|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(cos(c(x)));
> end;
exact_soln_y := proc(x) return cos(c(x)) end proc
> exact_soln_yp := proc(x)
> return(neg(sin(c(x))));
> end;
exact_soln_yp := proc(x) return neg(sin(c(x))) end proc
> exact_soln_ypp := proc(x)
> return(neg(cos(c(x))));
> end;
exact_soln_ypp := proc(x) return neg(cos(c(x))) end proc
> exact_soln_yppp := proc(x)
> return(sin(x));
> end;
exact_soln_yppp := proc(x) return sin(x) end proc
> exact_soln_ypppp := proc(x)
> return(cos(c(x)));
> end;
exact_soln_ypppp := proc(x) return cos(c(x)) 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_5,
> array_const_0D0,
> array_const_3,
#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_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_5, array_const_0D0, array_const_3,
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_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_5,
> array_const_0D0,
> array_const_3,
#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_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_5, array_const_0D0, array_const_3,
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_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_5,
> array_const_0D0,
> array_const_3,
#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_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_5, array_const_0D0, array_const_3,
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_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_5,
> array_const_0D0,
> array_const_3,
#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_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_5, array_const_0D0, array_const_3,
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_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_5,
> array_const_0D0,
> array_const_3,
#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_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_5, array_const_0D0, array_const_3,
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_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_5,
> array_const_0D0,
> array_const_3,
#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_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_5, array_const_0D0, array_const_3,
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_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_5,
> array_const_0D0,
> array_const_3,
#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_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 - 5 - 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 - 5 - 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 - 5 - 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_5, array_const_0D0, array_const_3,
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_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 - 15;
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 - 15;
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 - 15;
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_5,
> array_const_0D0,
> array_const_3,
#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_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 diff $eq_no = 1 i = 1 order_d = 3
> array_tmp1[1] := array_y_higher[4,1];
> #emit pre neg FULL $eq_no = 1
> array_tmp2[1] := neg(array_tmp1[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[1]) * (expt((glob_h) , c(5))) * c(factorial_3(0,5));
> 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);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[3,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[4,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[5,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[6,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2 order_d = 3
> array_tmp1[2] := array_y_higher[4,2];
> #emit pre neg FULL $eq_no = 1
> array_tmp2[2] := neg(array_tmp1[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,7]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[2]) * (expt((glob_h) , c(5))) * c(factorial_3(1,6));
> if (7 <= ATS_MAX_TERMS) then # if number 3
> array_y[7] := temporary;
> array_y_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y_higher[2,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[3,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[4,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[5,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[6,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3 order_d = 3
> array_tmp1[3] := array_y_higher[4,3];
> #emit pre neg FULL $eq_no = 1
> array_tmp2[3] := neg(array_tmp1[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,8]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[3]) * (expt((glob_h) , c(5))) * c(factorial_3(2,7));
> if (8 <= ATS_MAX_TERMS) then # if number 3
> array_y[8] := temporary;
> array_y_higher[1,8] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(7);
> array_y_higher[2,7] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y_higher[3,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[4,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[5,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[6,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4 order_d = 3
> array_tmp1[4] := array_y_higher[4,4];
> #emit pre neg FULL $eq_no = 1
> array_tmp2[4] := neg(array_tmp1[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,9]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[4]) * (expt((glob_h) , c(5))) * c(factorial_3(3,8));
> if (9 <= ATS_MAX_TERMS) then # if number 3
> array_y[9] := temporary;
> array_y_higher[1,9] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(8);
> array_y_higher[2,8] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(7);
> array_y_higher[3,7] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y_higher[4,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[5,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[6,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5 order_d = 3
> array_tmp1[5] := array_y_higher[4,5];
> #emit pre neg FULL $eq_no = 1
> array_tmp2[5] := neg(array_tmp1[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,10]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[5]) * (expt((glob_h) , c(5))) * c(factorial_3(4,9));
> if (10 <= ATS_MAX_TERMS) then # if number 3
> array_y[10] := temporary;
> array_y_higher[1,10] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(9);
> array_y_higher[2,9] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(8);
> array_y_higher[3,8] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(7);
> array_y_higher[4,7] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y_higher[5,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[6,5] := 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 diff $eq_no = 1
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp1[kkk] := array_y_higher[4,kkk];
> fi;# end if 1;
> #emit neg FULL $eq_no = 1
> array_tmp2[kkk] := neg(array_tmp1[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 5;
> 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_tmp3[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_5, array_const_0D0, array_const_3,
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_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_y_higher[4, 1];
array_tmp2[1] := neg(array_tmp1[1]);
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y_set_initial[1, 6] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[1])*expt(glob_h, c(5))*c(factorial_3(0, 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);
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[3, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[4, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[5, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[6, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_y_higher[4, 2];
array_tmp2[2] := neg(array_tmp1[2]);
array_tmp3[2] := array_tmp2[2];
if not array_y_set_initial[1, 7] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[2])*expt(glob_h, c(5))*c(factorial_3(1, 6));
if 7 <= ATS_MAX_TERMS then
array_y[7] := temporary; array_y_higher[1, 7] := temporary
end if;
temporary := c(temporary)*c(6)/c(glob_h);
array_y_higher[2, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[3, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[4, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[5, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[6, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_y_higher[4, 3];
array_tmp2[3] := neg(array_tmp1[3]);
array_tmp3[3] := array_tmp2[3];
if not array_y_set_initial[1, 8] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[3])*expt(glob_h, c(5))*c(factorial_3(2, 7));
if 8 <= ATS_MAX_TERMS then
array_y[8] := temporary; array_y_higher[1, 8] := temporary
end if;
temporary := c(temporary)*c(7)/c(glob_h);
array_y_higher[2, 7] := c(temporary);
temporary := c(temporary)*c(6)/c(glob_h);
array_y_higher[3, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[4, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[5, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[6, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_y_higher[4, 4];
array_tmp2[4] := neg(array_tmp1[4]);
array_tmp3[4] := array_tmp2[4];
if not array_y_set_initial[1, 9] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[4])*expt(glob_h, c(5))*c(factorial_3(3, 8));
if 9 <= ATS_MAX_TERMS then
array_y[9] := temporary; array_y_higher[1, 9] := temporary
end if;
temporary := c(temporary)*c(8)/c(glob_h);
array_y_higher[2, 8] := c(temporary);
temporary := c(temporary)*c(7)/c(glob_h);
array_y_higher[3, 7] := c(temporary);
temporary := c(temporary)*c(6)/c(glob_h);
array_y_higher[4, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[5, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[6, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_y_higher[4, 5];
array_tmp2[5] := neg(array_tmp1[5]);
array_tmp3[5] := array_tmp2[5];
if not array_y_set_initial[1, 10] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[5])*expt(glob_h, c(5))*c(factorial_3(4, 9));
if 10 <= ATS_MAX_TERMS then
array_y[10] := temporary;
array_y_higher[1, 10] := temporary
end if;
temporary := c(temporary)*c(9)/c(glob_h);
array_y_higher[2, 9] := c(temporary);
temporary := c(temporary)*c(8)/c(glob_h);
array_y_higher[3, 8] := c(temporary);
temporary := c(temporary)*c(7)/c(glob_h);
array_y_higher[4, 7] := c(temporary);
temporary := c(temporary)*c(6)/c(glob_h);
array_y_higher[5, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[6, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
if kkk <= ATS_MAX_TERMS then
array_tmp1[kkk] := array_y_higher[4, kkk]
end if;
array_tmp2[kkk] := neg(array_tmp1[kkk]);
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 5;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp3[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_5,
> array_const_0D0,
> array_const_3,
> #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_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:=64;
> 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_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(6) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(6) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(6) ,(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_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=6) 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 <=6) 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 <=6) 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_m1);
> zero_ats_ar(array_const_5);
> array_const_5[1] := c(5);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_3);
> array_const_3[1] := c(3);
> 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] := true;
> array_y_set_initial[1,3] := true;
> array_y_set_initial[1,4] := true;
> array_y_set_initial[1,5] := true;
> 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/h5h3postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 5 ) = neg ( diff ( y , x , 3 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> 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 := 0.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);");
> omniout_str(ALWAYS,"array_y_init[2 + 1] := exact_soln_ypp(x_start);");
> omniout_str(ALWAYS,"array_y_init[3 + 1] := exact_soln_yppp(x_start);");
> omniout_str(ALWAYS,"array_y_init[4 + 1] := exact_soln_ypppp(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> 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 := 3;");
> 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(cos(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"return(neg(sin(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_ypp := proc(x)");
> omniout_str(ALWAYS,"return(neg(cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yppp := proc(x)");
> omniout_str(ALWAYS,"return(sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_ypppp := proc(x)");
> omniout_str(ALWAYS,"return(cos(c(x)));");
> 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 := 0.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> array_y_init[2 + 1] := exact_soln_ypp(x_start);
> array_y_init[3 + 1] := exact_soln_yppp(x_start);
> array_y_init[4 + 1] := exact_soln_ypppp(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #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 := 5;
> #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 := 6;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 6;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[6,iii] := array_y_higher[6,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 := 6;
> 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 := 5;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[5,iii] := array_y_higher[5,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 := 5;
> 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 := 5;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[5,iii] := array_y_higher[5,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 := 5;
> 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 := 4;
> calc_term := 3;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[4,iii] := array_y_higher[4,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 := 4;
> calc_term := 3;
> #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 := 4;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[4,iii] := array_y_higher[4,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 := 4;
> 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 := 4;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[4,iii] := array_y_higher[4,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 := 4;
> 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 := 3;
> calc_term := 4;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> calc_term := 4;
> #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 := 3;
> calc_term := 3;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> calc_term := 3;
> #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 := 3;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> 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 := 3;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> 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 := 2;
> calc_term := 5;
> #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 := 5;
> #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 := 2;
> calc_term := 4;
> #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 := 4;
> #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 := 2;
> calc_term := 3;
> #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 := 3;
> #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 := 2;
> calc_term := 2;
> #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 := 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 := 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 := 6;
> #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 := 6;
> #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 := 5;
> #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 := 5;
> #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 := 4;
> #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 := 4;
> #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 := 3;
> #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 := 3;
> #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 , 5 ) = neg ( diff ( y , x , 3 ) ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T14:58:05-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"h5h3")
> ;
> logitem_str(html_log_file,"diff ( y , x , 5 ) = neg ( diff ( y , x , 3 ) ) ; ")
> ;
> 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,"h5h3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"h5h3 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_5, array_const_0D0, array_const_3,
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_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 := 64;
