|\^/| 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(tan(sqrt(c(2.0)*c(x) + c(1.0))));
> end;
exact_soln_y := proc(x) return tan(sqrt(c(2.0)*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_1D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> 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_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, 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_1D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> 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_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, 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_1D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> 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_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, 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_1D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> 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_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, 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_1D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> 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_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, 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_1D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> 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_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, 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_1D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> 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_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, 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_1D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> array_tmp4_a1[1] := sin(array_tmp3[1]);
> array_tmp4_a2[1] := cos(array_tmp3[1]);
> array_tmp4[1] := (array_tmp4_a1[1] / array_tmp4_a2[1]);
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_tmp5[1] + array_const_1D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp7[1] := sqrt(array_tmp6[1]);
> array_tmp8_a1[1] := sin(array_tmp7[1]);
> array_tmp8_a2[1] := cos(array_tmp7[1]);
> array_tmp8[1] := (array_tmp8_a1[1] / array_tmp8_a2[1]);
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp9[1] := (array_tmp4[1] * (array_tmp8[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp10[1] := array_const_1D0[1] + array_tmp9[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp11[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp12[1] := array_tmp11[1] + array_const_1D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp13[1] := sqrt(array_tmp12[1]);
> #emit pre div FULL - FULL $eq_no = 1 i = 1
> array_tmp14[1] := (array_tmp10[1] / (array_tmp13[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp15[1] := array_const_0D0[1] + array_tmp14[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_tmp15[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2;
> #emit pre tan $eq_no = 1
> array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[2] := neg(att(1,array_tmp4_a1,array_tmp3,1));
> array_tmp4[2] := (array_tmp4_a1[2] - ats(2,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp7[2] := array_tmp6[2] / array_tmp7[1]/glob__2;
> #emit pre tan $eq_no = 1
> array_tmp8_a1[2] := att(1,array_tmp8_a2,array_tmp7,1);
> array_tmp8_a2[2] := neg(att(1,array_tmp8_a1,array_tmp7,1));
> array_tmp8[2] := (array_tmp8_a1[2] - ats(2,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp9[2] := ats(2,array_tmp4,array_tmp8,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp11[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp12[2] := array_tmp11[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp13[2] := array_tmp12[2] / array_tmp13[1]/glob__2;
> #emit pre div FULL - FULL $eq_no = 1 i = 2
> array_tmp14[2] := ((array_tmp10[2] - ats(2,array_tmp13,array_tmp14,2))/array_tmp13[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp15[2] := array_tmp14[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_tmp15[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 tan $eq_no = 1
> array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[3] := neg(att(2,array_tmp4_a1,array_tmp3,1));
> array_tmp4[3] := (array_tmp4_a1[3] - ats(3,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp7[3] := 0;
> array_tmp7[3] := neg(ats(3,array_tmp7,array_tmp7,2)) / array_tmp7[1] /glob__2;
> #emit pre tan $eq_no = 1
> array_tmp8_a1[3] := att(2,array_tmp8_a2,array_tmp7,1);
> array_tmp8_a2[3] := neg(att(2,array_tmp8_a1,array_tmp7,1));
> array_tmp8[3] := (array_tmp8_a1[3] - ats(3,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp9[3] := ats(3,array_tmp4,array_tmp8,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3];
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp13[3] := 0;
> array_tmp13[3] := neg(ats(3,array_tmp13,array_tmp13,2)) / array_tmp13[1] /glob__2;
> #emit pre div FULL - FULL $eq_no = 1 i = 3
> array_tmp14[3] := ((array_tmp10[3] - ats(3,array_tmp13,array_tmp14,2))/array_tmp13[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp15[3] := array_tmp14[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_tmp15[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 tan $eq_no = 1
> array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[4] := neg(att(3,array_tmp4_a1,array_tmp3,1));
> array_tmp4[4] := (array_tmp4_a1[4] - ats(4,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp7[4] := 0;
> array_tmp7[4] := neg(ats(4,array_tmp7,array_tmp7,2)) / array_tmp7[1] /glob__2;
> #emit pre tan $eq_no = 1
> array_tmp8_a1[4] := att(3,array_tmp8_a2,array_tmp7,1);
> array_tmp8_a2[4] := neg(att(3,array_tmp8_a1,array_tmp7,1));
> array_tmp8[4] := (array_tmp8_a1[4] - ats(4,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp9[4] := ats(4,array_tmp4,array_tmp8,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4];
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp13[4] := 0;
> array_tmp13[4] := neg(ats(4,array_tmp13,array_tmp13,2)) / array_tmp13[1] /glob__2;
> #emit pre div FULL - FULL $eq_no = 1 i = 4
> array_tmp14[4] := ((array_tmp10[4] - ats(4,array_tmp13,array_tmp14,2))/array_tmp13[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp15[4] := array_tmp14[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_tmp15[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 tan $eq_no = 1
> array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[5] := neg(att(4,array_tmp4_a1,array_tmp3,1));
> array_tmp4[5] := (array_tmp4_a1[5] - ats(5,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp7[5] := 0;
> array_tmp7[5] := neg(ats(5,array_tmp7,array_tmp7,2)) / array_tmp7[1] /glob__2;
> #emit pre tan $eq_no = 1
> array_tmp8_a1[5] := att(4,array_tmp8_a2,array_tmp7,1);
> array_tmp8_a2[5] := neg(att(4,array_tmp8_a1,array_tmp7,1));
> array_tmp8[5] := (array_tmp8_a1[5] - ats(5,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp9[5] := ats(5,array_tmp4,array_tmp8,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5];
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp13[5] := 0;
> array_tmp13[5] := neg(ats(5,array_tmp13,array_tmp13,2)) / array_tmp13[1] /glob__2;
> #emit pre div FULL - FULL $eq_no = 1 i = 5
> array_tmp14[5] := ((array_tmp10[5] - ats(5,array_tmp13,array_tmp14,2))/array_tmp13[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp15[5] := array_tmp14[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_tmp15[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;
> array_tmp4_a1[kkk] := att(kkk-1 ,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[kkk] := neg(att(kkk-1,array_tmp4_a1,array_tmp3,1));
> array_tmp4[kkk] := (array_tmp4_a1[kkk] - ats(kkk ,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit sqrt LINEAR $eq_no = 1
> array_tmp7[kkk] := 0;
> array_tmp7[kkk] := neg(ats(kkk,array_tmp7,array_tmp7,2)) /array_tmp7[1] / glob__2;
> array_tmp8_a1[kkk] := att(kkk-1 ,array_tmp8_a2,array_tmp7,1);
> array_tmp8_a2[kkk] := neg(att(kkk-1,array_tmp8_a1,array_tmp7,1));
> array_tmp8[kkk] := (array_tmp8_a1[kkk] - ats(kkk ,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1];
> #emit mult FULL FULL $eq_no = 1
> array_tmp9[kkk] := ats(kkk,array_tmp4,array_tmp8,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk];
> #emit sqrt LINEAR $eq_no = 1
> array_tmp13[kkk] := 0;
> array_tmp13[kkk] := neg(ats(kkk,array_tmp13,array_tmp13,2)) /array_tmp13[1] / glob__2;
> #emit div FULL FULL $eq_no = 1
> array_tmp14[kkk] := ((array_tmp10[kkk] - ats(kkk,array_tmp13,array_tmp14,2)) /array_tmp13[1]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp15[kkk] := array_tmp14[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_tmp15[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_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
array_tmp1[1] := array_const_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_a1[1] := sin(array_tmp3[1]);
array_tmp4_a2[1] := cos(array_tmp3[1]);
array_tmp4[1] := array_tmp4_a1[1]/array_tmp4_a2[1];
array_tmp5[1] := array_const_2D0[1]*array_x[1];
array_tmp6[1] := array_tmp5[1] + array_const_1D0[1];
array_tmp7[1] := sqrt(array_tmp6[1]);
array_tmp8_a1[1] := sin(array_tmp7[1]);
array_tmp8_a2[1] := cos(array_tmp7[1]);
array_tmp8[1] := array_tmp8_a1[1]/array_tmp8_a2[1];
array_tmp9[1] := array_tmp4[1]*array_tmp8[1];
array_tmp10[1] := array_const_1D0[1] + array_tmp9[1];
array_tmp11[1] := array_const_2D0[1]*array_x[1];
array_tmp12[1] := array_tmp11[1] + array_const_1D0[1];
array_tmp13[1] := sqrt(array_tmp12[1]);
array_tmp14[1] := array_tmp10[1]/array_tmp13[1];
array_tmp15[1] := array_const_0D0[1] + array_tmp14[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp15[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[2] := neg(att(1, array_tmp4_a1, array_tmp3, 1));
array_tmp4[2] := (
array_tmp4_a1[2] - ats(2, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[2] := array_const_2D0[1]*array_x[2];
array_tmp6[2] := array_tmp5[2];
array_tmp7[2] := array_tmp6[2]/(array_tmp7[1]*glob__2);
array_tmp8_a1[2] := att(1, array_tmp8_a2, array_tmp7, 1);
array_tmp8_a2[2] := neg(att(1, array_tmp8_a1, array_tmp7, 1));
array_tmp8[2] := (
array_tmp8_a1[2] - ats(2, array_tmp8_a2, array_tmp8, 2))/
array_tmp8_a2[1];
array_tmp9[2] := ats(2, array_tmp4, array_tmp8, 1);
array_tmp10[2] := array_tmp9[2];
array_tmp11[2] := array_const_2D0[1]*array_x[2];
array_tmp12[2] := array_tmp11[2];
array_tmp13[2] := array_tmp12[2]/(array_tmp13[1]*glob__2);
array_tmp14[2] := (array_tmp10[2] - ats(2, array_tmp13, array_tmp14, 2)
)/array_tmp13[1];
array_tmp15[2] := array_tmp14[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp15[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_a1[3] := att(2, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[3] := neg(att(2, array_tmp4_a1, array_tmp3, 1));
array_tmp4[3] := (
array_tmp4_a1[3] - ats(3, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp7[3] := 0;
array_tmp7[3] :=
neg(ats(3, array_tmp7, array_tmp7, 2))/(array_tmp7[1]*glob__2);
array_tmp8_a1[3] := att(2, array_tmp8_a2, array_tmp7, 1);
array_tmp8_a2[3] := neg(att(2, array_tmp8_a1, array_tmp7, 1));
array_tmp8[3] := (
array_tmp8_a1[3] - ats(3, array_tmp8_a2, array_tmp8, 2))/
array_tmp8_a2[1];
array_tmp9[3] := ats(3, array_tmp4, array_tmp8, 1);
array_tmp10[3] := array_tmp9[3];
array_tmp13[3] := 0;
array_tmp13[3] :=
neg(ats(3, array_tmp13, array_tmp13, 2))/(array_tmp13[1]*glob__2);
array_tmp14[3] := (array_tmp10[3] - ats(3, array_tmp13, array_tmp14, 2)
)/array_tmp13[1];
array_tmp15[3] := array_tmp14[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp15[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_a1[4] := att(3, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[4] := neg(att(3, array_tmp4_a1, array_tmp3, 1));
array_tmp4[4] := (
array_tmp4_a1[4] - ats(4, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp7[4] := 0;
array_tmp7[4] :=
neg(ats(4, array_tmp7, array_tmp7, 2))/(array_tmp7[1]*glob__2);
array_tmp8_a1[4] := att(3, array_tmp8_a2, array_tmp7, 1);
array_tmp8_a2[4] := neg(att(3, array_tmp8_a1, array_tmp7, 1));
array_tmp8[4] := (
array_tmp8_a1[4] - ats(4, array_tmp8_a2, array_tmp8, 2))/
array_tmp8_a2[1];
array_tmp9[4] := ats(4, array_tmp4, array_tmp8, 1);
array_tmp10[4] := array_tmp9[4];
array_tmp13[4] := 0;
array_tmp13[4] :=
neg(ats(4, array_tmp13, array_tmp13, 2))/(array_tmp13[1]*glob__2);
array_tmp14[4] := (array_tmp10[4] - ats(4, array_tmp13, array_tmp14, 2)
)/array_tmp13[1];
array_tmp15[4] := array_tmp14[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp15[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_a1[5] := att(4, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[5] := neg(att(4, array_tmp4_a1, array_tmp3, 1));
array_tmp4[5] := (
array_tmp4_a1[5] - ats(5, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp7[5] := 0;
array_tmp7[5] :=
neg(ats(5, array_tmp7, array_tmp7, 2))/(array_tmp7[1]*glob__2);
array_tmp8_a1[5] := att(4, array_tmp8_a2, array_tmp7, 1);
array_tmp8_a2[5] := neg(att(4, array_tmp8_a1, array_tmp7, 1));
array_tmp8[5] := (
array_tmp8_a1[5] - ats(5, array_tmp8_a2, array_tmp8, 2))/
array_tmp8_a2[1];
array_tmp9[5] := ats(5, array_tmp4, array_tmp8, 1);
array_tmp10[5] := array_tmp9[5];
array_tmp13[5] := 0;
array_tmp13[5] :=
neg(ats(5, array_tmp13, array_tmp13, 2))/(array_tmp13[1]*glob__2);
array_tmp14[5] := (array_tmp10[5] - ats(5, array_tmp13, array_tmp14, 2)
)/array_tmp13[1];
array_tmp15[5] := array_tmp14[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp15[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_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[kkk] :=
neg(att(kkk - 1, array_tmp4_a1, array_tmp3, 1));
array_tmp4[kkk] := (
array_tmp4_a1[kkk] - ats(kkk, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp7[kkk] := 0;
array_tmp7[kkk] := neg(ats(kkk, array_tmp7, array_tmp7, 2))/(
array_tmp7[1]*glob__2);
array_tmp8_a1[kkk] := att(kkk - 1, array_tmp8_a2, array_tmp7, 1);
array_tmp8_a2[kkk] :=
neg(att(kkk - 1, array_tmp8_a1, array_tmp7, 1));
array_tmp8[kkk] := (
array_tmp8_a1[kkk] - ats(kkk, array_tmp8_a2, array_tmp8, 2))/
array_tmp8_a2[1];
array_tmp9[kkk] := ats(kkk, array_tmp4, array_tmp8, 1);
array_tmp10[kkk] := array_tmp9[kkk];
array_tmp13[kkk] := 0;
array_tmp13[kkk] := neg(ats(kkk, array_tmp13, array_tmp13, 2))/(
array_tmp13[1]*glob__2);
array_tmp14[kkk] := (
array_tmp10[kkk] - ats(kkk, array_tmp13, array_tmp14, 2))/
array_tmp13[1];
array_tmp15[kkk] := array_tmp14[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_tmp15[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_1D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8_g,
> array_tmp8_a1,
> array_tmp8_a2,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> 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_g:= Array(0..(40),[]);
> array_tmp4_a1:= Array(0..(40),[]);
> array_tmp4_a2:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_tmp6:= Array(0..(40),[]);
> array_tmp7:= Array(0..(40),[]);
> array_tmp8_g:= Array(0..(40),[]);
> array_tmp8_a1:= Array(0..(40),[]);
> array_tmp8_a2:= Array(0..(40),[]);
> array_tmp8:= Array(0..(40),[]);
> array_tmp9:= Array(0..(40),[]);
> array_tmp10:= Array(0..(40),[]);
> array_tmp11:= Array(0..(40),[]);
> array_tmp12:= Array(0..(40),[]);
> array_tmp13:= Array(0..(40),[]);
> array_tmp14:= Array(0..(40),[]);
> array_tmp15:= 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_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp8_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp8_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp8_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp8[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp9[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp10[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp11[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp12[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp13[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp14[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp15[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_g);
> zero_ats_ar(array_tmp4_a1);
> zero_ats_ar(array_tmp4_a2);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_tmp8_g);
> zero_ats_ar(array_tmp8_a1);
> zero_ats_ar(array_tmp8_a2);
> zero_ats_ar(array_tmp8);
> zero_ats_ar(array_tmp9);
> zero_ats_ar(array_tmp10);
> zero_ats_ar(array_tmp11);
> zero_ats_ar(array_tmp12);
> zero_ats_ar(array_tmp13);
> zero_ats_ar(array_tmp14);
> zero_ats_ar(array_tmp15);
> 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_1D0);
> array_const_1D0[1] := c(1.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> 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/tan_sqrtpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 1.4 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.0001);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> 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,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(tan(sqrt(c(2.0)*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 := 1.4 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.0001);
> 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 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:41:07-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"tan_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"tan_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"tan_sqrt maple results")
> ;
> logitem_str(html_log_file,"Poor Accuracy")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0,
array_const_2D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g,
array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, 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_g := Array(0 .. 40, []);
array_tmp4_a1 := Array(0 .. 40, []);
array_tmp4_a2 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_tmp6 := Array(0 .. 40, []);
array_tmp7 := Array(0 .. 40, []);
array_tmp8_g := Array(0 .. 40, []);
array_tmp8_a1 := Array(0 .. 40, []);
array_tmp8_a2 := Array(0 .. 40, []);
array_tmp8 := Array(0 .. 40, []);
array_tmp9 := Array(0 .. 40, []);
array_tmp10 := Array(0 .. 40, []);
array_tmp11 := Array(0 .. 40, []);
array_tmp12 := Array(0 .. 40, []);
array_tmp13 := Array(0 .. 40, []);
array_tmp14 := Array(0 .. 40, []);
array_tmp15 := 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_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp8_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp8_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp8_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp8[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp9[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp10[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp11[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp12[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp13[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp14[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp15[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_g);
zero_ats_ar(array_tmp4_a1);
zero_ats_ar(array_tmp4_a2);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_tmp8_g);
zero_ats_ar(array_tmp8_a1);
zero_ats_ar(array_tmp8_a2);
zero_ats_ar(array_tmp8);
zero_ats_ar(array_tmp9);
zero_ats_ar(array_tmp10);
zero_ats_ar(array_tmp11);
zero_ats_ar(array_tmp12);
zero_ats_ar(array_tmp13);
zero_ats_ar(array_tmp14);
zero_ats_ar(array_tmp15);
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_1D0);
array_const_1D0[1] := c(1.0);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
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/tan_sqrtpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 1.0 + ( t\
an ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.\
0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 \
) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 1.4 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.0001);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
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, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(tan(sqrt(c(2.0)*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,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 1.4 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.0001);
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 ) = ( 1.0 + ( \
tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt \
( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x\
+ 1.0 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:41:07-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"tan_sqrt");
logitem_str(html_log_file, "diff ( y , x , 1 ) = (\
1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) \
* tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) \
/ sqrt ( 2.0 * x + 1.0 ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file, "tan_sqrt diffeq.mxt");
logitem_str(html_log_file, "tan_sqrt maple results");
logitem_str(html_log_file, "Poor Accuracy");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.7MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/tan_sqrtpostcpx.cpx#################
diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 1.4 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.0001);
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(tan(sqrt(c(2.0)*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
memory used=39.4MB, alloc=40.3MB, time=0.50
x[1] = 1.4 0.1
h = 0.0001 0.005
y[1] (numeric) = -2.46195285409 0.367754104928
y[1] (closed_form) = -2.46195285409 0.367754104928
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 3.401
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=85.0MB, alloc=44.3MB, time=1.08
x[1] = 1.4001 0.105
h = 0.0001 0.003
y[1] (numeric) = -2.45648498841 0.385272668433
y[1] (closed_form) = -2.45638031504 0.385215316265
absolute error = 0.0001194
relative error = 0.0048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=130.5MB, alloc=44.3MB, time=1.64
x[1] = 1.4002 0.108
h = 0.001 0.001
y[1] (numeric) = -2.45292698799 0.39566681201
y[1] (closed_form) = -2.45278917715 0.395588610341
absolute error = 0.0001585
relative error = 0.006378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=176.1MB, alloc=44.3MB, time=2.21
x[1] = 1.4012 0.109
h = 0.001 0.003
y[1] (numeric) = -2.44834590178 0.398057159904
y[1] (closed_form) = -2.44821360221 0.397971765614
absolute error = 0.0001575
relative error = 0.006349 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=221.7MB, alloc=44.3MB, time=2.77
x[1] = 1.4022 0.112
h = 0.0001 0.004
y[1] (numeric) = -2.44157812761 0.407374063702
y[1] (closed_form) = -2.44142437643 0.407244711586
absolute error = 0.0002009
relative error = 0.008118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.404
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=267.2MB, alloc=44.3MB, time=3.33
x[1] = 1.4023 0.116
h = 0.003 0.006
y[1] (numeric) = -2.43674667417 0.421054547769
y[1] (closed_form) = -2.43652838859 0.420886665868
absolute error = 0.0002754
relative error = 0.01114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.404
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=312.8MB, alloc=44.3MB, time=3.90
x[1] = 1.4053 0.122
h = 0.0001 0.005
y[1] (numeric) = -2.41951981018 0.438150335909
y[1] (closed_form) = -2.41928208246 0.43776790359
absolute error = 0.0004503
relative error = 0.01832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.407
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=358.3MB, alloc=44.3MB, time=4.46
x[1] = 1.4054 0.127
h = 0.0001 0.003
y[1] (numeric) = -2.4132107805 0.454881549689
y[1] (closed_form) = -2.41287943868 0.454442936133
absolute error = 0.0005497
relative error = 0.02239 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.408
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=403.9MB, alloc=44.3MB, time=5.02
x[1] = 1.4055 0.13
h = 0.001 0.001
y[1] (numeric) = -2.40916747837 0.464792574739
y[1] (closed_form) = -2.40880638535 0.464330999344
absolute error = 0.000586
relative error = 0.02389 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.408
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=449.4MB, alloc=44.3MB, time=5.58
x[1] = 1.4065 0.131
h = 0.001 0.003
y[1] (numeric) = -2.40457900272 0.466861252792
y[1] (closed_form) = -2.40422385926 0.466393282554
absolute error = 0.0005875
relative error = 0.02399 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.409
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=494.9MB, alloc=44.3MB, time=6.14
x[1] = 1.4075 0.134
h = 0.0001 0.004
y[1] (numeric) = -2.39747857863 0.475544441865
y[1] (closed_form) = -2.3971067871 0.475032568464
absolute error = 0.0006326
relative error = 0.02589 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.41
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=540.6MB, alloc=44.3MB, time=6.71
x[1] = 1.4076 0.138
h = 0.003 0.006
y[1] (numeric) = -2.39202240592 0.488577665146
y[1] (closed_form) = -2.39159236873 0.488023298245
absolute error = 0.0007016
relative error = 0.02874 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.41
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=586.2MB, alloc=44.3MB, time=7.27
x[1] = 1.4106 0.144
h = 0.0001 0.005
y[1] (numeric) = -2.37433459919 0.504243042023
y[1] (closed_form) = -2.37390476171 0.50348183641
absolute error = 0.0008742
relative error = 0.03602 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.414
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=631.8MB, alloc=44.3MB, time=7.83
x[1] = 1.4107 0.149
h = 0.0001 0.003
y[1] (numeric) = -2.36729039712 0.520155926911
y[1] (closed_form) = -2.36677626721 0.519332979283
absolute error = 0.0009703
relative error = 0.04005 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.414
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=677.3MB, alloc=44.3MB, time=8.39
x[1] = 1.4108 0.152
h = 0.001 0.001
y[1] (numeric) = -2.36282479863 0.529563052353
y[1] (closed_form) = -2.36228434323 0.528715555058
memory used=722.9MB, alloc=44.3MB, time=8.96
absolute error = 0.001005
relative error = 0.04152 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.414
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=768.3MB, alloc=44.3MB, time=9.52
x[1] = 1.4118 0.153
h = 0.001 0.003
y[1] (numeric) = -2.35825696788 0.531323611119
y[1] (closed_form) = -2.35772278135 0.530470521411
absolute error = 0.001007
relative error = 0.04165 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.415
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=813.7MB, alloc=44.3MB, time=10.08
x[1] = 1.4128 0.156
h = 0.0001 0.004
y[1] (numeric) = -2.35089303278 0.539372454112
y[1] (closed_form) = -2.35034670304 0.538476058099
absolute error = 0.00105
relative error = 0.04354 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.416
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=859.0MB, alloc=44.3MB, time=10.64
x[1] = 1.4129 0.16
h = 0.003 0.006
y[1] (numeric) = -2.3448952255 0.551733664025
y[1] (closed_form) = -2.34429700185 0.550791769527
absolute error = 0.001116
relative error = 0.04634 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.417
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=904.4MB, alloc=44.3MB, time=11.20
x[1] = 1.4159 0.166
h = 0.0001 0.005
y[1] (numeric) = -2.32688895894 0.56599337281
y[1] (closed_form) = -2.32630850628 0.564854098137
absolute error = 0.001279
relative error = 0.05341 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.42
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=949.9MB, alloc=44.3MB, time=11.76
x[1] = 1.416 0.171
h = 0.0001 0.003
y[1] (numeric) = -2.31921173761 0.5810628265
y[1] (closed_form) = -2.31855634656 0.579857650496
absolute error = 0.001372
relative error = 0.0574 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.42
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=995.3MB, alloc=44.3MB, time=12.32
x[1] = 1.4161 0.174
h = 0.001 0.001
y[1] (numeric) = -2.3143853446 0.589953603454
y[1] (closed_form) = -2.31370701641 0.58872277869
absolute error = 0.001405
relative error = 0.05887 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1040.7MB, alloc=44.3MB, time=12.88
x[1] = 1.4171 0.175
h = 0.001 0.003
y[1] (numeric) = -2.3098629615 0.591421897535
y[1] (closed_form) = -2.30919111098 0.590186270345
absolute error = 0.001406
relative error = 0.05901 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.422
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1086.1MB, alloc=44.3MB, time=13.45
x[1] = 1.4181 0.178
h = 0.0001 0.004
y[1] (numeric) = -2.30230049047 0.598843513016
y[1] (closed_form) = -2.30162065177 0.597565634846
absolute error = 0.001447
relative error = 0.06087 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.423
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1131.7MB, alloc=44.3MB, time=14.02
x[1] = 1.4182 0.182
h = 0.003 0.006
y[1] (numeric) = -2.29584177137 0.610518704237
y[1] (closed_form) = -2.29511631675 0.609193213968
absolute error = 0.001511
relative error = 0.06363 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.423
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1177.2MB, alloc=44.3MB, time=14.58
x[1] = 1.4212 0.188
h = 0.0001 0.005
y[1] (numeric) = -2.277647959 0.623411700533
y[1] (closed_form) = -2.27695570106 0.621899614651
absolute error = 0.001663
relative error = 0.07046 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.426
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1222.6MB, alloc=44.3MB, time=15.14
x[1] = 1.4213 0.193
h = 0.0001 0.003
y[1] (numeric) = -2.2694362457 0.637625360316
y[1] (closed_form) = -2.26867824296 0.636044505868
absolute error = 0.001753
relative error = 0.07441 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.427
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1268.0MB, alloc=44.3MB, time=15.70
x[1] = 1.4214 0.196
h = 0.001 0.001
y[1] (numeric) = -2.26430804094 0.645994811647
y[1] (closed_form) = -2.26353038854 0.644387653294
absolute error = 0.001785
relative error = 0.07586 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.427
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1313.5MB, alloc=44.3MB, time=16.26
x[1] = 1.4224 0.197
h = 0.0001 0.004
y[1] (numeric) = -2.25985262001 0.647188379156
y[1] (closed_form) = -2.25908155399 0.64557718183
absolute error = 0.001786
relative error = 0.07602 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.428
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1358.9MB, alloc=44.3MB, time=16.82
x[1] = 1.4225 0.201
h = 0.003 0.006
y[1] (numeric) = -2.2530535028 0.658275494237
y[1] (closed_form) = -2.25223940731 0.656613399689
absolute error = 0.001851
relative error = 0.07889 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.428
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1404.4MB, alloc=44.3MB, time=17.39
x[1] = 1.4255 0.207
h = 0.0001 0.005
y[1] (numeric) = -2.23477808541 0.67003248107
y[1] (closed_form) = -2.23400888664 0.668193686668
absolute error = 0.001993
relative error = 0.08548 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1450.0MB, alloc=44.3MB, time=17.95
x[1] = 1.4256 0.212
h = 0.0001 0.003
y[1] (numeric) = -2.22617120286 0.683513087739
y[1] (closed_form) = -2.22534390829 0.681603889316
absolute error = 0.002081
relative error = 0.0894 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1495.5MB, alloc=44.3MB, time=18.52
x[1] = 1.4257 0.215
h = 0.001 0.001
y[1] (numeric) = -2.22082176655 0.691437530293
y[1] (closed_form) = -2.21997753112 0.689501744582
absolute error = 0.002112
relative error = 0.09085 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1541.1MB, alloc=44.3MB, time=19.08
x[1] = 1.4267 0.216
h = 0.001 0.003
y[1] (numeric) = -2.21643576623 0.692408445163
y[1] (closed_form) = -2.21559814796 0.690469247975
absolute error = 0.002112
relative error = 0.09102 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.434
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1586.4MB, alloc=44.3MB, time=19.64
x[1] = 1.4277 0.219
h = 0.0001 0.004
y[1] (numeric) = -2.20865274161 0.698704305879
y[1] (closed_form) = -2.20781385688 0.696725718617
absolute error = 0.002149
relative error = 0.09283 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1632.0MB, alloc=44.3MB, time=20.20
x[1] = 1.4278 0.223
h = 0.003 0.006
y[1] (numeric) = -2.2015299639 0.709100983425
y[1] (closed_form) = -2.20065657652 0.707072865875
absolute error = 0.002208
relative error = 0.09553 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1677.5MB, alloc=44.3MB, time=20.76
x[1] = 1.4308 0.229
h = 0.0001 0.005
y[1] (numeric) = -2.18327757747 0.719591251131
y[1] (closed_form) = -2.18246056926 0.717398697472
absolute error = 0.00234
relative error = 0.1018 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.438
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1723.1MB, alloc=44.3MB, time=21.32
x[1] = 1.4309 0.234
h = 0.0001 0.003
y[1] (numeric) = -2.17430551289 0.732220749301
y[1] (closed_form) = -2.17343892625 0.729956983012
absolute error = 0.002424
relative error = 0.1057 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.439
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1768.7MB, alloc=44.3MB, time=21.89
x[1] = 1.431 0.237
h = 0.001 0.001
y[1] (numeric) = -2.16875490959 0.739630660625
y[1] (closed_form) = -2.16787436202 0.737340344435
absolute error = 0.002454
relative error = 0.1072 %
Correct digits = 3
memory used=1814.3MB, alloc=44.3MB, time=22.45
Radius of convergence (given) for eq 1 = 3.439