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_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 6, 0 .. 41, []);
array_y_higher_work := Array(0 .. 6, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 6, 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_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 6 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 <= 6 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 <= 6 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_m1);
zero_ats_ar(array_const_5);
array_const_5[1] := c(5);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_3);
array_const_3[1] := c(3);
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] := true;
array_y_set_initial[1, 3] := true;
array_y_set_initial[1, 4] := true;
array_y_set_initial[1, 5] := true;
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/h5h3postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 5 ) = neg ( diff ( y \
, x , 3 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
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 := 0.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);");
omniout_str(ALWAYS, "array_y_init[2 + 1] := exact_soln_ypp(x_start);");
omniout_str(ALWAYS, "array_y_init[3 + 1] := exact_soln_yppp(x_start);")
;
omniout_str(ALWAYS, "array_y_init[4 + 1] := exact_soln_ypppp(x_start);")
;
omniout_str(ALWAYS, "glob_look_poles := true;");
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 := 3;");
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(cos(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "return(neg(sin(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_ypp := proc(x)");
omniout_str(ALWAYS, "return(neg(cos(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yppp := proc(x)");
omniout_str(ALWAYS, "return(sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_ypppp := proc(x)");
omniout_str(ALWAYS, "return(cos(c(x)));");
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,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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 := 0.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
array_y_init[3] := exact_soln_ypp(x_start);
array_y_init[4] := exact_soln_yppp(x_start);
array_y_init[5] := exact_soln_ypppp(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
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 := 5;
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 := 6;
ord := 6;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[6, iii] := array_y_higher[6, 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 := 6;
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 := 5;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[5, iii] := array_y_higher[5, 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 := 5;
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 := 5;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[5, iii] := array_y_higher[5, 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 := 5;
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 := 4;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[4, iii] := array_y_higher[4, 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 := 4;
calc_term := 3;
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 := 4;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[4, iii] := array_y_higher[4, 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 := 4;
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 := 4;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[4, iii] := array_y_higher[4, 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 := 4;
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 := 3;
calc_term := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, 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 := 3;
calc_term := 4;
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 := 3;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, 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 := 3;
calc_term := 3;
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 := 3;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, 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 := 3;
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 := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, 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 := 3;
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 := 2;
calc_term := 5;
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 := 5;
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 := 2;
calc_term := 4;
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 := 4;
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 := 2;
calc_term := 3;
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 := 3;
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 := 2;
calc_term := 2;
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 := 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 := 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 := 6;
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 := 6;
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 := 5;
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 := 5;
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 := 4;
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 := 4;
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 := 3;
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 := 3;
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 , 5 ) = neg ( diff ( \
y , x , 3 ) ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T14:58:05-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "h5h3")
;
logitem_str(html_log_file, "diff ( y , x , 5 ) = ne\
g ( diff ( y , x , 3 ) ) ; ");
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,
"h5h3 diffeq.mxt");
logitem_str(html_log_file,
"h5h3 maple results");
logitem_str(html_log_file, "Poor Accuracy");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.10
##############ECHO OF PROBLEM#################
##############temp/h5h3postcpx.cpx#################
diff ( y , x , 5 ) = neg ( diff ( y , x , 3 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
array_y_init[2 + 1] := exact_soln_ypp(x_start);
array_y_init[3 + 1] := exact_soln_yppp(x_start);
array_y_init[4 + 1] := exact_soln_ypppp(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(cos(c(x)));
end;
exact_soln_yp := proc(x)
return(neg(sin(c(x))));
end;
exact_soln_ypp := proc(x)
return(neg(cos(c(x))));
end;
exact_soln_yppp := proc(x)
return(sin(x));
end;
exact_soln_ypppp := proc(x)
return(cos(c(x)));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.999983333337 -0.00999998888889
y[1] (closed_form) = 0.999983333337 -0.00999998888889
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1768
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 1.00037995723 -0.010411768614
y[1] (closed_form) = 1.00048412347 -0.0105122476776
absolute error = 0.0001447
relative error = 0.01447 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1083
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 1.00079256889 -0.0108245151296
y[1] (closed_form) = 1.00079256889 -0.0108245151295
absolute error = 7.637e-14
relative error = 7.631e-12 %
Correct digits = 13
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0519
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=37.8MB, alloc=40.3MB, time=0.55
x[1] = 0.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 1.00122117458 -0.0112382353659
y[1] (closed_form) = 1.00079960894 -0.0110337996083
absolute error = 0.0004685
relative error = 0.04681 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.118
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 1.00166578084 -0.0116529362815
y[1] (closed_form) = 1.00102792236 -0.0114503883919
absolute error = 0.0006692
relative error = 0.06685 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1539
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.1023 0.116
h = 0.00518991310064 0
y[1] (numeric) = 1.00212639442 -0.0120686248635
y[1] (closed_form) = 1.00147225055 -0.0118726973391
absolute error = 0.0006829
relative error = 0.06818 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2007
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.107489913101 0.116
h = 0.0001 0.005
y[1] (numeric) = 1.00249374305 -0.0123909113217
y[1] (closed_form) = 1.00092519315 -0.0124727612031
absolute error = 0.001571
relative error = 0.1569 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2013
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.107589913101 0.121
h = 0.0001 0.003
y[1] (numeric) = 1.0028706806 -0.012713796417
y[1] (closed_form) = 1.00150484185 -0.0130250070976
absolute error = 0.001401
relative error = 0.1399 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1225
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.107689913101 0.124
h = 0.001 0.001
y[1] (numeric) = 1.00325721052 -0.0130372834208
y[1] (closed_form) = 1.00186030562 -0.0133619345983
absolute error = 0.001434
relative error = 0.1431 %
Correct digits = 3
memory used=81.7MB, alloc=44.3MB, time=1.05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05848
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.108689913101 0.125
h = 0.001 0.003
y[1] (numeric) = 1.00365333634 -0.0133613756155
y[1] (closed_form) = 1.00187558076 -0.0135948435749
absolute error = 0.001793
relative error = 0.1789 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1331
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.109689913101 0.128
h = 0.0001 0.004
y[1] (numeric) = 1.00405906172 -0.0136860762947
y[1] (closed_form) = 1.00214398147 -0.0140504645225
absolute error = 0.001949
relative error = 0.1945 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1742
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.109789913101 0.132
h = 0.00518991310064 0
y[1] (numeric) = 1.00447439037 -0.0140113887631
y[1] (closed_form) = 1.00265126623 -0.0145052091831
absolute error = 0.001889
relative error = 0.1884 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2231
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.114979826201 0.132
h = 0.0001 0.005
y[1] (numeric) = 1.00480230762 -0.014263494003
y[1] (closed_form) = 1.00206414811 -0.0151879337787
absolute error = 0.00289
relative error = 0.2884 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2283
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.115079826201 0.137
h = 0.0001 0.003
y[1] (numeric) = 1.00513597709 -0.0145159689601
y[1] (closed_form) = 1.0027226389 -0.015780416106
absolute error = 0.002725
relative error = 0.2717 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1379
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=125.5MB, alloc=44.3MB, time=1.55
x[1] = 0.115179826201 0.14
h = 0.001 0.001
y[1] (numeric) = 1.00547540062 -0.0147688151793
y[1] (closed_form) = 1.0031251113 -0.0161421562067
absolute error = 0.002722
relative error = 0.2713 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06545
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.116179826201 0.141
h = 0.001 0.003
y[1] (numeric) = 1.00582058009 -0.0150220342102
y[1] (closed_form) = 1.00314856877 -0.0163987399008
absolute error = 0.003006
relative error = 0.2996 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1491
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.117179826201 0.144
h = 0.0001 0.004
y[1] (numeric) = 1.0061715174 -0.0152756276075
y[1] (closed_form) = 1.00345700122 -0.0168935484225
absolute error = 0.00316
relative error = 0.3149 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.196
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.117279826201 0.148
h = 0.00518991310064 0
y[1] (numeric) = 1.00652821448 -0.0155295969308
y[1] (closed_form) = 1.00402723496 -0.0173809412885
absolute error = 0.003112
relative error = 0.3099 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2457
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.122469739302 0.148
h = 0.0001 0.005
y[1] (numeric) = 1.00680813219 -0.0157263434253
y[1] (closed_form) = 1.00339977512 -0.0181463223687
absolute error = 0.00418
relative error = 0.4165 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2575
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=169.5MB, alloc=44.3MB, time=2.05
x[1] = 0.122569739302 0.153
h = 0.0001 0.003
y[1] (numeric) = 1.00709149958 -0.0159233165973
y[1] (closed_form) = 1.00413709761 -0.0187793173964
absolute error = 0.004109
relative error = 0.4092 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1541
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.122669739302 0.156
h = 0.001 0.001
y[1] (numeric) = 1.00737831758 -0.0161205171762
y[1] (closed_form) = 1.00458657241 -0.0191660388755
absolute error = 0.004131
relative error = 0.4112 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0727
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.123669739302 0.157
h = 0.001 0.003
y[1] (numeric) = 1.00766858714 -0.016317945894
y[1] (closed_form) = 1.00461815539 -0.0194463542005
absolute error = 0.004369
relative error = 0.4349 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1659
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.124669739302 0.16
h = 0.0001 0.004
y[1] (numeric) = 1.00796230922 -0.0165156034855
y[1] (closed_form) = 1.00496656264 -0.0199805231351
absolute error = 0.00458
relative error = 0.4557 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2191
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.124769739302 0.164
h = 0.00518991310064 0
y[1] (numeric) = 1.0082594848 -0.0167134906888
y[1] (closed_form) = 1.00559974252 -0.0205007983129
absolute error = 0.004628
relative error = 0.4601 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2681
Order of pole (three term test) = 32.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.129959652403 0.164
h = 0.0001 0.005
y[1] (numeric) = 1.00849176972 -0.0168667474112
y[1] (closed_form) = 1.00493163209 -0.0213488384843
absolute error = 0.005724
relative error = 0.5695 %
Correct digits = 2
memory used=213.5MB, alloc=44.3MB, time=2.56
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2887
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.130059652403 0.169
h = 0.0001 0.003
y[1] (numeric) = 1.00872612282 -0.0170201423579
y[1] (closed_form) = 1.00574778195 -0.0220226494732
absolute error = 0.005822
relative error = 0.5787 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1711
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.130159652403 0.172
h = 0.001 0.001
y[1] (numeric) = 1.00896254455 -0.0171736758749
y[1] (closed_form) = 1.0062442563 -0.0224345373686
absolute error = 0.005922
relative error = 0.5883 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08014
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.131159652403 0.173
h = 0.0001 0.004
y[1] (numeric) = 1.00920103539 -0.0173273483108
y[1] (closed_form) = 1.00628390392 -0.0227386479295
absolute error = 0.006148
relative error = 0.6108 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2393
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.131259652403 0.177
h = 0.00518991310064 0
y[1] (numeric) = 1.00944159582 -0.0174811600161
y[1] (closed_form) = 1.00696815084 -0.0232874545794
absolute error = 0.006311
relative error = 0.6266 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2863
Order of pole (three term test) = 32.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.136449565503 0.177
h = 0.0001 0.005
y[1] (numeric) = 1.00962912965 -0.0176002547683
y[1] (closed_form) = 1.00626465254 -0.0242026121084
absolute error = 0.00741
relative error = 0.7362 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3163
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=257.5MB, alloc=44.3MB, time=3.06
x[1] = 0.136549565503 0.182
h = 0.0001 0.003
y[1] (numeric) = 1.00981790276 -0.0177194332573
y[1] (closed_form) = 1.00714476029 -0.0249118624477
absolute error = 0.007673
relative error = 0.7616 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1857
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.136649565503 0.185
h = 0.001 0.001
y[1] (numeric) = 1.01000791538 -0.0178386956494
y[1] (closed_form) = 1.00767935084 -0.0253455666389
absolute error = 0.00786
relative error = 0.7797 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08644
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.137649565503 0.186
h = 0.001 0.003
y[1] (numeric) = 1.01019916772 -0.0179580421126
y[1] (closed_form) = 1.00772508554 -0.0256694594665
absolute error = 0.008099
relative error = 0.8034 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1982
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.138649565503 0.189
h = 0.0001 0.004
y[1] (numeric) = 1.01039166003 -0.018077472817
y[1] (closed_form) = 1.00814535822 -0.0262766784717
absolute error = 0.008501