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1859.8MB, alloc=44.3MB, time=23.01
x[1] = 1.432 0.238
h = 0.001 0.003
y[1] (numeric) = -2.1644676049 0.740361895087
y[1] (closed_form) = -2.16359362781 0.738068855129
absolute error = 0.002454
relative error = 0.1073 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.44
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=1905.3MB, alloc=44.3MB, time=23.58
x[1] = 1.433 0.241
h = 0.0001 0.004
y[1] (numeric) = -2.15664383079 0.746082641888
y[1] (closed_form) = -2.15577161644 0.743752133885
absolute error = 0.002488
relative error = 0.1091 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.441
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1950.8MB, alloc=44.3MB, time=24.14
x[1] = 1.4331 0.245
h = 0.003 0.006
y[1] (numeric) = -2.14926817518 0.755801027372
y[1] (closed_form) = -2.1483669914 0.753420946294
absolute error = 0.002545
relative error = 0.1118 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.442
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1996.3MB, alloc=44.3MB, time=24.70
x[1] = 1.4361 0.251
h = 0.0001 0.005
y[1] (numeric) = -2.13113300303 0.765089948412
y[1] (closed_form) = -2.13029767845 0.762558007511
absolute error = 0.002666
relative error = 0.1178 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.445
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2041.7MB, alloc=44.3MB, time=25.26
x[1] = 1.4362 0.256
h = 0.0001 0.003
y[1] (numeric) = -2.12187752414 0.776884020111
y[1] (closed_form) = -2.12100062151 0.774280959582
absolute error = 0.002747
relative error = 0.1217 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.446
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2087.2MB, alloc=44.3MB, time=25.82
x[1] = 1.4363 0.259
h = 0.001 0.001
y[1] (numeric) = -2.11617401221 0.783790613797
y[1] (closed_form) = -2.11528591683 0.781161336237
absolute error = 0.002775
relative error = 0.1231 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.446
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2132.7MB, alloc=44.3MB, time=26.39
x[1] = 1.4373 0.26
h = 0.001 0.003
y[1] (numeric) = -2.11199803468 0.784301638954
y[1] (closed_form) = -2.11111639723 0.781670274499
absolute error = 0.002775
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.447
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2178.1MB, alloc=44.3MB, time=26.95
x[1] = 1.4383 0.263
h = 0.0001 0.004
y[1] (numeric) = -2.10417785342 0.789473533763
y[1] (closed_form) = -2.10330061168 0.786806783981
absolute error = 0.002807
relative error = 0.125 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.448
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2223.6MB, alloc=44.3MB, time=27.51
x[1] = 1.4384 0.267
h = 0.003 0.006
y[1] (numeric) = -2.09661181712 0.798529709728
y[1] (closed_form) = -2.09571075706 0.795813883981
absolute error = 0.002861
relative error = 0.1276 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.449
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2269.2MB, alloc=44.3MB, time=28.07
x[1] = 1.4414 0.273
h = 0.0001 0.005
y[1] (numeric) = -2.07867523386 0.806687355892
y[1] (closed_form) = -2.07784764593 0.80383229141
absolute error = 0.002973
relative error = 0.1334 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.452
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2314.7MB, alloc=44.3MB, time=28.64
x[1] = 1.4415 0.278
h = 0.0001 0.003
y[1] (numeric) = -2.06921099405 0.817668485522
y[1] (closed_form) = -2.06834924939 0.814743154748
absolute error = 0.00305
relative error = 0.1372 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.453
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2360.3MB, alloc=44.3MB, time=29.20
x[1] = 1.4416 0.281
h = 0.001 0.001
y[1] (numeric) = -2.0633984323 0.824086819409
y[1] (closed_form) = -2.06252803454 0.821135848552
absolute error = 0.003077
relative error = 0.1386 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.453
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2405.8MB, alloc=44.3MB, time=29.77
x[1] = 1.4426 0.282
h = 0.001 0.003
y[1] (numeric) = -2.05934368462 0.824396963162
y[1] (closed_form) = -2.05847957811 0.821444487906
absolute error = 0.003076
relative error = 0.1388 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.454
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2451.3MB, alloc=44.3MB, time=30.33
x[1] = 1.4436 0.285
h = 0.0001 0.004
y[1] (numeric) = -2.05156587719 0.829048668375
y[1] (closed_form) = -2.05070841907 0.826062990715
absolute error = 0.003106
relative error = 0.1405 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.455
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2496.8MB, alloc=44.3MB, time=30.89
x[1] = 1.4437 0.289
h = 0.003 0.006
y[1] (numeric) = -2.04386610968 0.837463516065
y[1] (closed_form) = -2.04298957276 0.83442970718
absolute error = 0.003158
relative error = 0.1431 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.456
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2542.4MB, alloc=44.3MB, time=31.46
x[1] = 1.4467 0.295
h = 0.0001 0.005
y[1] (numeric) = -2.02619724054 0.844562741963
y[1] (closed_form) = -2.0254000799 0.841402139456
absolute error = 0.00326
relative error = 0.1486 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.459
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2587.9MB, alloc=44.3MB, time=32.02
x[1] = 1.4468 0.3
h = 0.0001 0.003
y[1] (numeric) = -2.0165916051 0.854758796033
y[1] (closed_form) = -2.01576709405 0.851529406133
absolute error = 0.003333
relative error = 0.1523 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.46
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=2633.4MB, alloc=44.3MB, time=32.59
x[1] = 1.4469 0.303
h = 0.001 0.001
y[1] (numeric) = -2.0107093926 0.860706927287
y[1] (closed_form) = -2.0098785317 0.857452670091
absolute error = 0.003359
relative error = 0.1537 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.46
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=2679.0MB, alloc=44.3MB, time=33.15
x[1] = 1.4479 0.304
h = 0.0001 0.004
y[1] (numeric) = -2.0067833043 0.860835072572
y[1] (closed_form) = -2.00595852488 0.857579837554
absolute error = 0.003358
relative error = 0.1539 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2724.6MB, alloc=44.3MB, time=33.71
x[1] = 1.448 0.308
h = 0.003 0.006
y[1] (numeric) = -1.99900372075 0.868720505767
y[1] (closed_form) = -1.99816195832 0.865415940227
absolute error = 0.00341
relative error = 0.1566 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.462
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2770.2MB, alloc=44.3MB, time=34.27
x[1] = 1.451 0.314
h = 0.0001 0.005
y[1] (numeric) = -1.98160044209 0.874963834136
y[1] (closed_form) = -1.98084204237 0.871542865036
absolute error = 0.003504
relative error = 0.1619 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.465
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2815.6MB, alloc=44.3MB, time=34.84
x[1] = 1.4511 0.319
h = 0.0001 0.003
y[1] (numeric) = -1.97191267482 0.884510316532
y[1] (closed_form) = -1.97113230505 0.881022167315
absolute error = 0.003574
relative error = 0.1656 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.466
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2861.1MB, alloc=44.3MB, time=35.40
x[1] = 1.4512 0.322
h = 0.001 0.001
y[1] (numeric) = -1.96599342781 0.890070171335
y[1] (closed_form) = -1.96520851241 0.886557919439
absolute error = 0.003599
relative error = 0.1669 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.466
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2906.7MB, alloc=44.3MB, time=35.96
x[1] = 1.4522 0.323
h = 0.001 0.003
memory used=2952.2MB, alloc=44.3MB, time=36.52
y[1] (numeric) = -1.96218046932 0.890054652386
y[1] (closed_form) = -1.96140143341 0.886541834195
absolute error = 0.003598
relative error = 0.1672 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.467
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2997.7MB, alloc=44.3MB, time=37.08
x[1] = 1.4532 0.326
h = 0.0001 0.004
y[1] (numeric) = -1.95456129067 0.89381811227
y[1] (closed_form) = -1.95379218922 0.890276231539
absolute error = 0.003624
relative error = 0.1688 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.469
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3043.2MB, alloc=44.3MB, time=37.65
x[1] = 1.4533 0.33
h = 0.003 0.006
y[1] (numeric) = -1.94673648483 0.901107427369
y[1] (closed_form) = -1.94595601033 0.897520029805
absolute error = 0.003671
relative error = 0.1713 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.469
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3088.7MB, alloc=44.3MB, time=38.21
x[1] = 1.4563 0.336
h = 0.0001 0.005
y[1] (numeric) = -1.92970052869 0.906429383894
y[1] (closed_form) = -1.92900659422 0.902737278857
absolute error = 0.003757
relative error = 0.1764 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.473
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3134.2MB, alloc=44.3MB, time=38.78
x[1] = 1.4564 0.341
h = 0.0001 0.003
y[1] (numeric) = -1.91997799165 0.915252040104
y[1] (closed_form) = -1.91926772926 0.911495081479
absolute error = 0.003824
relative error = 0.18 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.473
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3179.8MB, alloc=44.3MB, time=39.34
x[1] = 1.4565 0.344
h = 0.001 0.001
y[1] (numeric) = -1.91405107458 0.920380378178
y[1] (closed_form) = -1.91333813396 0.916600343041
absolute error = 0.003847
relative error = 0.1813 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.474
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3225.4MB, alloc=44.3MB, time=39.91
x[1] = 1.4575 0.345
h = 0.001 0.003
y[1] (numeric) = -1.91037514214 0.920216019256
y[1] (closed_form) = -1.90966781636 0.916435841834
absolute error = 0.003846
relative error = 0.1816 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.475
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3270.9MB, alloc=44.3MB, time=40.47
x[1] = 1.4585 0.348
h = 0.0001 0.004
y[1] (numeric) = -1.90288118716 0.923547171077
y[1] (closed_form) = -1.90218509748 0.919740146404
absolute error = 0.00387
relative error = 0.1832 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.476
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3316.4MB, alloc=44.3MB, time=41.03
x[1] = 1.4586 0.352
h = 0.003 0.006
y[1] (numeric) = -1.89505304157 0.930271667571
y[1] (closed_form) = -1.89434910851 0.926420905524
absolute error = 0.003915
relative error = 0.1856 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.476
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3361.9MB, alloc=44.3MB, time=41.60
x[1] = 1.4616 0.358
h = 0.0001 0.005
y[1] (numeric) = -1.87842309542 0.934745065895
y[1] (closed_form) = -1.87780766633 0.930800716725
absolute error = 0.003992
relative error = 0.1905 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.48
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=3407.4MB, alloc=44.3MB, time=42.16
x[1] = 1.4617 0.363
h = 0.0001 0.003
y[1] (numeric) = -1.86871305744 0.942880587604
y[1] (closed_form) = -1.86808632993 0.938874011194
absolute error = 0.004055
relative error = 0.194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3452.9MB, alloc=44.3MB, time=42.72
x[1] = 1.4618 0.366
h = 0.001 0.001
y[1] (numeric) = -1.86280574726 0.947600186266
y[1] (closed_form) = -1.86217798466 0.943571641819
absolute error = 0.004077
relative error = 0.1953 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3498.4MB, alloc=44.3MB, time=43.28
x[1] = 1.4628 0.367
h = 0.001 0.003
y[1] (numeric) = -1.85926866591 0.94730351528
y[1] (closed_form) = -1.85864623627 0.943275199997
absolute error = 0.004076
relative error = 0.1956 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.482
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3543.9MB, alloc=44.3MB, time=43.85
x[1] = 1.4638 0.37
h = 0.0001 0.004
y[1] (numeric) = -1.85191991412 0.95023341939
y[1] (closed_form) = -1.85130974644 0.946180416961
absolute error = 0.004099
relative error = 0.1971 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.484
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3589.4MB, alloc=44.3MB, time=44.41
x[1] = 1.4639 0.374
h = 0.003 0.006
y[1] (numeric) = -1.84412335694 0.956423366582
y[1] (closed_form) = -1.84350847126 0.952328564246
absolute error = 0.004141
relative error = 0.1996 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.484
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3634.9MB, alloc=44.3MB, time=44.98
x[1] = 1.4669 0.38
h = 0.0001 0.005
y[1] (numeric) = -1.82792934346 0.960118932313
y[1] (closed_form) = -1.8274038804 0.955941016674
absolute error = 0.004211
relative error = 0.2042 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.488
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3680.5MB, alloc=44.3MB, time=45.54
x[1] = 1.467 0.385
h = 0.0001 0.003
y[1] (numeric) = -1.81827268672 0.967605197771
y[1] (closed_form) = -1.81774036841 0.963367891828
absolute error = 0.004271
relative error = 0.2076 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.488
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3726.1MB, alloc=44.3MB, time=46.10
x[1] = 1.4671 0.388
h = 0.001 0.001
y[1] (numeric) = -1.81240845288 0.971939381735
y[1] (closed_form) = -1.81187653063 0.967681268318
absolute error = 0.004291
relative error = 0.2089 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.489
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3771.6MB, alloc=44.3MB, time=46.66
x[1] = 1.4681 0.389
h = 0.001 0.003
y[1] (numeric) = -1.809010591 0.971525874795
y[1] (closed_form) = -1.80848370948 0.967268312394
absolute error = 0.00429
relative error = 0.2092 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.49
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=3817.1MB, alloc=44.3MB, time=47.23
x[1] = 1.4691 0.392
h = 0.0001 0.004
y[1] (numeric) = -1.80182309162 0.974084940247
y[1] (closed_form) = -1.80130925268 0.969804773492
absolute error = 0.004311
relative error = 0.2107 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.491
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3862.6MB, alloc=44.3MB, time=47.79
x[1] = 1.4692 0.396
h = 0.003 0.006
y[1] (numeric) = -1.79408811357 0.979771194269
y[1] (closed_form) = -1.79357229919 0.975451268847
absolute error = 0.004351
relative error = 0.2131 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.492
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3908.3MB, alloc=44.3MB, time=48.35
x[1] = 1.4722 0.402
h = 0.0001 0.005
y[1] (numeric) = -1.7783521917 0.982756886348
y[1] (closed_form) = -1.77792583141 0.978363631504
absolute error = 0.004414
relative error = 0.2175 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.495
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3953.8MB, alloc=44.3MB, time=48.92
x[1] = 1.4723 0.407
h = 0.0001 0.003
y[1] (numeric) = -1.76878387333 0.989632227363
y[1] (closed_form) = -1.76835454836 0.985182553388
absolute error = 0.00447
relative error = 0.2208 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.496
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3999.4MB, alloc=44.3MB, time=49.48
x[1] = 1.4724 0.41
h = 0.001 0.001
y[1] (numeric) = -1.76298266995 0.993604448948
y[1] (closed_form) = -1.7625549746 0.98913515468
absolute error = 0.00449
relative error = 0.2221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.497
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4045.1MB, alloc=44.3MB, time=50.04
x[1] = 1.4734 0.411
h = 0.0001 0.004
y[1] (numeric) = -1.75972317335 0.993088484947
y[1] (closed_form) = -1.75930022195 0.988620017398
absolute error = 0.004488
relative error = 0.2224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.498
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4090.6MB, alloc=44.3MB, time=50.60
memory used=4136.2MB, alloc=44.3MB, time=51.17
x[1] = 1.4735 0.415
h = 0.003 0.006
y[1] (numeric) = -1.75205712162 0.998366930688
y[1] (closed_form) = -1.75163340671 0.993858358709
absolute error = 0.004528
relative error = 0.2249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.498
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4181.7MB, alloc=44.3MB, time=51.73
x[1] = 1.4765 0.421
h = 0.0001 0.005
y[1] (numeric) = -1.73672062593 1.00078783907
y[1] (closed_form) = -1.7363858984 0.996213801717
absolute error = 0.004586
relative error = 0.2291 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.502
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4227.2MB, alloc=44.3MB, time=52.30
x[1] = 1.4766 0.426
h = 0.0001 0.003
y[1] (numeric) = -1.7272455195 1.00716639418
y[1] (closed_form) = -1.72691079939 1.00253851529
absolute error = 0.00464
relative error = 0.2324 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.503
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4272.8MB, alloc=44.3MB, time=52.86
x[1] = 1.4767 0.429
h = 0.001 0.001
y[1] (numeric) = -1.72150815573 1.01084466015
y[1] (closed_form) = -1.72117599502 1.00619817621
absolute error = 0.004658
relative error = 0.2337 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.503
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4318.4MB, alloc=44.3MB, time=53.43
x[1] = 1.4777 0.43
h = 0.001 0.003
y[1] (numeric) = -1.71836529163 1.01024955407
y[1] (closed_form) = -1.718037622 1.00560410356
absolute error = 0.004657
relative error = 0.2339 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4363.8MB, alloc=44.3MB, time=53.99
x[1] = 1.4787 0.433
h = 0.0001 0.004
y[1] (numeric) = -1.71150522563 1.01219378821
y[1] (closed_form) = -1.71119152127 1.00752934757
absolute error = 0.004675
relative error = 0.2354 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.506
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4409.4MB, alloc=44.3MB, time=54.56
x[1] = 1.4788 0.437
h = 0.003 0.006
y[1] (numeric) = -1.70394424552 1.01702342551
y[1] (closed_form) = -1.70363276354 1.01232312629
absolute error = 0.004711
relative error = 0.2377 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.506
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4454.8MB, alloc=44.3MB, time=55.12
x[1] = 1.4818 0.443
h = 0.0001 0.005
y[1] (numeric) = -1.68909040616 1.01885190351
y[1] (closed_form) = -1.68886666118 1.01409460421
absolute error = 0.004763
relative error = 0.2418 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.51
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=4500.4MB, alloc=44.3MB, time=55.68
x[1] = 1.4819 0.448
h = 0.0001 0.003
y[1] (numeric) = -1.67975506195 1.02468982497
y[1] (closed_form) = -1.6795342914 1.01988174846
absolute error = 0.004813
relative error = 0.245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.511
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4545.9MB, alloc=44.3MB, time=56.25
x[1] = 1.482 0.451
h = 0.001 0.001
y[1] (numeric) = -1.67410982681 1.02804883796
y[1] (closed_form) = -1.67389252364 1.02322334207
absolute error = 0.00483
relative error = 0.2462 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.511
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4591.3MB, alloc=44.3MB, time=56.81
x[1] = 1.483 0.452
h = 0.001 0.003
y[1] (numeric) = -1.67110134049 1.0273751148
y[1] (closed_form) = -1.67088823464 1.02255085211
absolute error = 0.004829
relative error = 0.2465 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.512
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4637.0MB, alloc=44.3MB, time=57.38
x[1] = 1.484 0.455
h = 0.0001 0.004
y[1] (numeric) = -1.66443075437 1.02902930238
y[1] (closed_form) = -1.66423185044 1.02418784004
absolute error = 0.004846
relative error = 0.248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4682.4MB, alloc=44.3MB, time=57.94
x[1] = 1.4841 0.459
h = 0.003 0.006
y[1] (numeric) = -1.65699379472 1.03344225705
y[1] (closed_form) = -1.65679890661 1.02856705076
absolute error = 0.004879
relative error = 0.2502 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4728.0MB, alloc=44.3MB, time=58.50
x[1] = 1.4871 0.465
h = 0.0001 0.005
y[1] (numeric) = -1.64262768277 1.03473623023
y[1] (closed_form) = -1.64251877449 1.0298117835
absolute error = 0.004926
relative error = 0.2541 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.518
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4773.6MB, alloc=44.3MB, time=59.07
x[1] = 1.4872 0.47
h = 0.0001 0.003
y[1] (numeric) = -1.63345285386 1.04007027884
y[1] (closed_form) = -1.63334945004 1.03509809856
absolute error = 0.004973
relative error = 0.2572 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.519
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4819.1MB, alloc=44.3MB, time=59.63
x[1] = 1.4873 0.473
h = 0.001 0.001
y[1] (numeric) = -1.62791133927 1.04313223737
y[1] (closed_form) = -1.62781215907 1.03814379997
absolute error = 0.004989
relative error = 0.2584 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.519
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4864.8MB, alloc=44.3MB, time=60.20
x[1] = 1.4883 0.474
h = 0.001 0.003
y[1] (numeric) = -1.62503397131 1.04239114559
y[1] (closed_form) = -1.62493870141 1.03740410583
absolute error = 0.004988
relative error = 0.2587 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.52
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=4910.4MB, alloc=44.3MB, time=60.77
x[1] = 1.4893 0.477
h = 0.0001 0.004
y[1] (numeric) = -1.61855753383 1.04378088465
y[1] (closed_form) = -1.61847656261 1.03877832058
absolute error = 0.005003
relative error = 0.2602 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4955.9MB, alloc=44.3MB, time=61.33
x[1] = 1.4894 0.481
h = 0.003 0.006
y[1] (numeric) = -1.61125926903 1.04780622445
y[1] (closed_form) = -1.61118382987 1.04277199807
absolute error = 0.005035
relative error = 0.2623 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5001.4MB, alloc=44.3MB, time=61.90
x[1] = 1.4924 0.487
h = 0.0001 0.005
y[1] (numeric) = -1.59738160785 1.04861974805
y[1] (closed_form) = -1.59738999057 1.04354335622
absolute error = 0.005076
relative error = 0.2661 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.526
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5046.9MB, alloc=44.3MB, time=62.46
x[1] = 1.4925 0.492
h = 0.0001 0.003
y[1] (numeric) = -1.58838404157 1.05348542543
y[1] (closed_form) = -1.58840006389 1.04836428806
absolute error = 0.005121
relative error = 0.2691 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.527
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5092.5MB, alloc=44.3MB, time=63.02
x[1] = 1.4926 0.495
h = 0.001 0.001
y[1] (numeric) = -1.58295549973 1.05627169565
y[1] (closed_form) = -1.58297636607 1.05113542925
absolute error = 0.005136
relative error = 0.2703 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.528
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5138.0MB, alloc=44.3MB, time=63.58
x[1] = 1.4936 0.496
h = 0.001 0.003
y[1] (numeric) = -1.58020547295 1.05547344665
y[1] (closed_form) = -1.58022997171 1.05033871074
absolute error = 0.005135
relative error = 0.2706 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.529
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5183.6MB, alloc=44.3MB, time=64.15
x[1] = 1.4946 0.499
h = 0.0001 0.004
y[1] (numeric) = -1.57392579895 1.05662278801
y[1] (closed_form) = -1.57396457549 1.0514740869
absolute error = 0.005149
relative error = 0.272 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.53
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=5229.3MB, alloc=44.3MB, time=64.72
memory used=5274.8MB, alloc=44.3MB, time=65.29
x[1] = 1.4947 0.503
h = 0.003 0.006
y[1] (numeric) = -1.56677790062 1.06028844817
y[1] (closed_form) = -1.56682347634 1.05511011358
absolute error = 0.005179
relative error = 0.2741 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.531
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5320.3MB, alloc=44.3MB, time=65.86
x[1] = 1.4977 0.509
h = 0.0001 0.005
y[1] (numeric) = -1.55338578127 1.06067169735
y[1] (closed_form) = -1.55351271256 1.05545761681
absolute error = 0.005216
relative error = 0.2777 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.535
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5365.8MB, alloc=44.3MB, time=66.43
x[1] = 1.4978 0.514
h = 0.0001 0.003
y[1] (numeric) = -1.54457868481 1.06510303085
y[1] (closed_form) = -1.54471503679 1.05984711009
absolute error = 0.005258
relative error = 0.2807 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.535
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5411.3MB, alloc=44.3MB, time=67.00
x[1] = 1.4979 0.517
h = 0.001 0.001
y[1] (numeric) = -1.53927030776 1.06763403124
y[1] (closed_form) = -1.53941200357 1.06236406736
absolute error = 0.005272
relative error = 0.2819 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.536
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5456.9MB, alloc=44.3MB, time=67.84
x[1] = 1.4989 0.518
h = 0.0001 0.004
y[1] (numeric) = -1.53664345817 1.06678785124
y[1] (closed_form) = -1.53678851948 1.06151952269
absolute error = 0.00527
relative error = 0.2822 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.537
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5502.5MB, alloc=44.3MB, time=68.43
x[1] = 1.499 0.522
h = 0.003 0.006
y[1] (numeric) = -1.52962881713 1.07016522485
y[1] (closed_form) = -1.52978125119 1.06486709949
absolute error = 0.0053
relative error = 0.2844 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.538
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5548.0MB, alloc=44.3MB, time=69.02
x[1] = 1.502 0.528
h = 0.0001 0.005
y[1] (numeric) = -1.51664562238 1.07020968582
y[1] (closed_form) = -1.51687716981 1.06488087464
absolute error = 0.005334
relative error = 0.2878 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5593.4MB, alloc=44.3MB, time=69.62
x[1] = 1.5021 0.533
h = 0.0001 0.003
y[1] (numeric) = -1.50800601795 1.07429073734
y[1] (closed_form) = -1.50824829836 1.06892248872
absolute error = 0.005374
relative error = 0.2907 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5639.0MB, alloc=44.3MB, time=70.22
x[1] = 1.5022 0.536
h = 0.001 0.001
y[1] (numeric) = -1.5028027241 1.07661606509
y[1] (closed_form) = -1.50305070512 1.07123466562
absolute error = 0.005387
relative error = 0.2919 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.543
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5684.5MB, alloc=44.3MB, time=70.81
x[1] = 1.5032 0.537
h = 0.001 0.003
y[1] (numeric) = -1.50027791589 1.07573391183
y[1] (closed_form) = -1.50052904322 1.07035422106
absolute error = 0.005386
relative error = 0.2922 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.544
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5730.3MB, alloc=44.3MB, time=71.40
x[1] = 1.5042 0.54
h = 0.0001 0.004
y[1] (numeric) = -1.49436330857 1.0764922139
y[1] (closed_form) = -1.49462844365 1.07110115776
absolute error = 0.005398
relative error = 0.2935 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5775.7MB, alloc=44.3MB, time=71.99
x[1] = 1.5043 0.544
h = 0.003 0.006
y[1] (numeric) = -1.48751391658 1.07955651769
y[1] (closed_form) = -1.48778765857 1.07413940488
absolute error = 0.005424
relative error = 0.2956 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5821.3MB, alloc=44.3MB, time=72.58
x[1] = 1.5073 0.55
h = 0.0001 0.005
y[1] (numeric) = -1.47500380878 1.079254095
y[1] (closed_form) = -1.47535382033 1.07381159304
absolute error = 0.005454
relative error = 0.2989 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.55
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=5866.9MB, alloc=44.3MB, time=73.20
x[1] = 1.5074 0.555
h = 0.0001 0.003
y[1] (numeric) = -1.46657165348 1.08295965417
y[1] (closed_form) = -1.46693362066 1.07748041993
absolute error = 0.005491
relative error = 0.3017 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.551
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5912.4MB, alloc=44.3MB, time=73.81
x[1] = 1.5075 0.558
h = 0.001 0.001
y[1] (numeric) = -1.46149751325 1.0850649062
y[1] (closed_form) = -1.46186549321 1.07957351589
absolute error = 0.005504
relative error = 0.3029 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.552
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5957.9MB, alloc=44.3MB, time=74.42
x[1] = 1.5085 0.559
h = 0.001 0.003
y[1] (numeric) = -1.45908756013 1.08414962687
y[1] (closed_form) = -1.45945844256 1.07866000661
absolute error = 0.005502
relative error = 0.3032 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.553
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6003.6MB, alloc=44.3MB, time=75.03
x[1] = 1.5095 0.562
h = 0.0001 0.004
y[1] (numeric) = -1.45336873152 1.08472770923
y[1] (closed_form) = -1.45375336535 1.07922796298
absolute error = 0.005513
relative error = 0.3045 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.554
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6049.2MB, alloc=44.3MB, time=75.64
x[1] = 1.5096 0.566
h = 0.003 0.006
y[1] (numeric) = -1.44668992508 1.08750489568
y[1] (closed_form) = -1.44708386223 1.08198090301
absolute error = 0.005538
relative error = 0.3065 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.555
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6094.8MB, alloc=44.3MB, time=76.23
x[1] = 1.5126 0.572
h = 0.0001 0.005
y[1] (numeric) = -1.43464283777 1.08689518738
y[1] (closed_form) = -1.43511009026 1.08135055365
absolute error = 0.005564
relative error = 0.3097 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.559
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6140.3MB, alloc=44.3MB, time=76.84
x[1] = 1.5127 0.577
h = 0.0001 0.003
y[1] (numeric) = -1.42642348112 1.09025445894
y[1] (closed_form) = -1.42690366253 1.08467567162
absolute error = 0.005599
relative error = 0.3124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.56
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=6185.8MB, alloc=44.3MB, time=77.44
x[1] = 1.5128 0.58
h = 0.001 0.001
y[1] (numeric) = -1.42148114423 1.09215704038
y[1] (closed_form) = -1.42196756819 1.08656703802
absolute error = 0.005611
relative error = 0.3135 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.56
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=6231.4MB, alloc=44.3MB, time=78.05
x[1] = 1.5138 0.581
h = 0.001 0.003
y[1] (numeric) = -1.41918132638 1.09121537881
y[1] (closed_form) = -1.41967042242 1.08562718876
absolute error = 0.00561
relative error = 0.3139 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.562
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6277.0MB, alloc=44.3MB, time=78.65
x[1] = 1.5148 0.584
h = 0.0001 0.004
y[1] (numeric) = -1.41365558597 1.09163133931
y[1] (closed_form) = -1.41415812432 1.08603415883
absolute error = 0.00562
relative error = 0.3152 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.563
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6322.5MB, alloc=44.3MB, time=79.25
x[1] = 1.5149 0.588
h = 0.003 0.006
y[1] (numeric) = -1.40715058737 1.09414408262
y[1] (closed_form) = -1.40766297088 1.08852437527
absolute error = 0.005643
relative error = 0.3171 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.564
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6368.0MB, alloc=44.3MB, time=79.83
x[1] = 1.5179 0.594
h = 0.0001 0.005
y[1] (numeric) = -1.39555489269 1.09326327755
y[1] (closed_form) = -1.39613757592 1.08762716951
absolute error = 0.005666
relative error = 0.3202 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.568
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6413.5MB, alloc=44.3MB, time=80.41
memory used=6459.1MB, alloc=44.3MB, time=80.99
x[1] = 1.518 0.599
h = 0.0001 0.003
y[1] (numeric) = -1.3875516378 1.0963036921
y[1] (closed_form) = -1.38814800535 1.09063587643
absolute error = 0.005699
relative error = 0.3228 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.569
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6504.5MB, alloc=44.3MB, time=81.57
x[1] = 1.5181 0.602
h = 0.001 0.001
y[1] (numeric) = -1.38274258064 1.09801991882
y[1] (closed_form) = -1.38334534936 1.09234177426
absolute error = 0.00571
relative error = 0.324 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.569
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6550.0MB, alloc=44.3MB, time=82.15
x[1] = 1.5191 0.603
h = 0.001 0.003
y[1] (numeric) = -1.38054813458 1.09705787297
y[1] (closed_form) = -1.38115335861 1.09138156661
absolute error = 0.005708
relative error = 0.3243 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.57
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=6595.5MB, alloc=44.3MB, time=82.73
x[1] = 1.5201 0.606
h = 0.0001 0.004
y[1] (numeric) = -1.37521196587 1.0973283715
y[1] (closed_form) = -1.37583028227 1.09164411196
absolute error = 0.005718
relative error = 0.3256 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.572
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6641.0MB, alloc=44.3MB, time=83.31
x[1] = 1.5202 0.61
h = 0.003 0.006
y[1] (numeric) = -1.36888250024 1.09959791591
y[1] (closed_form) = -1.36951106917 1.09389275573
absolute error = 0.00574
relative error = 0.3275 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.573
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6686.6MB, alloc=44.3MB, time=83.90
x[1] = 1.5232 0.616
h = 0.0001 0.005
y[1] (numeric) = -1.35772538477 1.09847898688
y[1] (closed_form) = -1.35842121687 1.09276119929
absolute error = 0.00576
relative error = 0.3304 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.577
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6732.2MB, alloc=44.3MB, time=84.47
x[1] = 1.5233 0.621
h = 0.0001 0.003
y[1] (numeric) = -1.34993979135 1.10122621629
y[1] (closed_form) = -1.35064987393 1.09547903122
absolute error = 0.005791
relative error = 0.333 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.578
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6777.8MB, alloc=44.3MB, time=85.04
x[1] = 1.5234 0.624
h = 0.001 0.001
y[1] (numeric) = -1.34526449507 1.10277133066
y[1] (closed_form) = -1.34598107641 1.09701464798
absolute error = 0.005801
relative error = 0.3341 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.578
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6823.2MB, alloc=44.3MB, time=85.61
x[1] = 1.5244 0.625
h = 0.0001 0.004
y[1] (numeric) = -1.34317066828 1.1017942155
y[1] (closed_form) = -1.34388950176 1.09603938285
absolute error = 0.0058
relative error = 0.3344 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.579
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6868.8MB, alloc=44.3MB, time=86.19
x[1] = 1.5245 0.629
h = 0.003 0.006
y[1] (numeric) = -1.33699015962 1.10386979806
y[1] (closed_form) = -1.33771948481 1.09809385263
absolute error = 0.005822
relative error = 0.3364 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.58
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=6914.4MB, alloc=44.3MB, time=86.76
x[1] = 1.5275 0.635
h = 0.0001 0.005
y[1] (numeric) = -1.32619727207 1.10256499668
y[1] (closed_form) = -1.32699129335 1.09677936384
absolute error = 0.00584
relative error = 0.3392 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.584
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6959.8MB, alloc=44.3MB, time=87.34
x[1] = 1.5276 0.64
h = 0.0001 0.003
y[1] (numeric) = -1.31859604352 1.10507651314
y[1] (closed_form) = -1.31940469617 1.09926335803
absolute error = 0.005869
relative error = 0.3418 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.585
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7005.4MB, alloc=44.3MB, time=87.90
x[1] = 1.5277 0.643
h = 0.001 0.001
y[1] (numeric) = -1.3140338158 1.10648416056
y[1] (closed_form) = -1.31484901833 1.10066217966
absolute error = 0.005879
relative error = 0.3428 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.586
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7050.9MB, alloc=44.3MB, time=88.47
x[1] = 1.5287 0.644
h = 0.001 0.003
y[1] (numeric) = -1.31202272916 1.10549673085
y[1] (closed_form) = -1.31284001961 1.09967660278
absolute error = 0.005877
relative error = 0.3432 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.587
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7096.5MB, alloc=44.3MB, time=89.05
x[1] = 1.5297 0.647
h = 0.0001 0.004
y[1] (numeric) = -1.30702648728 1.10553414059
y[1] (closed_form) = -1.30785615384 1.09970775321
absolute error = 0.005885
relative error = 0.3444 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.589
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7142.1MB, alloc=44.3MB, time=89.63
x[1] = 1.5298 0.651
h = 0.003 0.006
y[1] (numeric) = -1.30102167933 1.10740082201
y[1] (closed_form) = -1.30186207611 1.10155630831
absolute error = 0.005905
relative error = 0.3462 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.589
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7187.6MB, alloc=44.3MB, time=90.20
x[1] = 1.5328 0.657
h = 0.0001 0.005
y[1] (numeric) = -1.29064174619 1.10591156266
y[1] (closed_form) = -1.29154384181 1.10006036912
absolute error = 0.00592
relative error = 0.349 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.593
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7233.3MB, alloc=44.3MB, time=90.78
x[1] = 1.5329 0.662
h = 0.0001 0.003
y[1] (numeric) = -1.28325760138 1.10817314343
y[1] (closed_form) = -1.28417460745 1.10229648707
absolute error = 0.005948
relative error = 0.3514 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.594
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7278.8MB, alloc=44.3MB, time=91.36
x[1] = 1.533 0.665
h = 0.001 0.001
y[1] (numeric) = -1.27882806166 1.10943530277
y[1] (closed_form) = -1.27975162443 1.10355055281
absolute error = 0.005957
relative error = 0.3525 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.595
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7324.2MB, alloc=44.3MB, time=91.93
x[1] = 1.534 0.666
h = 0.001 0.003
y[1] (numeric) = -1.27690897082 1.10844113542
y[1] (closed_form) = -1.27783444279 1.10255822933
absolute error = 0.005955
relative error = 0.3529 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.596
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7369.8MB, alloc=44.3MB, time=92.51
x[1] = 1.535 0.669
h = 0.0001 0.004
y[1] (numeric) = -1.27208925704 1.10837351801
y[1] (closed_form) = -1.27302668852 1.10248514213
absolute error = 0.005963
relative error = 0.3541 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.598
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7415.4MB, alloc=44.3MB, time=93.09
x[1] = 1.5351 0.673
h = 0.003 0.006
y[1] (numeric) = -1.26625878683 1.11005018002
y[1] (closed_form) = -1.26720706413 1.10414503873
absolute error = 0.005981
relative error = 0.3558 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.599
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7461.0MB, alloc=44.3MB, time=93.66
x[1] = 1.5381 0.679
h = 0.0001 0.005
y[1] (numeric) = -1.25627717829 1.10840137003
y[1] (closed_form) = -1.25728421439 1.1024921978
absolute error = 0.005994
relative error = 0.3585 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.603
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7506.6MB, alloc=44.3MB, time=94.24
x[1] = 1.5382 0.684
h = 0.0001 0.003
y[1] (numeric) = -1.24910805667 1.11043393109
y[1] (closed_form) = -1.25013015995 1.10450122319
absolute error = 0.00602
relative error = 0.3609 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7552.2MB, alloc=44.3MB, time=94.82
memory used=7597.8MB, alloc=44.3MB, time=95.39
x[1] = 1.5383 0.687
h = 0.001 0.001
y[1] (numeric) = -1.24480963807 1.11156296562
y[1] (closed_form) = -1.24583826718 1.1056228451
absolute error = 0.006029
relative error = 0.3619 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7643.4MB, alloc=44.3MB, time=95.96
x[1] = 1.5393 0.688
h = 0.001 0.003
y[1] (numeric) = -1.24297802833 1.11056574404
y[1] (closed_form) = -1.24400840052 1.10462744987
absolute error = 0.006027
relative error = 0.3623 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.606
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7689.1MB, alloc=44.3MB, time=96.54
x[1] = 1.5403 0.691
h = 0.0001 0.004
y[1] (numeric) = -1.23832952436 1.11040491505
y[1] (closed_form) = -1.23937143018 1.10446186562
absolute error = 0.006034
relative error = 0.3635 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.607
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7734.5MB, alloc=44.3MB, time=97.11
x[1] = 1.5404 0.695
h = 0.003 0.006
y[1] (numeric) = -1.23267124265 1.11190763981
y[1] (closed_form) = -1.23372403566 1.10594909661
absolute error = 0.006051
relative error = 0.3652 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.608
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7780.1MB, alloc=44.3MB, time=97.70
x[1] = 1.5434 0.701
h = 0.0001 0.005
y[1] (numeric) = -1.22307312969 1.11012175793
y[1] (closed_form) = -1.22418181543 1.10416150818
absolute error = 0.006062
relative error = 0.3677 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.612
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7825.5MB, alloc=44.3MB, time=98.28
x[1] = 1.5435 0.706
h = 0.0001 0.003
y[1] (numeric) = -1.21611610663 1.11194467875
y[1] (closed_form) = -1.21723991252 1.10596269238
absolute error = 0.006087
relative error = 0.3701 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.613
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7871.1MB, alloc=44.3MB, time=98.86
x[1] = 1.5436 0.709
h = 0.001 0.001
y[1] (numeric) = -1.21194676017 1.11295202796
y[1] (closed_form) = -1.21307702971 1.10696326085
absolute error = 0.006094
relative error = 0.3711 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.614
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7916.6MB, alloc=44.3MB, time=99.43
x[1] = 1.5446 0.71
h = 0.001 0.003
y[1] (numeric) = -1.21019825185 1.11195496839
y[1] (closed_form) = -1.21133011042 1.10596800305
absolute error = 0.006093
relative error = 0.3715 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.615
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7962.1MB, alloc=44.3MB, time=100.00
x[1] = 1.5456 0.713
h = 0.0001 0.004
y[1] (numeric) = -1.20571544391 1.11171168123
y[1] (closed_form) = -1.20685840608 1.10572060605
absolute error = 0.006099
relative error = 0.3726 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.617
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8007.7MB, alloc=44.3MB, time=100.57
x[1] = 1.5457 0.717
h = 0.003 0.006
y[1] (numeric) = -1.20022658973 1.11305534856
y[1] (closed_form) = -1.20138041787 1.10704996527
absolute error = 0.006115
relative error = 0.3743 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.617
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8053.3MB, alloc=44.3MB, time=101.14
x[1] = 1.5487 0.723
h = 0.0001 0.005
y[1] (numeric) = -1.19099710395 1.1111526404
y[1] (closed_form) = -1.19220404541 1.10514758234
absolute error = 0.006125
relative error = 0.3768 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.622
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8098.9MB, alloc=44.3MB, time=101.71
x[1] = 1.5488 0.728
h = 0.0001 0.003
y[1] (numeric) = -1.18424855377 1.11278384414
y[1] (closed_form) = -1.18547058095 1.10675872542
absolute error = 0.006148
relative error = 0.3791 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.623
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8144.4MB, alloc=44.3MB, time=102.29
x[1] = 1.5489 0.731
h = 0.001 0.001
y[1] (numeric) = -1.18020584267 1.1136800742
y[1] (closed_form) = -1.18143424557 1.10764875993
absolute error = 0.006155
relative error = 0.3801 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.623
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8189.9MB, alloc=44.3MB, time=102.87
x[1] = 1.5499 0.732
h = 0.0001 0.004
y[1] (numeric) = -1.1785362066 1.11268597313
y[1] (closed_form) = -1.17976605594 1.10665643029
absolute error = 0.006154
relative error = 0.3804 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8235.5MB, alloc=44.3MB, time=103.45
x[1] = 1.55 0.736
h = 0.003 0.006
y[1] (numeric) = -1.17318877596 1.11390305815
y[1] (closed_form) = -1.1744295942 1.1078589158
absolute error = 0.00617
relative error = 0.3822 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8281.1MB, alloc=44.3MB, time=104.03
x[1] = 1.553 0.742
h = 0.0001 0.005
y[1] (numeric) = -1.16426365117 1.11191028259
y[1] (closed_form) = -1.16555528679 1.10586803417
absolute error = 0.006179
relative error = 0.3846 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.63
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=8326.6MB, alloc=44.3MB, time=104.61
x[1] = 1.5531 0.747
h = 0.0001 0.003
y[1] (numeric) = -1.15768919454 1.11338734995
y[1] (closed_form) = -1.15899584536 1.10732639076
absolute error = 0.0062
relative error = 0.3868 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.631
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8372.3MB, alloc=44.3MB, time=105.19
x[1] = 1.5532 0.75
h = 0.001 0.001
y[1] (numeric) = -1.15375213221 1.11419430144
y[1] (closed_form) = -1.15506507243 1.10812761629
absolute error = 0.006207
relative error = 0.3878 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.631
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8417.8MB, alloc=44.3MB, time=106.03
x[1] = 1.5542 0.751
h = 0.001 0.003
y[1] (numeric) = -1.1521471966 1.11320382405
y[1] (closed_form) = -1.15346146883 1.10713888199
absolute error = 0.006206
relative error = 0.3881 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.633
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8463.3MB, alloc=44.3MB, time=107.09
x[1] = 1.5552 0.754
h = 0.0001 0.004
y[1] (numeric) = -1.14795695481 1.11283059551
y[1] (closed_form) = -1.14928153951 1.10676258473
absolute error = 0.006211
relative error = 0.3893 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.634
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8508.9MB, alloc=44.3MB, time=108.01
x[1] = 1.5553 0.758
h = 0.0001 0.004
y[1] (numeric) = -1.14277288403 1.1139121381
y[1] (closed_form) = -1.14410817449 1.10783181131
absolute error = 0.006225
relative error = 0.3909 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.635
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8554.3MB, alloc=44.3MB, time=108.59
x[1] = 1.5554 0.762
h = 0.003 0.006
y[1] (numeric) = -1.13761151972 1.11496504674
y[1] (closed_form) = -1.13895796944 1.10887325536
absolute error = 0.006239
relative error = 0.3925 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.636
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8599.8MB, alloc=44.3MB, time=109.18
x[1] = 1.5584 0.768
h = 0.0001 0.005
y[1] (numeric) = -1.12908269549 1.11286263735
y[1] (closed_form) = -1.13047697793 1.10677464443
absolute error = 0.006246
relative error = 0.3948 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.64
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=8645.5MB, alloc=44.3MB, time=109.76
x[1] = 1.5585 0.773
h = 0.0001 0.003
y[1] (numeric) = -1.12273727415 1.11414396228
y[1] (closed_form) = -1.12414642855 1.10803897076
absolute error = 0.006266
relative error = 0.3969 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.641
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8691.0MB, alloc=44.3MB, time=110.34
memory used=8736.7MB, alloc=44.3MB, time=110.93
x[1] = 1.5586 0.776
h = 0.001 0.001
y[1] (numeric) = -1.11893907879 1.11483760201
y[1] (closed_form) = -1.12035439353 1.10872747795
absolute error = 0.006272
relative error = 0.3979 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.642
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8782.2MB, alloc=44.3MB, time=111.52
x[1] = 1.5596 0.777
h = 0.001 0.003
y[1] (numeric) = -1.11741789028 1.11385324815
y[1] (closed_form) = -1.11883439233 1.10774482627
absolute error = 0.006271
relative error = 0.3983 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.643
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8827.7MB, alloc=44.3MB, time=112.10
x[1] = 1.5606 0.78
h = 0.0001 0.004
y[1] (numeric) = -1.11340059234 1.11340875388
y[1] (closed_form) = -1.11482692973 1.10729783395
absolute error = 0.006275
relative error = 0.3994 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.645
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8873.2MB, alloc=44.3MB, time=112.69
x[1] = 1.5607 0.784
h = 0.003 0.006
y[1] (numeric) = -1.10839867816 1.11434195436
y[1] (closed_form) = -1.10983557715 1.10821984557
absolute error = 0.006288
relative error = 0.4009 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.646
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8918.7MB, alloc=44.3MB, time=113.28
x[1] = 1.5637 0.79
h = 0.0001 0.005
y[1] (numeric) = -1.10019501836 1.11217302952
y[1] (closed_form) = -1.10167726892 1.10605602894
absolute error = 0.006294
relative error = 0.4032 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.65
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=8964.2MB, alloc=44.3MB, time=113.87
x[1] = 1.5638 0.795
h = 0.0001 0.003
y[1] (numeric) = -1.09404478916 1.11330920739
y[1] (closed_form) = -1.09554168774 1.10717654863
absolute error = 0.006313
relative error = 0.4053 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.651
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9009.8MB, alloc=44.3MB, time=114.45
x[1] = 1.5639 0.798
h = 0.001 0.001
y[1] (numeric) = -1.09036462875 1.11391912947
y[1] (closed_form) = -1.0918675468 1.10778179776
absolute error = 0.006319
relative error = 0.4062 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.652
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9055.3MB, alloc=44.3MB, time=115.04
x[1] = 1.5649 0.799
h = 0.001 0.003
y[1] (numeric) = -1.08891057367 1.11294425718
y[1] (closed_form) = -1.0904145673 1.10680858569
absolute error = 0.006317
relative error = 0.4066 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.653
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9100.9MB, alloc=44.3MB, time=115.69
x[1] = 1.5659 0.802
h = 0.0001 0.004
y[1] (numeric) = -1.08503647618 1.11245173449
y[1] (closed_form) = -1.08654989192 1.10631398521
absolute error = 0.006322
relative error = 0.4077 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9146.4MB, alloc=44.3MB, time=116.34
x[1] = 1.566 0.806
h = 0.003 0.006
y[1] (numeric) = -1.08018936264 1.1132752749
y[1] (closed_form) = -1.08171315408 1.10712721742
absolute error = 0.006334
relative error = 0.4092 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.656
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9191.9MB, alloc=44.3MB, time=116.92
x[1] = 1.569 0.812
h = 0.0001 0.005
y[1] (numeric) = -1.07229684864 1.11105284072
y[1] (closed_form) = -1.07386361996 1.10491101356
absolute error = 0.006339
relative error = 0.4114 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.66
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=9237.4MB, alloc=44.3MB, time=117.49
x[1] = 1.5691 0.817
h = 0.0001 0.003
y[1] (numeric) = -1.06633654773 1.11205677575
y[1] (closed_form) = -1.06791770365 1.10590053154
absolute error = 0.006356
relative error = 0.4134 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.661
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9283.0MB, alloc=44.3MB, time=118.07
x[1] = 1.5692 0.82
h = 0.001 0.001
y[1] (numeric) = -1.0627711053 1.11259055143
y[1] (closed_form) = -1.06435813006 1.10643005729
absolute error = 0.006362
relative error = 0.4144 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.662
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9328.6MB, alloc=44.3MB, time=118.65
x[1] = 1.5702 0.821
h = 0.001 0.003
y[1] (numeric) = -1.06138062154 1.11162666189
y[1] (closed_form) = -1.0629686191 1.105467784
absolute error = 0.00636
relative error = 0.4147 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.663
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9374.1MB, alloc=44.3MB, time=119.23
x[1] = 1.5712 0.824
h = 0.0001 0.004
y[1] (numeric) = -1.05764413116 1.11109264406
y[1] (closed_form) = -1.05924114815 1.10493206467
absolute error = 0.006364
relative error = 0.4158 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9419.8MB, alloc=44.3MB, time=119.81
x[1] = 1.5713 0.828
h = 0.003 0.006
y[1] (numeric) = -1.0529474573 1.1118163785
y[1] (closed_form) = -1.05455464136 1.10564630606
absolute error = 0.006376
relative error = 0.4173 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.666
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9465.3MB, alloc=44.3MB, time=120.39
x[1] = 1.5743 0.834
h = 0.0001 0.005
y[1] (numeric) = -1.04535247154 1.10955203675
y[1] (closed_form) = -1.0470003737 1.1033891497
absolute error = 0.006379
relative error = 0.4194 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.67
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=9510.9MB, alloc=44.3MB, time=120.97
x[1] = 1.5744 0.839
h = 0.0001 0.003
y[1] (numeric) = -1.03957667114 1.1104355872
y[1] (closed_form) = -1.04123866315 1.10425943115
absolute error = 0.006396
relative error = 0.4214 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.672
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9556.5MB, alloc=44.3MB, time=121.55
x[1] = 1.5745 0.842
h = 0.001 0.001
y[1] (numeric) = -1.03612255046 1.11090016665
y[1] (closed_form) = -1.0377902535 1.10472014964
absolute error = 0.006401
relative error = 0.4223 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.672
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9602.1MB, alloc=44.3MB, time=122.13
x[1] = 1.5755 0.843
h = 0.001 0.003
y[1] (numeric) = -1.03479224897 1.10994852554
y[1] (closed_form) = -1.03646083041 1.10377007941
absolute error = 0.0064
relative error = 0.4227 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.674
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9647.7MB, alloc=44.3MB, time=122.70
x[1] = 1.5765 0.846
h = 0.0001 0.004
y[1] (numeric) = -1.03118788216 1.10937890569
y[1] (closed_form) = -1.03286509214 1.10319909447
absolute error = 0.006403
relative error = 0.4237 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.675
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9693.2MB, alloc=44.3MB, time=123.28
x[1] = 1.5766 0.85
h = 0.003 0.006
y[1] (numeric) = -1.02663718954 1.11001188227
y[1] (closed_form) = -1.02832434024 1.10382333182
absolute error = 0.006414
relative error = 0.4252 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.676
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9738.9MB, alloc=44.3MB, time=123.86
x[1] = 1.5796 0.856
h = 0.0001 0.005
y[1] (numeric) = -1.0193265508 1.10771596283
y[1] (closed_form) = -1.0210522669 1.1015354045
absolute error = 0.006417
relative error = 0.4272 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.681
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9784.5MB, alloc=44.3MB, time=124.44
x[1] = 1.5797 0.861
h = 0.0001 0.003
y[1] (numeric) = -1.01372972227 1.10849001709
y[1] (closed_form) = -1.01546920909 1.10229725083
absolute error = 0.006432
relative error = 0.4292 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.682
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9829.9MB, alloc=44.3MB, time=125.01
x[1] = 1.5798 0.864
h = 0.001 0.001
y[1] (numeric) = -1.01038348356 1.10889177545
y[1] (closed_form) = -1.01212851869 1.10269550557
absolute error = 0.006437
relative error = 0.4301 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.683
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9875.5MB, alloc=44.3MB, time=125.59
memory used=9921.2MB, alloc=44.3MB, time=126.17
x[1] = 1.5808 0.865
h = 0.0001 0.004
y[1] (numeric) = -1.00911014562 1.10795343997
y[1] (closed_form) = -1.0108559725 1.10175869469
absolute error = 0.006436
relative error = 0.4304 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.684
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9966.8MB, alloc=44.3MB, time=126.74
x[1] = 1.5809 0.869
h = 0.003 0.006
y[1] (numeric) = -1.00468028725 1.10851425622
y[1] (closed_form) = -1.00643611958 1.10231042494
absolute error = 0.006448
relative error = 0.432 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.685
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10012.3MB, alloc=44.3MB, time=127.32
x[1] = 1.5839 0.875
h = 0.0001 0.005
y[1] (numeric) = -0.9976039712 1.10619536437
y[1] (closed_form) = -0.999396609456 1.10000013761
absolute error = 0.006449
relative error = 0.434 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.689
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10057.7MB, alloc=44.3MB, time=127.90
x[1] = 1.584 0.88
h = 0.0001 0.003
y[1] (numeric) = -0.992155586141 1.10688115851
y[1] (closed_form) = -0.993961716868 1.1006745761
absolute error = 0.006464
relative error = 0.4359 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.69
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=10103.4MB, alloc=44.3MB, time=128.48
x[1] = 1.5841 0.883
h = 0.001 0.001
y[1] (numeric) = -0.988898788206 1.1072323116
y[1] (closed_form) = -0.990710328449 1.10102251157
absolute error = 0.006469
relative error = 0.4367 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.691
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10149.0MB, alloc=44.3MB, time=129.07
x[1] = 1.5851 0.884
h = 0.001 0.003
y[1] (numeric) = -0.987672204488 1.10630550503
y[1] (closed_form) = -0.989484467123 1.10009719031
absolute error = 0.006467
relative error = 0.4371 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.692
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10194.6MB, alloc=44.3MB, time=129.65
x[1] = 1.5861 0.887
h = 0.0001 0.004
y[1] (numeric) = -0.984299270739 1.10568193589
y[1] (closed_form) = -0.986119471938 1.09947279275
absolute error = 0.00647
relative error = 0.4381 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.694
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10240.3MB, alloc=44.3MB, time=130.22
x[1] = 1.5862 0.891
h = 0.003 0.006
y[1] (numeric) = -0.98000733881 1.10616598919
y[1] (closed_form) = -0.981837033986 1.09994936329
absolute error = 0.00648
relative error = 0.4395 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10285.7MB, alloc=44.3MB, time=130.79
x[1] = 1.5892 0.897
h = 0.0001 0.005
y[1] (numeric) = -0.973192173775 1.10383190936
y[1] (closed_form) = -0.975056718515 1.09762446096
absolute error = 0.006481
relative error = 0.4415 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.7
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=10331.3MB, alloc=44.3MB, time=131.36
x[1] = 1.5893 0.902
h = 0.0001 0.003
y[1] (numeric) = -0.967912484661 1.10442619815
y[1] (closed_form) = -0.969790171786 1.09820830895
absolute error = 0.006495
relative error = 0.4433 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.701
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10376.9MB, alloc=44.3MB, time=131.93
x[1] = 1.5894 0.905
h = 0.001 0.001
y[1] (numeric) = -0.96475721236 1.10472505074
y[1] (closed_form) = -0.96664014156 1.09850424845
absolute error = 0.0065
relative error = 0.4442 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.702
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10422.5MB, alloc=44.3MB, time=132.53
x[1] = 1.5904 0.906
h = 0.001 0.003
y[1] (numeric) = -0.963582049683 1.10381307722
y[1] (closed_form) = -0.965465627587 1.09759371334
absolute error = 0.006498
relative error = 0.4445 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.703
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10467.9MB, alloc=44.3MB, time=133.09
x[1] = 1.5914 0.909
h = 0.0001 0.004
y[1] (numeric) = -0.96032637815 1.10316777632
y[1] (closed_form) = -0.962217541223 1.09694782576
absolute error = 0.006501
relative error = 0.4455 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.705
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10513.5MB, alloc=44.3MB, time=133.66
x[1] = 1.5915 0.913
h = 0.003 0.006
y[1] (numeric) = -0.956167592026 1.10358308046
y[1] (closed_form) = -0.958067992969 1.09735624774
absolute error = 0.00651
relative error = 0.4469 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.706
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10559.0MB, alloc=44.3MB, time=134.23
x[1] = 1.5945 0.919
h = 0.0001 0.005
y[1] (numeric) = -0.949601739873 1.10124113622
y[1] (closed_form) = -0.951535136333 1.09502394944
absolute error = 0.006511
relative error = 0.4488 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.71
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=10604.6MB, alloc=44.3MB, time=134.80
x[1] = 1.5946 0.924
h = 0.0001 0.003
y[1] (numeric) = -0.944485182853 1.10175241897
y[1] (closed_form) = -0.946431362141 1.09552563544
absolute error = 0.006524
relative error = 0.4506 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.711
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10650.2MB, alloc=44.3MB, time=135.37
x[1] = 1.5947 0.927
h = 0.001 0.001
y[1] (numeric) = -0.941428014302 1.10200393295
y[1] (closed_form) = -0.943379267923 1.09577451547
absolute error = 0.006528
relative error = 0.4515 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.712
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10695.8MB, alloc=44.3MB, time=135.94
x[1] = 1.5957 0.928
h = 0.001 0.003
y[1] (numeric) = -0.940301514591 1.10110737717
y[1] (closed_form) = -0.942253349455 1.09487935141
absolute error = 0.006527
relative error = 0.4518 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.714
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10741.3MB, alloc=44.3MB, time=136.50
x[1] = 1.5967 0.931
h = 0.0001 0.004
y[1] (numeric) = -0.937158198431 1.10044425634
y[1] (closed_form) = -0.939117278987 1.09421585854
absolute error = 0.006529
relative error = 0.4528 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10786.8MB, alloc=44.3MB, time=137.07
x[1] = 1.5968 0.935
h = 0.003 0.006
y[1] (numeric) = -0.933128080473 1.10079727919
y[1] (closed_form) = -0.935096138416 1.09456255337
absolute error = 0.006538
relative error = 0.4541 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.716
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10832.4MB, alloc=44.3MB, time=137.63
x[1] = 1.5998 0.941
h = 0.0001 0.005
y[1] (numeric) = -0.926800190869 1.09845393802
y[1] (closed_form) = -0.928799489155 1.09222923451
absolute error = 0.006538
relative error = 0.456 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.721
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10878.0MB, alloc=44.3MB, time=138.20
x[1] = 1.5999 0.946
h = 0.0001 0.003
y[1] (numeric) = -0.921841260896 1.09889000107
y[1] (closed_form) = -0.923852976716 1.09265647914
absolute error = 0.00655
relative error = 0.4578 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.722
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10923.7MB, alloc=44.3MB, time=138.76
x[1] = 1.6 0.949
h = 0.001 0.001
y[1] (numeric) = -0.918878820243 1.09909871753
y[1] (closed_form) = -0.920895443464 1.09286281739
absolute error = 0.006554
relative error = 0.4586 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.723
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10969.4MB, alloc=44.3MB, time=139.33
x[1] = 1.601 0.95
h = 0.001 0.003
y[1] (numeric) = -0.917798376316 1.09821803656
y[1] (closed_form) = -0.919815519065 1.09198348187
absolute error = 0.006553
relative error = 0.459 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.724
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11015.0MB, alloc=44.3MB, time=139.90
x[1] = 1.602 0.953
h = 0.0001 0.004
y[1] (numeric) = -0.914762681597 1.09754060359
y[1] (closed_form) = -0.916786744522 1.09130586712
absolute error = 0.006555
relative error = 0.4599 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.726
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11060.6MB, alloc=44.3MB, time=140.46
memory used=11106.2MB, alloc=44.3MB, time=141.03
x[1] = 1.6021 0.957
h = 0.003 0.006
y[1] (numeric) = -0.910856816266 1.0978372669
y[1] (closed_form) = -0.91288959398 1.09159671346
absolute error = 0.006563
relative error = 0.4612 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11151.8MB, alloc=44.3MB, time=141.60
x[1] = 1.6051 0.963
h = 0.0001 0.005
y[1] (numeric) = -0.904756024631 1.09549822595
y[1] (closed_form) = -0.906818382642 1.08926799019
absolute error = 0.006563
relative error = 0.463 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.732
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11197.3MB, alloc=44.3MB, time=142.17
x[1] = 1.6052 0.968
h = 0.0001 0.003
y[1] (numeric) = -0.899949300181 1.09586619941
y[1] (closed_form) = -0.902023707822 1.08962786275
absolute error = 0.006574
relative error = 0.4648 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.733
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11242.8MB, alloc=44.3MB, time=142.73
x[1] = 1.6053 0.971
h = 0.001 0.001
y[1] (numeric) = -0.8970782712 1.0960362726
y[1] (closed_form) = -0.899157421041 1.08979579191
absolute error = 0.006578
relative error = 0.4656 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.734
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11288.4MB, alloc=44.3MB, time=143.30
x[1] = 1.6063 0.972
h = 0.0001 0.004
y[1] (numeric) = -0.89604142045 1.09517181164
y[1] (closed_form) = -0.898121033398 1.08893263079
absolute error = 0.006577
relative error = 0.4659 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.735
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11333.9MB, alloc=44.3MB, time=143.86
x[1] = 1.6064 0.976
h = 0.003 0.006
y[1] (numeric) = -0.89223815349 1.09542367484
y[1] (closed_form) = -0.89432655427 1.08917832311
absolute error = 0.006585
relative error = 0.4673 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.736
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11379.4MB, alloc=44.3MB, time=144.43
x[1] = 1.6094 0.982
h = 0.0001 0.005
y[1] (numeric) = -0.8863246375 1.09308982881
y[1] (closed_form) = -0.888441265224 1.08685501005
absolute error = 0.006584
relative error = 0.469 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.741
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11424.9MB, alloc=44.3MB, time=145.00
x[1] = 1.6095 0.987
h = 0.0001 0.003
y[1] (numeric) = -0.881643956837 1.09340271347
y[1] (closed_form) = -0.88377232508 1.08716037057
absolute error = 0.006595
relative error = 0.4707 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11470.5MB, alloc=44.3MB, time=145.56
x[1] = 1.6096 0.99
h = 0.001 0.001
y[1] (numeric) = -0.878848610393 1.09354154187
y[1] (closed_form) = -0.88098158306 1.08729724245
absolute error = 0.006599
relative error = 0.4715 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.743
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11516.2MB, alloc=44.3MB, time=146.14
x[1] = 1.6106 0.991
h = 0.001 0.003
y[1] (numeric) = -0.877847613822 1.09269076209
y[1] (closed_form) = -0.87998100442 1.08644772451
absolute error = 0.006597
relative error = 0.4719 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.744