relative error = 0.843 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2645
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.138749565503 0.193
h = 0.00518991310064 0
y[1] (numeric) = 1.01058539253 -0.0181969879351
y[1] (closed_form) = 1.00889255228 -0.0268588499158
absolute error = 0.008826
relative error = 0.8745 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3074
Order of pole (three term test) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=301.3MB, alloc=44.3MB, time=3.56
x[1] = 0.143939478604 0.193
h = 0.0001 0.005
y[1] (numeric) = 1.01073612795 -0.0182895108139
y[1] (closed_form) = 1.00814776828 -0.027856680913
absolute error = 0.009911
relative error = 0.9827 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3513
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.144039478604 0.198
h = 0.0001 0.003
y[1] (numeric) = 1.01088760594 -0.0183820844056
y[1] (closed_form) = 1.00910670324 -0.0286073696142
absolute error = 0.01038
relative error = 1.028 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2037
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.144139478604 0.201
h = 0.001 0.001
y[1] (numeric) = 1.01103982662 -0.0184747087938
y[1] (closed_form) = 1.00968829214 -0.0290666194269
absolute error = 0.01068
relative error = 1.057 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09408
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.145139478604 0.202
h = 0.001 0.003
y[1] (numeric) = 1.0111927901 -0.018567384064
y[1] (closed_form) = 1.00974196839 -0.0294144391303
absolute error = 0.01094
relative error = 1.083 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2165
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.146139478604 0.205
h = 0.0001 0.004
y[1] (numeric) = 1.01134649648 -0.018660110304
y[1] (closed_form) = 1.0102020424 -0.0300615992417
absolute error = 0.01146
relative error = 1.134 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2909
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
memory used=345.1MB, alloc=44.3MB, time=4.06
x[1] = 0.146239478604 0.209
h = 0.00518991310064 0
y[1] (numeric) = 1.01150094589 -0.0187528876036
y[1] (closed_form) = 1.01101219342 -0.0306774309473
absolute error = 0.01193
relative error = 1.18 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3274
Order of pole (three term test) = 32.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151429391704 0.209
h = 0.0001 0.005
y[1] (numeric) = 1.0116209481 -0.0188247013894
y[1] (closed_form) = 1.01022573567 -0.031757956365
absolute error = 0.01301
relative error = 1.287 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3886
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151529391704 0.214
h = 0.0001 0.003
y[1] (numeric) = 1.01174139517 -0.0188965458365
y[1] (closed_form) = 1.01126350959 -0.0325504633332
absolute error = 0.01366
relative error = 1.35 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2222
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151629391704 0.217
h = 0.001 0.001
y[1] (numeric) = 1.01186228716 -0.0189684209904
y[1] (closed_form) = 1.01189210305 -0.0330354899695
absolute error = 0.01407
relative error = 1.389 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1018
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.152629391704 0.218
h = 0.001 0.003
y[1] (numeric) = 1.01198362412 -0.0190403268988
y[1] (closed_form) = 1.01195364819 -0.0334073189432
absolute error = 0.01437
relative error = 1.419 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2352
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.153629391704 0.221
h = 0.0001 0.004
y[1] (numeric) = 1.01210540611 -0.0191122636118
y[1] (closed_form) = 1.01245346038 -0.0340946598009
absolute error = 0.01499
relative error = 1.479 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3184
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=389.1MB, alloc=44.3MB, time=4.56
SETTING H FOR POLE
x[1] = 0.153729391704 0.225
h = 0.00518991310064 0
y[1] (numeric) = 1.01222763318 -0.0191842311817
y[1] (closed_form) = 1.01332658271 -0.0347444690538
absolute error = 0.0156
relative error = 1.538 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3464
Order of pole (three term test) = 32.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.158919304805 0.225
h = 0.0001 0.005
y[1] (numeric) = 1.0123225016 -0.0192399312904
y[1] (closed_form) = 1.01249803502 -0.0359077163866
absolute error = 0.01667
relative error = 1.645 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4284
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.159019304805 0.23
h = 0.0001 0.003
y[1] (numeric) = 1.01241763648 -0.019295649928
y[1] (closed_form) = 1.01361466539 -0.0367424487826
absolute error = 0.01749
relative error = 1.724 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2412
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.159119304805 0.233
h = 0.001 0.001
y[1] (numeric) = 1.01251303786 -0.0193513871232
y[1] (closed_form) = 1.0142902728 -0.0372534998638
absolute error = 0.01799
relative error = 1.772 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1095
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.160119304805 0.234
h = 0.001 0.003
y[1] (numeric) = 1.01260870576 -0.0194071429066
y[1] (closed_form) = 1.01435961002 -0.0376494271879
absolute error = 0.01833
relative error = 1.805 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2543
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=433.0MB, alloc=44.3MB, time=5.07
x[1] = 0.161119304805 0.237
h = 0.0001 0.004
y[1] (numeric) = 1.01270464021 -0.0194629173114
y[1] (closed_form) = 1.01489909557 -0.0383772059886
absolute error = 0.01904
relative error = 1.875 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3472
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.161219304805 0.241
h = 0.00518991310064 0
y[1] (numeric) = 1.01280084125 -0.0195187103733
y[1] (closed_form) = 1.01583520799 -0.03906133196
absolute error = 0.01978
relative error = 1.945 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3641
Order of pole (three term test) = 32.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.166409217906 0.241
h = 0.0001 0.005
y[1] (numeric) = 1.01287545171 -0.019561888425
y[1] (closed_form) = 1.01496412591 -0.0403073351501
absolute error = 0.02085
relative error = 2.053 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.471
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.166509217906 0.246
h = 0.0001 0.003
y[1] (numeric) = 1.01295022176 -0.019605077686
y[1] (closed_form) = 1.01615963589 -0.0411847274766
absolute error = 0.02182
relative error = 2.145 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2608
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.166609217906 0.249
h = 0.001 0.001
y[1] (numeric) = 1.01302515142 -0.0196482781773
y[1] (closed_form) = 1.01688226981 -0.0417220670947
absolute error = 0.02241
relative error = 2.202 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1173
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=476.9MB, alloc=44.3MB, time=5.58
x[1] = 0.167609217906 0.25
h = 0.0001 0.004
y[1] (numeric) = 1.01310024072 -0.0196914899224
y[1] (closed_form) = 1.01695931808 -0.042142188534
absolute error = 0.02278
relative error = 2.238 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3723
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.167709217906 0.254
h = 0.00518991310064 0
y[1] (numeric) = 1.01317548966 -0.0197347129474
y[1] (closed_form) = 1.01794651699 -0.042856105737
absolute error = 0.02361
relative error = 2.317 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.378
Order of pole (three term test) = 32.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.172899131006 0.254
h = 0.0001 0.005
y[1] (numeric) = 1.0132338168 -0.0197681609142
y[1] (closed_form) = 1.01703839354 -0.0441692862312
absolute error = 0.0247
relative error = 2.426 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.509
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.172999131006 0.259
h = 0.0001 0.003
y[1] (numeric) = 1.01329223951 -0.0198016156646
y[1] (closed_form) = 1.01829788279 -0.0450837344032
absolute error = 0.02577
relative error = 2.529 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2775
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.173099131006 0.262
h = 0.001 0.001
y[1] (numeric) = 1.01335075781 -0.0198350772154
y[1] (closed_form) = 1.01905864099 -0.0456438732673
absolute error = 0.02643
relative error = 2.591 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1238
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.174099131006 0.263
h = 0.001 0.003
y[1] (numeric) = 1.01340937171 -0.0198685455859
y[1] (closed_form) = 1.01914146125 -0.0460841211266
absolute error = 0.02683
relative error = 2.63 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2903
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=520.9MB, alloc=44.3MB, time=6.08
x[1] = 0.175099131006 0.266
h = 0.0001 0.004
y[1] (numeric) = 1.01346808121 -0.0199020207982
y[1] (closed_form) = 1.01975221518 -0.0468871241951
absolute error = 0.02771
relative error = 2.714 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4036
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.175199131006 0.27
h = 0.00518991310064 0
y[1] (numeric) = 1.01352688633 -0.0199355028771
y[1] (closed_form) = 1.0208024415 -0.0476360332628
absolute error = 0.02864
relative error = 2.803 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3935
Order of pole (three term test) = 32.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.180389044107 0.27
h = 0.0001 0.005
y[1] (numeric) = 1.01357244751 -0.0199614115708
y[1] (closed_form) = 1.01985089987 -0.0490320371308
absolute error = 0.02974
relative error = 2.913 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5577
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.180489044107 0.275
h = 0.0001 0.003
y[1] (numeric) = 1.01361806593 -0.0199873244054
y[1] (closed_form) = 1.02118931473 -0.0499900083341
absolute error = 0.03094
relative error = 3.026 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2981
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.180589044107 0.278
h = 0.001 0.001
y[1] (numeric) = 1.0136637416 -0.0200132413975
y[1] (closed_form) = 1.02199712399 -0.0505769599062
absolute error = 0.03168
relative error = 3.096 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1315
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=564.8MB, alloc=44.3MB, time=6.57
x[1] = 0.181589044107 0.279
h = 0.001 0.003
y[1] (numeric) = 1.01370947454 -0.0200391625664
y[1] (closed_form) = 1.02208749434 -0.0510415916845
absolute error = 0.03211
relative error = 3.138 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3104
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.182589044107 0.282
h = 0.0001 0.004
y[1] (numeric) = 1.01375526476 -0.0200650879342
y[1] (closed_form) = 1.02273772233 -0.0518858520986
absolute error = 0.03306
relative error = 3.229 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4365
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.182689044107 0.286
h = 0.00518991310064 0
y[1] (numeric) = 1.01380111226 -0.0200910175261
y[1] (closed_form) = 1.0238510065 -0.0526701544615
absolute error = 0.03409
relative error = 3.326 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4077
Order of pole (three term test) = 32.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.187878957208 0.286
h = 0.0001 0.005
y[1] (numeric) = 1.01383662224 -0.0201110813004
y[1] (closed_form) = 1.02285552187 -0.0541490326937
absolute error = 0.03521
relative error = 3.438 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6105
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.187978957208 0.291
h = 0.0001 0.003
y[1] (numeric) = 1.01387216653 -0.0201311476345
y[1] (closed_form) = 1.02427290029 -0.0551510392247
absolute error = 0.03653
relative error = 3.561 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3192
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=608.8MB, alloc=44.3MB, time=7.08
x[1] = 0.188078957208 0.294
h = 0.001 0.001
y[1] (numeric) = 1.01390774513 -0.0201512165455
y[1] (closed_form) = 1.0251277814 -0.0557651144561
absolute error = 0.03734
relative error = 3.637 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1392
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.189078957208 0.295
h = 0.001 0.003
y[1] (numeric) = 1.01394335804 -0.0201712880533
y[1] (closed_form) = 1.02522560854 -0.0562542446937
absolute error = 0.03781
relative error = 3.682 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.331
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.190078957208 0.298
h = 0.0001 0.004
y[1] (numeric) = 1.01397900528 -0.020191362181
y[1] (closed_form) = 1.02591523823 -0.0571400870708
absolute error = 0.03883
relative error = 3.779 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4712
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.190178957208 0.302
h = 0.00518991310064 0
y[1] (numeric) = 1.01401468685 -0.0202114389546
y[1] (closed_form) = 1.0270916148 -0.0579602063485
absolute error = 0.03995
relative error = 3.883 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4207
Order of pole (three term test) = 32.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.195368870308 0.302
h = 0.0001 0.005
y[1] (numeric) = 1.01404231605 -0.0202269735171
y[1] (closed_form) = 1.02605163371 -0.0595220159694
absolute error = 0.04109
relative error = 3.998 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.668
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.195468870308 0.307
h = 0.0001 0.003
y[1] (numeric) = 1.01406996582 -0.0202425096962
y[1] (closed_form) = 1.02754801885 -0.0605685978537
absolute error = 0.04252
relative error = 4.131 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3409
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=652.9MB, alloc=44.3MB, time=7.58
x[1] = 0.195568870308 0.31
h = 0.001 0.001
y[1] (numeric) = 1.01409763615 -0.0202580475097
y[1] (closed_form) = 1.02844999552 -0.0612101244002
absolute error = 0.04339
relative error = 4.212 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.147
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.196568870308 0.311
h = 0.001 0.003
y[1] (numeric) = 1.01412532707 -0.0202735869785
y[1] (closed_form) = 1.02855518177 -0.0617238743217
absolute error = 0.04389
relative error = 4.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.352
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.197568870308 0.314
h = 0.0001 0.004
y[1] (numeric) = 1.01415303858 -0.0202891281268
y[1] (closed_form) = 1.02928413869 -0.0626516410356
absolute error = 0.04498
relative error = 4.362 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5078
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.197668870308 0.318
h = 0.00518991310064 0
y[1] (numeric) = 1.01418077068 -0.020304670982
y[1] (closed_form) = 1.03052364624 -0.0635080231298
absolute error = 0.04619
relative error = 4.474 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4324
Order of pole (three term test) = 32.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.202858783409 0.318
h = 0.0001 0.005
y[1] (numeric) = 1.01420224023 -0.02031669716
y[1] (closed_form) = 1.02943858646 -0.0651528270766
absolute error = 0.04735
relative error = 4.591 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7308
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=697.0MB, alloc=44.3MB, time=8.08
x[1] = 0.202958783409 0.323
h = 0.0001 0.003
y[1] (numeric) = 1.01422372211 -0.0203287243942
y[1] (closed_form) = 1.0310140266 -0.0662445521869
absolute error = 0.04889
relative error = 4.732 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3633
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.203058783409 0.326
h = 0.001 0.001
y[1] (numeric) = 1.01424521635 -0.0203407527033
y[1] (closed_form) = 1.03196312537 -0.06691387448
absolute error = 0.04983
relative error = 4.818 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1547
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.204058783409 0.327
h = 0.0001 0.004
y[1] (numeric) = 1.01426672295 -0.0203527821094
y[1] (closed_form) = 1.03207556862 -0.0674523719956
absolute error = 0.05035
relative error = 4.869 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.54
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.204158783409 0.331
h = 0.00518991310064 0
y[1] (numeric) = 1.01428824192 -0.0203648126377
y[1] (closed_form) = 1.03336624976 -0.0683402290879
absolute error = 0.05163
relative error = 4.985 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4414
Order of pole (three term test) = 32.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.20934869651 0.331
h = 0.0001 0.005
y[1] (numeric) = 1.01430489891 -0.0203741210435
y[1] (closed_form) = 1.03224194735 -0.0700523711905
absolute error = 0.05282
relative error = 5.105 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7881