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11561.7MB, alloc=44.3MB, time=146.72
x[1] = 1.6116 0.994
h = 0.0001 0.004
y[1] (numeric) = -0.875000093694 1.09199364756
y[1] (closed_form) = -0.87713983723 1.08575072875
absolute error = 0.006599
relative error = 0.4728 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.746
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11607.2MB, alloc=44.3MB, time=147.28
x[1] = 1.6117 0.998
h = 0.003 0.006
y[1] (numeric) = -0.871313435896 1.09219814999
y[1] (closed_form) = -0.873461411204 1.08595026454
absolute error = 0.006607
relative error = 0.4741 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.747
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11652.7MB, alloc=44.3MB, time=147.85
x[1] = 1.6147 1.004
h = 0.0001 0.005
y[1] (numeric) = -0.865608121181 1.08987753226
y[1] (closed_form) = -0.867782829121 1.08364034898
absolute error = 0.006605
relative error = 0.4758 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.752
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11698.3MB, alloc=44.3MB, time=148.41
x[1] = 1.6148 1.009
h = 0.0001 0.003
y[1] (numeric) = -0.86106991358 1.0901340879
y[1] (closed_form) = -0.863255995299 1.0838899967
absolute error = 0.006616
relative error = 0.4774 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.753
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11743.9MB, alloc=44.3MB, time=148.98
x[1] = 1.6149 1.012
h = 0.001 0.001
y[1] (numeric) = -0.858360041894 1.09024111707
y[1] (closed_form) = -0.860550567702 1.08399526781
absolute error = 0.006619
relative error = 0.4782 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.754
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11789.6MB, alloc=44.3MB, time=149.54
x[1] = 1.6159 1.013
h = 0.001 0.003
y[1] (numeric) = -0.857398420253 1.08940697471
y[1] (closed_form) = -0.85958931634 1.08316234326
absolute error = 0.006618
relative error = 0.4786 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11835.2MB, alloc=44.3MB, time=150.11
x[1] = 1.6169 1.016
h = 0.0001 0.004
y[1] (numeric) = -0.854645982635 1.08870372544
y[1] (closed_form) = -0.85684294506 1.08245934556
absolute error = 0.00662
relative error = 0.4795 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.757
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11880.8MB, alloc=44.3MB, time=150.68
x[1] = 1.617 1.02
h = 0.003 0.006
y[1] (numeric) = -0.851071480765 1.08886622215
y[1] (closed_form) = -0.853276415273 1.08261728047
absolute error = 0.006627
relative error = 0.4807 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.758
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11926.3MB, alloc=44.3MB, time=151.25
x[1] = 1.62 1.026
h = 0.0001 0.005
y[1] (numeric) = -0.845564842843 1.08656272601
y[1] (closed_form) = -0.847795099381 1.08032460037
absolute error = 0.006625
relative error = 0.4824 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.763
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11971.8MB, alloc=44.3MB, time=151.81
x[1] = 1.6201 1.031
h = 0.0001 0.003
y[1] (numeric) = -0.841164014993 1.08676848283
y[1] (closed_form) = -0.843405282347 1.0805240169
absolute error = 0.006635
relative error = 0.484 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.764
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12017.4MB, alloc=44.3MB, time=152.38
x[1] = 1.6202 1.034
h = 0.001 0.001
y[1] (numeric) = -0.838536520405 1.08684692544
y[1] (closed_form) = -0.840782075007 1.08060088293
absolute error = 0.006637
relative error = 0.4848 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.765
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12063.1MB, alloc=44.3MB, time=152.94
x[1] = 1.6212 1.035
h = 0.001 0.003
y[1] (numeric) = -0.837612187815 1.08602951692
y[1] (closed_form) = -0.839858069212 1.07978464926
absolute error = 0.006636
relative error = 0.4851 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.766
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12108.6MB, alloc=44.3MB, time=153.51
x[1] = 1.6222 1.038
h = 0.0001 0.004
y[1] (numeric) = -0.834950776225 1.0853224046
y[1] (closed_form) = -0.837202450505 1.07907790503
absolute error = 0.006638
relative error = 0.486 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.768
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12154.3MB, alloc=44.3MB, time=154.07
x[1] = 1.6223 1.042
h = 0.003 0.006
y[1] (numeric) = -0.831484381946 1.08544709226
y[1] (closed_form) = -0.8337437722 1.07919840395
absolute error = 0.006645
relative error = 0.4872 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.769
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12199.9MB, alloc=44.3MB, time=154.64
x[1] = 1.6253 1.048
h = 0.0001 0.005
y[1] (numeric) = -0.826167344865 1.08316410317
y[1] (closed_form) = -0.828450726162 1.07692629653
absolute error = 0.006643
relative error = 0.4889 %
Correct digits = 2
memory used=12245.5MB, alloc=44.3MB, time=155.20
Radius of convergence (given) for eq 1 = 3.774
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12291.1MB, alloc=44.3MB, time=155.77
x[1] = 1.6254 1.053
h = 0.0001 0.003
y[1] (numeric) = -0.821898942579 1.08332411866
y[1] (closed_form) = -0.824192976997 1.07708049455
absolute error = 0.006652
relative error = 0.4905 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.775
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12336.6MB, alloc=44.3MB, time=156.34
x[1] = 1.6255 1.056
h = 0.001 0.001
y[1] (numeric) = -0.819350816798 1.08337690969
y[1] (closed_form) = -0.821648985493 1.07713187487
absolute error = 0.006654
relative error = 0.4912 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.776
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12382.2MB, alloc=44.3MB, time=156.90
x[1] = 1.6265 1.057
h = 0.001 0.003
y[1] (numeric) = -0.81846180691 1.08257626605
y[1] (closed_form) = -0.820760262746 1.07633236425
absolute error = 0.006654
relative error = 0.4916 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12427.8MB, alloc=44.3MB, time=157.47
x[1] = 1.6275 1.06
h = 0.0001 0.004
y[1] (numeric) = -0.81588753742 1.0818673132
y[1] (closed_form) = -0.818191525447 1.07562388141
absolute error = 0.006655
relative error = 0.4924 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.779
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12473.4MB, alloc=44.3MB, time=158.04
x[1] = 1.6276 1.064
h = 0.003 0.006
y[1] (numeric) = -0.812525319454 1.08195802772
y[1] (closed_form) = -0.814836771802 1.07571075089
absolute error = 0.006661
relative error = 0.4936 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.78
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=12519.0MB, alloc=44.3MB, time=158.60
x[1] = 1.6306 1.07
h = 0.0001 0.005
y[1] (numeric) = -0.807389241284 1.0796984762
y[1] (closed_form) = -0.809723429258 1.07346210482
absolute error = 0.006659
relative error = 0.4952 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.785
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12564.5MB, alloc=44.3MB, time=159.17
x[1] = 1.6307 1.075
h = 0.0001 0.003
y[1] (numeric) = -0.803248456163 1.07981737431
y[1] (closed_form) = -0.805592946032 1.07357566693
absolute error = 0.006667
relative error = 0.4968 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.787
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12610.1MB, alloc=44.3MB, time=159.74
x[1] = 1.6308 1.078
h = 0.001 0.001
y[1] (numeric) = -0.800776783571 1.07984719428
y[1] (closed_form) = -0.803125258898 1.07360422775
absolute error = 0.00667
relative error = 0.4975 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.787
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12655.7MB, alloc=44.3MB, time=160.30
x[1] = 1.6318 1.079
h = 0.0001 0.004
y[1] (numeric) = -0.799921243223 1.07906329007
y[1] (closed_form) = -0.80226996955 1.07282141592
absolute error = 0.006669
relative error = 0.4978 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.789
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12701.2MB, alloc=44.3MB, time=160.87
x[1] = 1.6319 1.083
h = 0.003 0.006
y[1] (numeric) = -0.796644995286 1.07912701666
y[1] (closed_form) = -0.799001274329 1.07288095835
absolute error = 0.006676
relative error = 0.499 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.79
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=12746.7MB, alloc=44.3MB, time=161.44
x[1] = 1.6349 1.089
h = 0.0001 0.005
y[1] (numeric) = -0.791658399486 1.07688765079
y[1] (closed_form) = -0.794036390729 1.07065250297
absolute error = 0.006673
relative error = 0.5006 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.795
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12792.4MB, alloc=44.3MB, time=162.01
x[1] = 1.635 1.094
h = 0.0001 0.003
y[1] (numeric) = -0.787623304999 1.07697310973
y[1] (closed_form) = -0.790011306851 1.0707330138
absolute error = 0.006681
relative error = 0.5021 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.796
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12838.0MB, alloc=44.3MB, time=162.58
x[1] = 1.6351 1.097
h = 0.001 0.001
y[1] (numeric) = -0.785214943823 1.07698425977
y[1] (closed_form) = -0.787606808114 1.07074302629
absolute error = 0.006684
relative error = 0.5028 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.797
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12883.7MB, alloc=44.3MB, time=163.14
x[1] = 1.6361 1.098
h = 0.001 0.003
y[1] (numeric) = -0.784387008947 1.07621433597
y[1] (closed_form) = -0.786779095256 1.06997416125
absolute error = 0.006683
relative error = 0.5032 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.798
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=12929.2MB, alloc=44.3MB, time=163.71
x[1] = 1.6371 1.101
h = 0.0001 0.004
y[1] (numeric) = -0.7819651532 1.07550564977
y[1] (closed_form) = -0.78436232001 1.06926610365
absolute error = 0.006684
relative error = 0.504 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.8
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=12974.8MB, alloc=44.3MB, time=164.27
x[1] = 1.6372 1.105
h = 0.003 0.006
y[1] (numeric) = -0.778786425094 1.07554110911
y[1] (closed_form) = -0.781190605463 1.06929828991
absolute error = 0.00669
relative error = 0.5052 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.801
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13020.2MB, alloc=44.3MB, time=164.84
x[1] = 1.6402 1.111
h = 0.0001 0.005
y[1] (numeric) = -0.773965833589 1.07332967467
y[1] (closed_form) = -0.776390600547 1.06709772549
absolute error = 0.006687
relative error = 0.5067 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.806
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13066.0MB, alloc=44.3MB, time=165.40
x[1] = 1.6403 1.116
h = 0.0001 0.003
y[1] (numeric) = -0.770049855463 1.07338164089
y[1] (closed_form) = -0.772484295805 1.06714515648
absolute error = 0.006695
relative error = 0.5082 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.808
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13111.6MB, alloc=44.3MB, time=165.97
x[1] = 1.6404 1.119
h = 0.001 0.001
y[1] (numeric) = -0.767712800879 1.07337423444
y[1] (closed_form) = -0.770150962923 1.06713674044
absolute error = 0.006697
relative error = 0.5089 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.809
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13157.3MB, alloc=44.3MB, time=166.54
x[1] = 1.6414 1.12
h = 0.001 0.003
y[1] (numeric) = -0.766915165982 1.07262089783
y[1] (closed_form) = -0.7693535197 1.06638442425
absolute error = 0.006696
relative error = 0.5092 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.81
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=13202.9MB, alloc=44.3MB, time=167.11
x[1] = 1.6424 1.123
h = 0.0001 0.004
y[1] (numeric) = -0.764570274217 1.07191502679
y[1] (closed_form) = -0.767013481758 1.06567924959
absolute error = 0.006697
relative error = 0.5101 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.812
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13248.5MB, alloc=44.3MB, time=167.67
x[1] = 1.6425 1.127
h = 0.003 0.006
y[1] (numeric) = -0.761485186744 1.07192579519
y[1] (closed_form) = -0.763935172014 1.06568701662
absolute error = 0.006703
relative error = 0.5112 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.813
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13294.1MB, alloc=44.3MB, time=168.24
x[1] = 1.6455 1.133
h = 0.0001 0.005
y[1] (numeric) = -0.756823108217 1.06974416478
y[1] (closed_form) = -0.759292619058 1.06351618837
absolute error = 0.0067
relative error = 0.5127 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13339.7MB, alloc=44.3MB, time=168.80
x[1] = 1.6456 1.138
h = 0.0001 0.003
y[1] (numeric) = -0.753021869922 1.06976620965
y[1] (closed_form) = -0.755500725606 1.06353407818
absolute error = 0.006707
relative error = 0.5141 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13385.3MB, alloc=44.3MB, time=169.37
x[1] = 1.6457 1.141
h = 0.001 0.001
y[1] (numeric) = -0.750753477168 1.06974231035
y[1] (closed_form) = -0.7532359184 1.06350928606
memory used=13430.9MB, alloc=44.3MB, time=169.94
absolute error = 0.006709
relative error = 0.5148 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.82
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=13476.5MB, alloc=44.3MB, time=170.50
x[1] = 1.6467 1.142
h = 0.001 0.003
y[1] (numeric) = -0.749984579166 1.06900541325
y[1] (closed_form) = -0.752467184468 1.0627733723
absolute error = 0.006708
relative error = 0.5152 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13522.1MB, alloc=44.3MB, time=171.07
x[1] = 1.6477 1.145
h = 0.0001 0.004
y[1] (numeric) = -0.747713391438 1.06830362253
y[1] (closed_form) = -0.750200634945 1.06207233619
absolute error = 0.006709
relative error = 0.516 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13567.8MB, alloc=44.3MB, time=171.64
x[1] = 1.6478 1.149
h = 0.003 0.006
y[1] (numeric) = -0.744718488117 1.06829240283
y[1] (closed_form) = -0.747212279926 1.06205836538
absolute error = 0.006714
relative error = 0.5171 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13613.2MB, alloc=44.3MB, time=172.20
x[1] = 1.6508 1.155
h = 0.0001 0.005
y[1] (numeric) = -0.740207803471 1.06614215424
y[1] (closed_form) = -0.742720120811 1.05991882768
absolute error = 0.006711
relative error = 0.5186 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13658.8MB, alloc=44.3MB, time=172.78
x[1] = 1.6509 1.16
h = 0.0001 0.003
y[1] (numeric) = -0.736517082765 1.06613753965
y[1] (closed_form) = -0.739038425517 1.05991040807
absolute error = 0.006718
relative error = 0.5199 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13704.5MB, alloc=44.3MB, time=173.34
x[1] = 1.651 1.163
h = 0.001 0.001
y[1] (numeric) = -0.734314802818 1.06609903006
y[1] (closed_form) = -0.736839599589 1.05987111221
absolute error = 0.00672
relative error = 0.5206 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13750.1MB, alloc=44.3MB, time=173.91
x[1] = 1.652 1.164
h = 0.001 0.003
y[1] (numeric) = -0.733573169281 1.06537839408
y[1] (closed_form) = -0.736098105028 1.05915142378
absolute error = 0.006719
relative error = 0.521 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13795.9MB, alloc=44.3MB, time=174.48
x[1] = 1.653 1.167
h = 0.0001 0.004
y[1] (numeric) = -0.731372575392 1.06468179745
y[1] (closed_form) = -0.733901944317 1.0584556314
absolute error = 0.00672
relative error = 0.5218 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13841.5MB, alloc=44.3MB, time=175.05
x[1] = 1.6531 1.171
h = 0.003 0.006
y[1] (numeric) = -0.728464524584 1.06465105679
y[1] (closed_form) = -0.731000219006 1.05842237014
absolute error = 0.006725
relative error = 0.5228 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13887.2MB, alloc=44.3MB, time=175.62
x[1] = 1.6561 1.177
h = 0.0001 0.005
y[1] (numeric) = -0.7240984704 1.06253350494
y[1] (closed_form) = -0.726651747829 1.05631541801
absolute error = 0.006722
relative error = 0.5243 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13932.7MB, alloc=44.3MB, time=176.18
x[1] = 1.6562 1.182
h = 0.0001 0.003
y[1] (numeric) = -0.720514198269 1.06250520934
y[1] (closed_form) = -0.723076191085 1.0562836397
absolute error = 0.006728
relative error = 0.5256 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=13978.3MB, alloc=44.3MB, time=176.75
x[1] = 1.6563 1.185
h = 0.001 0.001
y[1] (numeric) = -0.71837557682 1.06245380631
y[1] (closed_form) = -0.720940896754 1.05623154756
absolute error = 0.00673
relative error = 0.5263 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14023.9MB, alloc=44.3MB, time=177.32
x[1] = 1.6573 1.186
h = 0.0001 0.004
y[1] (numeric) = -0.717659820698 1.06174922724
y[1] (closed_form) = -0.720225256812 1.05552788152
absolute error = 0.00673
relative error = 0.5266 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.845
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14069.5MB, alloc=44.3MB, time=177.88
x[1] = 1.6574 1.19
h = 0.003 0.006
y[1] (numeric) = -0.714823474311 1.06170301013
y[1] (closed_form) = -0.717395337239 1.05547883112
absolute error = 0.006735
relative error = 0.5277 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14115.1MB, alloc=44.3MB, time=178.45
x[1] = 1.6604 1.196
h = 0.0001 0.005
y[1] (numeric) = -0.710577163248 1.05961285647
y[1] (closed_form) = -0.713165839825 1.05339917828
absolute error = 0.006731
relative error = 0.5291 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14160.7MB, alloc=44.3MB, time=179.01
x[1] = 1.6605 1.201
h = 0.0001 0.003
y[1] (numeric) = -0.707081137141 1.05956515846
y[1] (closed_form) = -0.709678273349 1.053348258
absolute error = 0.006738
relative error = 0.5305 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14206.3MB, alloc=44.3MB, time=179.58
x[1] = 1.6606 1.204
h = 0.001 0.001
y[1] (numeric) = -0.704995288129 1.0595031956
y[1] (closed_form) = -0.707595646928 1.05328568419
absolute error = 0.006739
relative error = 0.5311 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14252.0MB, alloc=44.3MB, time=180.15
x[1] = 1.6616 1.205
h = 0.001 0.003
y[1] (numeric) = -0.704300944754 1.05881197045
y[1] (closed_form) = -0.706901401413 1.05259534361
absolute error = 0.006739
relative error = 0.5315 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14297.5MB, alloc=44.3MB, time=180.72
x[1] = 1.6626 1.208
h = 0.0001 0.004
y[1] (numeric) = -0.702224008052 1.05812678554
y[1] (closed_form) = -0.704828543361 1.05191103772
absolute error = 0.006739
relative error = 0.5322 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14343.1MB, alloc=44.3MB, time=181.28
x[1] = 1.6627 1.212
h = 0.003 0.006
y[1] (numeric) = -0.699468950765 1.05806461515
y[1] (closed_form) = -0.702079417318 1.05184673086
absolute error = 0.006744
relative error = 0.5332 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14388.7MB, alloc=44.3MB, time=181.85
x[1] = 1.6657 1.218
h = 0.0001 0.005
y[1] (numeric) = -0.695355585456 1.05600907276
y[1] (closed_form) = -0.69798202131 1.04980154845
absolute error = 0.00674
relative error = 0.5347 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.863
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14434.3MB, alloc=44.3MB, time=182.41
x[1] = 1.6658 1.223
h = 0.0001 0.003
y[1] (numeric) = -0.691958865781 1.05594260614
y[1] (closed_form) = -0.694593468884 1.04973213587
absolute error = 0.006746
relative error = 0.536 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14479.9MB, alloc=44.3MB, time=182.97
x[1] = 1.6659 1.226
h = 0.001 0.001
y[1] (numeric) = -0.689932371495 1.05587057742
y[1] (closed_form) = -0.692570078714 1.04965957789
absolute error = 0.006748
relative error = 0.5366 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14525.4MB, alloc=44.3MB, time=183.53
x[1] = 1.6669 1.227
h = 0.001 0.003
y[1] (numeric) = -0.689261531796 1.05519498911
y[1] (closed_form) = -0.691899317866 1.04898484195
absolute error = 0.006747
relative error = 0.5369 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14571.0MB, alloc=44.3MB, time=184.10
x[1] = 1.6679 1.23
h = 0.0001 0.004
y[1] (numeric) = -0.687247075988 1.05451750766
y[1] (closed_form) = -0.689888763348 1.04830826925
absolute error = 0.006748
relative error = 0.5377 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14616.6MB, alloc=44.3MB, time=184.66
memory used=14662.2MB, alloc=44.3MB, time=185.22
x[1] = 1.668 1.234
h = 0.003 0.006
y[1] (numeric) = -0.684570036424 1.05444177891
y[1] (closed_form) = -0.687217451563 1.04823058618
absolute error = 0.006752
relative error = 0.5387 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.87
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=14707.9MB, alloc=44.3MB, time=185.79
x[1] = 1.671 1.24
h = 0.0001 0.005
y[1] (numeric) = -0.680583779683 1.05242155579
y[1] (closed_form) = -0.683246368268 1.04622057026
absolute error = 0.006748
relative error = 0.5401 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14753.3MB, alloc=44.3MB, time=186.35
x[1] = 1.6711 1.245
h = 0.0001 0.003
y[1] (numeric) = -0.677282720443 1.0523386116
y[1] (closed_form) = -0.679953193611 1.04613493452
absolute error = 0.006754
relative error = 0.5413 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14799.0MB, alloc=44.3MB, time=186.92
x[1] = 1.6712 1.248
h = 0.001 0.001
y[1] (numeric) = -0.675313386611 1.05225783247
y[1] (closed_form) = -0.677986849908 1.04605370055
absolute error = 0.006756
relative error = 0.5419 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14844.6MB, alloc=44.3MB, time=187.48
x[1] = 1.6722 1.249
h = 0.001 0.003
y[1] (numeric) = -0.674664880739 1.05159762403
y[1] (closed_form) = -0.677338405663 1.04539431351
absolute error = 0.006755
relative error = 0.5423 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14890.2MB, alloc=44.3MB, time=188.04
x[1] = 1.6732 1.252
h = 0.0001 0.004
y[1] (numeric) = -0.672710319268 1.05092850171
y[1] (closed_form) = -0.675387576955 1.04472612412
absolute error = 0.006756
relative error = 0.543 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.881
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14935.8MB, alloc=44.3MB, time=188.61
x[1] = 1.6733 1.256
h = 0.003 0.006
y[1] (numeric) = -0.670108428079 1.05084094296
y[1] (closed_form) = -0.672791216939 1.04463677885
absolute error = 0.006759
relative error = 0.544 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.882
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=14981.4MB, alloc=44.3MB, time=189.17
x[1] = 1.6763 1.262
h = 0.0001 0.005
y[1] (numeric) = -0.666243737495 1.04885658012
y[1] (closed_form) = -0.66894094957 1.04266246064
absolute error = 0.006756
relative error = 0.5454 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15027.0MB, alloc=44.3MB, time=189.74
x[1] = 1.6764 1.267
h = 0.0001 0.003
y[1] (numeric) = -0.663034835422 1.04875924773
y[1] (closed_form) = -0.665739659087 1.04256267096
absolute error = 0.006761
relative error = 0.5466 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.889
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15072.7MB, alloc=44.3MB, time=190.31
x[1] = 1.6765 1.27
h = 0.001 0.001
y[1] (numeric) = -0.66112055506 1.04867091611
y[1] (closed_form) = -0.663828259267 1.04247395225
absolute error = 0.006763
relative error = 0.5472 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.89
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=15118.3MB, alloc=44.3MB, time=190.88
x[1] = 1.6775 1.271
h = 0.001 0.003
y[1] (numeric) = -0.660493280571 1.04802581867
y[1] (closed_form) = -0.66320103081 1.04182964641
absolute error = 0.006762
relative error = 0.5475 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.891
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15163.9MB, alloc=44.3MB, time=191.44
x[1] = 1.6785 1.274
h = 0.0001 0.004
y[1] (numeric) = -0.65859614913 1.04736562024
y[1] (closed_form) = -0.66130747201 1.04117040019
absolute error = 0.006763
relative error = 0.5483 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.893
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15209.5MB, alloc=44.3MB, time=192.00
x[1] = 1.6786 1.278
h = 0.003 0.006
y[1] (numeric) = -0.656066650691 1.04726780654
y[1] (closed_form) = -0.658783314935 1.04107095453
absolute error = 0.006766
relative error = 0.5492 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15255.0MB, alloc=44.3MB, time=192.58
x[1] = 1.6816 1.284
h = 0.0001 0.005
y[1] (numeric) = -0.652318263846 1.04531969698
y[1] (closed_form) = -0.655048643987 1.03913271912
absolute error = 0.006763
relative error = 0.5505 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15300.6MB, alloc=44.3MB, time=193.14
x[1] = 1.6817 1.289
h = 0.0001 0.003
y[1] (numeric) = -0.649198154533 1.04520988112
y[1] (closed_form) = -0.651935882846 1.03902066169
absolute error = 0.006768
relative error = 0.5517 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.901
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15346.1MB, alloc=44.3MB, time=193.70
x[1] = 1.6818 1.292
h = 0.001 0.001
y[1] (numeric) = -0.647336905418 1.04511508737
y[1] (closed_form) = -0.65007740898 1.03892554247
absolute error = 0.006769
relative error = 0.5523 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.902
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15391.7MB, alloc=44.3MB, time=194.27
x[1] = 1.6828 1.293
h = 0.0001 0.004
y[1] (numeric) = -0.646729823197 1.04448482271
y[1] (closed_form) = -0.64947035869 1.03829604081
absolute error = 0.006768
relative error = 0.5527 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.903
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15437.4MB, alloc=44.3MB, time=194.83
x[1] = 1.6829 1.297
h = 0.003 0.006
y[1] (numeric) = -0.644260151073 1.04437892314
y[1] (closed_form) = -0.647006137069 1.03818822748
absolute error = 0.006772
relative error = 0.5536 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.905
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15483.0MB, alloc=44.3MB, time=195.40
x[1] = 1.6859 1.303
h = 0.0001 0.005
y[1] (numeric) = -0.640608299699 1.04246092843
y[1] (closed_form) = -0.643367423029 1.0362799629
absolute error = 0.006769
relative error = 0.5549 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.909
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15528.7MB, alloc=44.3MB, time=195.96
x[1] = 1.686 1.308
h = 0.0001 0.003
y[1] (numeric) = -0.637561908159 1.04234075734
y[1] (closed_form) = -0.640328162779 1.03615772519
absolute error = 0.006774
relative error = 0.5561 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.911
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15574.3MB, alloc=44.3MB, time=196.53
x[1] = 1.6861 1.311
h = 0.001 0.001
y[1] (numeric) = -0.635744688874 1.04224059852
y[1] (closed_form) = -0.638513632106 1.03605729064
absolute error = 0.006775
relative error = 0.5567 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.912
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15619.9MB, alloc=44.3MB, time=197.09
x[1] = 1.6871 1.312
h = 0.001 0.003
y[1] (numeric) = -0.635154372964 1.04162264843
y[1] (closed_form) = -0.637923336763 1.03544007996
absolute error = 0.006774
relative error = 0.557 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.914
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15665.5MB, alloc=44.3MB, time=197.66
x[1] = 1.6881 1.315
h = 0.0001 0.004
y[1] (numeric) = -0.633358060931 1.04097966451
y[1] (closed_form) = -0.636130320483 1.03479807452
absolute error = 0.006775
relative error = 0.5577 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15711.1MB, alloc=44.3MB, time=198.22
x[1] = 1.6882 1.319
h = 0.003 0.006
y[1] (numeric) = -0.630956225768 1.04086569898
y[1] (closed_form) = -0.633733492766 1.03468273501
absolute error = 0.006778
relative error = 0.5586 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15756.7MB, alloc=44.3MB, time=198.79
x[1] = 1.6912 1.325
h = 0.0001 0.005
y[1] (numeric) = -0.627411584142 1.03898440736
y[1] (closed_form) = -0.63020135424 1.03281099214
absolute error = 0.006775
relative error = 0.5599 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.922
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15802.3MB, alloc=44.3MB, time=199.35
memory used=15847.9MB, alloc=44.3MB, time=199.91
x[1] = 1.6913 1.33
h = 0.0001 0.003
y[1] (numeric) = -0.624448098573 1.03885489444
y[1] (closed_form) = -0.627244753781 1.03267959753
absolute error = 0.006779
relative error = 0.5611 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.924
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15893.5MB, alloc=44.3MB, time=200.48
x[1] = 1.6914 1.333
h = 0.001 0.001
y[1] (numeric) = -0.622680374466 1.03875006876
y[1] (closed_form) = -0.625479620615 1.03257454768
absolute error = 0.00678
relative error = 0.5616 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.925
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15939.2MB, alloc=44.3MB, time=201.04
x[1] = 1.6924 1.334
h = 0.001 0.003
y[1] (numeric) = -0.622108469376 1.03814642725
y[1] (closed_form) = -0.624907724448 1.03197161904
absolute error = 0.00678
relative error = 0.562 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.926
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=15984.9MB, alloc=44.3MB, time=201.61
x[1] = 1.6934 1.337
h = 0.0001 0.004
y[1] (numeric) = -0.620363167683 1.03751358439
y[1] (closed_form) = -0.623165580135 1.03133976255
absolute error = 0.00678
relative error = 0.5627 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.928
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16030.4MB, alloc=44.3MB, time=202.17
x[1] = 1.6935 1.341
h = 0.003 0.006
y[1] (numeric) = -0.618026453611 1.03739316334
y[1] (closed_form) = -0.620833702434 1.03121808967
absolute error = 0.006783
relative error = 0.5635 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.929
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16076.0MB, alloc=44.3MB, time=202.74
x[1] = 1.6965 1.347
h = 0.0001 0.005
y[1] (numeric) = -0.614584482459 1.03554862971
y[1] (closed_form) = -0.617403636118 1.02938291974
absolute error = 0.00678
relative error = 0.5648 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.934
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16121.7MB, alloc=44.3MB, time=203.30
x[1] = 1.6966 1.352
h = 0.0001 0.003
y[1] (numeric) = -0.611700910848 1.03541123168
y[1] (closed_form) = -0.61452671254 1.0292438103
absolute error = 0.006784
relative error = 0.5659 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.936
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16167.3MB, alloc=44.3MB, time=203.87
x[1] = 1.6967 1.355
h = 0.001 0.001
y[1] (numeric) = -0.609980886322 1.03530256886
y[1] (closed_form) = -0.612809185237 1.02913497013
absolute error = 0.006785
relative error = 0.5665 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.937
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16213.0MB, alloc=44.3MB, time=204.44
x[1] = 1.6977 1.356
h = 0.001 0.003
y[1] (numeric) = -0.609426513645 1.03471294193
y[1] (closed_form) = -0.612254810993 1.02854603059
absolute error = 0.006785
relative error = 0.5668 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.938
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16258.5MB, alloc=44.3MB, time=205.00
x[1] = 1.6987 1.359
h = 0.0001 0.004
y[1] (numeric) = -0.607730178775 1.03409053136
y[1] (closed_form) = -0.610561502015 1.02792461121
absolute error = 0.006785
relative error = 0.5675 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.94
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=16304.1MB, alloc=44.3MB, time=205.56
x[1] = 1.6988 1.363
h = 0.003 0.006
y[1] (numeric) = -0.605456235847 1.03396474914
y[1] (closed_form) = -0.608292230708 1.02779768966
absolute error = 0.006788
relative error = 0.5684 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.942
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16349.7MB, alloc=44.3MB, time=206.13
x[1] = 1.7018 1.369
h = 0.0001 0.005
y[1] (numeric) = -0.602112624196 1.03215693719
y[1] (closed_form) = -0.604959959434 1.02599905381
absolute error = 0.006784
relative error = 0.5696 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.947
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16395.4MB, alloc=44.3MB, time=206.70
x[1] = 1.7019 1.374
h = 0.0001 0.003
y[1] (numeric) = -0.599306096937 1.03201297944
y[1] (closed_form) = -0.602159852011 1.02585354147
absolute error = 0.006788
relative error = 0.5707 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.949
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16441.0MB, alloc=44.3MB, time=207.26
x[1] = 1.702 1.377
h = 0.001 0.001
y[1] (numeric) = -0.597632050667 1.03190123295
y[1] (closed_form) = -0.600488213071 1.0257416601
absolute error = 0.00679
relative error = 0.5712 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.95
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=16486.6MB, alloc=44.3MB, time=207.83
x[1] = 1.703 1.378
h = 0.001 0.003
y[1] (numeric) = -0.597094381726 1.03132532451
y[1] (closed_form) = -0.599950533128 1.02516641461
absolute error = 0.006789
relative error = 0.5715 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.951
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16532.2MB, alloc=44.3MB, time=208.39
x[1] = 1.704 1.381
h = 0.0001 0.004
y[1] (numeric) = -0.595445067077 1.03071358373
y[1] (closed_form) = -0.598304119408 1.02455566707
absolute error = 0.006789
relative error = 0.5722 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.953
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16577.7MB, alloc=44.3MB, time=208.96
x[1] = 1.7041 1.385
h = 0.003 0.006
y[1] (numeric) = -0.593231642123 1.03058343501
y[1] (closed_form) = -0.596095207488 1.02442448266
absolute error = 0.006792
relative error = 0.5731 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.955
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16623.4MB, alloc=44.3MB, time=209.52
x[1] = 1.7071 1.391
h = 0.0001 0.005
y[1] (numeric) = -0.589982295267 1.02881222835
y[1] (closed_form) = -0.592856668312 1.02266226294
absolute error = 0.006789
relative error = 0.5743 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.959
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16669.0MB, alloc=44.3MB, time=210.09
x[1] = 1.7072 1.396
h = 0.0001 0.003
y[1] (numeric) = -0.587250060693 1.02866291605
y[1] (closed_form) = -0.590130634019 1.02251154045
absolute error = 0.006792
relative error = 0.5753 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.961
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16714.6MB, alloc=44.3MB, time=210.66
x[1] = 1.7073 1.399
h = 0.001 0.001
y[1] (numeric) = -0.585620342829 1.0285487696
y[1] (closed_form) = -0.588503237281 1.02239729762
absolute error = 0.006794
relative error = 0.5759 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.962
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16760.3MB, alloc=44.3MB, time=211.22
x[1] = 1.7083 1.4
h = 0.003 0.006
y[1] (numeric) = -0.585098595649 1.0279862828
y[1] (closed_form) = -0.587981470627 1.02183545032
absolute error = 0.006793
relative error = 0.5762 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.964
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16805.9MB, alloc=44.3MB, time=211.79
x[1] = 1.7113 1.406
h = 0.0001 0.005
y[1] (numeric) = -0.581910147564 1.02624318667
y[1] (closed_form) = -0.584804245353 1.02010042203
absolute error = 0.00679
relative error = 0.5775 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.969
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16851.5MB, alloc=44.3MB, time=212.35
x[1] = 1.7114 1.411
h = 0.0001 0.003
y[1] (numeric) = -0.579227582834 1.02609262547
y[1] (closed_form) = -0.582127731461 1.019948538
absolute error = 0.006794
relative error = 0.5785 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.971
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16897.1MB, alloc=44.3MB, time=212.91
x[1] = 1.7115 1.414
h = 0.001 0.001
y[1] (numeric) = -0.577627478448 1.02597826089
y[1] (closed_form) = -0.580529890112 1.01983409934
absolute error = 0.006795
relative error = 0.5791 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16942.8MB, alloc=44.3MB, time=213.48
x[1] = 1.7125 1.415
h = 0.001 0.003
y[1] (numeric) = -0.577115923588 1.02542521362
y[1] (closed_form) = -0.580018311028 1.01928167581
absolute error = 0.006795
relative error = 0.5794 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.973
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=16988.4MB, alloc=44.3MB, time=214.04
x[1] = 1.7135 1.418
h = 0.0001 0.004
y[1] (numeric) = -0.575541535596 1.02483297415
y[1] (closed_form) = -0.57844662698 1.01869042487
absolute error = 0.006795
relative error = 0.58 %
Correct digits = 2
memory used=17034.2MB, alloc=44.3MB, time=214.61
Radius of convergence (given) for eq 1 = 3.975
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17079.9MB, alloc=44.3MB, time=215.17
x[1] = 1.7136 1.422
h = 0.003 0.006
y[1] (numeric) = -0.573425468494 1.02469886893
y[1] (closed_form) = -0.576334816539 1.01855543703
absolute error = 0.006798
relative error = 0.5808 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17125.6MB, alloc=44.3MB, time=215.74
x[1] = 1.7166 1.428
h = 0.0001 0.005
y[1] (numeric) = -0.570325598471 1.02299115925
y[1] (closed_form) = -0.573244926603 1.01685638192
absolute error = 0.006794
relative error = 0.582 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.981
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17171.1MB, alloc=44.3MB, time=216.30
x[1] = 1.7167 1.433
h = 0.0001 0.003
y[1] (numeric) = -0.567712912449 1.02283696965
y[1] (closed_form) = -0.570638086137 1.0167009953
absolute error = 0.006798
relative error = 0.583 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.983
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17216.7MB, alloc=44.3MB, time=216.86
x[1] = 1.7168 1.436
h = 0.001 0.001
y[1] (numeric) = -0.566154492234 1.02272117932
y[1] (closed_form) = -0.569081848761 1.01658516353
absolute error = 0.006799
relative error = 0.5835 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.985
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17262.2MB, alloc=44.3MB, time=217.43
x[1] = 1.7178 1.437
h = 0.001 0.003
y[1] (numeric) = -0.565657644755 1.02218103654
y[1] (closed_form) = -0.568584970005 1.01604562267
absolute error = 0.006798
relative error = 0.5839 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.986
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17307.8MB, alloc=44.3MB, time=217.99
x[1] = 1.7188 1.44
h = 0.0001 0.004
y[1] (numeric) = -0.564125486502 1.02159983845
y[1] (closed_form) = -0.567055406682 1.01546540942
absolute error = 0.006798
relative error = 0.5845 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.988
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17353.3MB, alloc=44.3MB, time=218.56
x[1] = 1.7189 1.444
h = 0.003 0.006
y[1] (numeric) = -0.562064314349 1.02146355971
y[1] (closed_form) = -0.564998348457 1.01532833129
absolute error = 0.006801
relative error = 0.5853 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.989
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17398.9MB, alloc=44.3MB, time=219.12
x[1] = 1.7219 1.45
h = 0.0001 0.005
y[1] (numeric) = -0.559048695647 1.01979173214
y[1] (closed_form) = -0.561992253322 1.01366496945
absolute error = 0.006797
relative error = 0.5865 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.994
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17444.5MB, alloc=44.3MB, time=219.69
x[1] = 1.722 1.455
h = 0.0001 0.003
y[1] (numeric) = -0.556503434037 1.01963484663
y[1] (closed_form) = -0.559452639914 1.01350700279
absolute error = 0.006801
relative error = 0.5874 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.996
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17490.1MB, alloc=44.3MB, time=220.26
x[1] = 1.7221 1.458
h = 0.001 0.001
y[1] (numeric) = -0.554985227957 1.01951815634
y[1] (closed_form) = -0.557936539801 1.01339030055
absolute error = 0.006802
relative error = 0.5879 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.997
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17535.7MB, alloc=44.3MB, time=220.82
x[1] = 1.7231 1.459
h = 0.001 0.003
y[1] (numeric) = -0.55450241774 1.0189906252
y[1] (closed_form) = -0.557453692009 1.01286335041
absolute error = 0.006801
relative error = 0.5883 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 3.999
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17581.3MB, alloc=44.3MB, time=221.38
x[1] = 1.7241 1.462
h = 0.0001 0.004
y[1] (numeric) = -0.553010861481 1.01842055418
y[1] (closed_form) = -0.555964627013 1.01229425883
absolute error = 0.006801
relative error = 0.5889 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.001
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17626.8MB, alloc=44.3MB, time=221.95
x[1] = 1.7242 1.466
h = 0.003 0.006
y[1] (numeric) = -0.551002658658 1.0182827986
y[1] (closed_form) = -0.55396040086 1.01215578052
absolute error = 0.006804
relative error = 0.5896 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.002
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17672.4MB, alloc=44.3MB, time=222.51
x[1] = 1.7272 1.472
h = 0.0001 0.005
y[1] (numeric) = -0.548067900419 1.01664652452
y[1] (closed_form) = -0.551034734907 1.01052778431
absolute error = 0.0068
relative error = 0.5908 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.007
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17718.1MB, alloc=44.3MB, time=223.08
x[1] = 1.7273 1.477
h = 0.0001 0.003
y[1] (numeric) = -0.545587710545 1.01648778859
y[1] (closed_form) = -0.548560003543 1.01036807391
absolute error = 0.006803
relative error = 0.5918 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.009
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17763.7MB, alloc=44.3MB, time=223.64
x[1] = 1.7274 1.48
h = 0.001 0.001
y[1] (numeric) = -0.54410830993 1.01637067376
y[1] (closed_form) = -0.547082635217 1.01025097378
absolute error = 0.006804
relative error = 0.5923 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.01
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
memory used=17809.5MB, alloc=44.3MB, time=224.21
x[1] = 1.7284 1.481
h = 0.0001 0.004
y[1] (numeric) = -0.543638903892 1.015855464
y[1] (closed_form) = -0.546613185998 1.00973632494
absolute error = 0.006804
relative error = 0.5926 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.012
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17855.1MB, alloc=44.3MB, time=224.78
x[1] = 1.7285 1.485
h = 0.003 0.006
y[1] (numeric) = -0.541674582651 1.01571663408
y[1] (closed_form) = -0.544652952676 1.00959654421
absolute error = 0.006806
relative error = 0.5933 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17900.6MB, alloc=44.3MB, time=225.34
x[1] = 1.7315 1.491
h = 0.0001 0.005
y[1] (numeric) = -0.538807256332 1.01410975678
y[1] (closed_form) = -0.541794364245 1.00799778899
absolute error = 0.006803
relative error = 0.5945 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.018
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17946.3MB, alloc=44.3MB, time=225.90
x[1] = 1.7316 1.496
h = 0.0001 0.003
y[1] (numeric) = -0.536381258787 1.01394930527
y[1] (closed_form) = -0.539373668997 1.00783645016
absolute error = 0.006806
relative error = 0.5954 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=17992.0MB, alloc=44.3MB, time=226.47
x[1] = 1.7317 1.499
h = 0.001 0.001
y[1] (numeric) = -0.534934179362 1.01383172996
y[1] (closed_form) = -0.537928561178 1.00771891119
absolute error = 0.006807
relative error = 0.5959 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.022
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18037.7MB, alloc=44.3MB, time=227.03
x[1] = 1.7327 1.5
h = 0.001 0.003
y[1] (numeric) = -0.534475972992 1.01332674595
y[1] (closed_form) = -0.537470307082 1.00721447156
absolute error = 0.006806
relative error = 0.5962 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.023
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18083.2MB, alloc=44.3MB, time=227.60
x[1] = 1.7337 1.503
h = 0.0001 0.004
y[1] (numeric) = -0.533056027321 1.01277706001
y[1] (closed_form) = -0.536052672937 1.00666575226
absolute error = 0.006806
relative error = 0.5968 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.025
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18128.8MB, alloc=44.3MB, time=228.16
x[1] = 1.7338 1.507
h = 0.003 0.006
y[1] (numeric) = -0.531141533576 1.01263760831
y[1] (closed_form) = -0.534141915156 1.00652570622
absolute error = 0.006809
relative error = 0.5975 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.026
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18174.6MB, alloc=44.3MB, time=228.72
x[1] = 1.7368 1.513
h = 0.0001 0.005
y[1] (numeric) = -0.528349190981 1.01106560249
y[1] (closed_form) = -0.531357922185 1.00496163743
absolute error = 0.006805
relative error = 0.5986 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18220.3MB, alloc=44.3MB, time=229.30
memory used=18266.0MB, alloc=44.3MB, time=229.86
x[1] = 1.7369 1.518
h = 0.0001 0.003
y[1] (numeric) = -0.525984151614 1.01090469218
y[1] (closed_form) = -0.528998008884 1.00479993118
absolute error = 0.006808
relative error = 0.5996 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.033
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18311.6MB, alloc=44.3MB, time=230.43
x[1] = 1.737 1.521
h = 0.001 0.001
y[1] (numeric) = -0.524573415492 1.0107874726
y[1] (closed_form) = -0.527589176267 1.00468276984
absolute error = 0.006809
relative error = 0.6 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.035
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18357.2MB, alloc=44.3MB, time=230.99
x[1] = 1.738 1.522
h = 0.001 0.003
y[1] (numeric) = -0.524127522926 1.01029428535
y[1] (closed_form) = -0.527143231508 1.00419010841
absolute error = 0.006808
relative error = 0.6003 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.036
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18402.7MB, alloc=44.3MB, time=231.56
x[1] = 1.739 1.525
h = 0.0001 0.004
y[1] (numeric) = -0.522743930935 1.00975582395
y[1] (closed_form) = -0.525761861142 1.00365260439
absolute error = 0.006809
relative error = 0.6009 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18448.3MB, alloc=44.3MB, time=232.12
x[1] = 1.7391 1.529
h = 0.003 0.006
y[1] (numeric) = -0.520877334212 1.00961656282
y[1] (closed_form) = -0.52389887771 1.00351280941
absolute error = 0.006811
relative error = 0.6016 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18493.9MB, alloc=44.3MB, time=232.69
x[1] = 1.7421 1.535
h = 0.0001 0.005
y[1] (numeric) = -0.518157038632 1.00807899421
y[1] (closed_form) = -0.521186564635 1.001982995
absolute error = 0.006807
relative error = 0.6027 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.045
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18539.6MB, alloc=44.3MB, time=233.27
x[1] = 1.7422 1.54
h = 0.0001 0.003
y[1] (numeric) = -0.515850872074 1.00791825893
y[1] (closed_form) = -0.518885354824 1.00182154788
absolute error = 0.00681
relative error = 0.6036 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.047
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18585.2MB, alloc=44.3MB, time=233.84
x[1] = 1.7423 1.543
h = 0.001 0.001
y[1] (numeric) = -0.514475231789 1.00780174827
y[1] (closed_form) = -0.517511552782 1.00170511513
absolute error = 0.006811
relative error = 0.6041 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.048
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18630.9MB, alloc=44.3MB, time=234.41
x[1] = 1.7433 1.544
h = 0.001 0.003
y[1] (numeric) = -0.514041114049 1.00732007765
y[1] (closed_form) = -0.517077378911 1.00122395254
absolute error = 0.00681
relative error = 0.6044 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.049
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18676.6MB, alloc=44.3MB, time=234.99
x[1] = 1.7443 1.547
h = 0.0001 0.004
y[1] (numeric) = -0.512692521785 1.00679282088
y[1] (closed_form) = -0.515730922707 1.0006976429
absolute error = 0.006811
relative error = 0.605 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.051
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18722.2MB, alloc=44.3MB, time=235.62
x[1] = 1.7444 1.551
h = 0.003 0.006
y[1] (numeric) = -0.510872186739 1.00665422066
y[1] (closed_form) = -0.513914083046 1.00055856453
absolute error = 0.006813
relative error = 0.6057 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18767.8MB, alloc=44.3MB, time=236.22
x[1] = 1.7474 1.557
h = 0.0001 0.005
y[1] (numeric) = -0.508221144218 1.00515062878
y[1] (closed_form) = -0.511270675794 0.999062546516
absolute error = 0.006809
relative error = 0.6067 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.058
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18813.4MB, alloc=44.3MB, time=236.78
x[1] = 1.7475 1.562
h = 0.0001 0.003
y[1] (numeric) = -0.505971851323 1.00499064042
y[1] (closed_form) = -0.509026176977 0.998901923704
absolute error = 0.006812
relative error = 0.6076 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.06
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=18859.1MB, alloc=44.3MB, time=237.37
x[1] = 1.7476 1.565
h = 0.001 0.001
y[1] (numeric) = -0.504630111335 1.00487515616
y[1] (closed_form) = -0.507686212687 0.998786534993
absolute error = 0.006813
relative error = 0.608 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.061
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18904.7MB, alloc=44.3MB, time=237.95
x[1] = 1.7486 1.566
h = 0.001 0.003
y[1] (numeric) = -0.504207258577 1.00440472655
y[1] (closed_form) = -0.507263300347 0.998316596356
absolute error = 0.006812
relative error = 0.6083 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.063
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18950.5MB, alloc=44.3MB, time=238.53
x[1] = 1.7496 1.569
h = 0.0001 0.004
y[1] (numeric) = -0.502892374609 1.00388863438
y[1] (closed_form) = -0.505950470977 0.997801440206
absolute error = 0.006812
relative error = 0.6089 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.065
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=18996.0MB, alloc=44.3MB, time=239.10
x[1] = 1.7497 1.573
h = 0.003 0.006
y[1] (numeric) = -0.501116733643 1.00375111853
y[1] (closed_form) = -0.504178212077 0.997663497473
absolute error = 0.006814
relative error = 0.6096 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.066
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19041.7MB, alloc=44.3MB, time=239.67
x[1] = 1.7527 1.579
h = 0.0001 0.005
y[1] (numeric) = -0.498532285322 1.00228102097
y[1] (closed_form) = -0.501601070486 0.996200796201
absolute error = 0.006811
relative error = 0.6106 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.071
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19087.4MB, alloc=44.3MB, time=240.24
x[1] = 1.7528 1.584
h = 0.0001 0.003
y[1] (numeric) = -0.496337949458 1.00212229467
y[1] (closed_form) = -0.499411372426 0.996041506641
absolute error = 0.006813
relative error = 0.6115 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.073
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19133.1MB, alloc=44.3MB, time=240.81
x[1] = 1.7529 1.587
h = 0.001 0.001
y[1] (numeric) = -0.49502896388 1.00200812161
y[1] (closed_form) = -0.498104102605 0.995927444914
absolute error = 0.006814
relative error = 0.6119 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.075
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19178.7MB, alloc=44.3MB, time=241.38
x[1] = 1.7539 1.588
h = 0.0001 0.004
y[1] (numeric) = -0.494616893655 1.0015486622
y[1] (closed_form) = -0.497691969787 0.995468460122
absolute error = 0.006814
relative error = 0.6122 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.076
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19224.4MB, alloc=44.3MB, time=241.95
x[1] = 1.754 1.592
h = 0.003 0.006
y[1] (numeric) = -0.492878335695 1.00141212079
y[1] (closed_form) = -0.495956901859 0.995331290916
absolute error = 0.006816
relative error = 0.6129 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.078
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19270.1MB, alloc=44.3MB, time=242.52
x[1] = 1.757 1.598
h = 0.0001 0.005
y[1] (numeric) = -0.490349568945 0.999969701254
y[1] (closed_form) = -0.493435171098 0.993896120814
absolute error = 0.006812
relative error = 0.6139 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.083
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19315.6MB, alloc=44.3MB, time=243.08
x[1] = 1.7571 1.603
h = 0.0001 0.003
y[1] (numeric) = -0.488201086254 0.999811808951
y[1] (closed_form) = -0.491291197383 0.993737723704
absolute error = 0.006815
relative error = 0.6148 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.085
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19361.2MB, alloc=44.3MB, time=243.65
x[1] = 1.7572 1.606
h = 0.001 0.001
y[1] (numeric) = -0.486919432975 0.999698597224
y[1] (closed_form) = -0.490011210423 0.9936246362
absolute error = 0.006816
relative error = 0.6152 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.086
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19406.8MB, alloc=44.3MB, time=244.22
x[1] = 1.7582 1.607
h = 0.001 0.003
y[1] (numeric) = -0.486516403754 0.999248246502
y[1] (closed_form) = -0.489608116159 0.993174746585
absolute error = 0.006815
relative error = 0.6155 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.087
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19452.6MB, alloc=44.3MB, time=244.79
memory used=19498.3MB, alloc=44.3MB, time=245.36
x[1] = 1.7592 1.61
h = 0.0001 0.004
y[1] (numeric) = -0.485261138015 0.998752395317
y[1] (closed_form) = -0.488354763476 0.992679809776
absolute error = 0.006815
relative error = 0.616 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.089
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19543.9MB, alloc=44.3MB, time=245.96
x[1] = 1.7593 1.614
h = 0.003 0.006
y[1] (numeric) = -0.483564732842 0.998617388621
y[1] (closed_form) = -0.486661541612 0.992544462149
absolute error = 0.006817
relative error = 0.6167 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.091
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19589.6MB, alloc=44.3MB, time=246.53
x[1] = 1.7623 1.62
h = 0.0001 0.005
y[1] (numeric) = -0.481097941657 0.997207548344
y[1] (closed_form) = -0.484201489801 0.991141699189
absolute error = 0.006814
relative error = 0.6177 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.096
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19635.2MB, alloc=44.3MB, time=247.09
x[1] = 1.7624 1.625
h = 0.0001 0.003
y[1] (numeric) = -0.47900106178 0.99705176234
y[1] (closed_form) = -0.482108973805 0.990985469228
absolute error = 0.006816
relative error = 0.6185 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.098
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19680.9MB, alloc=44.3MB, time=247.66
x[1] = 1.7625 1.628
h = 0.001 0.001
y[1] (numeric) = -0.47775015803 0.996940326512
y[1] (closed_form) = -0.48085968096 0.990874170325
absolute error = 0.006817
relative error = 0.6189 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.1
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=19726.5MB, alloc=44.3MB, time=248.22
x[1] = 1.7635 1.629
h = 0.001 0.003
y[1] (numeric) = -0.477357077923 0.996500460743
y[1] (closed_form) = -0.480466533529 0.99043475053
absolute error = 0.006816
relative error = 0.6192 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19772.2MB, alloc=44.3MB, time=248.79
x[1] = 1.7645 1.632
h = 0.0001 0.004
y[1] (numeric) = -0.476132142491 0.996015581797
y[1] (closed_form) = -0.479243440267 0.989950773031
absolute error = 0.006816
relative error = 0.6197 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19817.9MB, alloc=44.3MB, time=249.36
x[1] = 1.7646 1.636
h = 0.003 0.006
y[1] (numeric) = -0.474476298586 0.995882662189
y[1] (closed_form) = -0.477590678469 0.98981755281
absolute error = 0.006818
relative error = 0.6204 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.105
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19863.5MB, alloc=44.3MB, time=249.92
x[1] = 1.7676 1.642
h = 0.0001 0.005
y[1] (numeric) = -0.472069171849 0.994504874369
y[1] (closed_form) = -0.475190010194 0.988446673445
absolute error = 0.006815
relative error = 0.6214 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19909.0MB, alloc=44.3MB, time=250.48
x[1] = 1.7677 1.647
h = 0.0001 0.003
y[1] (numeric) = -0.470022194364 0.994351571626
y[1] (closed_form) = -0.473147257195 0.988292982677
absolute error = 0.006817
relative error = 0.6222 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.112
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=19954.7MB, alloc=44.3MB, time=251.05
x[1] = 1.7678 1.65
h = 0.001 0.001
y[1] (numeric) = -0.468801024253 0.994242117084
y[1] (closed_form) = -0.471927644868 0.988183676322
absolute error = 0.006818
relative error = 0.6226 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20000.3MB, alloc=44.3MB, time=251.61
x[1] = 1.7688 1.651
h = 0.001 0.003
y[1] (numeric) = -0.468417480568 0.993812480138
y[1] (closed_form) = -0.471544031918 0.987754470838
absolute error = 0.006817
relative error = 0.6228 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20046.0MB, alloc=44.3MB, time=252.18
x[1] = 1.7698 1.654
h = 0.0001 0.004
y[1] (numeric) = -0.467221796945 0.993338475214
y[1] (closed_form) = -0.470350122909 0.987281353999
absolute error = 0.006817
relative error = 0.6234 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.117
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20091.7MB, alloc=44.3MB, time=252.75
x[1] = 1.7699 1.658
h = 0.003 0.006
y[1] (numeric) = -0.465605181224 0.993207918729
y[1] (closed_form) = -0.468736492021 0.987150533962
absolute error = 0.006819
relative error = 0.624 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.118
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20137.4MB, alloc=44.3MB, time=253.32
x[1] = 1.7729 1.664
h = 0.0001 0.005
y[1] (numeric) = -0.46325551714 0.991861647277
y[1] (closed_form) = -0.466393020266 0.985811005465
absolute error = 0.006816
relative error = 0.625 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.124
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20183.1MB, alloc=44.3MB, time=253.89
x[1] = 1.773 1.669
h = 0.0001 0.003
y[1] (numeric) = -0.461256811075 0.991711164379
y[1] (closed_form) = -0.464398404762 0.985660185935
absolute error = 0.006818
relative error = 0.6257 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20228.8MB, alloc=44.3MB, time=254.45
x[1] = 1.7731 1.672
h = 0.001 0.001
y[1] (numeric) = -0.460064400423 0.991603873364
y[1] (closed_form) = -0.463207500967 0.985553053051
absolute error = 0.006818
relative error = 0.6261 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.127
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20274.5MB, alloc=44.3MB, time=255.02
x[1] = 1.7741 1.673
h = 0.001 0.003
y[1] (numeric) = -0.459690002106 0.991184214617
y[1] (closed_form) = -0.462833031749 0.985133811846
absolute error = 0.006818
relative error = 0.6264 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.128
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20320.3MB, alloc=44.3MB, time=255.58
x[1] = 1.7751 1.676
h = 0.0001 0.004
y[1] (numeric) = -0.458522540382 0.990720974848
y[1] (closed_form) = -0.461667280238 0.98467144645
absolute error = 0.006818
relative error = 0.6269 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.13
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=20365.9MB, alloc=44.3MB, time=256.15
x[1] = 1.7752 1.68
h = 0.003 0.006
y[1] (numeric) = -0.456943874236 0.990593027025
y[1] (closed_form) = -0.460091505423 0.984543269129
absolute error = 0.00682
relative error = 0.6275 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20411.7MB, alloc=44.3MB, time=256.71
x[1] = 1.7782 1.686
h = 0.0001 0.005
y[1] (numeric) = -0.454649574521 0.989277728984
y[1] (closed_form) = -0.457803145818 0.983234551986
absolute error = 0.006817
relative error = 0.6285 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.137
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20457.2MB, alloc=44.3MB, time=257.28
x[1] = 1.7783 1.691
h = 0.0001 0.003
y[1] (numeric) = -0.452697575279 0.989130365547
y[1] (closed_form) = -0.455855108456 0.983086899115
absolute error = 0.006819
relative error = 0.6292 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.139
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20502.8MB, alloc=44.3MB, time=257.84
x[1] = 1.7784 1.694
h = 0.001 0.001
y[1] (numeric) = -0.451532989749 0.989025399132
y[1] (closed_form) = -0.454691980949 0.982982099573
absolute error = 0.006819
relative error = 0.6296 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.141
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20548.5MB, alloc=44.3MB, time=258.40
x[1] = 1.7794 1.695
h = 0.0001 0.004
y[1] (numeric) = -0.451167366111 0.988615473536
y[1] (closed_form) = -0.454326285057 0.982572578163
absolute error = 0.006819
relative error = 0.6299 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.142
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20594.3MB, alloc=44.3MB, time=258.97
x[1] = 1.7795 1.699
h = 0.003 0.006
y[1] (numeric) = -0.449620236254 0.988489719081
y[1] (closed_form) = -0.452782149218 0.982446417381
absolute error = 0.00682
relative error = 0.6305 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20640.0MB, alloc=44.3MB, time=259.53
x[1] = 1.7825 1.705
h = 0.0001 0.005
y[1] (numeric) = -0.447372347153 0.98720001617
y[1] (closed_form) = -0.45053999177 0.981163161466
absolute error = 0.006817
relative error = 0.6314 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.149
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20685.7MB, alloc=44.3MB, time=260.09
x[1] = 1.7826 1.71
h = 0.0001 0.003
y[1] (numeric) = -0.445459388589 0.987055019676
y[1] (closed_form) = -0.448630888856 0.981017914505
absolute error = 0.006819
relative error = 0.6322 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20731.4MB, alloc=44.3MB, time=260.66
memory used=20776.9MB, alloc=44.3MB, time=261.22
x[1] = 1.7827 1.713
h = 0.001 0.001
y[1] (numeric) = -0.444318064852 0.986951851347
y[1] (closed_form) = -0.447490982803 0.980914920238
absolute error = 0.00682
relative error = 0.6326 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.152
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20822.6MB, alloc=44.3MB, time=261.78
x[1] = 1.7837 1.714
h = 0.001 0.003
y[1] (numeric) = -0.443959824075 0.986550012915
y[1] (closed_form) = -0.44713266866 0.980513474943
absolute error = 0.00682
relative error = 0.6328 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.154
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20868.3MB, alloc=44.3MB, time=262.35
x[1] = 1.7847 1.717
h = 0.0001 0.004
y[1] (numeric) = -0.442842416647 0.986106174822
y[1] (closed_form) = -0.446016859271 0.980070485711
absolute error = 0.00682
relative error = 0.6333 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.156
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20913.9MB, alloc=44.3MB, time=262.91
x[1] = 1.7848 1.721
h = 0.003 0.006
y[1] (numeric) = -0.441331176009 0.985983222309
y[1] (closed_form) = -0.444508345824 0.979947360849
absolute error = 0.006821
relative error = 0.6339 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.158
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=20959.5MB, alloc=44.3MB, time=263.48
x[1] = 1.7878 1.727
h = 0.0001 0.005
y[1] (numeric) = -0.439134997242 0.984723493699
y[1] (closed_form) = -0.4423176703 0.978693923571
absolute error = 0.006818
relative error = 0.6348 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21005.2MB, alloc=44.3MB, time=264.04
x[1] = 1.7879 1.732
h = 0.0001 0.003
y[1] (numeric) = -0.437266003452 0.984582103193
y[1] (closed_form) = -0.440452412625 0.978552322774
absolute error = 0.00682
relative error = 0.6355 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.165
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21050.8MB, alloc=44.3MB, time=264.61
x[1] = 1.788 1.735
h = 0.001 0.001
y[1] (numeric) = -0.436150867639 0.984481519041
y[1] (closed_form) = -0.439338649305 0.978451919429
absolute error = 0.00682
relative error = 0.6359 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.166
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21096.3MB, alloc=44.3MB, time=265.18
x[1] = 1.789 1.736
h = 0.001 0.003
y[1] (numeric) = -0.435800759203 0.984088976651
y[1] (closed_form) = -0.438988466611 0.978059757808
absolute error = 0.00682
relative error = 0.6362 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.168
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21141.9MB, alloc=44.3MB, time=265.74
x[1] = 1.79 1.739
h = 0.0001 0.004
y[1] (numeric) = -0.434708872635 0.983655556075
y[1] (closed_form) = -0.437898121818 0.977627171726
absolute error = 0.00682
relative error = 0.6367 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21187.6MB, alloc=44.3MB, time=266.31
x[1] = 1.7901 1.743
h = 0.003 0.006
y[1] (numeric) = -0.433232205216 0.983535781781
y[1] (closed_form) = -0.436424098016 0.977507251701
absolute error = 0.006821
relative error = 0.6372 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.172
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21233.3MB, alloc=44.3MB, time=266.87
x[1] = 1.7931 1.749
h = 0.0001 0.005
y[1] (numeric) = -0.431085905371 0.982305474834
y[1] (closed_form) = -0.434283084728 0.976283083977
absolute error = 0.006818
relative error = 0.6381 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.177
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21278.9MB, alloc=44.3MB, time=267.44
x[1] = 1.7932 1.754
h = 0.0001 0.003
y[1] (numeric) = -0.429259485431 0.98216789987
y[1] (closed_form) = -0.432460286015 0.976145335558
absolute error = 0.00682
relative error = 0.6388 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.179
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21324.6MB, alloc=44.3MB, time=268.00
x[1] = 1.7933 1.757
h = 0.001 0.001
y[1] (numeric) = -0.428169707393 0.982070009515
y[1] (closed_form) = -0.431371837119 0.976047631829
absolute error = 0.006821
relative error = 0.6392 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21370.1MB, alloc=44.3MB, time=268.57
x[1] = 1.7943 1.758
h = 0.001 0.003
y[1] (numeric) = -0.427827412622 0.981686534025
y[1] (closed_form) = -0.431029467411 0.975664525236
absolute error = 0.00682
relative error = 0.6394 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.182
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21415.7MB, alloc=44.3MB, time=269.14
x[1] = 1.7953 1.761
h = 0.0001 0.004
y[1] (numeric) = -0.426760182635 0.981263392593