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=741.0MB, alloc=44.3MB, time=8.59
x[1] = 0.20944869651 0.336
h = 0.0001 0.003
y[1] (numeric) = 1.01432156333 -0.0203834301535
y[1] (closed_form) = 1.03388147425 -0.0711832984881
absolute error = 0.05444
relative error = 5.253 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3825
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.20954869651 0.339
h = 0.001 0.001
y[1] (numeric) = 1.01433823517 -0.0203927399858
y[1] (closed_form) = 1.03486875267 -0.0718767220087
absolute error = 0.05543
relative error = 5.343 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1611
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.21054869651 0.34
h = 0.001 0.003
y[1] (numeric) = 1.01435491444 -0.0204020505615
y[1] (closed_form) = 1.03498656629 -0.0724358150947
absolute error = 0.05597
relative error = 5.395 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3915
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.21154869651 0.343
h = 0.0001 0.004
y[1] (numeric) = 1.01437160115 -0.0204113619055
y[1] (closed_form) = 1.03578609977 -0.0734417266252
absolute error = 0.05719
relative error = 5.508 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5806
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.21164869651 0.347
h = 0.00518991310064 0
y[1] (numeric) = 1.01438829532 -0.0204206740462
y[1] (closed_form) = 1.03713998192 -0.0743667176591
absolute error = 0.05855
relative error = 5.631 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.451
Order of pole (three term test) = 32.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.21683860961 0.347
h = 0.0001 0.005
y[1] (numeric) = 1.01440121616 -0.020427879105
y[1] (closed_form) = 1.03596946388 -0.0761619700895
absolute error = 0.05976
relative error = 5.753 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8633
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=785.1MB, alloc=44.3MB, time=9.16
x[1] = 0.21693860961 0.352
h = 0.0001 0.003
y[1] (numeric) = 1.01441414148 -0.0204350846767
y[1] (closed_form) = 1.03768813334 -0.0773391486425
absolute error = 0.06148
relative error = 5.908 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4062
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.21703860961 0.355
h = 0.001 0.001
y[1] (numeric) = 1.01442707128 -0.0204422907808
y[1] (closed_form) = 1.0387225813 -0.0780610395953
absolute error = 0.06253
relative error = 6.003 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1687
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.21803860961 0.356
h = 0.001 0.003
y[1] (numeric) = 1.01444000558 -0.0204494974408
y[1] (closed_form) = 1.03884745132 -0.0786451282119
absolute error = 0.06311
relative error = 6.057 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4137
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.21903860961 0.359
h = 0.0001 0.004
y[1] (numeric) = 1.01445294438 -0.0204567046837
y[1] (closed_form) = 1.03968608141 -0.0796940248404
absolute error = 0.06439
relative error = 6.175 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6239
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.21913860961 0.363
h = 0.00518991310064 0
y[1] (numeric) = 1.0144658877 -0.02046391254
y[1] (closed_form) = 1.0411032135 -0.0806566592268
absolute error = 0.06582
relative error = 6.304 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4596
Order of pole (three term test) = 32.28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=829.1MB, alloc=44.3MB, time=9.66
x[1] = 0.224328522711 0.363
h = 0.0001 0.005
y[1] (numeric) = 1.01447590462 -0.0204694894603
y[1] (closed_form) = 1.03988581553 -0.0825351002997
absolute error = 0.06707
relative error = 6.429 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9472
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.224428522711 0.368
h = 0.0001 0.003
y[1] (numeric) = 1.01448592427 -0.0204750667867
y[1] (closed_form) = 1.04168368897 -0.0837591773654
absolute error = 0.06888
relative error = 6.591 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4306
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.224528522711 0.371
h = 0.001 0.001
y[1] (numeric) = 1.01449594665 -0.0204806445402
y[1] (closed_form) = 1.04276534023 -0.0845099279982
absolute error = 0.06999
relative error = 6.69 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1763
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.225528522711 0.372
h = 0.001 0.003
y[1] (numeric) = 1.01450597176 -0.0204862227459
y[1] (closed_form) = 1.04289715162 -0.085119158834
absolute error = 0.07059
relative error = 6.747 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4364
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.226528522711 0.375
h = 0.0001 0.004
y[1] (numeric) = 1.01451599963 -0.0204918014324
y[1] (closed_form) = 1.04377479455 -0.0862114512419
absolute error = 0.07194
relative error = 6.869 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6701
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=872.9MB, alloc=44.3MB, time=10.15
SETTING H FOR POLE
x[1] = 0.226628522711 0.379
h = 0.00518991310064 0
y[1] (numeric) = 1.01452603027 -0.0204973806325
y[1] (closed_form) = 1.04525522913 -0.0872122610768
absolute error = 0.07345
relative error = 7.003 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4672
Order of pole (three term test) = 32.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.231818435811 0.379
h = 0.0001 0.005
y[1] (numeric) = 1.01453379254 -0.0205016974487
y[1] (closed_form) = 1.04399025766 -0.0891739744998
absolute error = 0.07472
relative error = 7.131 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.041
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.231918435811 0.384
h = 0.0001 0.003
y[1] (numeric) = 1.0145415565 -0.0205060146135
y[1] (closed_form) = 1.04586740107 -0.0904456256946
absolute error = 0.07663
relative error = 7.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4559
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.232018435811 0.387
h = 0.001 0.001
y[1] (numeric) = 1.01454932213 -0.0205103321494
y[1] (closed_form) = 1.04699629192 -0.091225645338
absolute error = 0.0778
relative error = 7.403 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1838
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.233018435811 0.388
h = 0.001 0.003
y[1] (numeric) = 1.01455708946 -0.0205146500826
y[1] (closed_form) = 1.04713492499 -0.0918601717714
absolute error = 0.07843
relative error = 7.461 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4596
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.234018435811 0.391
h = 0.0001 0.004
y[1] (numeric) = 1.0145648585 -0.0205189684435
y[1] (closed_form) = 1.0480514944 -0.0929962886657
absolute error = 0.07984
relative error = 7.588 %
Correct digits = 1
memory used=917.0MB, alloc=44.3MB, time=10.65
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7195
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.234118435811 0.395
h = 0.00518991310064 0
y[1] (numeric) = 1.01457262926 -0.0205232872668
y[1] (closed_form) = 1.04959528753 -0.094035828849
absolute error = 0.08143
relative error = 7.727 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4738
Order of pole (three term test) = 32.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.239308348912 0.395
h = 0.0001 0.005
y[1] (numeric) = 1.01457864244 -0.0205266289375
y[1] (closed_form) = 1.04828201949 -0.0960809035731
absolute error = 0.08273
relative error = 7.859 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.148
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.239408348912 0.4
h = 0.0001 0.003
y[1] (numeric) = 1.01458465666 -0.0205299709283
y[1] (closed_form) = 1.05023850332 -0.0974008330232
absolute error = 0.08474
relative error = 8.034 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.482
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.239508348912 0.403
h = 0.001 0.001
y[1] (numeric) = 1.01459067195 -0.0205333132628
y[1] (closed_form) = 1.05141467245 -0.0982105481814
absolute error = 0.08596
relative error = 8.141 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1913
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.240508348912 0.404
h = 0.0001 0.004
y[1] (numeric) = 1.01459668831 -0.0205366559685
y[1] (closed_form) = 1.05156000283 -0.0988705302824
absolute error = 0.08662
relative error = 8.201 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7638
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=961.0MB, alloc=44.3MB, time=11.15
SETTING H FOR POLE
x[1] = 0.240608348912 0.408
h = 0.00518991310064 0
y[1] (numeric) = 1.01460270575 -0.0205399990773
y[1] (closed_form) = 1.0531551152 -0.0999436614711
absolute error = 0.08827
relative error = 8.344 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4787
Order of pole (three term test) = 32.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.245798262013 0.408
h = 0.0001 0.005
y[1] (numeric) = 1.01460736201 -0.0205425858283
y[1] (closed_form) = 1.05179984451 -0.102056324482
absolute error = 0.0896
relative error = 8.479 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.248
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.245898262013 0.413
h = 0.0001 0.003
y[1] (numeric) = 1.01461201893 -0.0205451728613
y[1] (closed_form) = 1.05382059715 -0.103418142784
absolute error = 0.09168
relative error = 8.658 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5047
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.245998262013 0.416
h = 0.001 0.001
y[1] (numeric) = 1.01461667654 -0.0205477601987
y[1] (closed_form) = 1.0550350415 -0.104253586482
absolute error = 0.09295
relative error = 8.768 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1975
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.246998262013 0.417
h = 0.001 0.003
y[1] (numeric) = 1.01462133483 -0.0205503478672
y[1] (closed_form) = 1.05518524966 -0.104934758203
absolute error = 0.09363
relative error = 8.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5034
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1005.1MB, alloc=44.3MB, time=11.65
x[1] = 0.247998262013 0.42
h = 0.0001 0.004
y[1] (numeric) = 1.01462599383 -0.0205529358978
y[1] (closed_form) = 1.05617158946 -0.106152696361
absolute error = 0.09515
relative error = 8.964 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8204
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.248098262013 0.424
h = 0.00518991310064 0
y[1] (numeric) = 1.01463065356 -0.0205555243257
y[1] (closed_form) = 1.05783015853 -0.107265629403
absolute error = 0.09688
relative error = 9.111 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4838
Order of pole (three term test) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253288175113 0.424
h = 0.0001 0.005
y[1] (numeric) = 1.01463425914 -0.0205575272037
y[1] (closed_form) = 1.05642519529 -0.109461812349
absolute error = 0.09824
relative error = 9.249 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253388175113 0.429
h = 0.0001 0.003
y[1] (numeric) = 1.01463786517 -0.0205595303642
y[1] (closed_form) = 1.05852541165 -0.110873267452
absolute error = 0.1004
relative error = 9.434 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5326
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253488175113 0.432
h = 0.001 0.001
y[1] (numeric) = 1.01464147167 -0.0205615338319
y[1] (closed_form) = 1.05978720107 -0.111739229221
absolute error = 0.1017
relative error = 9.547 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2049
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.254488175113 0.433
h = 0.001 0.003
y[1] (numeric) = 1.01464507864 -0.0205635376356
y[1] (closed_form) = 1.05994386398 -0.112446162692
absolute error = 0.1024
relative error = 9.611 %
Correct digits = 1
memory used=1049.3MB, alloc=44.3MB, time=12.14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.528
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.255488175113 0.436
h = 0.0001 0.004
y[1] (numeric) = 1.01464868611 -0.0205655418086
y[1] (closed_form) = 1.06096886128 -0.113709231041
absolute error = 0.104
relative error = 9.749 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8817
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.255588175113 0.44
h = 0.00518991310064 0
y[1] (numeric) = 1.01465229409 -0.020567546389
y[1] (closed_form) = 1.06269095184 -0.114862585944
absolute error = 0.1058
relative error = 9.901 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4881
Order of pole (three term test) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.260778088214 0.44
h = 0.0001 0.005
y[1] (numeric) = 1.01465508582 -0.0205690975724
y[1] (closed_form) = 1.06123548883 -0.117142391093
absolute error = 0.1072
relative error = 10.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 31.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.260878088214 0.445
h = 0.0001 0.003
y[1] (numeric) = 1.01465787789 -0.0205706490476
y[1] (closed_form) = 1.06341525043 -0.118604268538
absolute error = 0.1095
relative error = 10.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5616
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.260978088214 0.448
h = 0.001 0.001
y[1] (numeric) = 1.0146606703 -0.0205722008406
y[1] (closed_form) = 1.06472442959 -0.119501223916
absolute error = 0.1109
relative error = 10.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2122
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1093.2MB, alloc=44.3MB, time=12.62
x[1] = 0.261978088214 0.449
h = 0.001 0.003
y[1] (numeric) = 1.01466346306 -0.0205737529821
y[1] (closed_form) = 1.06488740912 -0.120234098003
absolute error = 0.1116
relative error = 10.41 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5532
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.262978088214 0.452
h = 0.0001 0.004
y[1] (numeric) = 1.01466625619 -0.0205753055075
y[1] (closed_form) = 1.06595096608 -0.121542794705
absolute error = 0.1132
relative error = 10.56 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9483
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.263078088214 0.456
h = 0.00518991310064 0
y[1] (numeric) = 1.01466904972 -0.020576858457
y[1] (closed_form) = 1.06773664595 -0.122737214785
absolute error = 0.1151
relative error = 10.71 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4917
Order of pole (three term test) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.268268001315 0.456
h = 0.0001 0.005
y[1] (numeric) = 1.01467121126 -0.0205780602416
y[1] (closed_form) = 1.06622984577 -0.125100749016
absolute error = 0.1165
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.726
Order of pole (three term test) = 30.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.268368001315 0.461
h = 0.0001 0.003
y[1] (numeric) = 1.01467337306 -0.0205792623305
y[1] (closed_form) = 1.06848923796 -0.126613863489
absolute error = 0.1189
relative error = 11.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5918
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1137.4MB, alloc=44.3MB, time=13.11
x[1] = 0.268468001315 0.464
h = 0.001 0.001
y[1] (numeric) = 1.01467553513 -0.0205804647512
y[1] (closed_form) = 1.06984585358 -0.127542305568
absolute error = 0.1204
relative error = 11.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2194
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.269468001315 0.465
h = 0.001 0.003
y[1] (numeric) = 1.01467769749 -0.020581667536
y[1] (closed_form) = 1.07001500666 -0.128301305836
absolute error = 0.1211
relative error = 11.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5789
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.270468001315 0.468
h = 0.0001 0.004
y[1] (numeric) = 1.01467986015 -0.0205828707218
y[1] (closed_form) = 1.0711170222 -0.129656147418
absolute error = 0.1228
relative error = 11.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.021
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.270568001315 0.472
h = 0.00518991310064 0
y[1] (numeric) = 1.01468202313 -0.0205840743507
y[1] (closed_form) = 1.07296636204 -0.13089229944
absolute error = 0.1248
relative error = 11.54 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4946
Order of pole (three term test) = 32.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.275757914415 0.472
h = 0.0001 0.005
y[1] (numeric) = 1.0146836968 -0.0205850058921
y[1] (closed_form) = 1.07140735699 -0.133339674066
absolute error = 0.1262
relative error = 11.69 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.945
Order of pole (three term test) = 30.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.275857914415 0.477
h = 0.0001 0.003
y[1] (numeric) = 1.01468537069 -0.0205859377515
y[1] (closed_form) = 1.07374646874 -0.13490486958
memory used=1181.5MB, alloc=44.3MB, time=13.60
absolute error = 0.1287
relative error = 11.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6233