y[1] (closed_form) = -0.429963725498 0.975242203825
absolute error = 0.00682
relative error = 0.6399 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.184
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21461.4MB, alloc=44.3MB, time=269.71
x[1] = 1.7954 1.765
h = 0.003 0.006
y[1] (numeric) = -0.425316998023 0.981146946228
y[1] (closed_form) = -0.428523104136 0.97512563613
absolute error = 0.006822
relative error = 0.6405 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.186
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21507.0MB, alloc=44.3MB, time=270.27
x[1] = 1.7984 1.771
h = 0.0001 0.005
y[1] (numeric) = -0.423218829685 0.979945508471
y[1] (closed_form) = -0.426430016718 0.973930189051
absolute error = 0.006819
relative error = 0.6413 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.191
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21552.6MB, alloc=44.3MB, time=270.84
x[1] = 1.7985 1.776
h = 0.0001 0.003
y[1] (numeric) = -0.421433648356 0.979811932365
y[1] (closed_form) = -0.424648346181 0.97379647324
absolute error = 0.006821
relative error = 0.642 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.193
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21598.2MB, alloc=44.3MB, time=271.40
x[1] = 1.7986 1.779
h = 0.001 0.001
y[1] (numeric) = -0.420368431321 0.979716830491
y[1] (closed_form) = -0.423584416695 0.973701562961
absolute error = 0.006821
relative error = 0.6424 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.195
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21643.7MB, alloc=44.3MB, time=271.97
x[1] = 1.7996 1.78
h = 0.001 0.003
y[1] (numeric) = -0.420033647712 0.979342198382
y[1] (closed_form) = -0.423249557661 0.973327288353
absolute error = 0.006821
relative error = 0.6426 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.196
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21689.4MB, alloc=44.3MB, time=272.53
x[1] = 1.8006 1.783
h = 0.0001 0.004
y[1] (numeric) = -0.418990247849 0.978929192766
y[1] (closed_form) = -0.422207594604 0.972915088221
absolute error = 0.006821
relative error = 0.6431 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21735.1MB, alloc=44.3MB, time=273.10
x[1] = 1.8007 1.787
h = 0.003 0.006
y[1] (numeric) = -0.417579499267 0.978816204284
y[1] (closed_form) = -0.420799331977 0.972802000765
absolute error = 0.006822
relative error = 0.6436 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21780.7MB, alloc=44.3MB, time=273.66
x[1] = 1.8037 1.793
h = 0.0001 0.005
y[1] (numeric) = -0.415527794628 0.977643084723
y[1] (closed_form) = -0.418752513036 0.971634726889
absolute error = 0.006819
relative error = 0.6445 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21826.3MB, alloc=44.3MB, time=274.22
x[1] = 1.8038 1.798
h = 0.0001 0.003
y[1] (numeric) = -0.413782569867 0.977513666793
y[1] (closed_form) = -0.417010692895 0.971505200155
absolute error = 0.006821
relative error = 0.6452 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.207
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21871.9MB, alloc=44.3MB, time=274.78
x[1] = 1.8039 1.801
h = 0.001 0.001
y[1] (numeric) = -0.412741148938 0.97742143444
y[1] (closed_form) = -0.415970519599 0.97141316359
absolute error = 0.006821
relative error = 0.6455 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.209
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=21917.5MB, alloc=44.3MB, time=275.36
memory used=21963.3MB, alloc=44.3MB, time=275.92
x[1] = 1.8049 1.802
h = 0.0001 0.004
y[1] (numeric) = -0.412413589227 0.97705542777
y[1] (closed_form) = -0.415642884153 0.97104750348
absolute error = 0.006821
relative error = 0.6457 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.21
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=22009.0MB, alloc=44.3MB, time=276.48
x[1] = 1.805 1.806
h = 0.003 0.006
y[1] (numeric) = -0.411029836942 0.976945310203
y[1] (closed_form) = -0.41426171405 0.970937131103
absolute error = 0.006822
relative error = 0.6463 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.212
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22054.7MB, alloc=44.3MB, time=277.05
x[1] = 1.808 1.812
h = 0.0001 0.005
y[1] (numeric) = -0.40901717734 0.975795598918
y[1] (closed_form) = -0.412253778322 0.969793145695
absolute error = 0.006819
relative error = 0.6471 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.217
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22100.2MB, alloc=44.3MB, time=277.61
x[1] = 1.8081 1.817
h = 0.0001 0.003
y[1] (numeric) = -0.407305409808 0.975669414855
y[1] (closed_form) = -0.410545327624 0.969666878506
absolute error = 0.006821
relative error = 0.6478 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.219
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22145.8MB, alloc=44.3MB, time=278.18
x[1] = 1.8082 1.82
h = 0.001 0.001
y[1] (numeric) = -0.40628391781 0.975579436219
y[1] (closed_form) = -0.409525050226 0.969577099152
absolute error = 0.006822
relative error = 0.6481 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22191.4MB, alloc=44.3MB, time=278.74
x[1] = 1.8092 1.821
h = 0.001 0.003
y[1] (numeric) = -0.405962456472 0.975220602078
y[1] (closed_form) = -0.409203512888 0.969218602502
absolute error = 0.006821
relative error = 0.6484 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.222
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22237.0MB, alloc=44.3MB, time=279.30
x[1] = 1.8102 1.824
h = 0.0001 0.004
y[1] (numeric) = -0.404961437576 0.974825799585
y[1] (closed_form) = -0.408203841272 0.968824578962
absolute error = 0.006821
relative error = 0.6488 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.224
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22282.6MB, alloc=44.3MB, time=279.87
x[1] = 1.8103 1.828
h = 0.003 0.006
y[1] (numeric) = -0.403608444246 0.974719171757
y[1] (closed_form) = -0.406853198026 0.968717889671
absolute error = 0.006822
relative error = 0.6493 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.226
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22328.2MB, alloc=44.3MB, time=280.44
x[1] = 1.8133 1.834
h = 0.0001 0.005
y[1] (numeric) = -0.401639336322 0.973596778972
y[1] (closed_form) = -0.404888636623 0.967601084211
absolute error = 0.00682
relative error = 0.6502 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.231
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22373.9MB, alloc=44.3MB, time=281.00
x[1] = 1.8134 1.839
h = 0.0001 0.003
y[1] (numeric) = -0.39996527461 0.97347500646
y[1] (closed_form) = -0.403217793003 0.967479254685
absolute error = 0.006821
relative error = 0.6508 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.234
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22419.7MB, alloc=44.3MB, time=281.57
x[1] = 1.8135 1.842
h = 0.001 0.001
y[1] (numeric) = -0.398966236028 0.973388024111
y[1] (closed_form) = -0.402219932024 0.967392474528
absolute error = 0.006822
relative error = 0.6511 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.235
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22465.4MB, alloc=44.3MB, time=282.13
x[1] = 1.8145 1.843
h = 0.001 0.003
y[1] (numeric) = -0.398651499251 0.973037427555
y[1] (closed_form) = -0.401905119222 0.967042205312
absolute error = 0.006821
relative error = 0.6514 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22510.9MB, alloc=44.3MB, time=282.70
x[1] = 1.8155 1.846
h = 0.0001 0.004
y[1] (numeric) = -0.397672136767 0.972652339161
y[1] (closed_form) = -0.400927059035 0.966657881343
absolute error = 0.006821
relative error = 0.6518 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22556.6MB, alloc=44.3MB, time=283.26
x[1] = 1.8156 1.85
h = 0.003 0.006
y[1] (numeric) = -0.396348809606 0.972549457411
y[1] (closed_form) = -0.399606012742 0.96655495541
absolute error = 0.006822
relative error = 0.6523 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.24
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=22602.2MB, alloc=44.3MB, time=283.83
x[1] = 1.8186 1.856
h = 0.0001 0.005
y[1] (numeric) = -0.394421791247 0.97145384142
y[1] (closed_form) = -0.397683372364 0.965464791667
absolute error = 0.00682
relative error = 0.6531 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.246
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22647.9MB, alloc=44.3MB, time=284.40
x[1] = 1.8187 1.861
h = 0.0001 0.003
y[1] (numeric) = -0.392784292519 0.971336581354
y[1] (closed_form) = -0.396048996754 0.965347498424
absolute error = 0.006821
relative error = 0.6537 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.248
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22693.6MB, alloc=44.3MB, time=284.96
x[1] = 1.8188 1.864
h = 0.001 0.001
y[1] (numeric) = -0.391807025824 0.971252643209
y[1] (closed_form) = -0.395072872136 0.965263764788
absolute error = 0.006821
relative error = 0.654 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.249
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22739.2MB, alloc=44.3MB, time=285.53
x[1] = 1.8198 1.865
h = 0.001 0.003
y[1] (numeric) = -0.391498765396 0.970910081762
y[1] (closed_form) = -0.394764535791 0.964921520929
absolute error = 0.006821
relative error = 0.6543 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.251
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22784.9MB, alloc=44.3MB, time=286.09
x[1] = 1.8208 1.868
h = 0.0001 0.004
y[1] (numeric) = -0.390540362058 0.97053455182
y[1] (closed_form) = -0.39380739175 0.964546740953
absolute error = 0.006821
relative error = 0.6547 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.253
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22830.5MB, alloc=44.3MB, time=286.66
x[1] = 1.8209 1.872
h = 0.003 0.006
y[1] (numeric) = -0.389245805017 0.970435484144
y[1] (closed_form) = -0.392515048966 0.964447644866
absolute error = 0.006822
relative error = 0.6552 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.255
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22876.2MB, alloc=44.3MB, time=287.22
x[1] = 1.8239 1.878
h = 0.0001 0.005
y[1] (numeric) = -0.38735947897 0.969366108436
y[1] (closed_form) = -0.390632940673 0.963383589758
absolute error = 0.00682
relative error = 0.656 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22921.9MB, alloc=44.3MB, time=287.78
x[1] = 1.824 1.883
h = 0.0001 0.003
y[1] (numeric) = -0.385757445004 0.969253444781
y[1] (closed_form) = -0.38903393846 0.96327091466
absolute error = 0.006821
relative error = 0.6566 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=22967.5MB, alloc=44.3MB, time=288.35
x[1] = 1.8241 1.886
h = 0.001 0.001
y[1] (numeric) = -0.384801295368 0.969172589202
y[1] (closed_form) = -0.388078896781 0.963190265368
absolute error = 0.006821
relative error = 0.6569 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.264
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23013.1MB, alloc=44.3MB, time=288.91
x[1] = 1.8251 1.887
h = 0.001 0.003
y[1] (numeric) = -0.38449927525 0.968837865699
y[1] (closed_form) = -0.387776800971 0.962855850081
absolute error = 0.006821
relative error = 0.6571 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.265
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23058.8MB, alloc=44.3MB, time=289.47
x[1] = 1.8261 1.89
h = 0.0001 0.004
y[1] (numeric) = -0.383561163347 0.96847173698
y[1] (closed_form) = -0.386839907251 0.962490456966
absolute error = 0.006821
relative error = 0.6576 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.267
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23104.4MB, alloc=44.3MB, time=290.04
x[1] = 1.8262 1.894
h = 0.003 0.006
y[1] (numeric) = -0.382294515322 0.968376538685
y[1] (closed_form) = -0.385575409366 0.962395244632
absolute error = 0.006822
relative error = 0.658 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23150.0MB, alloc=44.3MB, time=290.60
memory used=23195.7MB, alloc=44.3MB, time=291.16
x[1] = 1.8292 1.9
h = 0.0001 0.005
y[1] (numeric) = -0.380447545868 0.967332872605
y[1] (closed_form) = -0.383732505291 0.961356770885
absolute error = 0.006819
relative error = 0.6588 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.275
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23241.4MB, alloc=44.3MB, time=291.73
x[1] = 1.8293 1.905
h = 0.0001 0.003
y[1] (numeric) = -0.378879921073 0.967224873871
y[1] (closed_form) = -0.382167824337 0.961248780498
absolute error = 0.006821
relative error = 0.6594 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.277
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23287.0MB, alloc=44.3MB, time=292.29
x[1] = 1.8294 1.908
h = 0.001 0.001
y[1] (numeric) = -0.377944259175 0.967147130519
y[1] (closed_form) = -0.381233237619 0.961171244716
absolute error = 0.006821
relative error = 0.6597 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.278
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23332.7MB, alloc=44.3MB, time=292.86
x[1] = 1.8304 1.909
h = 0.0001 0.004
y[1] (numeric) = -0.37764825482 0.966820053011
y[1] (closed_form) = -0.380937157903 0.960844466417
absolute error = 0.006821
relative error = 0.6599 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.28
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23378.4MB, alloc=44.3MB, time=293.43
x[1] = 1.8305 1.913
h = 0.003 0.006
y[1] (numeric) = -0.376404870388 0.966728051406
y[1] (closed_form) = -0.379696012802 0.960752313085
absolute error = 0.006822
relative error = 0.6604 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.282
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23424.0MB, alloc=44.3MB, time=293.99
x[1] = 1.8335 1.919
h = 0.0001 0.005
y[1] (numeric) = -0.37459105062 0.965705647027
y[1] (closed_form) = -0.377886131732 0.959734994991
absolute error = 0.00682
relative error = 0.6612 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.287
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23469.5MB, alloc=44.3MB, time=294.56
x[1] = 1.8336 1.924
h = 0.0001 0.003
y[1] (numeric) = -0.373052286374 0.965601314238
y[1] (closed_form) = -0.376350238516 0.95963068713
absolute error = 0.006821
relative error = 0.6617 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.289
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23515.0MB, alloc=44.3MB, time=295.12
x[1] = 1.8337 1.927
h = 0.001 0.001
y[1] (numeric) = -0.372133811737 0.965526033167
y[1] (closed_form) = -0.375432811882 0.959555614745
absolute error = 0.006821
relative error = 0.662 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.291
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23560.7MB, alloc=44.3MB, time=295.68
x[1] = 1.8347 1.928
h = 0.001 0.003
y[1] (numeric) = -0.371842902104 0.965205319059
y[1] (closed_form) = -0.375141827149 0.959235192368
absolute error = 0.006821
relative error = 0.6622 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.292
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23606.3MB, alloc=44.3MB, time=296.25
x[1] = 1.8357 1.931
h = 0.0001 0.004
y[1] (numeric) = -0.370940973482 0.964856037737
y[1] (closed_form) = -0.374241044726 0.958886620692
absolute error = 0.006821
relative error = 0.6627 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.294
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23652.0MB, alloc=44.3MB, time=296.82
x[1] = 1.8358 1.935
h = 0.003 0.006
y[1] (numeric) = -0.369724126133 0.964767838006
y[1] (closed_form) = -0.37302623463 0.958798431
absolute error = 0.006822
relative error = 0.6631 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.296
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23697.7MB, alloc=44.3MB, time=297.38
x[1] = 1.8388 1.941
h = 0.0001 0.005
y[1] (numeric) = -0.367947324555 0.963770187619
y[1] (closed_form) = -0.371253232879 0.957805744684
absolute error = 0.006819
relative error = 0.6639 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.302
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23743.3MB, alloc=44.3MB, time=297.95
x[1] = 1.8389 1.946
h = 0.0001 0.003
y[1] (numeric) = -0.366441112753 0.963670622121
y[1] (closed_form) = -0.369749810216 0.95770622063
absolute error = 0.006821
relative error = 0.6644 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.304
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23789.0MB, alloc=44.3MB, time=298.51
x[1] = 1.839 1.949
h = 0.001 0.001
y[1] (numeric) = -0.365542019001 0.963598494757
y[1] (closed_form) = -0.368851734027 0.957634302422
absolute error = 0.006821
relative error = 0.6647 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.305
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23834.7MB, alloc=44.3MB, time=299.08
x[1] = 1.84 1.95
h = 0.001 0.003
y[1] (numeric) = -0.365256733582 0.963285085398
y[1] (closed_form) = -0.368566374013 0.957321176419
absolute error = 0.006821
relative error = 0.6649 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.307
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23880.4MB, alloc=44.3MB, time=299.64
x[1] = 1.841 1.953
h = 0.0001 0.004
y[1] (numeric) = -0.364373334927 0.962944757866
y[1] (closed_form) = -0.367684085322 0.956981544535
absolute error = 0.006821
relative error = 0.6653 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.309
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23926.0MB, alloc=44.3MB, time=300.21
x[1] = 1.8411 1.957
h = 0.003 0.006
y[1] (numeric) = -0.363182112739 0.962860534264
y[1] (closed_form) = -0.366494842829 0.956897341876
absolute error = 0.006822
relative error = 0.6657 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=23971.7MB, alloc=44.3MB, time=300.78
x[1] = 1.8441 1.963
h = 0.0001 0.005
y[1] (numeric) = -0.361441153061 0.961887126192
y[1] (closed_form) = -0.364757550775 0.955928778876
absolute error = 0.006819
relative error = 0.6665 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.316
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24017.3MB, alloc=44.3MB, time=301.34
x[1] = 1.8442 1.968
h = 0.0001 0.003
y[1] (numeric) = -0.359966549772 0.961792358959
y[1] (closed_form) = -0.363285657785 0.955834068049
absolute error = 0.00682
relative error = 0.667 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.319
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24062.8MB, alloc=44.3MB, time=301.90
x[1] = 1.8443 1.971
h = 0.001 0.001
y[1] (numeric) = -0.359086274367 0.961723393898
y[1] (closed_form) = -0.36240637068 0.955765312239
absolute error = 0.006821
relative error = 0.6673 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.32
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24108.4MB, alloc=44.3MB, time=302.47
x[1] = 1.8453 1.972
h = 0.001 0.003
y[1] (numeric) = -0.358806418153 0.961417111587
y[1] (closed_form) = -0.362126440454 0.955459305231
absolute error = 0.00682
relative error = 0.6675 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.321
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24154.1MB, alloc=44.3MB, time=303.03
x[1] = 1.8463 1.975
h = 0.0001 0.004
y[1] (numeric) = -0.35794098296 0.961085578403
y[1] (closed_form) = -0.361262080535 0.955128453863
absolute error = 0.00682
relative error = 0.6679 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.324
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24199.7MB, alloc=44.3MB, time=303.60
x[1] = 1.8464 1.979
h = 0.003 0.006
y[1] (numeric) = -0.356774645654 0.961005346602
y[1] (closed_form) = -0.360097667479 0.955048252874
absolute error = 0.006821
relative error = 0.6683 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.326
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24245.4MB, alloc=44.3MB, time=304.16
x[1] = 1.8494 1.985
h = 0.0001 0.005
y[1] (numeric) = -0.355068401957 0.960055676801
y[1] (closed_form) = -0.358394965508 0.954103312295
absolute error = 0.006819
relative error = 0.669 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.331
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24291.1MB, alloc=44.3MB, time=304.72
x[1] = 1.8495 1.99
h = 0.0001 0.003
y[1] (numeric) = -0.353624499057 0.959965728021
y[1] (closed_form) = -0.356953696988 0.954013433447
absolute error = 0.00682
relative error = 0.6695 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.333
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24336.9MB, alloc=44.3MB, time=305.29
x[1] = 1.8496 1.993
h = 0.001 0.001
y[1] (numeric) = -0.352762500865 0.959899927844
y[1] (closed_form) = -0.356092658958 0.953947842277
absolute error = 0.00682
relative error = 0.6698 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.335
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24382.6MB, alloc=44.3MB, time=305.85
x[1] = 1.8506 1.994
h = 0.001 0.003
y[1] (numeric) = -0.352487888078 0.959600599699
y[1] (closed_form) = -0.355817972812 0.953648781687
absolute error = 0.00682
relative error = 0.67 %
Correct digits = 2
memory used=24428.4MB, alloc=44.3MB, time=306.42
Radius of convergence (given) for eq 1 = 4.336
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24474.0MB, alloc=44.3MB, time=306.98
x[1] = 1.8516 1.997
h = 0.0001 0.004
y[1] (numeric) = -0.351639873052 0.959277701797
y[1] (closed_form) = -0.354970999837 0.953326551944
absolute error = 0.00682
relative error = 0.6704 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.339
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24519.8MB, alloc=44.3MB, time=307.55
x[1] = 1.8517 2.001
h = 0.003 0.006
y[1] (numeric) = -0.350497708384 0.959201469432
y[1] (closed_form) = -0.353830705999 0.953250359307
absolute error = 0.006821
relative error = 0.6708 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.34
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=24565.4MB, alloc=44.3MB, time=308.12
x[1] = 1.8547 2.007
h = 0.0001 0.005
y[1] (numeric) = -0.348825102612 0.958275041773
y[1] (closed_form) = -0.352161522013 0.952328548099
absolute error = 0.006819
relative error = 0.6715 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.346
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24611.0MB, alloc=44.3MB, time=308.68
x[1] = 1.8548 2.012
h = 0.0001 0.003
y[1] (numeric) = -0.347411026207 0.958189921827
y[1] (closed_form) = -0.350750006867 0.952243510282
absolute error = 0.00682
relative error = 0.672 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.348
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24656.7MB, alloc=44.3MB, time=309.24
x[1] = 1.8549 2.015
h = 0.001 0.001
y[1] (numeric) = -0.34656678455 0.958127283661
y[1] (closed_form) = -0.349906698311 0.952181080572
absolute error = 0.00682
relative error = 0.6723 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.35
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24702.2MB, alloc=44.3MB, time=309.82
x[1] = 1.8559 2.016
h = 0.0001 0.004
y[1] (numeric) = -0.346297238143 0.957834741504
y[1] (closed_form) = -0.349637079258 0.951888798516
absolute error = 0.00682
relative error = 0.6725 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.351
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24747.9MB, alloc=44.3MB, time=310.38
x[1] = 1.856 2.02
h = 0.003 0.006
y[1] (numeric) = -0.345175251933 0.95776180499
y[1] (closed_form) = -0.348517045868 0.95181577966
absolute error = 0.006821
relative error = 0.6729 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.353
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24793.5MB, alloc=44.3MB, time=310.94
x[1] = 1.859 2.026
h = 0.0001 0.005
y[1] (numeric) = -0.343531041045 0.956854608254
y[1] (closed_form) = -0.346876156759 0.950913106056
absolute error = 0.006818
relative error = 0.6736 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.359
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24839.1MB, alloc=44.3MB, time=311.51
x[1] = 1.8591 2.031
h = 0.0001 0.003
y[1] (numeric) = -0.342142021058 0.956773304556
y[1] (closed_form) = -0.345489637364 0.950831894828
absolute error = 0.00682
relative error = 0.6741 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.361
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24884.8MB, alloc=44.3MB, time=312.07
x[1] = 1.8592 2.034
h = 0.001 0.001
y[1] (numeric) = -0.341312699174 0.956713178621
y[1] (closed_form) = -0.344661226101 0.950771976958
absolute error = 0.00682
relative error = 0.6744 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.362
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24930.4MB, alloc=44.3MB, time=312.66
x[1] = 1.8602 2.035
h = 0.001 0.003
y[1] (numeric) = -0.341047456473 0.956426288818
y[1] (closed_form) = -0.34439591133 0.950485341054
absolute error = 0.00682
relative error = 0.6746 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.364
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=24976.0MB, alloc=44.3MB, time=313.22
x[1] = 1.8612 2.038
h = 0.0001 0.004
y[1] (numeric) = -0.340230583651 0.956118844966
y[1] (closed_form) = -0.343580022239 0.950178540811
absolute error = 0.00682
relative error = 0.6749 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.366
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25021.7MB, alloc=44.3MB, time=313.78
x[1] = 1.8613 2.042
h = 0.003 0.006
y[1] (numeric) = -0.339131641419 0.956049781313
y[1] (closed_form) = -0.342482856617 0.950109531758
absolute error = 0.00682
relative error = 0.6753 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.368
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25067.4MB, alloc=44.3MB, time=314.35
x[1] = 1.8643 2.048
h = 0.0001 0.005
y[1] (numeric) = -0.337519176101 0.955164936951
y[1] (closed_form) = -0.340873603418 0.949229103241
absolute error = 0.006818
relative error = 0.676 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.373
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25112.9MB, alloc=44.3MB, time=314.92
x[1] = 1.8644 2.053
h = 0.0001 0.003
y[1] (numeric) = -0.336158442406 0.955088467826
y[1] (closed_form) = -0.339515302073 0.949152736542
absolute error = 0.006819
relative error = 0.6765 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.376
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25158.5MB, alloc=44.3MB, time=315.48
x[1] = 1.8645 2.056
h = 0.001 0.001
y[1] (numeric) = -0.335345959429 0.95503149144
y[1] (closed_form) = -0.338703704529 0.949095967164
absolute error = 0.006819
relative error = 0.6767 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.377
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25204.2MB, alloc=44.3MB, time=316.04
x[1] = 1.8655 2.057
h = 0.001 0.003
y[1] (numeric) = -0.335085473426 0.954751088703
y[1] (closed_form) = -0.33844314727 0.94881581138
absolute error = 0.006819
relative error = 0.6769 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.379
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25249.8MB, alloc=44.3MB, time=316.61
x[1] = 1.8665 2.06
h = 0.0001 0.004
y[1] (numeric) = -0.334284583141 0.954451835126
y[1] (closed_form) = -0.337643211306 0.948517188296
absolute error = 0.006819
relative error = 0.6773 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.381
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25295.5MB, alloc=44.3MB, time=317.18
x[1] = 1.8666 2.064
h = 0.003 0.006
y[1] (numeric) = -0.333207919839 0.954386762214
y[1] (closed_form) = -0.336568276519 0.948452176525
absolute error = 0.00682
relative error = 0.6777 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.383
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25341.2MB, alloc=44.3MB, time=317.74
x[1] = 1.8696 2.07
h = 0.0001 0.005
y[1] (numeric) = -0.331626246366 0.953523797352
y[1] (closed_form) = -0.334989710592 0.947593523103
absolute error = 0.006818
relative error = 0.6783 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.388
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25386.7MB, alloc=44.3MB, time=318.31
x[1] = 1.8697 2.075
h = 0.0001 0.003
y[1] (numeric) = -0.330293014866 0.953452149472
y[1] (closed_form) = -0.333658845671 0.947521986545
absolute error = 0.006819
relative error = 0.6788 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.391
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25432.3MB, alloc=44.3MB, time=318.88
x[1] = 1.8698 2.078
h = 0.001 0.001
y[1] (numeric) = -0.329496903767 0.95339830665
y[1] (closed_form) = -0.332863595763 0.947468349444
absolute error = 0.006819
relative error = 0.679 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.392
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25478.1MB, alloc=44.3MB, time=319.44
x[1] = 1.8708 2.079
h = 0.001 0.003
y[1] (numeric) = -0.32924101993 0.953124235543
y[1] (closed_form) = -0.332607641527 0.947194518602
absolute error = 0.006819
relative error = 0.6792 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.394
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25523.7MB, alloc=44.3MB, time=320.00
x[1] = 1.8718 2.082
h = 0.0001 0.004
y[1] (numeric) = -0.328455648591 0.952833016719
y[1] (closed_form) = -0.331823196308 0.946903917363
absolute error = 0.006819
relative error = 0.6796 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.396
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25569.3MB, alloc=44.3MB, time=320.56
x[1] = 1.8719 2.086
h = 0.003 0.006
y[1] (numeric) = -0.327400649088 0.9527719173
y[1] (closed_form) = -0.330769878943 0.946842884921
absolute error = 0.006819
relative error = 0.6799 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.398
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25615.0MB, alloc=44.3MB, time=321.13
x[1] = 1.8749 2.092
h = 0.0001 0.005
y[1] (numeric) = -0.325848853114 0.951930367633
y[1] (closed_form) = -0.329221090754 0.946005545099
absolute error = 0.006817
relative error = 0.6806 %
Correct digits = 2
memory used=25660.7MB, alloc=44.3MB, time=321.69
Radius of convergence (given) for eq 1 = 4.404
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25706.1MB, alloc=44.3MB, time=322.26
x[1] = 1.875 2.097
h = 0.0001 0.003
y[1] (numeric) = -0.324542368537 0.951863520953
y[1] (closed_form) = -0.327916909354 0.945938817657
absolute error = 0.006818
relative error = 0.681 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.406
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25751.8MB, alloc=44.3MB, time=322.82
x[1] = 1.8751 2.1
h = 0.001 0.001
y[1] (numeric) = -0.323762179503 0.951812792027
y[1] (closed_form) = -0.327137558171 0.94588829296
absolute error = 0.006819
relative error = 0.6813 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.408
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25797.5MB, alloc=44.3MB, time=323.39
x[1] = 1.8761 2.101
h = 0.001 0.003
y[1] (numeric) = -0.323510750354 0.951544901384
y[1] (closed_form) = -0.326886059519 0.945620636139
absolute error = 0.006818
relative error = 0.6815 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.409
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25843.1MB, alloc=44.3MB, time=323.96
x[1] = 1.8771 2.104
h = 0.0001 0.004
y[1] (numeric) = -0.3227404527 0.951261563244
y[1] (closed_form) = -0.326116660932 0.94533790289
absolute error = 0.006818
relative error = 0.6818 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.411
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25888.7MB, alloc=44.3MB, time=324.52
x[1] = 1.8772 2.108
h = 0.003 0.006
y[1] (numeric) = -0.321706524434 0.951204415115
y[1] (closed_form) = -0.325084370073 0.945280826922
absolute error = 0.006819
relative error = 0.6822 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.413
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25934.3MB, alloc=44.3MB, time=325.08
x[1] = 1.8802 2.114
h = 0.0001 0.005
y[1] (numeric) = -0.320183729075 0.950383824971
y[1] (closed_form) = -0.323564487298 0.944464347768
absolute error = 0.006817
relative error = 0.6828 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.419
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=25979.9MB, alloc=44.3MB, time=325.65
x[1] = 1.8803 2.119
h = 0.0001 0.003
y[1] (numeric) = -0.31890326373 0.950321753378
y[1] (closed_form) = -0.322286263995 0.94440240242
absolute error = 0.006818
relative error = 0.6832 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26025.5MB, alloc=44.3MB, time=326.21
x[1] = 1.8804 2.122
h = 0.001 0.001
y[1] (numeric) = -0.318138563411 0.950274115369
y[1] (closed_form) = -0.321522379053 0.944354966964
absolute error = 0.006818
relative error = 0.6835 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.423
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26071.2MB, alloc=44.3MB, time=326.78
x[1] = 1.8814 2.123
h = 0.0001 0.004
y[1] (numeric) = -0.317891448157 0.950012258179
y[1] (closed_form) = -0.321275195224 0.944093337387
absolute error = 0.006818
relative error = 0.6837 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.424
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26116.8MB, alloc=44.3MB, time=327.35
x[1] = 1.8815 2.127
h = 0.003 0.006
y[1] (numeric) = -0.316875133856 0.94995836132
y[1] (closed_form) = -0.320260593228 0.944039404044
absolute error = 0.006819
relative error = 0.684 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.426
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26162.4MB, alloc=44.3MB, time=327.92
x[1] = 1.8845 2.133
h = 0.0001 0.005
y[1] (numeric) = -0.315376868789 0.949155122263
y[1] (closed_form) = -0.318765161131 0.943240194091
absolute error = 0.006817
relative error = 0.6846 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26208.0MB, alloc=44.3MB, time=328.48
x[1] = 1.8846 2.138
h = 0.0001 0.003
y[1] (numeric) = -0.314118293752 0.949096837161
y[1] (closed_form) = -0.31750877733 0.943182041287