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.275957914415 0.48
h = 0.001 0.001
y[1] (numeric) = 1.01468704481 -0.0205868699577
y[1] (closed_form) = 1.07515056948 -0.135865309116
absolute error = 0.1302
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2266
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.276957914415 0.481
h = 0.0001 0.004
y[1] (numeric) = 1.01468871918 -0.0205878025442
y[1] (closed_form) = 1.07532574799 -0.136650627832
absolute error = 0.1309
relative error = 12.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.088
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.277057914415 0.485
h = 0.00518991310064 0
y[1] (numeric) = 1.01469039382 -0.0205887355497
y[1] (closed_form) = 1.07722660006 -0.137922929659
absolute error = 0.133
relative error = 12.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4967
Order of pole (three term test) = 32.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.282247827516 0.485
h = 0.0001 0.005
y[1] (numeric) = 1.01469168964 -0.0205894576999
y[1] (closed_form) = 1.07562225945 -0.140438217628
absolute error = 0.1344
relative error = 12.39 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.158
Order of pole (three term test) = 30.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.282347827516 0.49
h = 0.0001 0.003
y[1] (numeric) = 1.01469298563 -0.0205901801502
y[1] (closed_form) = 1.07802588235 -0.142048542362
absolute error = 0.137
relative error = 12.6 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6508
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1225.6MB, alloc=44.3MB, time=14.10
x[1] = 0.282447827516 0.493
h = 0.001 0.001
y[1] (numeric) = 1.01469428183 -0.0205909029276
y[1] (closed_form) = 1.07946838542 -0.143036671102
absolute error = 0.1385
relative error = 12.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2326
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.283447827516 0.494
h = 0.001 0.003
y[1] (numeric) = 1.01469557824 -0.0205916260644
y[1] (closed_form) = 1.0796478525 -0.143843898352
absolute error = 0.1393
relative error = 12.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6276
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.284447827516 0.497
h = 0.0001 0.004
y[1] (numeric) = 1.01469687488 -0.0205923495978
y[1] (closed_form) = 1.08081869353 -0.145285005927
absolute error = 0.1411
relative error = 12.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.174
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.284547827516 0.501
h = 0.00518991310064 0
y[1] (numeric) = 1.01469817177 -0.0205930735705
y[1] (closed_form) = 1.08278332629 -0.146600317058
absolute error = 0.1432
relative error = 13.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4986
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.289737740617 0.501
h = 0.0001 0.005
y[1] (numeric) = 1.01469917532 -0.0205936340156
y[1] (closed_form) = 1.0811251185 -0.149199639575
absolute error = 0.1447
relative error = 13.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.462
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1269.6MB, alloc=44.3MB, time=14.60
x[1] = 0.289837740617 0.506
h = 0.0001 0.003
y[1] (numeric) = 1.01470017905 -0.0205941947774
y[1] (closed_form) = 1.08360861293 -0.150863661355
absolute error = 0.1474
relative error = 13.47 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6848
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.289937740617 0.509
h = 0.001 0.001
y[1] (numeric) = 1.01470118298 -0.0205947558853
y[1] (closed_form) = 1.08509868292 -0.151884765138
absolute error = 0.149
relative error = 13.6 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2397
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.290937740617 0.51
h = 0.001 0.003
y[1] (numeric) = 1.01470218711 -0.020595317374
y[1] (closed_form) = 1.08528388807 -0.152718675111
absolute error = 0.1498
relative error = 13.67 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.655
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.291937740617 0.513
h = 0.0001 0.004
y[1] (numeric) = 1.01470319147 -0.0205958792836
y[1] (closed_form) = 1.08649287179 -0.154207482706
absolute error = 0.1517
relative error = 13.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.27
Order of pole (three term test) = 31.22 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.292037740617 0.517
h = 0.00518991310064 0
y[1] (numeric) = 1.01470419609 -0.0205964416594
y[1] (closed_form) = 1.08852136269 -0.155566536966
absolute error = 0.1538
relative error = 13.99 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.297227653717 0.517
h = 0.0001 0.005
y[1] (numeric) = 1.01470497352 -0.0205968771031
y[1] (closed_form) = 1.08680833324 -0.158250016188
memory used=1313.7MB, alloc=44.3MB, time=15.10
absolute error = 0.1554
relative error = 14.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.829
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.297327653717 0.522
h = 0.0001 0.003
y[1] (numeric) = 1.01470575113 -0.0205973128832
y[1] (closed_form) = 1.0893717968 -0.159968662907
absolute error = 0.1581
relative error = 14.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7204
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.297427653717 0.525
h = 0.001 0.001
y[1] (numeric) = 1.01470652894 -0.0205977490308
y[1] (closed_form) = 1.09090948685 -0.161023302999
absolute error = 0.1598
relative error = 14.49 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2467
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.298427653717 0.526
h = 0.001 0.003
y[1] (numeric) = 1.01470730696 -0.0205981855827
y[1] (closed_form) = 1.09110026721 -0.161884106784
absolute error = 0.1606
relative error = 14.56 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.683
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.299427653717 0.529
h = 0.0001 0.004
y[1] (numeric) = 1.01470808522 -0.0205986225809
y[1] (closed_form) = 1.09234727844 -0.163421201788
absolute error = 0.1626
relative error = 14.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.377
Order of pole (three term test) = 31.13 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.299527653717 0.533
h = 0.00518991310064 0
y[1] (numeric) = 1.01470886373 -0.0205990600733
y[1] (closed_form) = 1.09443970725 -0.164824757051
absolute error = 0.1648
relative error = 14.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.501
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1357.7MB, alloc=44.3MB, time=15.61
x[1] = 0.304717566818 0.533
h = 0.0001 0.005
y[1] (numeric) = 1.01470946624 -0.0205993989196
y[1] (closed_form) = 1.0926708705 -0.167592518816
absolute error = 0.1664
relative error = 15.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.27
Order of pole (three term test) = 30.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.304817566818 0.538
h = 0.0001 0.003
y[1] (numeric) = 1.01471006894 -0.0205997381218
y[1] (closed_form) = 1.0953144037 -0.169366748457
absolute error = 0.1692
relative error = 15.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7577
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.304917566818 0.541
h = 0.001 0.001
y[1] (numeric) = 1.01471067183 -0.0206000777125
y[1] (closed_form) = 1.0968997684 -0.170455504241
absolute error = 0.1709
relative error = 15.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2536
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.305917566818 0.542
h = 0.001 0.003
y[1] (numeric) = 1.01471127495 -0.0206004177299
y[1] (closed_form) = 1.09709595579 -0.171343419639
absolute error = 0.1718
relative error = 15.47 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7117
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.306917566818 0.545
h = 0.0001 0.004
y[1] (numeric) = 1.01471187832 -0.0206007582181
y[1] (closed_form) = 1.0983808754 -0.172929408207
absolute error = 0.1738
relative error = 15.63 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.497
Order of pole (three term test) = 31.03 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1401.8MB, alloc=44.3MB, time=16.12
SETTING H FOR POLE
x[1] = 0.307017566818 0.549
h = 0.00518991310064 0
y[1] (numeric) = 1.01471248195 -0.0206010992269
y[1] (closed_form) = 1.10053732396 -0.174378246567
absolute error = 0.1761
relative error = 15.8 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5015
Order of pole (three term test) = 32.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.312207479918 0.549
h = 0.0001 0.005
y[1] (numeric) = 1.01471294916 -0.0206013634465
y[1] (closed_form) = 1.09871166294 -0.177230420187
absolute error = 0.1777
relative error = 15.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.786
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.312307479918 0.554
h = 0.0001 0.003
y[1] (numeric) = 1.01471341657 -0.0206016280402
y[1] (closed_form) = 1.10143536897 -0.179061221033
absolute error = 0.1806
relative error = 16.19 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7968
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.312407479918 0.557
h = 0.001 0.001
y[1] (numeric) = 1.01471388419 -0.020601893042
y[1] (closed_form) = 1.10306846427 -0.18018469014
absolute error = 0.1824
relative error = 16.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2604
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.313407479918 0.558
h = 0.0001 0.004
y[1] (numeric) = 1.01471435204 -0.0206021584915
y[1] (closed_form) = 1.10326988509 -0.18109994167
absolute error = 0.1833
relative error = 16.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 30.94 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
memory used=1446.0MB, alloc=44.3MB, time=16.62
x[1] = 0.313507479918 0.562
h = 0.00518991310064 0
y[1] (numeric) = 1.01471482014 -0.0206024244343
y[1] (closed_form) = 1.10547807275 -0.182587944278
absolute error = 0.1857
relative error = 16.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5018
Order of pole (three term test) = 32.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.318697393019 0.562
h = 0.0001 0.005
y[1] (numeric) = 1.01471518249 -0.0206026305565
y[1] (closed_form) = 1.10360315324 -0.185508413995
absolute error = 0.1873
relative error = 16.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.237
Order of pole (three term test) = 30.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.318797393019 0.567
h = 0.0001 0.003
y[1] (numeric) = 1.01471554502 -0.0206028370321
y[1] (closed_form) = 1.10639165596 -0.187388154397
absolute error = 0.1903
relative error = 16.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8314
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.318897393019 0.57
h = 0.001 0.001
y[1] (numeric) = 1.01471590774 -0.0206030438929
y[1] (closed_form) = 1.10806330178 -0.188541616459
absolute error = 0.1921
relative error = 17.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2662
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.319897393019 0.571
h = 0.001 0.003
y[1] (numeric) = 1.01471627069 -0.020603251177
y[1] (closed_form) = 1.10826831862 -0.189479620296
absolute error = 0.1931
relative error = 17.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7657
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.320897393019 0.574
h = 0.0001 0.004
y[1] (numeric) = 1.01471663387 -0.0206034589281
y[1] (closed_form) = 1.10962095078 -0.191157103
absolute error = 0.1952
relative error = 17.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.761
Order of pole (three term test) = 30.82 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1490.1MB, alloc=44.3MB, time=17.12
x[1] = 0.320997393019 0.578
h = 0.0001 0.004
y[1] (numeric) = 1.01471699732 -0.0206036671962
y[1] (closed_form) = 1.11189329486 -0.19269187848
absolute error = 0.1976
relative error = 17.51 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.775
Order of pole (three term test) = 30.81 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.321097393019 0.582
h = 0.00518991310064 0
y[1] (numeric) = 1.01471736107 -0.0206038760377
y[1] (closed_form) = 1.11418326398 -0.194230624625
absolute error = 0.2001
relative error = 17.69 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5016
Order of pole (three term test) = 32.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32628730612 0.582
h = 0.0001 0.005
y[1] (numeric) = 1.01471764271 -0.0206040380446
y[1] (closed_form) = 1.11224495816 -0.197258712452
absolute error = 0.2018
relative error = 17.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32638730612 0.587
h = 0.0001 0.003
y[1] (numeric) = 1.01471792457 -0.0206042004649
y[1] (closed_form) = 1.1151358679 -0.199201854065
absolute error = 0.2049
relative error = 18.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8781
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32648730612 0.59
h = 0.001 0.001
y[1] (numeric) = 1.01471820666 -0.0206043633364
y[1] (closed_form) = 1.11686856371 -0.200394333581
absolute error = 0.2068
relative error = 18.22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2734
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1534.3MB, alloc=44.3MB, time=17.63
x[1] = 0.32748730612 0.591
h = 0.001 0.003
y[1] (numeric) = 1.01471848902 -0.0206045267031
y[1] (closed_form) = 1.11708200973 -0.201365451272
absolute error = 0.2077
relative error = 18.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7988
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32848730612 0.594
h = 0.0001 0.004
y[1] (numeric) = 1.01471877166 -0.0206046906153
y[1] (closed_form) = 1.11848459876 -0.203100836112
absolute error = 0.2099
relative error = 18.47 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.951
Order of pole (three term test) = 30.67 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.32858730612 0.598
h = 0.00518991310064 0
y[1] (numeric) = 1.01471905462 -0.0206048551299
y[1] (closed_form) = 1.12083890775 -0.204687378289
absolute error = 0.2125
relative error = 18.65 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5012
Order of pole (three term test) = 32.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.33377721922 0.598
h = 0.0001 0.005
y[1] (numeric) = 1.01471927378 -0.0206049828627
y[1] (closed_form) = 1.11884051258 -0.207800367885
absolute error = 0.2142
relative error = 18.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.2
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.33387721922 0.603
h = 0.0001 0.003
y[1] (numeric) = 1.01471949318 -0.020605111027
y[1] (closed_form) = 1.12181199882 -0.209803254305
absolute error = 0.2174
relative error = 19.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9235
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1578.5MB, alloc=44.3MB, time=18.13
x[1] = 0.33397721922 0.606
h = 0.001 0.001
y[1] (numeric) = 1.01471971282 -0.020605239661
y[1] (closed_form) = 1.12359264816 -0.211032366299
absolute error = 0.2194
relative error = 19.19 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2801
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.33497721922 0.607
h = 0.001 0.003
y[1] (numeric) = 1.01471993274 -0.0206053688093
y[1] (closed_form) = 1.12381078509 -0.212031554911
absolute error = 0.2203
relative error = 19.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8298
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.33597721922 0.61
h = 0.0001 0.004
y[1] (numeric) = 1.01472015297 -0.0206054985231
y[1] (closed_form) = 1.12525080719 -0.213818477758
absolute error = 0.2226
relative error = 19.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.154
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.33607721922 0.614
h = 0.00518991310064 0
y[1] (numeric) = 1.01472037353 -0.02060562886
y[1] (closed_form) = 1.1276695464 -0.215453697411
absolute error = 0.2252
relative error = 19.62 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5006
Order of pole (three term test) = 32.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.341267132321 0.614
h = 0.0001 0.005
y[1] (numeric) = 1.01472054443 -0.0206057301656
y[1] (closed_form) = 1.12560991625 -0.218651732077
absolute error = 0.227
relative error = 19.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.264
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.341367132321 0.619
h = 0.0001 0.003
y[1] (numeric) = 1.01472071556 -0.0206058319165
y[1] (closed_form) = 1.12866209295 -0.220715475901
absolute error = 0.2303
relative error = 20.02 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9715
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1622.8MB, alloc=44.3MB, time=18.62
x[1] = 0.341467132321 0.622
h = 0.001 0.001
y[1] (numeric) = 1.01472088696 -0.0206059341515
y[1] (closed_form) = 1.13049075716 -0.221981892866
absolute error = 0.2323
relative error = 20.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2866
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.342467132321 0.623
h = 0.001 0.003
y[1] (numeric) = 1.01472105865 -0.0206060369162
y[1] (closed_form) = 1.13071338911 -0.223009404422