absolute error = 0.006818
relative error = 0.6851 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.434
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26253.7MB, alloc=44.3MB, time=329.05
x[1] = 1.8847 2.141
h = 0.001 0.001
y[1] (numeric) = -0.313366627031 0.949051661262
y[1] (closed_form) = -0.316757907279 0.943137066619
absolute error = 0.006818
relative error = 0.6853 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.436
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26299.2MB, alloc=44.3MB, time=329.61
x[1] = 1.8857 2.142
h = 0.001 0.003
y[1] (numeric) = -0.313123186697 0.94879483361
y[1] (closed_form) = -0.316514399121 0.942880461406
absolute error = 0.006818
relative error = 0.6855 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.437
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26344.9MB, alloc=44.3MB, time=330.19
x[1] = 1.8867 2.145
h = 0.0001 0.004
y[1] (numeric) = -0.312379901434 0.94852558726
y[1] (closed_form) = -0.315771965317 0.942611797194
absolute error = 0.006818
relative error = 0.6858 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.439
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26390.6MB, alloc=44.3MB, time=330.75
x[1] = 1.8868 2.149
h = 0.003 0.006
y[1] (numeric) = -0.311383724217 0.948475482166
y[1] (closed_form) = -0.314777346463 0.942561772827
absolute error = 0.006818
relative error = 0.6861 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.441
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26436.3MB, alloc=44.3MB, time=331.32
x[1] = 1.8898 2.155
h = 0.0001 0.005
y[1] (numeric) = -0.309912916485 0.947692387295
y[1] (closed_form) = -0.313309284383 0.941782613064
absolute error = 0.006816
relative error = 0.6868 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.447
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26481.9MB, alloc=44.3MB, time=331.89
x[1] = 1.8899 2.16
h = 0.0001 0.003
y[1] (numeric) = -0.308679075537 0.947638822471
y[1] (closed_form) = -0.312077577499 0.941729186014
absolute error = 0.006817
relative error = 0.6871 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.449
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26527.5MB, alloc=44.3MB, time=332.45
x[1] = 1.89 2.163
h = 0.001 0.001
y[1] (numeric) = -0.307942132235 0.947596691789
y[1] (closed_form) = -0.311341409901 0.941687254582
absolute error = 0.006817
relative error = 0.6874 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.451
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26573.2MB, alloc=44.3MB, time=333.02
x[1] = 1.891 2.164
h = 0.001 0.003
y[1] (numeric) = -0.307702758773 0.94734563621
y[1] (closed_form) = -0.311101969594 0.941436415646
absolute error = 0.006817
relative error = 0.6876 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.452
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26618.8MB, alloc=44.3MB, time=333.58
x[1] = 1.892 2.167
h = 0.0001 0.004
y[1] (numeric) = -0.306973365374 0.947083843686
y[1] (closed_form) = -0.310373403601 0.941175193178
absolute error = 0.006817
relative error = 0.6879 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.455
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26664.4MB, alloc=44.3MB, time=334.14
x[1] = 1.8921 2.171
h = 0.003 0.006
y[1] (numeric) = -0.305996679887 0.947037609433
y[1] (closed_form) = -0.309398236078 0.941129043213
absolute error = 0.006818
relative error = 0.6882 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.457
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26710.1MB, alloc=44.3MB, time=334.71
x[1] = 1.8951 2.177
h = 0.0001 0.005
y[1] (numeric) = -0.304552550211 0.946274227512
y[1] (closed_form) = -0.307956768641 0.940369504944
absolute error = 0.006816
relative error = 0.6888 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.462
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26755.6MB, alloc=44.3MB, time=335.27
x[1] = 1.8952 2.182
h = 0.0001 0.003
y[1] (numeric) = -0.303342788138 0.946225342313
y[1] (closed_form) = -0.30674908547 0.940320762274
absolute error = 0.006817
relative error = 0.6892 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.465
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26801.3MB, alloc=44.3MB, time=335.83
x[1] = 1.8953 2.185
h = 0.001 0.001
y[1] (numeric) = -0.302620178174 0.946186226002
y[1] (closed_form) = -0.306027231002 0.940281843099
absolute error = 0.006817
relative error = 0.6894 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.466
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26847.0MB, alloc=44.3MB, time=336.39
memory used=26892.8MB, alloc=44.3MB, time=336.96
x[1] = 1.8963 2.186
h = 0.001 0.003
y[1] (numeric) = -0.302384748084 0.945940806684
y[1] (closed_form) = -0.305791735069 0.940036634835
absolute error = 0.006817
relative error = 0.6896 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.468
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26938.3MB, alloc=44.3MB, time=337.52
x[1] = 1.8973 2.189
h = 0.0001 0.004
y[1] (numeric) = -0.301668864425 0.945686320554
y[1] (closed_form) = -0.305076655713 0.9397827069
absolute error = 0.006817
relative error = 0.6899 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=26984.0MB, alloc=44.3MB, time=338.10
x[1] = 1.8974 2.193
h = 0.003 0.006
y[1] (numeric) = -0.300711156453 0.945643919815
y[1] (closed_form) = -0.304120426707 0.93974039353
absolute error = 0.006817
relative error = 0.6902 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.472
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27029.7MB, alloc=44.3MB, time=338.66
x[1] = 1.9004 2.199
h = 0.0001 0.005
y[1] (numeric) = -0.299292956541 0.944899828264
y[1] (closed_form) = -0.302704809324 0.939000056647
absolute error = 0.006815
relative error = 0.6908 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.478
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27075.3MB, alloc=44.3MB, time=339.23
x[1] = 1.9005 2.204
h = 0.0001 0.003
y[1] (numeric) = -0.298106641432 0.944855578018
y[1] (closed_form) = -0.301520519878 0.938955953015
absolute error = 0.006816
relative error = 0.6912 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.48
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27121.0MB, alloc=44.3MB, time=339.80
x[1] = 1.9006 2.207
h = 0.001 0.001
y[1] (numeric) = -0.297397988625 0.944819443088
y[1] (closed_form) = -0.300812603089 0.938920012989
absolute error = 0.006816
relative error = 0.6914 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.482
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27166.7MB, alloc=44.3MB, time=340.36
x[1] = 1.9016 2.208
h = 0.001 0.003
y[1] (numeric) = -0.297166383843 0.944579527949
y[1] (closed_form) = -0.300580933482 0.938680303513
absolute error = 0.006816
relative error = 0.6916 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.483
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27212.2MB, alloc=44.3MB, time=340.92
x[1] = 1.9026 2.211
h = 0.0001 0.004
y[1] (numeric) = -0.29646364236 0.944332202784
y[1] (closed_form) = -0.299878974108 0.938433524904
absolute error = 0.006816
relative error = 0.6919 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27257.8MB, alloc=44.3MB, time=341.48
x[1] = 1.9027 2.215
h = 0.003 0.006
y[1] (numeric) = -0.295524415933 0.944293595311
y[1] (closed_form) = -0.298941188988 0.938395007438
absolute error = 0.006817
relative error = 0.6922 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.487
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27303.3MB, alloc=44.3MB, time=342.05
x[1] = 1.9057 2.221
h = 0.0001 0.005
y[1] (numeric) = -0.294131427016 0.943568380156
y[1] (closed_form) = -0.297550706404 0.937673460367
absolute error = 0.006815
relative error = 0.6927 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.493
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27349.0MB, alloc=44.3MB, time=342.61
x[1] = 1.9058 2.226
h = 0.0001 0.003
y[1] (numeric) = -0.292967949271 0.943528716592
y[1] (closed_form) = -0.296389202928 0.937633946887
absolute error = 0.006816
relative error = 0.6931 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.496
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27394.6MB, alloc=44.3MB, time=343.18
x[1] = 1.9059 2.229
h = 0.001 0.001
y[1] (numeric) = -0.292272890754 0.943495528153
y[1] (closed_form) = -0.295694861647 0.937600951016
absolute error = 0.006816
relative error = 0.6933 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.497
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27440.3MB, alloc=44.3MB, time=343.74
x[1] = 1.9069 2.23
h = 0.0001 0.004
y[1] (numeric) = -0.29204499837 0.943260988734
y[1] (closed_form) = -0.295466905471 0.937366612058
absolute error = 0.006816
relative error = 0.6935 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.499
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27485.9MB, alloc=44.3MB, time=344.31
x[1] = 1.907 2.234
h = 0.003 0.006
y[1] (numeric) = -0.291121241477 0.943225499185
y[1] (closed_form) = -0.294544657978 0.937331115419
absolute error = 0.006816
relative error = 0.6938 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.501
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27531.5MB, alloc=44.3MB, time=344.87
x[1] = 1.91 2.24
h = 0.0001 0.005
y[1] (numeric) = -0.289749617595 0.94251591804
y[1] (closed_form) = -0.293175476521 0.936625130555
absolute error = 0.006815
relative error = 0.6943 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.506
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27577.2MB, alloc=44.3MB, time=345.44
x[1] = 1.9101 2.245
h = 0.0001 0.003
y[1] (numeric) = -0.288605379479 0.942479898878
y[1] (closed_form) = -0.292033169889 0.936589264591
absolute error = 0.006815
relative error = 0.6947 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.509
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27622.8MB, alloc=44.3MB, time=346.00
x[1] = 1.9102 2.248
h = 0.001 0.001
y[1] (numeric) = -0.28792177615 0.942449061164
y[1] (closed_form) = -0.291350268136 0.936558617571
absolute error = 0.006816
relative error = 0.6949 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.51
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=27668.6MB, alloc=44.3MB, time=346.56
x[1] = 1.9112 2.249
h = 0.001 0.003
y[1] (numeric) = -0.287697054621 0.942219006325
y[1] (closed_form) = -0.291125483654 0.936328758851
absolute error = 0.006815
relative error = 0.6951 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.512
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27714.3MB, alloc=44.3MB, time=347.13
x[1] = 1.9122 2.252
h = 0.0001 0.004
y[1] (numeric) = -0.287017917826 0.941984479254
y[1] (closed_form) = -0.29044708981 0.93609475751
absolute error = 0.006815
relative error = 0.6954 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27759.9MB, alloc=44.3MB, time=347.69
x[1] = 1.9123 2.256
h = 0.003 0.006
y[1] (numeric) = -0.28611186444 0.941952607347
y[1] (closed_form) = -0.28954241106 0.936062979867
absolute error = 0.006816
relative error = 0.6956 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27805.5MB, alloc=44.3MB, time=348.26
x[1] = 1.9153 2.262
h = 0.0001 0.005
y[1] (numeric) = -0.284764183272 0.941261162745
y[1] (closed_form) = -0.288197102209 0.935375049216
absolute error = 0.006814
relative error = 0.6962 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27851.1MB, alloc=44.3MB, time=348.82
x[1] = 1.9154 2.267
h = 0.0001 0.003
y[1] (numeric) = -0.283641703738 0.941229638876
y[1] (closed_form) = -0.287076505994 0.935343680971
absolute error = 0.006815
relative error = 0.6965 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.524
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27896.8MB, alloc=44.3MB, time=349.38
x[1] = 1.9155 2.27
h = 0.001 0.001
y[1] (numeric) = -0.282971052551 0.941201682391
y[1] (closed_form) = -0.286406538818 0.935315912673
absolute error = 0.006815
relative error = 0.6967 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.526
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27942.6MB, alloc=44.3MB, time=349.95
x[1] = 1.9165 2.271
h = 0.001 0.003
y[1] (numeric) = -0.282749844721 0.940976774737
y[1] (closed_form) = -0.286185269089 0.93509119627
absolute error = 0.006815
relative error = 0.6969 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.527
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=27988.3MB, alloc=44.3MB, time=350.52
x[1] = 1.9175 2.274
h = 0.0001 0.004
y[1] (numeric) = -0.282082871563 0.940749008046
y[1] (closed_form) = -0.285519019059 0.934863944292
absolute error = 0.006815
relative error = 0.6972 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.53
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=28034.0MB, alloc=44.3MB, time=351.08
x[1] = 1.9176 2.278
h = 0.003 0.006
y[1] (numeric) = -0.281193974291 0.940720806138
y[1] (closed_form) = -0.284631462303 0.934835838184
absolute error = 0.006815
relative error = 0.6974 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.532
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28079.7MB, alloc=44.3MB, time=351.64
x[1] = 1.9206 2.284
h = 0.0001 0.005
y[1] (numeric) = -0.279869594204 0.940047108006
y[1] (closed_form) = -0.283309387448 0.934165573886
absolute error = 0.006814
relative error = 0.698 %
Correct digits = 2
memory used=28125.6MB, alloc=44.3MB, time=352.21
Radius of convergence (given) for eq 1 = 4.537
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28171.3MB, alloc=44.3MB, time=352.78
x[1] = 1.9207 2.289
h = 0.0001 0.003
y[1] (numeric) = -0.278768322412 0.940020022701
y[1] (closed_form) = -0.282209952447 0.934138646143
absolute error = 0.006814
relative error = 0.6983 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.54
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=28216.8MB, alloc=44.3MB, time=353.35
x[1] = 1.9208 2.292
h = 0.001 0.001
y[1] (numeric) = -0.278110295549 0.939994908143
y[1] (closed_form) = -0.281552592645 0.934113717195
absolute error = 0.006815
relative error = 0.6985 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28262.5MB, alloc=44.3MB, time=353.92
x[1] = 1.9218 2.293
h = 0.001 0.003
y[1] (numeric) = -0.277892501893 0.939775028958
y[1] (closed_form) = -0.281334738151 0.933894024561
absolute error = 0.006814
relative error = 0.6987 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.543
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28308.1MB, alloc=44.3MB, time=354.48
x[1] = 1.9228 2.296
h = 0.0001 0.004
y[1] (numeric) = -0.277237375128 0.939553885327
y[1] (closed_form) = -0.280680315447 0.933673384845
absolute error = 0.006814
relative error = 0.6989 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.545
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28353.7MB, alloc=44.3MB, time=355.04
x[1] = 1.9229 2.3
h = 0.003 0.006
y[1] (numeric) = -0.27636520149 0.939529304499
y[1] (closed_form) = -0.279809449346 0.933648901028
absolute error = 0.006815
relative error = 0.6992 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.547
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28399.3MB, alloc=44.3MB, time=355.61
x[1] = 1.9259 2.306
h = 0.0001 0.005
y[1] (numeric) = -0.275063505401 0.938872971051
y[1] (closed_form) = -0.278509994275 0.932995923447
absolute error = 0.006813
relative error = 0.6997 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.553
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28445.0MB, alloc=44.3MB, time=356.17
x[1] = 1.926 2.311
h = 0.0001 0.003
y[1] (numeric) = -0.273982909432 0.938850265342
y[1] (closed_form) = -0.277431190138 0.932973376787
absolute error = 0.006814
relative error = 0.7 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.556
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28490.6MB, alloc=44.3MB, time=356.74
x[1] = 1.9261 2.314
h = 0.001 0.001
y[1] (numeric) = -0.273337190356 0.938827952275
y[1] (closed_form) = -0.276786121763 0.932951246691
absolute error = 0.006814
relative error = 0.7002 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.557
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28536.4MB, alloc=44.3MB, time=357.30
x[1] = 1.9271 2.315
h = 0.001 0.003
y[1] (numeric) = -0.273122715567 0.938612986076
y[1] (closed_form) = -0.276571587201 0.932736462503
absolute error = 0.006814
relative error = 0.7004 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.559
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28582.1MB, alloc=44.3MB, time=357.87
x[1] = 1.9281 2.318
h = 0.0001 0.004
y[1] (numeric) = -0.272479129591 0.938398330415
y[1] (closed_form) = -0.275928686941 0.932522300177
absolute error = 0.006814
relative error = 0.7007 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.561
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28627.7MB, alloc=44.3MB, time=358.44
x[1] = 1.9282 2.322
h = 0.003 0.006
y[1] (numeric) = -0.271623261925 0.938377320165
y[1] (closed_form) = -0.27507409493 0.932501387851
absolute error = 0.006814
relative error = 0.7009 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.563
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28673.1MB, alloc=44.3MB, time=359.00
x[1] = 1.9312 2.328
h = 0.0001 0.005
y[1] (numeric) = -0.270343656172 0.937737977793
y[1] (closed_form) = -0.273796668705 0.931865325466
absolute error = 0.006813
relative error = 0.7014 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.569
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28718.8MB, alloc=44.3MB, time=359.56
x[1] = 1.9313 2.333
h = 0.0001 0.003
y[1] (numeric) = -0.269283222244 0.937719590752
y[1] (closed_form) = -0.272737983158 0.931847098545
absolute error = 0.006813
relative error = 0.7017 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.571
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28764.3MB, alloc=44.3MB, time=360.13
x[1] = 1.9314 2.336
h = 0.001 0.001
y[1] (numeric) = -0.268649505233 0.937700037764
y[1] (closed_form) = -0.272104901052 0.931827725837
absolute error = 0.006814
relative error = 0.7019 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.573
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28810.0MB, alloc=44.3MB, time=360.69
x[1] = 1.9324 2.337
h = 0.0001 0.004
y[1] (numeric) = -0.268438258011 0.937489872205
y[1] (closed_form) = -0.271893595125 0.931617737904
absolute error = 0.006813
relative error = 0.7021 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.574
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28855.8MB, alloc=44.3MB, time=361.26
x[1] = 1.9325 2.341
h = 0.003 0.006
y[1] (numeric) = -0.267596055818 0.937471794238
y[1] (closed_form) = -0.271052730258 0.931599670718
absolute error = 0.006814
relative error = 0.7023 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.577
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28901.4MB, alloc=44.3MB, time=361.82
x[1] = 1.9355 2.347
h = 0.0001 0.005
y[1] (numeric) = -0.266335202886 0.936846530266
y[1] (closed_form) = -0.269794005132 0.930977623734
absolute error = 0.006812
relative error = 0.7028 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.582
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28947.1MB, alloc=44.3MB, time=362.39
x[1] = 1.9356 2.352
h = 0.0001 0.003
y[1] (numeric) = -0.265291776072 0.93683157833
y[1] (closed_form) = -0.268752290463 0.930962833026
absolute error = 0.006813
relative error = 0.7031 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.585
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=28992.9MB, alloc=44.3MB, time=362.95
x[1] = 1.9357 2.355
h = 0.001 0.001
y[1] (numeric) = -0.264668185345 0.93681422912
y[1] (closed_form) = -0.268129321445 0.930945661924
absolute error = 0.006813
relative error = 0.7033 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.586
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29038.6MB, alloc=44.3MB, time=363.52
x[1] = 1.9367 2.356
h = 0.001 0.003
y[1] (numeric) = -0.264459701527 0.936608071118
y[1] (closed_form) = -0.267920779792 0.930739677879
absolute error = 0.006813
relative error = 0.7034 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.588
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29084.3MB, alloc=44.3MB, time=364.08
x[1] = 1.9377 2.359
h = 0.0001 0.004
y[1] (numeric) = -0.263836888222 0.936405006831
y[1] (closed_form) = -0.267298619753 0.93053708801
absolute error = 0.006813
relative error = 0.7037 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.59
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=29129.8MB, alloc=44.3MB, time=364.65
x[1] = 1.9378 2.363
h = 0.003 0.006
y[1] (numeric) = -0.263010339814 0.936390318489
y[1] (closed_form) = -0.266473290451 0.930522498924
absolute error = 0.006813
relative error = 0.7039 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.592
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29175.6MB, alloc=44.3MB, time=365.21
x[1] = 1.9408 2.369
h = 0.0001 0.005
y[1] (numeric) = -0.261770527037 0.935781378206
y[1] (closed_form) = -0.265235548728 0.929916703444
absolute error = 0.006812
relative error = 0.7044 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.598
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29221.3MB, alloc=44.3MB, time=365.77
x[1] = 1.9409 2.374
h = 0.0001 0.003
y[1] (numeric) = -0.260746351207 0.935770632859
y[1] (closed_form) = -0.264213044231 0.929906119692
absolute error = 0.006813
relative error = 0.7047 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.601
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29267.0MB, alloc=44.3MB, time=366.34
x[1] = 1.941 2.377
h = 0.001 0.001
y[1] (numeric) = -0.260134220421 0.935755967917
y[1] (closed_form) = -0.263601520346 0.929891630085
absolute error = 0.006813
relative error = 0.7049 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29312.8MB, alloc=44.3MB, time=366.90
x[1] = 1.942 2.378
h = 0.001 0.003
y[1] (numeric) = -0.259928803019 0.93555441052
y[1] (closed_form) = -0.263396046179 0.929690242531
absolute error = 0.006813
relative error = 0.705 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29358.4MB, alloc=44.3MB, time=367.46
x[1] = 1.943 2.381
h = 0.0001 0.004
y[1] (numeric) = -0.259316714496 0.935357463416
y[1] (closed_form) = -0.262784594465 0.929493759865
absolute error = 0.006812
relative error = 0.7053 %
Correct digits = 2
memory used=29404.1MB, alloc=44.3MB, time=368.03
Radius of convergence (given) for eq 1 = 4.606
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29449.7MB, alloc=44.3MB, time=368.59
x[1] = 1.9431 2.385
h = 0.003 0.006
y[1] (numeric) = -0.258505353042 0.935346198696
y[1] (closed_form) = -0.261974423134 0.929482594572
absolute error = 0.006813
relative error = 0.7055 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.608
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29495.3MB, alloc=44.3MB, time=369.16
x[1] = 1.9461 2.391
h = 0.0001 0.005
y[1] (numeric) = -0.257286048126 0.934753230967
y[1] (closed_form) = -0.260757134876 0.928892701378
absolute error = 0.006811
relative error = 0.706 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.614
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29541.0MB, alloc=44.3MB, time=369.72
x[1] = 1.9462 2.396
h = 0.0001 0.003
y[1] (numeric) = -0.256280657366 0.934746626838
y[1] (closed_form) = -0.259753375975 0.928886258883
absolute error = 0.006812
relative error = 0.7063 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.617
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29586.6MB, alloc=44.3MB, time=370.28
x[1] = 1.9463 2.399
h = 0.001 0.001
y[1] (numeric) = -0.255679709333 0.934734602607
y[1] (closed_form) = -0.259153020534 0.928874407184
absolute error = 0.006812
relative error = 0.7064 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.618
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29632.2MB, alloc=44.3MB, time=370.86
x[1] = 1.9473 2.4
h = 0.001 0.003
y[1] (numeric) = -0.255477277482 0.934537541895
y[1] (closed_form) = -0.258950532985 0.928677512336
absolute error = 0.006812
relative error = 0.7066 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.62
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=29677.9MB, alloc=44.3MB, time=371.42
x[1] = 1.9483 2.403
h = 0.0001 0.004
y[1] (numeric) = -0.25487564849 0.934346585497
y[1] (closed_form) = -0.258349524949 0.928487010603
absolute error = 0.006812
relative error = 0.7068 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.622
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29723.6MB, alloc=44.3MB, time=371.99
x[1] = 1.9484 2.407
h = 0.003 0.006
y[1] (numeric) = -0.254079108025 0.934338689473
y[1] (closed_form) = -0.257554146563 0.928479213961
absolute error = 0.006812
relative error = 0.707 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.624
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29769.3MB, alloc=44.3MB, time=372.56
x[1] = 1.9514 2.413
h = 0.0001 0.005
y[1] (numeric) = -0.252879798259 0.933761350859
y[1] (closed_form) = -0.256356801297 0.927904881476
absolute error = 0.006811
relative error = 0.7075 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.63
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29815.0MB, alloc=44.3MB, time=373.12
x[1] = 1.9515 2.418
h = 0.0001 0.003
y[1] (numeric) = -0.251892742091 0.933758821506
y[1] (closed_form) = -0.255371338802 0.927902513496
absolute error = 0.006812
relative error = 0.7078 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.633
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29860.6MB, alloc=44.3MB, time=373.68
x[1] = 1.9516 2.421
h = 0.001 0.001
y[1] (numeric) = -0.251302708823 0.933749393951
y[1] (closed_form) = -0.254781884297 0.927893255646
absolute error = 0.006812
relative error = 0.7079 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.634
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29906.2MB, alloc=44.3MB, time=374.25
x[1] = 1.9526 2.422
h = 0.001 0.003
y[1] (numeric) = -0.251103184956 0.933556728794
y[1] (closed_form) = -0.254582305795 0.927700752507
absolute error = 0.006812
relative error = 0.7081 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.636
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29951.8MB, alloc=44.3MB, time=374.82
x[1] = 1.9536 2.425
h = 0.0001 0.004
y[1] (numeric) = -0.250511759607 0.933371638893
y[1] (closed_form) = -0.253991486125 0.927516107703
absolute error = 0.006811
relative error = 0.7083 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.638
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29997.5MB, alloc=44.3MB, time=375.38
x[1] = 1.9537 2.429
h = 0.003 0.006
y[1] (numeric) = -0.249729686263 0.933367055937
y[1] (closed_form) = -0.253210547716 0.927511623884
absolute error = 0.006812
relative error = 0.7085 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.64
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=30043.2MB, alloc=44.3MB, time=375.94
x[1] = 1.9567 2.435
h = 0.0001 0.005
y[1] (numeric) = -0.248549877638 0.932805010555
y[1] (closed_form) = -0.252032653565 0.92695251803
absolute error = 0.00681
relative error = 0.709 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.646
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30088.8MB, alloc=44.3MB, time=376.51
x[1] = 1.9568 2.44
h = 0.0001 0.003
y[1] (numeric) = -0.247580720404 0.932806488652
y[1] (closed_form) = -0.251065053052 0.926954156963
absolute error = 0.006811
relative error = 0.7092 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.649
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30134.5MB, alloc=44.3MB, time=377.08
x[1] = 1.9569 2.443
h = 0.001 0.001
y[1] (numeric) = -0.247001342745 0.932799613366
y[1] (closed_form) = -0.250486240784 0.926947448536
absolute error = 0.006811
relative error = 0.7094 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.65
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=30180.1MB, alloc=44.3MB, time=377.64
x[1] = 1.9579 2.444
h = 0.0001 0.004
y[1] (numeric) = -0.246804652429 0.932611245339
y[1] (closed_form) = -0.250289496893 0.926759238806
absolute error = 0.006811
relative error = 0.7095 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.652
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30225.8MB, alloc=44.3MB, time=378.21
x[1] = 1.958 2.448
h = 0.003 0.006
y[1] (numeric) = -0.246034717601 0.932609380856
y[1] (closed_form) = -0.249520752683 0.926757394926
absolute error = 0.006812
relative error = 0.7097 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.654
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30271.4MB, alloc=44.3MB, time=378.77
x[1] = 1.961 2.454
h = 0.0001 0.005
y[1] (numeric) = -0.244871489857 0.932060011456
y[1] (closed_form) = -0.248359397213 0.926210909694
absolute error = 0.00681
relative error = 0.7102 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.66
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=30317.1MB, alloc=44.3MB, time=379.33
x[1] = 1.9611 2.459
h = 0.0001 0.003
y[1] (numeric) = -0.24391744807 0.932064678153
y[1] (closed_form) = -0.247406881282 0.926215736981
absolute error = 0.006811
relative error = 0.7104 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.662
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30362.7MB, alloc=44.3MB, time=379.90
x[1] = 1.9612 2.462
h = 0.001 0.001
y[1] (numeric) = -0.243347071033 0.932059841111
y[1] (closed_form) = -0.246837058447 0.926211064492
absolute error = 0.006811
relative error = 0.7105 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.664
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30408.3MB, alloc=44.3MB, time=380.46
x[1] = 1.9622 2.463
h = 0.001 0.003
y[1] (numeric) = -0.243152812066 0.931875062499
y[1] (closed_form) = -0.246642746768 0.926026441057
absolute error = 0.006811
relative error = 0.7107 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30453.9MB, alloc=44.3MB, time=381.03
x[1] = 1.9632 2.466
h = 0.0001 0.004
y[1] (numeric) = -0.242579789158 0.931700451162
y[1] (closed_form) = -0.246070302451 0.925852257713
absolute error = 0.006811
relative error = 0.7109 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30499.6MB, alloc=44.3MB, time=381.59
x[1] = 1.9633 2.47
h = 0.003 0.006
y[1] (numeric) = -0.241823771205 0.931701720235
y[1] (closed_form) = -0.245315371195 0.925853625295
absolute error = 0.006811
relative error = 0.7111 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.67
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=30545.2MB, alloc=44.3MB, time=382.16
x[1] = 1.9663 2.476
h = 0.0001 0.005
y[1] (numeric) = -0.240679168545 0.931167044091
y[1] (closed_form) = -0.244172594494 0.925321769913
absolute error = 0.00681
relative error = 0.7116 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.676
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30590.9MB, alloc=44.3MB, time=382.72
x[1] = 1.9664 2.481
h = 0.0001 0.003
y[1] (numeric) = -0.239742251629 0.931175595965
y[1] (closed_form) = -0.243237168648 0.925330481372
absolute error = 0.00681
relative error = 0.7118 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.678
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30636.6MB, alloc=44.3MB, time=383.29
memory used=30682.3MB, alloc=44.3MB, time=383.86
x[1] = 1.9665 2.484
h = 0.001 0.001
y[1] (numeric) = -0.239182069725 0.931173230731
y[1] (closed_form) = -0.242677528381 0.925328277821
absolute error = 0.00681
relative error = 0.7119 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.68
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30727.9MB, alloc=44.3MB, time=384.43
x[1] = 1.9675 2.485
h = 0.001 0.003
y[1] (numeric) = -0.238990512546 0.930992573833
y[1] (closed_form) = -0.24248591954 0.9251477726
absolute error = 0.00681
relative error = 0.7121 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.681
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30773.6MB, alloc=44.3MB, time=385.00
x[1] = 1.9685 2.488
h = 0.0001 0.004
y[1] (numeric) = -0.238427008033 0.930823488798
y[1] (closed_form) = -0.241922979855 0.92497910655
absolute error = 0.00681
relative error = 0.7123 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.684
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30819.1MB, alloc=44.3MB, time=385.56
x[1] = 1.9686 2.492
h = 0.003 0.006
y[1] (numeric) = -0.237684506705 0.930827912867
y[1] (closed_form) = -0.241181540466 0.924983628393
absolute error = 0.006811
relative error = 0.7125 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.686
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30864.8MB, alloc=44.3MB, time=386.12
x[1] = 1.9716 2.498
h = 0.0001 0.005
y[1] (numeric) = -0.236558084271 0.930307614734
y[1] (closed_form) = -0.240056899524 0.924466089274
absolute error = 0.006809
relative error = 0.7129 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.692
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30910.5MB, alloc=44.3MB, time=386.69
x[1] = 1.9717 2.503
h = 0.0001 0.003
y[1] (numeric) = -0.235637895754 0.93031998265
y[1] (closed_form) = -0.239138168393 0.924478615555
absolute error = 0.00681
relative error = 0.7131 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30956.1MB, alloc=44.3MB, time=387.26
x[1] = 1.9718 2.506
h = 0.001 0.001
y[1] (numeric) = -0.235087673173 0.930320044143
y[1] (closed_form) = -0.238588475291 0.924478835856
absolute error = 0.00681
relative error = 0.7133 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.696
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31001.7MB, alloc=44.3MB, time=387.82
x[1] = 1.9728 2.507
h = 0.001 0.003
y[1] (numeric) = -0.234898751547 0.930143417798