absolute error = 0.2333
relative error = 20.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8614
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.343467132321 0.626
h = 0.0001 0.004
y[1] (numeric) = 1.01472123065 -0.0206061402628
y[1] (closed_form) = 1.13219070383 -0.224848567633
absolute error = 0.2356
relative error = 20.41 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.393
Order of pole (three term test) = 30.34 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.343567132321 0.63
h = 0.00518991310064 0
y[1] (numeric) = 1.014721403 -0.0206062442504
y[1] (closed_form) = 1.13467396483 -0.226533371378
absolute error = 0.2383
relative error = 20.6 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4997
Order of pole (three term test) = 32.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.348757045422 0.63
h = 0.0001 0.005
y[1] (numeric) = 1.0147215366 -0.0206063251835
y[1] (closed_form) = 1.13255192148 -0.229816596737
absolute error = 0.2401
relative error = 20.78 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.024
Order of pole (three term test) = 35.23 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1667.1MB, alloc=44.3MB, time=19.12
x[1] = 0.348857045422 0.635
h = 0.0001 0.003
y[1] (numeric) = 1.01472167046 -0.0206064065741
y[1] (closed_form) = 1.1356849041 -0.231942342068
absolute error = 0.2435
relative error = 21.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.022
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.348957045422 0.638
h = 0.001 0.001
y[1] (numeric) = 1.01472180458 -0.0206064884621
y[1] (closed_form) = 1.13756164521 -0.233246755465
absolute error = 0.2456
relative error = 21.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2931
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.349957045422 0.639
h = 0.001 0.003
y[1] (numeric) = 1.01472193899 -0.0206065708941
y[1] (closed_form) = 1.1377885704 -0.234302848727
absolute error = 0.2466
relative error = 21.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8936
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.350957045422 0.642
h = 0.0001 0.004
y[1] (numeric) = 1.01472207373 -0.0206066539236
y[1] (closed_form) = 1.13930303224 -0.23619497404
absolute error = 0.249
relative error = 21.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.676
Order of pole (three term test) = 30.13 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.351057045422 0.646
h = 0.00518991310064 0
y[1] (numeric) = 1.01472220882 -0.0206067376112
y[1] (closed_form) = 1.14185090761 -0.237930293869
absolute error = 0.2518
relative error = 21.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4986
Order of pole (three term test) = 32.55 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1711.3MB, alloc=44.3MB, time=19.61
x[1] = 0.356246958522 0.646
h = 0.0001 0.005
y[1] (numeric) = 1.01472231361 -0.0206068028517
y[1] (closed_form) = 1.1396652399 -0.241298857614
absolute error = 0.2536
relative error = 21.77 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.606
Order of pole (three term test) = 35.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.356346958522 0.651
h = 0.0001 0.003
y[1] (numeric) = 1.01472241864 -0.0206068685619
y[1] (closed_form) = 1.14287914523 -0.243487780319
absolute error = 0.2571
relative error = 22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.076
Order of pole (three term test) = 31.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.356446958522 0.654
h = 0.001 0.001
y[1] (numeric) = 1.01472252396 -0.0206069347826
y[1] (closed_form) = 1.14480402573 -0.244830900727
absolute error = 0.2592
relative error = 22.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2995
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.357446958522 0.655
h = 0.0001 0.004
y[1] (numeric) = 1.01472262958 -0.0206070015618
y[1] (closed_form) = 1.14503503641 -0.245915841197
absolute error = 0.2603
relative error = 22.22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.954
Order of pole (three term test) = 29.96 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.357546958522 0.659
h = 0.00518991310064 0
y[1] (numeric) = 1.01472273552 -0.0206070689543
y[1] (closed_form) = 1.14763503435 -0.247694753536
absolute error = 0.2631
relative error = 22.41 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4976
Order of pole (three term test) = 32.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.362736871623 0.659
h = 0.0001 0.005
y[1] (numeric) = 1.01472281774 -0.0206071215536
y[1] (closed_form) = 1.14539435093 -0.251132241593
absolute error = 0.265
relative error = 22.6 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.183
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1755.5MB, alloc=44.3MB, time=20.10
x[1] = 0.362836871623 0.664
h = 0.0001 0.003
y[1] (numeric) = 1.01472290019 -0.0206071745899
y[1] (closed_form) = 1.14867353654 -0.253375692879
absolute error = 0.2686
relative error = 22.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.124
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.362936871623 0.667
h = 0.001 0.001
y[1] (numeric) = 1.01472298289 -0.0206072281013
y[1] (closed_form) = 1.15063722205 -0.254752183711
absolute error = 0.2707
relative error = 22.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3049
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.363936871623 0.668
h = 0.001 0.003
y[1] (numeric) = 1.01472306588 -0.0206072821333
y[1] (closed_form) = 1.15087082645 -0.255861124865
absolute error = 0.2718
relative error = 23.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9535
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.364936871623 0.671
h = 0.0001 0.004
y[1] (numeric) = 1.01472314917 -0.0206073367382
y[1] (closed_form) = 1.15245145223 -0.257852440137
absolute error = 0.2743
relative error = 23.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.352
Order of pole (three term test) = 29.72 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.365036871623 0.675
h = 0.00518991310064 0
y[1] (numeric) = 1.0147232328 -0.020607391976
y[1] (closed_form) = 1.15511621462 -0.259683634726
absolute error = 0.2773
relative error = 23.42 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4961
Order of pole (three term test) = 32.57 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1799.6MB, alloc=44.3MB, time=20.61
x[1] = 0.370226784724 0.675
h = 0.0001 0.005
y[1] (numeric) = 1.01472329776 -0.0206074351881
y[1] (closed_form) = 1.15280961128 -0.263206708049
absolute error = 0.2791
relative error = 23.61 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.752
Order of pole (three term test) = 35.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.370326784724 0.68
h = 0.0001 0.003
y[1] (numeric) = 1.01472336297 -0.0206074788544
y[1] (closed_form) = 1.15616990892 -0.265515564366
absolute error = 0.2828
relative error = 23.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.184
Order of pole (three term test) = 31.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.370426784724 0.683
h = 0.001 0.001
y[1] (numeric) = 1.01472342844 -0.0206075230158
y[1] (closed_form) = 1.15818183285 -0.26693210801
absolute error = 0.2851
relative error = 23.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3111
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.371426784724 0.684
h = 0.001 0.003
y[1] (numeric) = 1.0147234942 -0.0206075677208
y[1] (closed_form) = 1.15841912256 -0.268070392915
absolute error = 0.2862
relative error = 24.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.987
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.372426784724 0.687
h = 0.0001 0.004
y[1] (numeric) = 1.01472356029 -0.0206076130251
y[1] (closed_form) = 1.1600364394 -0.270116809277
absolute error = 0.2887
relative error = 24.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.842
Order of pole (three term test) = 29.47 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
memory used=1843.5MB, alloc=44.3MB, time=21.11
x[1] = 0.372526784724 0.691
h = 0.00518991310064 0
y[1] (numeric) = 1.01472362673 -0.0206076589919
y[1] (closed_form) = 1.16276606 -0.272001290874
absolute error = 0.2917
relative error = 24.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4946
Order of pole (three term test) = 32.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.377716697824 0.691
h = 0.0001 0.005
y[1] (numeric) = 1.01472367841 -0.0206076950544
y[1] (closed_form) = 1.16039223123 -0.275610100865
absolute error = 0.2937
relative error = 24.62 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.373
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.377816697824 0.696
h = 0.0001 0.003
y[1] (numeric) = 1.01472373034 -0.020607731593
y[1] (closed_form) = 1.16383375922 -0.277985629168
absolute error = 0.2975
relative error = 24.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.249
Order of pole (three term test) = 31.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.377916697824 0.699
h = 0.001 0.001
y[1] (numeric) = 1.01472378256 -0.0206077686509
y[1] (closed_form) = 1.16589398423 -0.279442991018
absolute error = 0.2997
relative error = 25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3173
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.378916697824 0.7
h = 0.001 0.003
y[1] (numeric) = 1.01472383508 -0.0206078062788
y[1] (closed_form) = 1.16613473384 -0.280610904093
absolute error = 0.3009
relative error = 25.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.021
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.379916697824 0.703
h = 0.0001 0.004
y[1] (numeric) = 1.01472388794 -0.0206078445349
y[1] (closed_form) = 1.16778857454 -0.282713218269
absolute error = 0.3035
relative error = 25.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.452
Order of pole (three term test) = 29.24 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1887.7MB, alloc=44.3MB, time=21.61
SETTING H FOR POLE
x[1] = 0.380016697824 0.707
h = 0.00518991310064 0
y[1] (numeric) = 1.01472394117 -0.0206078834852
y[1] (closed_form) = 1.17058314734 -0.284652017832
absolute error = 0.3066
relative error = 25.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4929
Order of pole (three term test) = 32.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.385206610925 0.707
h = 0.0001 0.005
y[1] (numeric) = 1.01472398264 -0.0206079141428
y[1] (closed_form) = 1.16814075362 -0.28834671692
absolute error = 0.3086
relative error = 25.65 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.051
Order of pole (three term test) = 35.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.385306610925 0.712
h = 0.0001 0.003
y[1] (numeric) = 1.01472402438 -0.0206079452988
y[1] (closed_form) = 1.17166363055 -0.290790216959
absolute error = 0.3125
relative error = 25.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.317
Order of pole (three term test) = 31.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.385406610925 0.715
h = 0.001 0.001
y[1] (numeric) = 1.01472406641 -0.020607976998
y[1] (closed_form) = 1.17377221917 -0.292289182147
absolute error = 0.3148
relative error = 26.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3234
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.386406610925 0.716
h = 0.001 0.003
y[1] (numeric) = 1.01472410877 -0.0206080092929
y[1] (closed_form) = 1.17401619687 -0.293487014562
absolute error = 0.316
relative error = 26.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.055
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1931.6MB, alloc=44.3MB, time=22.11
x[1] = 0.387406610925 0.719
h = 0.0001 0.004
y[1] (numeric) = 1.01472415147 -0.0206080422438
y[1] (closed_form) = 1.17570638815 -0.295646043205
absolute error = 0.3187
relative error = 26.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.216
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.387506610925 0.723
h = 0.00518991310064 0
y[1] (numeric) = 1.01472419458 -0.0206080759191
y[1] (closed_form) = 1.17856600707 -0.297640218117
absolute error = 0.3219
relative error = 26.48 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4912
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.392696524025 0.723
h = 0.0001 0.005
y[1] (numeric) = 1.01472422822 -0.0206081025179
y[1] (closed_form) = 1.17605367461 -0.301420959465
absolute error = 0.3239
relative error = 26.68 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.78
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.392796524025 0.728
h = 0.0001 0.003
y[1] (numeric) = 1.01472426214 -0.0206081296357
y[1] (closed_form) = 1.17965801903 -0.303933764076
absolute error = 0.3278
relative error = 26.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.39
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.392896524025 0.731
h = 0.001 0.001
y[1] (numeric) = 1.01472429637 -0.0206081573191
y[1] (closed_form) = 1.18181503348 -0.305475137643
absolute error = 0.3303
relative error = 27.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3294
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1975.8MB, alloc=44.3MB, time=22.61
x[1] = 0.393896524025 0.732
h = 0.0001 0.004
y[1] (numeric) = 1.01472433093 -0.020608185622
y[1] (closed_form) = 1.18206200095 -0.306703187321
absolute error = 0.3314
relative error = 27.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.963
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.393996524025 0.736
h = 0.00518991310064 0
y[1] (numeric) = 1.01472436586 -0.0206082146066
y[1] (closed_form) = 1.18497399348 -0.308745053666
absolute error = 0.3347
relative error = 27.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4896
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.399186437126 0.736
h = 0.0001 0.005
y[1] (numeric) = 1.01472439317 -0.0206082375432
y[1] (closed_form) = 1.18240131606 -0.312595165786
absolute error = 0.3367
relative error = 27.53 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.575
Order of pole (three term test) = 34.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.399286437126 0.741
h = 0.0001 0.003
y[1] (numeric) = 1.01472442073 -0.0206082609668
y[1] (closed_form) = 1.18607125771 -0.315167666595
absolute error = 0.3408
relative error = 27.77 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.399386437126 0.744
h = 0.001 0.001
y[1] (numeric) = 1.01472444859 -0.0206082849208
y[1] (closed_form) = 1.18826723254 -0.31674553108
absolute error = 0.3432
relative error = 27.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3344
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.400386437126 0.745
h = 0.001 0.003
y[1] (numeric) = 1.01472447676 -0.0206083094567
y[1] (closed_form) = 1.18851584027 -0.317998708626
absolute error = 0.3444
relative error = 28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.118
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2020.1MB, alloc=44.3MB, time=23.11
x[1] = 0.401386437126 0.748
h = 0.0001 0.004
y[1] (numeric) = 1.01472450527 -0.0206083346337
y[1] (closed_form) = 1.19027058671 -0.320263992742
absolute error = 0.3473
relative error = 28.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.034
Order of pole (three term test) = 29.87 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.401486437126 0.752
h = 0.00518991310064 0
y[1] (numeric) = 1.01472453417 -0.0206083605197
y[1] (closed_form) = 1.19324777244 -0.322363231845
absolute error = 0.3506
relative error = 28.37 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4877
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.406676350227 0.752
h = 0.0001 0.005
y[1] (numeric) = 1.01472455682 -0.0206083810811
y[1] (closed_form) = 1.19060256057 -0.326299636073
absolute error = 0.3527
relative error = 28.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.379
Order of pole (three term test) = 34.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.406776350227 0.757
h = 0.0001 0.003
y[1] (numeric) = 1.01472457974 -0.0206084021523
y[1] (closed_form) = 1.19435415543 -0.328943958624
absolute error = 0.3568
relative error = 28.81 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 30.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.406876350227 0.76
h = 0.001 0.001
y[1] (numeric) = 1.01472460297 -0.0206084237796
y[1] (closed_form) = 1.19659865044 -0.330565751461
absolute error = 0.3594
relative error = 28.95 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3403
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2064.4MB, alloc=44.3MB, time=23.61
x[1] = 0.407876350227 0.761
h = 0.001 0.003
y[1] (numeric) = 1.01472462653 -0.0206084460177
y[1] (closed_form) = 1.19684978998 -0.331849701261
absolute error = 0.3606
relative error = 29.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.153
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.408876350227 0.764
h = 0.0001 0.004
y[1] (numeric) = 1.01472465046 -0.0206084689299
y[1] (closed_form) = 1.19864034471 -0.334174109103
absolute error = 0.3635
relative error = 29.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.157