y[1] (closed_form) = -0.238399503044 0.9243023578
absolute error = 0.00681
relative error = 0.7134 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.698
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31047.3MB, alloc=44.3MB, time=388.39
x[1] = 1.9738 2.51
h = 0.0001 0.004
y[1] (numeric) = -0.2343445421 0.929979743406
y[1] (closed_form) = -0.237845845147 0.924139093577
absolute error = 0.00681
relative error = 0.7136 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.7
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31092.9MB, alloc=44.3MB, time=388.95
x[1] = 1.9739 2.514
h = 0.003 0.006
y[1] (numeric) = -0.233615245841 0.929987265191
y[1] (closed_form) = -0.237117586841 0.924146712261
absolute error = 0.00681
relative error = 0.7138 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.702
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31138.4MB, alloc=44.3MB, time=389.51
x[1] = 1.9769 2.52
h = 0.0001 0.005
y[1] (numeric) = -0.232506574492 0.929481036838
y[1] (closed_form) = -0.236010654278 0.923643182779
absolute error = 0.006809
relative error = 0.7142 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.708
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31184.1MB, alloc=44.3MB, time=390.08
x[1] = 1.977 2.525
h = 0.0001 0.003
y[1] (numeric) = -0.231602730567 0.929497151353
y[1] (closed_form) = -0.235108235113 0.923659454242
absolute error = 0.006809
relative error = 0.7144 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.711
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31229.7MB, alloc=44.3MB, time=390.65
x[1] = 1.9771 2.528
h = 0.001 0.001
y[1] (numeric) = -0.231062239043 0.929499594438
y[1] (closed_form) = -0.234568261302 0.923662053262
absolute error = 0.006809
relative error = 0.7145 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.713
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31275.3MB, alloc=44.3MB, time=391.22
x[1] = 1.9781 2.529
h = 0.001 0.003
y[1] (numeric) = -0.230875889326 0.929326909889
y[1] (closed_form) = -0.234381861997 0.923489513721
absolute error = 0.006809
relative error = 0.7147 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.714
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31321.1MB, alloc=44.3MB, time=391.78
x[1] = 1.9791 2.532
h = 0.0001 0.004
y[1] (numeric) = -0.230330759198 0.929168532678
y[1] (closed_form) = -0.233837270604 0.92333153805
absolute error = 0.006809
relative error = 0.7149 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.716
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31366.7MB, alloc=44.3MB, time=392.35
x[1] = 1.9792 2.536
h = 0.003 0.006
y[1] (numeric) = -0.229614366373 0.929179094767
y[1] (closed_form) = -0.23312189249 0.923342196033
absolute error = 0.00681
relative error = 0.7151 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.719
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31412.4MB, alloc=44.3MB, time=392.91
x[1] = 1.9822 2.542
h = 0.0001 0.005
y[1] (numeric) = -0.228523032006 0.928686634827
y[1] (closed_form) = -0.232032255877 0.92285237638
absolute error = 0.006808
relative error = 0.7155 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.724
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31458.0MB, alloc=44.3MB, time=393.48
x[1] = 1.9823 2.547
h = 0.0001 0.003
y[1] (numeric) = -0.227635161031 0.928706426309
y[1] (closed_form) = -0.231145778054 0.922872323215
absolute error = 0.006809
relative error = 0.7157 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31503.6MB, alloc=44.3MB, time=394.04
x[1] = 1.9824 2.55
h = 0.001 0.001
y[1] (numeric) = -0.227104179543 0.928711205863
y[1] (closed_form) = -0.230615302889 0.922877255834
absolute error = 0.006809
relative error = 0.7158 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.729
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31549.4MB, alloc=44.3MB, time=394.61
x[1] = 1.9834 2.551
h = 0.0001 0.004
y[1] (numeric) = -0.226920340567 0.928542376684
y[1] (closed_form) = -0.230431415348 0.922708568484
absolute error = 0.006809
relative error = 0.7159 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.73
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31595.1MB, alloc=44.3MB, time=395.17
x[1] = 1.9835 2.555
h = 0.003 0.006
y[1] (numeric) = -0.226214786025 0.928555431128
y[1] (closed_form) = -0.229726925668 0.92272164776
absolute error = 0.006809
relative error = 0.7161 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.732
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31640.7MB, alloc=44.3MB, time=395.74
x[1] = 1.9865 2.561
h = 0.0001 0.005
y[1] (numeric) = -0.225138213403 0.928074386312
y[1] (closed_form) = -0.228652016089 0.922243194481
absolute error = 0.006808
relative error = 0.7165 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.738
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31686.4MB, alloc=44.3MB, time=396.30
x[1] = 1.9866 2.566
h = 0.0001 0.003
y[1] (numeric) = -0.224263845419 0.928097102521
y[1] (closed_form) = -0.227779014812 0.922266064898
absolute error = 0.006809
relative error = 0.7167 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.741
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31732.0MB, alloc=44.3MB, time=396.87
x[1] = 1.9867 2.569
h = 0.001 0.001
y[1] (numeric) = -0.223740905292 0.92810374732
y[1] (closed_form) = -0.227256571458 0.922272860427
absolute error = 0.006809
relative error = 0.7168 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.743
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31777.5MB, alloc=44.3MB, time=397.43
x[1] = 1.9877 2.57
h = 0.001 0.003
y[1] (numeric) = -0.223559224864 0.927938140271
y[1] (closed_form) = -0.227074843302 0.922107392539
absolute error = 0.006809
relative error = 0.717 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.744
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31823.2MB, alloc=44.3MB, time=397.99
x[1] = 1.9887 2.573
h = 0.0001 0.004
y[1] (numeric) = -0.223030499654 0.927789222899
y[1] (closed_form) = -0.226546634053 0.921958861282
absolute error = 0.006809
relative error = 0.7172 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.747
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31869.0MB, alloc=44.3MB, time=398.56
memory used=31914.8MB, alloc=44.3MB, time=399.13
x[1] = 1.9888 2.577
h = 0.003 0.006
y[1] (numeric) = -0.222337381279 0.927805143718
y[1] (closed_form) = -0.225854489007 0.921974876078
absolute error = 0.006809
relative error = 0.7173 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.749
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=31960.4MB, alloc=44.3MB, time=399.69
x[1] = 1.9918 2.583
h = 0.0001 0.005
y[1] (numeric) = -0.221277409505 0.927337328851
y[1] (closed_form) = -0.224796142173 0.921509596922
absolute error = 0.006808
relative error = 0.7177 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32006.0MB, alloc=44.3MB, time=400.25
x[1] = 1.9919 2.588
h = 0.0001 0.003
y[1] (numeric) = -0.220418352869 0.927363596428
y[1] (closed_form) = -0.223938422423 0.921536016809
absolute error = 0.006808
relative error = 0.7179 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.757
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32051.6MB, alloc=44.3MB, time=400.82
x[1] = 1.992 2.591
h = 0.001 0.001
y[1] (numeric) = -0.219904529298 0.927372496405
y[1] (closed_form) = -0.223425084894 0.921545064658
absolute error = 0.006808
relative error = 0.718 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.759
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32097.2MB, alloc=44.3MB, time=401.38
x[1] = 1.993 2.592
h = 0.001 0.003
y[1] (numeric) = -0.21972525101 0.927210590528
y[1] (closed_form) = -0.223245759884 0.921383294944
absolute error = 0.006808
relative error = 0.7181 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.761
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32142.7MB, alloc=44.3MB, time=401.94
x[1] = 1.994 2.595
h = 0.0001 0.004
y[1] (numeric) = -0.219205025711 0.927066659956
y[1] (closed_form) = -0.222726038953 0.921239742373
absolute error = 0.006808
relative error = 0.7183 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.763
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32188.4MB, alloc=44.3MB, time=402.52
x[1] = 1.9941 2.599
h = 0.003 0.006
y[1] (numeric) = -0.218523998567 0.927085460073
y[1] (closed_form) = -0.222045963869 0.921258635146
absolute error = 0.006809
relative error = 0.7185 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.765
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32234.1MB, alloc=44.3MB, time=403.08
x[1] = 1.9971 2.605
h = 0.0001 0.005
y[1] (numeric) = -0.217480253155 0.926630592468
y[1] (closed_form) = -0.221003806752 0.920806248856
absolute error = 0.006807
relative error = 0.7189 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.771
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32279.7MB, alloc=44.3MB, time=403.64
x[1] = 1.9972 2.61
h = 0.0001 0.003
y[1] (numeric) = -0.216636168474 0.926660341678
y[1] (closed_form) = -0.220161030044 0.920836148342
absolute error = 0.006808
relative error = 0.719 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.774
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32325.3MB, alloc=44.3MB, time=404.21
x[1] = 1.9973 2.613
h = 0.001 0.001
y[1] (numeric) = -0.216131259642 0.926671451978
y[1] (closed_form) = -0.219656596859 0.920847403667
absolute error = 0.006808
relative error = 0.7191 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.776
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32370.9MB, alloc=44.3MB, time=404.77
x[1] = 1.9983 2.614
h = 0.001 0.003
y[1] (numeric) = -0.215954328803 0.9265131671
y[1] (closed_form) = -0.219479620294 0.920689252048
absolute error = 0.006808
relative error = 0.7193 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32416.6MB, alloc=44.3MB, time=405.34
x[1] = 1.9993 2.617
h = 0.0001 0.004
y[1] (numeric) = -0.215442414099 0.926374118035
y[1] (closed_form) = -0.218968198757 0.920550573043
absolute error = 0.006808
relative error = 0.7195 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.779
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32462.2MB, alloc=44.3MB, time=405.90
x[1] = 1.9994 2.621
h = 0.003 0.006
y[1] (numeric) = -0.21477321136 0.926395740174
y[1] (closed_form) = -0.218299927448 0.92057228643
absolute error = 0.006808
relative error = 0.7196 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.782
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32507.8MB, alloc=44.3MB, time=406.47
x[1] = 2.0024 2.627
h = 0.0001 0.005
y[1] (numeric) = -0.213745330522 0.925953543456
y[1] (closed_form) = -0.217273599652 0.920132518016
absolute error = 0.006807
relative error = 0.72 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.788
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32553.4MB, alloc=44.3MB, time=407.03
x[1] = 2.0025 2.632
h = 0.0001 0.003
y[1] (numeric) = -0.212915888843 0.925986704747
y[1] (closed_form) = -0.21644543791 0.920165827425
absolute error = 0.006807
relative error = 0.7201 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.79
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=32599.0MB, alloc=44.3MB, time=407.60
x[1] = 2.0026 2.635
h = 0.001 0.001
y[1] (numeric) = -0.212419699151 0.925999980728
y[1] (closed_form) = -0.21594971379 0.9201792456
absolute error = 0.006807
relative error = 0.7202 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.792
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32644.7MB, alloc=44.3MB, time=408.16
x[1] = 2.0036 2.636
h = 0.001 0.003
y[1] (numeric) = -0.212245063128 0.925845238746
y[1] (closed_form) = -0.215775033024 0.92002463406
absolute error = 0.006807
relative error = 0.7204 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.793
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32690.4MB, alloc=44.3MB, time=408.73
x[1] = 2.0046 2.639
h = 0.0001 0.004
y[1] (numeric) = -0.211741275873 0.925710967965
y[1] (closed_form) = -0.215271728111 0.91989072557
absolute error = 0.006807
relative error = 0.7205 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.796
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32736.0MB, alloc=44.3MB, time=409.30
x[1] = 2.0047 2.643
h = 0.003 0.006
y[1] (numeric) = -0.211083638897 0.925735355076
y[1] (closed_form) = -0.214615002551 0.919915202441
absolute error = 0.006808
relative error = 0.7207 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.798
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32781.6MB, alloc=44.3MB, time=409.86
x[1] = 2.0077 2.649
h = 0.0001 0.005
y[1] (numeric) = -0.210071273008 0.925305559039
y[1] (closed_form) = -0.213604155779 0.919487783041
absolute error = 0.006806
relative error = 0.721 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32827.1MB, alloc=44.3MB, time=410.42
x[1] = 2.0078 2.654
h = 0.0001 0.003
y[1] (numeric) = -0.209256155421 0.925342063116
y[1] (closed_form) = -0.212790290933 0.919524432966
absolute error = 0.006807
relative error = 0.7212 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.807
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32872.7MB, alloc=44.3MB, time=410.98
x[1] = 2.0079 2.657
h = 0.001 0.001
y[1] (numeric) = -0.208768495248 0.925357460389
y[1] (closed_form) = -0.212303086566 0.919539969619
absolute error = 0.006807
relative error = 0.7213 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.809
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32918.3MB, alloc=44.3MB, time=411.55
x[1] = 2.0089 2.658
h = 0.0001 0.004
y[1] (numeric) = -0.208596103368 0.925206185204
y[1] (closed_form) = -0.212130650915 0.919388822146
absolute error = 0.006807
relative error = 0.7214 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.81
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=32964.0MB, alloc=44.3MB, time=412.11
x[1] = 2.009 2.662
h = 0.003 0.006
y[1] (numeric) = -0.207948190895 0.925232836551
y[1] (closed_form) = -0.211483694929 0.919415498708
absolute error = 0.006807
relative error = 0.7216 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.812
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33009.6MB, alloc=44.3MB, time=412.69
x[1] = 2.012 2.668
h = 0.0001 0.005
y[1] (numeric) = -0.206949052148 0.924813323477
y[1] (closed_form) = -0.210486046518 0.918998319229
absolute error = 0.006806
relative error = 0.7219 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.818
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33055.4MB, alloc=44.3MB, time=413.26
memory used=33101.0MB, alloc=44.3MB, time=413.82
x[1] = 2.0121 2.673
h = 0.0001 0.003
y[1] (numeric) = -0.206146054974 0.924852484029
y[1] (closed_form) = -0.209684279296 0.919037623906
absolute error = 0.006807
relative error = 0.7221 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.821
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33146.7MB, alloc=44.3MB, time=414.38
x[1] = 2.0122 2.676
h = 0.001 0.001
y[1] (numeric) = -0.205665613834 0.924869573279
y[1] (closed_form) = -0.209204285761 0.919054850241
absolute error = 0.006807
relative error = 0.7222 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.823
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33192.3MB, alloc=44.3MB, time=414.95
x[1] = 2.0132 2.677
h = 0.001 0.003
y[1] (numeric) = -0.205495154591 0.924721196803
y[1] (closed_form) = -0.209033783545 0.918906599179
absolute error = 0.006807
relative error = 0.7223 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.824
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33237.9MB, alloc=44.3MB, time=415.51
x[1] = 2.0142 2.68
h = 0.0001 0.004
y[1] (numeric) = -0.205006077378 0.924595457582
y[1] (closed_form) = -0.20854516939 0.918781208352
absolute error = 0.006807
relative error = 0.7225 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.827
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33283.4MB, alloc=44.3MB, time=416.08
x[1] = 2.0143 2.684
h = 0.003 0.006
y[1] (numeric) = -0.204369331287 0.924624707964
y[1] (closed_form) = -0.207909299014 0.91881054576
absolute error = 0.006807
relative error = 0.7226 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.829
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33329.0MB, alloc=44.3MB, time=416.64
x[1] = 2.0173 2.69
h = 0.0001 0.005
y[1] (numeric) = -0.203385084514 0.924217112566
y[1] (closed_form) = -0.206926510976 0.918405234672
absolute error = 0.006806
relative error = 0.7229 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.835
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33374.5MB, alloc=44.3MB, time=417.20
x[1] = 2.0174 2.695
h = 0.0001 0.003
y[1] (numeric) = -0.202595842626 0.924259491402
y[1] (closed_form) = -0.206138473325 0.918447755175
absolute error = 0.006806
relative error = 0.7231 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.838
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33420.3MB, alloc=44.3MB, time=417.77
x[1] = 2.0175 2.698
h = 0.001 0.001
y[1] (numeric) = -0.20212359278 0.924278622246
y[1] (closed_form) = -0.205666661862 0.918467020325
absolute error = 0.006806
relative error = 0.7232 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.839
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33465.8MB, alloc=44.3MB, time=418.34
x[1] = 2.0185 2.699
h = 0.001 0.003
y[1] (numeric) = -0.201955287457 0.924133576651
y[1] (closed_form) = -0.205498314516 0.918322097563
absolute error = 0.006806
relative error = 0.7233 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33511.5MB, alloc=44.3MB, time=418.90
x[1] = 2.0195 2.702
h = 0.0001 0.004
y[1] (numeric) = -0.201473844478 0.924012333516
y[1] (closed_form) = -0.205017324762 0.918201195517
absolute error = 0.006806
relative error = 0.7234 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.843
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33557.3MB, alloc=44.3MB, time=419.47
x[1] = 2.0196 2.706
h = 0.003 0.006
y[1] (numeric) = -0.200847966018 0.924044190166
y[1] (closed_form) = -0.204392303641 0.91823313751
absolute error = 0.006807
relative error = 0.7236 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.846
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33602.9MB, alloc=44.3MB, time=420.03
x[1] = 2.0226 2.712
h = 0.0001 0.005
y[1] (numeric) = -0.19987829373 0.923648258989
y[1] (closed_form) = -0.203424059646 0.917839442591
absolute error = 0.006805
relative error = 0.7239 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.851
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33648.5MB, alloc=44.3MB, time=420.60
x[1] = 2.0227 2.717
h = 0.0001 0.003
y[1] (numeric) = -0.19910251489 0.923693787791
y[1] (closed_form) = -0.202649460084 0.917885110522
absolute error = 0.006806
relative error = 0.7241 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.854
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33694.0MB, alloc=44.3MB, time=421.16
x[1] = 2.0228 2.72
h = 0.001 0.001
y[1] (numeric) = -0.198638282595 0.923714916693
y[1] (closed_form) = -0.202185657224 0.917906370972
absolute error = 0.006806
relative error = 0.7241 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.856
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33739.6MB, alloc=44.3MB, time=421.72
x[1] = 2.0238 2.721
h = 0.001 0.003
y[1] (numeric) = -0.198472085676 0.923573131269
y[1] (closed_form) = -0.202019419221 0.917764705875
absolute error = 0.006806
relative error = 0.7242 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33785.2MB, alloc=44.3MB, time=422.29
x[1] = 2.0248 2.724
h = 0.0001 0.004
y[1] (numeric) = -0.197998115373 0.923456288625
y[1] (closed_form) = -0.201545892629 0.917648197173
absolute error = 0.006806
relative error = 0.7244 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.86
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33830.8MB, alloc=44.3MB, time=422.86
x[1] = 2.0249 2.728
h = 0.003 0.006
y[1] (numeric) = -0.197382874687 0.923490695753
y[1] (closed_form) = -0.200931491438 0.91768268791
absolute error = 0.006806
relative error = 0.7245 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.862
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33876.4MB, alloc=44.3MB, time=423.42
x[1] = 2.0279 2.734
h = 0.0001 0.005
y[1] (numeric) = -0.196427469714 0.923106180984
y[1] (closed_form) = -0.199977485424 0.917300362542
absolute error = 0.006805
relative error = 0.7248 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.868
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33921.9MB, alloc=44.3MB, time=423.98
x[1] = 2.028 2.739
h = 0.0001 0.003
y[1] (numeric) = -0.19566487034 0.92315479192
y[1] (closed_form) = -0.199216041094 0.917349109996
absolute error = 0.006806
relative error = 0.725 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.871
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=33967.6MB, alloc=44.3MB, time=424.55
x[1] = 2.0281 2.742
h = 0.001 0.001
y[1] (numeric) = -0.195208487003 0.923177875719
y[1] (closed_form) = -0.198760078511 0.917372322611
absolute error = 0.006806
relative error = 0.7251 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.873
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34013.3MB, alloc=44.3MB, time=425.11
x[1] = 2.0291 2.743
h = 0.001 0.003
y[1] (numeric) = -0.195044354611 0.923039281539
y[1] (closed_form) = -0.198595905961 0.917233846325
absolute error = 0.006806
relative error = 0.7252 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.874
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34059.0MB, alloc=44.3MB, time=425.68
x[1] = 2.0301 2.746
h = 0.0001 0.004
y[1] (numeric) = -0.194577700481 0.922926745704
y[1] (closed_form) = -0.198129686333 0.917121637437
absolute error = 0.006806
relative error = 0.7253 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.877
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34104.6MB, alloc=44.3MB, time=426.24
x[1] = 2.0302 2.75
h = 0.003 0.006
y[1] (numeric) = -0.193972874494 0.92296364797
y[1] (closed_form) = -0.19752568251 0.917158621532
absolute error = 0.006806
relative error = 0.7254 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.879
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34150.2MB, alloc=44.3MB, time=426.81
x[1] = 2.0332 2.756
h = 0.0001 0.005
y[1] (numeric) = -0.193031439571 0.922590307303
y[1] (closed_form) = -0.196585618269 0.91678742457
absolute error = 0.006805
relative error = 0.7257 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.885
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34195.9MB, alloc=44.3MB, time=427.38
x[1] = 2.0333 2.761
h = 0.0001 0.003
y[1] (numeric) = -0.192281744409 0.922641933074
y[1] (closed_form) = -0.195837054617 0.916839184184
absolute error = 0.006805
relative error = 0.7259 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.888
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34241.6MB, alloc=44.3MB, time=427.94
x[1] = 2.0334 2.764
h = 0.001 0.001
y[1] (numeric) = -0.191833046396 0.922666929009
y[1] (closed_form) = -0.195388768931 0.916864306227
absolute error = 0.006805
relative error = 0.7259 %
Correct digits = 2
memory used=34287.3MB, alloc=44.3MB, time=428.50
Radius of convergence (given) for eq 1 = 4.89
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=34333.0MB, alloc=44.3MB, time=429.07
x[1] = 2.0344 2.765
h = 0.0001 0.004
y[1] (numeric) = -0.191670936221 0.922531458873
y[1] (closed_form) = -0.195226619513 0.916728951622
absolute error = 0.006805
relative error = 0.7261 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.891
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34378.7MB, alloc=44.3MB, time=429.64
x[1] = 2.0345 2.769
h = 0.003 0.006
y[1] (numeric) = -0.191074875087 0.922570401826
y[1] (closed_form) = -0.194631420969 0.91676791757
absolute error = 0.006806
relative error = 0.7262 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.893
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34424.3MB, alloc=44.3MB, time=430.20
x[1] = 2.0375 2.775
h = 0.0001 0.005
y[1] (numeric) = -0.190145363615 0.922206327762
y[1] (closed_form) = -0.193703256123 0.916405949099
absolute error = 0.006805
relative error = 0.7265 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.899
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34469.9MB, alloc=44.3MB, time=430.76
x[1] = 2.0376 2.78
h = 0.0001 0.003
y[1] (numeric) = -0.189406596519 0.922260345743
y[1] (closed_form) = -0.192965600787 0.916460098845
absolute error = 0.006805
relative error = 0.7266 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.902
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34515.4MB, alloc=44.3MB, time=431.33
x[1] = 2.0377 2.783
h = 0.001 0.001
y[1] (numeric) = -0.188964408483 0.922286864676
y[1] (closed_form) = -0.192523817991 0.916486741674
absolute error = 0.006805
relative error = 0.7267 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.904
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34561.1MB, alloc=44.3MB, time=431.89
x[1] = 2.0387 2.784
h = 0.001 0.003
y[1] (numeric) = -0.188804042386 0.922154007651
y[1] (closed_form) = -0.192363413399 0.916353998191
absolute error = 0.006805
relative error = 0.7268 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.905
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34606.8MB, alloc=44.3MB, time=432.46
x[1] = 2.0397 2.787
h = 0.0001 0.004
y[1] (numeric) = -0.188350650639 0.922049159886
y[1] (closed_form) = -0.191910439711 0.916249464858
absolute error = 0.006805
relative error = 0.7269 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.908
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34652.5MB, alloc=44.3MB, time=433.04
x[1] = 2.0398 2.791
h = 0.003 0.006
y[1] (numeric) = -0.18776466064 0.922090441317
y[1] (closed_form) = -0.191325240908 0.916290824895
absolute error = 0.006805
relative error = 0.727 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.91
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=34698.2MB, alloc=44.3MB, time=433.60
x[1] = 2.0428 2.797
h = 0.0001 0.005
y[1] (numeric) = -0.186848588321 0.921737107971
y[1] (closed_form) = -0.190410488793 0.915939553502
absolute error = 0.006804
relative error = 0.7273 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34743.8MB, alloc=44.3MB, time=434.17
x[1] = 2.0429 2.802
h = 0.0001 0.003
y[1] (numeric) = -0.186122233595 0.921794020164
y[1] (closed_form) = -0.189685223527 0.915996594678
absolute error = 0.006805
relative error = 0.7274 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.919
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34789.4MB, alloc=44.3MB, time=434.73
x[1] = 2.043 2.805
h = 0.001 0.001
y[1] (numeric) = -0.185687438467 0.921822374617
y[1] (closed_form) = -0.189250825662 0.916025070367
absolute error = 0.006805
relative error = 0.7275 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.921
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34835.1MB, alloc=44.3MB, time=435.30
x[1] = 2.044 2.806
h = 0.001 0.003
y[1] (numeric) = -0.18552901904 0.921692521478
y[1] (closed_form) = -0.18909236863 0.915895328531
absolute error = 0.006805
relative error = 0.7276 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.922
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34880.7MB, alloc=44.3MB, time=435.86
x[1] = 2.045 2.809
h = 0.0001 0.004
y[1] (numeric) = -0.185082520854 0.921591724464
y[1] (closed_form) = -0.188646280105 0.915794839373
absolute error = 0.006805
relative error = 0.7278 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.925
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34926.4MB, alloc=44.3MB, time=436.43
x[1] = 2.0451 2.813
h = 0.003 0.006
y[1] (numeric) = -0.184506342004 0.92163534788
y[1] (closed_form) = -0.188070876485 0.915838539507
absolute error = 0.006805
relative error = 0.7279 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.927
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=34972.1MB, alloc=44.3MB, time=437.00
x[1] = 2.0481 2.819
h = 0.0001 0.005
y[1] (numeric) = -0.183603437793 0.921292527884
y[1] (closed_form) = -0.187169266986 0.915497738889
absolute error = 0.006804
relative error = 0.7281 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.933
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35017.8MB, alloc=44.3MB, time=437.56
x[1] = 2.0482 2.824
h = 0.0001 0.003
y[1] (numeric) = -0.182889242361 0.921352268629
y[1] (closed_form) = -0.186456139341 0.915557605792
absolute error = 0.006804
relative error = 0.7283 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.936
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35063.4MB, alloc=44.3MB, time=438.12
x[1] = 2.0483 2.827
h = 0.001 0.001
y[1] (numeric) = -0.182461689703 0.921382417038
y[1] (closed_form) = -0.186028976199 0.915587872806
absolute error = 0.006805
relative error = 0.7283 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.938
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35109.2MB, alloc=44.3MB, time=438.69
x[1] = 2.0493 2.828
h = 0.001 0.003
y[1] (numeric) = -0.182305178765 0.921255505231
y[1] (closed_form) = -0.185872428533 0.915461070127
absolute error = 0.006804
relative error = 0.7284 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.939
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35154.7MB, alloc=44.3MB, time=439.25
x[1] = 2.0503 2.831
h = 0.0001 0.004
y[1] (numeric) = -0.181865435368 0.921158672304
y[1] (closed_form) = -0.18543308666 0.91536453862
absolute error = 0.006804
relative error = 0.7286 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.942
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35200.4MB, alloc=44.3MB, time=439.82
x[1] = 2.0504 2.835
h = 0.003 0.006
y[1] (numeric) = -0.181298868518 0.921204584306
y[1] (closed_form) = -0.18486727952 0.915410525425
absolute error = 0.006805
relative error = 0.7286 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.944
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35246.1MB, alloc=44.3MB, time=440.38
x[1] = 2.0534 2.841
h = 0.0001 0.005
y[1] (numeric) = -0.180408869813 0.920872055308
y[1] (closed_form) = -0.18397855092 0.915079974263
absolute error = 0.006804
relative error = 0.7289 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35291.8MB, alloc=44.3MB, time=440.95
x[1] = 2.0535 2.846
h = 0.0001 0.003
y[1] (numeric) = -0.179706587807 0.920934559612
y[1] (closed_form) = -0.183277315636 0.915142601862
absolute error = 0.006804
relative error = 0.729 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.953
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35337.4MB, alloc=44.3MB, time=441.51
x[1] = 2.0536 2.849
h = 0.001 0.001
y[1] (numeric) = -0.179286131469 0.920966460884
y[1] (closed_form) = -0.182857241286 0.915174619138
absolute error = 0.006804
relative error = 0.7291 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.955
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35383.0MB, alloc=44.3MB, time=442.07
x[1] = 2.0546 2.85
h = 0.001 0.003
y[1] (numeric) = -0.179131492156 0.920842429393
y[1] (closed_form) = -0.182702566108 0.91505069466
absolute error = 0.006804
relative error = 0.7292 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.956
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35428.7MB, alloc=44.3MB, time=442.63
x[1] = 2.0556 2.853
h = 0.0001 0.004
y[1] (numeric) = -0.17869836894 0.920749475639
y[1] (closed_form) = -0.182269836529 0.914958036028
absolute error = 0.006804
relative error = 0.7293 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.959
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35474.4MB, alloc=44.3MB, time=443.20
x[1] = 2.0557 2.857
h = 0.003 0.006
y[1] (numeric) = -0.178141220593 0.920797623404
y[1] (closed_form) = -0.181713432803 0.915006256659
absolute error = 0.006804
relative error = 0.7294 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.961
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35520.0MB, alloc=44.3MB, time=443.76
memory used=35565.7MB, alloc=44.3MB, time=444.35
x[1] = 2.0587 2.863
h = 0.0001 0.005
y[1] (numeric) = -0.1772638729 0.920475167951
y[1] (closed_form) = -0.180837331455 0.914685738502
absolute error = 0.006803
relative error = 0.7297 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.967
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35611.3MB, alloc=44.3MB, time=444.91
x[1] = 2.0588 2.868
h = 0.0001 0.003
y[1] (numeric) = -0.1765732654 0.920540371513
y[1] (closed_form) = -0.180147750194 0.914751062467
absolute error = 0.006804
relative error = 0.7298 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35657.1MB, alloc=44.3MB, time=445.50
x[1] = 2.0589 2.871
h = 0.001 0.001
y[1] (numeric) = -0.176159763364 0.920573985035
y[1] (closed_form) = -0.179734622831 0.914784789421
absolute error = 0.006804
relative error = 0.7298 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.972
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35702.8MB, alloc=44.3MB, time=446.06
x[1] = 2.0599 2.872
h = 0.001 0.003
y[1] (numeric) = -0.176006960068 0.920452774335
y[1] (closed_form) = -0.179581784522 0.914663683678
absolute error = 0.006804
relative error = 0.7299 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 4.973
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35748.5MB, alloc=44.3MB, time=446.63
Finished!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;
Iterations = 754
Total Elapsed Time = 7 Minutes 26 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 7 Minutes 26 Seconds
> quit
memory used=35756.9MB, alloc=44.3MB, time=446.72