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.408976350227 0.768
h = 0.00518991310064 0
y[1] (numeric) = 1.01472467479 -0.0206084925877
y[1] (closed_form) = 1.20168281564 -0.336331854188
absolute error = 0.3669
relative error = 29.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4857
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.414166263327 0.768
h = 0.0001 0.005
y[1] (numeric) = 1.01472469393 -0.0206085114532
y[1] (closed_form) = 1.19896359702 -0.340354703393
absolute error = 0.369
relative error = 29.61 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.212
Order of pole (three term test) = 34.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.414266263327 0.773
h = 0.0001 0.003
y[1] (numeric) = 1.01472471335 -0.020608530855
y[1] (closed_form) = 1.20279696124 -0.343072275487
absolute error = 0.3733
relative error = 29.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.632
Order of pole (three term test) = 30.84 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2108.5MB, alloc=44.3MB, time=24.12
x[1] = 0.414366263327 0.776
h = 0.001 0.001
y[1] (numeric) = 1.0147247331 -0.0206085508419
y[1] (closed_form) = 1.20509003639 -0.344738858844
absolute error = 0.3759
relative error = 29.99 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3461
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.415366263327 0.777
h = 0.001 0.003
y[1] (numeric) = 1.0147247532 -0.0206085714711
y[1] (closed_form) = 1.2053434502 -0.346053897752
absolute error = 0.3772
relative error = 30.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.187
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.416366263327 0.78
h = 0.0001 0.004
y[1] (numeric) = 1.01472477368 -0.0206085928086
y[1] (closed_form) = 1.20716961401 -0.348438323139
absolute error = 0.3801
relative error = 30.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.006
Order of pole (three term test) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.416466263327 0.784
h = 0.00518991310064 0
y[1] (numeric) = 1.01472479459 -0.0206086149288
y[1] (closed_form) = 1.21027746115 -0.350655734775
absolute error = 0.3836
relative error = 30.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4837
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.421656176428 0.784
h = 0.0001 0.005
y[1] (numeric) = 1.01472481109 -0.0206086326323
y[1] (closed_form) = 1.207482728 -0.354765181366
absolute error = 0.3858
relative error = 30.65 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.069
Order of pole (three term test) = 34.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.421756176428 0.789
h = 0.0001 0.003
y[1] (numeric) = 1.0147248279 -0.020608650898
y[1] (closed_form) = 1.2113979765 -0.357557465045
absolute error = 0.3901
relative error = 30.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.73
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2152.6MB, alloc=44.3MB, time=24.62
x[1] = 0.421856176428 0.792
h = 0.001 0.001
y[1] (numeric) = 1.01472484505 -0.0206086697763
y[1] (closed_form) = 1.21373969073 -0.359269721689
absolute error = 0.3928
relative error = 31.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3518
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.422856176428 0.793
h = 0.001 0.003
y[1] (numeric) = 1.01472486256 -0.0206086893267
y[1] (closed_form) = 1.21399511426 -0.360616173321
absolute error = 0.3941
relative error = 31.12 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.222
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.423856176428 0.796
h = 0.0001 0.004
y[1] (numeric) = 1.01472488048 -0.0206087096171
y[1] (closed_form) = 1.21585668071 -0.363061530602
absolute error = 0.3971
relative error = 31.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.171
Order of pole (three term test) = 36.34 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.423956176428 0.8
h = 0.00518991310064 0
y[1] (numeric) = 1.01472489885 -0.0206087307246
y[1] (closed_form) = 1.21902999382 -0.365339796954
absolute error = 0.4007
relative error = 31.49 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.429146089529 0.8
h = 0.0001 0.005
y[1] (numeric) = 1.01472491339 -0.0206087476699
y[1] (closed_form) = 1.21615820251 -0.369535992552
absolute error = 0.4029
relative error = 31.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.945
Order of pole (three term test) = 34.47 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2196.7MB, alloc=44.3MB, time=25.12
x[1] = 0.429246089529 0.805
h = 0.0001 0.003
y[1] (numeric) = 1.01472492826 -0.0206087652007
y[1] (closed_form) = 1.22015544868 -0.372404484422
absolute error = 0.4074
relative error = 31.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.836
Order of pole (three term test) = 30.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.429346089529 0.808
h = 0.001 0.001
y[1] (numeric) = 1.01472494348 -0.0206087833693
y[1] (closed_form) = 1.22254585968 -0.374163317906
absolute error = 0.4101
relative error = 32.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3574
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.430346089529 0.809
h = 0.0001 0.004
y[1] (numeric) = 1.01472495908 -0.0206088022367
y[1] (closed_form) = 1.22280302128 -0.375541512638
absolute error = 0.4114
relative error = 32.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.541
Order of pole (three term test) = 37.62 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.430446089529 0.813
h = 0.00518991310064 0
y[1] (numeric) = 1.0147249751 -0.0206088218728
y[1] (closed_form) = 1.22602893203 -0.377872082914
absolute error = 0.4151
relative error = 32.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4798
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.435636002629 0.813
h = 0.0001 0.005
y[1] (numeric) = 1.01472498781 -0.0206088376421
y[1] (closed_form) = 1.22309079927 -0.38213807583
absolute error = 0.4173
relative error = 32.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.848
Order of pole (three term test) = 34.39 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2240.8MB, alloc=44.3MB, time=25.63
x[1] = 0.435736002629 0.818
h = 0.0001 0.003
y[1] (numeric) = 1.01472500083 -0.0206088539604
y[1] (closed_form) = 1.22715392597 -0.385072074585
absolute error = 0.4219
relative error = 32.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.935
Order of pole (three term test) = 30.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.435836002629 0.821
h = 0.001 0.001
y[1] (numeric) = 1.01472501417 -0.0206088708767
y[1] (closed_form) = 1.22958342693 -0.386870906186
absolute error = 0.4246
relative error = 32.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3621
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.436836002629 0.822
h = 0.001 0.003
y[1] (numeric) = 1.01472502787 -0.0206088884486
y[1] (closed_form) = 1.22984114172 -0.388275480762
absolute error = 0.426
relative error = 33.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.284
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.437836002629 0.825
h = 0.0001 0.004
y[1] (numeric) = 1.01472504196 -0.0206089067429
y[1] (closed_form) = 1.23176535456 -0.3908350104
absolute error = 0.4292
relative error = 33.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.686
Order of pole (three term test) = 38.25 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.437936002629 0.829
h = 0.00518991310064 0
y[1] (numeric) = 1.01472505649 -0.0206089258359
y[1] (closed_form) = 1.23505686486 -0.393228674058
absolute error = 0.4329
relative error = 33.4 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4777
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.44312591573 0.829
h = 0.0001 0.005
y[1] (numeric) = 1.01472506807 -0.0206089412093
y[1] (closed_form) = 1.23203876471 -0.397581655366
absolute error = 0.4351
relative error = 33.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.751
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2285.0MB, alloc=44.3MB, time=26.13
x[1] = 0.44322591573 0.834
h = 0.0001 0.003
y[1] (numeric) = 1.01472507996 -0.0206089571566
y[1] (closed_form) = 1.23618405793 -0.400594681612
absolute error = 0.4398
relative error = 33.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.06
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.44332591573 0.837
h = 0.001 0.001
y[1] (numeric) = 1.01472509219 -0.02060897373
y[1] (closed_form) = 1.23866233724 -0.402441791721
absolute error = 0.4427
relative error = 33.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3676
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.44432591573 0.838
h = 0.001 0.003
y[1] (numeric) = 1.0147251048 -0.020608990991
y[1] (closed_form) = 1.23892126912 -0.403878722812
absolute error = 0.444
relative error = 34.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.317
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.44532591573 0.841
h = 0.0001 0.004
y[1] (numeric) = 1.01472511783 -0.0206090090104
y[1] (closed_form) = 1.24088024005 -0.406501871911
absolute error = 0.4473
relative error = 34.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.761
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.44542591573 0.845
h = 0.00518991310064 0
y[1] (numeric) = 1.01472513132 -0.0206090278686
y[1] (closed_form) = 1.24423743414 -0.40895989637
absolute error = 0.4511
relative error = 34.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4756
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2329.0MB, alloc=44.3MB, time=26.63
x[1] = 0.45061582883 0.845
h = 0.0001 0.005
y[1] (numeric) = 1.01472514211 -0.0206090430909
y[1] (closed_form) = 1.24113771995 -0.413400012837
absolute error = 0.4534
relative error = 34.66 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 34.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.45071582883 0.85
h = 0.0001 0.003
y[1] (numeric) = 1.01472515323 -0.0206090589163
y[1] (closed_form) = 1.24536528614 -0.416493662442
absolute error = 0.4582
relative error = 34.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.197
Order of pole (three term test) = 30.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.45081582883 0.853
h = 0.001 0.001
y[1] (numeric) = 1.01472516472 -0.0206090753994
y[1] (closed_form) = 1.24789239649 -0.418390014304
absolute error = 0.4611
relative error = 35.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.373
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.45181582883 0.854
h = 0.001 0.003
y[1] (numeric) = 1.0147251766 -0.0206090926044
y[1] (closed_form) = 1.24815225282 -0.419859651214
absolute error = 0.4625
relative error = 35.12 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.351
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.45281582883 0.857
h = 0.0001 0.004
y[1] (numeric) = 1.01472518892 -0.0206091106051
y[1] (closed_form) = 1.25014574471 -0.422547413677
absolute error = 0.4658
relative error = 35.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.935
Order of pole (three term test) = 37.84 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
memory used=2373.1MB, alloc=44.3MB, time=27.13
x[1] = 0.45291582883 0.861
h = 0.00518991310064 0
y[1] (numeric) = 1.01472520173 -0.0206091294852
y[1] (closed_form) = 1.25356870453 -0.425071094965
absolute error = 0.4697
relative error = 35.49 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4735
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.458105741931 0.861
h = 0.0001 0.005
y[1] (numeric) = 1.014725212 -0.0206091447545
y[1] (closed_form) = 1.25038569244 -0.429598491213
absolute error = 0.472
relative error = 35.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.591
Order of pole (three term test) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.458205741931 0.866
h = 0.0001 0.003
y[1] (numeric) = 1.01472522263 -0.0206091606548
y[1] (closed_form) = 1.25469563518 -0.432774395883
absolute error = 0.4769
relative error = 35.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.348
Order of pole (three term test) = 30.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.458305741931 0.869
h = 0.001 0.001
y[1] (numeric) = 1.01472523363 -0.020609177243
y[1] (closed_form) = 1.25727162722 -0.434720974288
absolute error = 0.4799
relative error = 36.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3783
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.459305741931 0.87
h = 0.001 0.003
y[1] (numeric) = 1.01472524506 -0.0206091945852
y[1] (closed_form) = 1.25753210768 -0.436223673081
absolute error = 0.4813
relative error = 36.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.460305741931 0.873
h = 0.0001 0.004
y[1] (numeric) = 1.01472525693 -0.0206092127577
y[1] (closed_form) = 1.25955987481 -0.438977064002
absolute error = 0.4847
relative error = 36.34 %
Correct digits = 0
memory used=2417.3MB, alloc=44.3MB, time=27.63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.247
Order of pole (three term test) = 37.41 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.460405741931 0.877
h = 0.00518991310064 0
y[1] (numeric) = 1.01472526932 -0.0206092318467
y[1] (closed_form) = 1.26304867973 -0.441567727035
absolute error = 0.4887
relative error = 36.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4713
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.465595655032 0.877
h = 0.0001 0.005
y[1] (numeric) = 1.01472527929 -0.0206092473049
y[1] (closed_form) = 1.2597806483 -0.446182545168
absolute error = 0.4911
relative error = 36.75 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.523
Order of pole (three term test) = 34.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.465695655032 0.882
h = 0.0001 0.003
y[1] (numeric) = 1.01472528961 -0.0206092634196
y[1] (closed_form) = 1.26417306794 -0.449442372794
absolute error = 0.4961
relative error = 36.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.516
Order of pole (three term test) = 30.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.465795655032 0.885
h = 0.001 0.001
y[1] (numeric) = 1.01472530034 -0.0206092802491
y[1] (closed_form) = 1.26679799004 -0.451440184291
absolute error = 0.4992
relative error = 37.12 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3835
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.466795655032 0.886
h = 0.0001 0.004
y[1] (numeric) = 1.0147253115 -0.0206092978616
y[1] (closed_form) = 1.26705878653 -0.452976307789
absolute error = 0.5006
relative error = 37.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.721
Order of pole (three term test) = 37.01 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2461.6MB, alloc=44.3MB, time=28.14
SETTING H FOR POLE
x[1] = 0.466895655032 0.89
h = 0.00518991310064 0
y[1] (numeric) = 1.01472532313 -0.0206093163352
y[1] (closed_form) = 1.27060036123 -0.455624423284
absolute error = 0.5047
relative error = 37.39 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4694
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.472085568132 0.89
h = 0.0001 0.005
y[1] (numeric) = 1.01472533248 -0.0206093312744
y[1] (closed_form) = 1.26725929462 -0.460309413642
absolute error = 0.5071
relative error = 37.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.468
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.472185568132 0.895
h = 0.0001 0.003
y[1] (numeric) = 1.01472534218 -0.0206093468283
y[1] (closed_form) = 1.27171781315 -0.463641230231
absolute error = 0.5122
relative error = 37.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.677
Order of pole (three term test) = 29.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.472285568132 0.898
h = 0.001 0.001
y[1] (numeric) = 1.01472535225 -0.0206093630515
y[1] (closed_form) = 1.27438190989 -0.465682950605
absolute error = 0.5153
relative error = 37.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3879
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.473285568132 0.899
h = 0.001 0.003
y[1] (numeric) = 1.01472536272 -0.0206093800085
y[1] (closed_form) = 1.27464202686 -0.467246830367
absolute error = 0.5168
relative error = 38.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.439
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2505.7MB, alloc=44.3MB, time=28.64
x[1] = 0.474285568132 0.902
h = 0.0001 0.004
y[1] (numeric) = 1.01472537363 -0.0206093977737
y[1] (closed_form) = 1.27673017839 -0.47012318759
absolute error = 0.5203
relative error = 38.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.26
Order of pole (three term test) = 36.64 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.474385568132 0.906
h = 0.00518991310064 0
y[1] (numeric) = 1.01472538504 -0.0206094164321
y[1] (closed_form) = 1.28033770627 -0.472840775801
absolute error = 0.5245
relative error = 38.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4673
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.479575481233 0.906
h = 0.0001 0.005
y[1] (numeric) = 1.01472539424 -0.0206094315405
y[1] (closed_form) = 1.27690838288 -0.477613401724
absolute error = 0.5269
relative error = 38.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.413
Order of pole (three term test) = 33.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.479675481233 0.911
h = 0.0001 0.003
y[1] (numeric) = 1.0147254038 -0.0206094472904
y[1] (closed_form) = 1.2814495152 -0.481032276618
absolute error = 0.5321
relative error = 38.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.883
Order of pole (three term test) = 29.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.479775481233 0.914
h = 0.001 0.001
y[1] (numeric) = 1.01472541374 -0.0206094637402
y[1] (closed_form) = 1.28416260162 -0.483127121732
absolute error = 0.5353
relative error = 39.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.393
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.480775481233 0.915
h = 0.001 0.003
y[1] (numeric) = 1.01472542411 -0.0206094809582
y[1] (closed_form) = 1.2844224448 -0.484725097934
absolute error = 0.5368
relative error = 39.1 %
Correct digits = 0
memory used=2549.7MB, alloc=44.3MB, time=29.15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.469
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.481775481233 0.918
h = 0.0001 0.004
y[1] (numeric) = 1.01472543494 -0.0206094990233
y[1] (closed_form) = 1.28654410672 -0.48767005823
absolute error = 0.5404
relative error = 39.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.88
Order of pole (three term test) = 36.32 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.481875481233 0.922
h = 0.00518991310064 0
y[1] (numeric) = 1.0147254463 -0.0206095180252
y[1] (closed_form) = 1.29021765755 -0.490458527072
absolute error = 0.5447
relative error = 39.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4652
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.487065394334 0.922
h = 0.0001 0.005
y[1] (numeric) = 1.01472545548 -0.0206095334324
y[1] (closed_form) = 1.28669824793 -0.49531892065
absolute error = 0.5471
relative error = 39.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.363
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.487165394334 0.927
h = 0.0001 0.003
y[1] (numeric) = 1.01472546503 -0.0206095495127
y[1] (closed_form) = 1.29132208236 -0.498826625724
absolute error = 0.5524
relative error = 39.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.115
Order of pole (three term test) = 29.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.487265394334 0.93
h = 0.001 0.001
y[1] (numeric) = 1.01472547499 -0.0206095663271
y[1] (closed_form) = 1.29408419871 -0.500975664623
absolute error = 0.5557
relative error = 40.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.398
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2593.9MB, alloc=44.3MB, time=29.76
x[1] = 0.488265394334 0.931
h = 0.001 0.003
y[1] (numeric) = 1.0147254854 -0.0206095839469
y[1] (closed_form) = 1.29434343703 -0.502608118981
absolute error = 0.5572
relative error = 40.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.489265394334 0.934
h = 0.0001 0.004
y[1] (numeric) = 1.0147254963 -0.0206096024543
y[1] (closed_form) = 1.29649832758 -0.505622779577
absolute error = 0.5609
relative error = 40.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.564
Order of pole (three term test) = 36.04 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.489365394334 0.938
h = 0.00518991310064 0
y[1] (numeric) = 1.01472550775 -0.0206096219422
y[1] (closed_form) = 1.30023796735 -0.508483566962
absolute error = 0.5653
relative error = 40.49 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4631
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.494555307434 0.938
h = 0.0001 0.005
y[1] (numeric) = 1.01472551701 -0.0206096377579
y[1] (closed_form) = 1.29662660302 -0.513431856235
absolute error = 0.5678
relative error = 40.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.317
Order of pole (three term test) = 33.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.494655307434 0.943
h = 0.0001 0.003
y[1] (numeric) = 1.01472552667 -0.0206096542771
y[1] (closed_form) = 1.30133322311 -0.517030200943
absolute error = 0.5732
relative error = 40.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.378
Order of pole (three term test) = 29.19 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2638.1MB, alloc=44.3MB, time=30.27
x[1] = 0.494755307434 0.946
h = 0.001 0.001
y[1] (numeric) = 1.01472553675 -0.0206096715628
y[1] (closed_form) = 1.30414440643 -0.519234525258
absolute error = 0.5765
relative error = 41.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4029
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.495755307434 0.947
h = 0.001 0.003
y[1] (numeric) = 1.0147255473 -0.0206096896886
y[1] (closed_form) = 1.30440270045 -0.520901846233
absolute error = 0.5781
relative error = 41.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.526
Order of pole (three term test) = 32.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.496755307434 0.95
h = 0.0001 0.004
y[1] (numeric) = 1.01472555837 -0.0206097087393
y[1] (closed_form) = 1.30659052783 -0.523987326256
absolute error = 0.5819
relative error = 41.33 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.299
Order of pole (three term test) = 35.8 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.496855307434 0.954
h = 0.00518991310064 0
y[1] (numeric) = 1.01472557 -0.0206097288107
y[1] (closed_form) = 1.31039631841 -0.526921900389
absolute error = 0.5863
relative error = 41.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4611
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.502045220535 0.954
h = 0.0001 0.005
y[1] (numeric) = 1.01472557942 -0.0206097451071
y[1] (closed_form) = 1.30669109141 -0.53195820893
absolute error = 0.5888
relative error = 41.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.275
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.502145220535 0.959
h = 0.0001 0.003
y[1] (numeric) = 1.01472558925 -0.0206097621343
y[1] (closed_form) = 1.31148057555 -0.535649040687
absolute error = 0.5944
relative error = 41.96 %
Correct digits = 0
memory used=2682.1MB, alloc=44.3MB, time=30.77
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.68
Order of pole (three term test) = 28.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.502245220535 0.962
h = 0.001 0.001
y[1] (numeric) = 1.01472559952 -0.0206097799571
y[1] (closed_form) = 1.31434085947 -0.53790976486
absolute error = 0.5978
relative error = 42.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4077
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.503245220535 0.963
h = 0.0001 0.004
y[1] (numeric) = 1.01472561028 -0.0206097986511
y[1] (closed_form) = 1.31459786118 -0.539612347661
absolute error = 0.5994
relative error = 42.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.09
Order of pole (three term test) = 35.6 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.503345220535 0.967
h = 0.00518991310064 0
y[1] (numeric) = 1.01472562157 -0.0206098183031
y[1] (closed_form) = 1.31845651364 -0.542610083485
absolute error = 0.6039
relative error = 42.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4592
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.508535133636 0.967
h = 0.0001 0.005
y[1] (numeric) = 1.0147256307 -0.0206098342265
y[1] (closed_form) = 1.31467082761 -0.547716851641
absolute error = 0.6065
relative error = 42.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.24
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.508635133636 0.972
h = 0.0001 0.003
y[1] (numeric) = 1.01472564021 -0.0206098508335
y[1] (closed_form) = 1.31952652862 -0.55148685687
absolute error = 0.6122
relative error = 42.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.983
Order of pole (three term test) = 28.62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2726.4MB, alloc=44.3MB, time=31.26
x[1] = 0.508735133636 0.975
h = 0.001 0.001
y[1] (numeric) = 1.01472565013 -0.0206098681847
y[1] (closed_form) = 1.32242600539 -0.553795822709
absolute error = 0.6156
relative error = 42.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4118
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.509735133636 0.976
h = 0.001 0.003
y[1] (numeric) = 1.01472566051 -0.0206098863515
y[1] (closed_form) = 1.3226809358 -0.555527662042
absolute error = 0.6172
relative error = 43.02 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.569
Order of pole (three term test) = 32.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.510735133636 0.979
h = 0.0001 0.004
y[1] (numeric) = 1.01472567138 -0.0206099054164
y[1] (closed_form) = 1.32492647258 -0.558745807115
absolute error = 0.6211
relative error = 43.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.896
Order of pole (three term test) = 35.42 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.510835133636 0.983
h = 0.00518991310064 0
y[1] (numeric) = 1.0147256828 -0.0206099254737
y[1] (closed_form) = 1.32885134495 -0.561820085028
absolute error = 0.6258
relative error = 43.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4572
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.516025046736 0.983
h = 0.0001 0.005
y[1] (numeric) = 1.01472569205 -0.0206099417389
y[1] (closed_form) = 1.3249682145 -0.567015043223
absolute error = 0.6283
relative error = 43.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.204
Order of pole (three term test) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2770.6MB, alloc=44.3MB, time=31.76
x[1] = 0.516125046736 0.988
h = 0.0001 0.003
y[1] (numeric) = 1.01472570169 -0.0206099587166
y[1] (closed_form) = 1.32990686752 -0.570881002088
absolute error = 0.6341
relative error = 43.82 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.383
Order of pole (three term test) = 28.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.516225046736 0.991
h = 0.001 0.001
y[1] (numeric) = 1.01472571177 -0.0206099764713
y[1] (closed_form) = 1.33285547219 -0.57324845845
absolute error = 0.6377
relative error = 43.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4165
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.517225046736 0.992
h = 0.001 0.003
y[1] (numeric) = 1.01472572233 -0.0206099950788
y[1] (closed_form) = 1.33310844515 -0.575016289439
absolute error = 0.6393
relative error = 44.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.593
Order of pole (three term test) = 32.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.518225046736 0.995
h = 0.0001 0.004
y[1] (numeric) = 1.0147257334 -0.0206100146266
y[1] (closed_form) = 1.33538601335 -0.578308524987
absolute error = 0.6433
relative error = 44.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.727
Order of pole (three term test) = 35.26 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.518325046736 0.999
h = 0.00518991310064 0
y[1] (numeric) = 1.01472574505 -0.0206100352138
y[1] (closed_form) = 1.33937715334 -0.581460900269
absolute error = 0.648
relative error = 44.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4552
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.523514959837 0.999
h = 0.0001 0.005
y[1] (numeric) = 1.0147257545 -0.0206100519248
y[1] (closed_form) = 1.33539455708 -0.586744156246
absolute error = 0.6506
relative error = 44.61 %
Correct digits = 0
memory used=2814.7MB, alloc=44.3MB, time=32.26
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.172
Order of pole (three term test) = 33.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.523614959837 1.004
h = 0.0001 0.003
y[1] (numeric) = 1.01472576437 -0.0206100693823
y[1] (closed_form) = 1.34041622273 -0.590708025273
absolute error = 0.6566
relative error = 44.82 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.855
Order of pole (three term test) = 27.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.523714959837 1.007
h = 0.001 0.001
y[1] (numeric) = 1.01472577469 -0.0206100876539
y[1] (closed_form) = 1.34341397729 -0.593135152148
absolute error = 0.6602
relative error = 44.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4211
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.524714959837 1.008
h = 0.001 0.003
y[1] (numeric) = 1.01472578551 -0.0206101068185
y[1] (closed_form) = 1.34366461963 -0.594939388815
absolute error = 0.6619
relative error = 45.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.615
Order of pole (three term test) = 32.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.525714959837 1.011
h = 0.0001 0.004
y[1] (numeric) = 1.01472579687 -0.0206101269671
y[1] (closed_form) = 1.34597388544 -0.598306918855
absolute error = 0.6659
relative error = 45.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.58
Order of pole (three term test) = 35.12 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.525814959837 1.015
h = 0.00518991310064 0
y[1] (numeric) = 1.01472580884 -0.0206101482024
y[1] (closed_form) = 1.3500313353 -0.601538978283
absolute error = 0.6708
relative error = 45.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4532
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2858.6MB, alloc=44.3MB, time=32.74
x[1] = 0.531004872937 1.015
h = 0.0001 0.005
y[1] (numeric) = 1.01472581855 -0.0206101654498
y[1] (closed_form) = 1.3459472108 -0.606910633592
absolute error = 0.6734
relative error = 45.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.141
Order of pole (three term test) = 33.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.531104872937 1.02
h = 0.0001 0.003
y[1] (numeric) = 1.0147258287 -0.0206101834766
y[1] (closed_form) = 1.35105194283 -0.610974408777
absolute error = 0.6794
relative error = 45.82 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.422
Order of pole (three term test) = 27.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.531204872937 1.023
h = 0.001 0.001
y[1] (numeric) = 1.01472583933 -0.0206102023525
y[1] (closed_form) = 1.35409886478 -0.613462409865
absolute error = 0.6831
relative error = 45.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4256
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.532204872937 1.024
h = 0.001 0.003
y[1] (numeric) = 1.01472585046 -0.0206102221588
y[1] (closed_form) = 1.35434679416 -0.615303472953
absolute error = 0.6848
relative error = 46.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.533204872937 1.027
h = 0.0001 0.004
y[1] (numeric) = 1.01472586217 -0.0206102429893
y[1] (closed_form) = 1.35668741205 -0.618747524149
absolute error = 0.689
relative error = 46.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.451
Order of pole (three term test) = 35 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2902.6MB, alloc=44.3MB, time=33.23
SETTING H FOR POLE
x[1] = 0.533304872937 1.031
h = 0.00518991310064 0
y[1] (numeric) = 1.01472587451 -0.0206102649497
y[1] (closed_form) = 1.36081120819 -0.622060886321
absolute error = 0.6939
relative error = 46.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4513
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.538494786038 1.031
h = 0.0001 0.005
y[1] (numeric) = 1.01472588452 -0.0206102827897
y[1] (closed_form) = 1.35662345153 -0.627521035852
absolute error = 0.6966
relative error = 46.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.113
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.538594786038 1.036
h = 0.0001 0.003
y[1] (numeric) = 1.01472589499 -0.0206103014385
y[1] (closed_form) = 1.36181129634 -0.631686753071
absolute error = 0.7028
relative error = 46.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.115
Order of pole (three term test) = 26.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.538694786038 1.039
h = 0.001 0.001
y[1] (numeric) = 1.01472590595 -0.0206103209675
y[1] (closed_form) = 1.36490739843 -0.634236856024
absolute error = 0.7065
relative error = 46.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4301
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.539694786038 1.04
h = 0.00518991310064 0
y[1] (numeric) = 1.01472591744 -0.0206103414604
y[1] (closed_form) = 1.36515222313 -0.636115172986
absolute error = 0.7083
relative error = 47.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4492
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.544884699139 1.04
h = 0.0001 0.005
y[1] (numeric) = 1.01472592673 -0.0206103580368
y[1] (closed_form) = 1.3608898241 -0.641617934924
absolute error = 0.711
relative error = 47.25 %
Correct digits = 0
memory used=2947.0MB, alloc=44.3MB, time=33.73
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.084
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.544984699139 1.045
h = 0.0001 0.003
y[1] (numeric) = 1.0147259364 -0.0206103752983
y[1] (closed_form) = 1.36611714637 -0.645856614813
absolute error = 0.7172
relative error = 47.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.031
Order of pole (three term test) = 25.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.545084699139 1.048
h = 0.001 0.001
y[1] (numeric) = 1.01472594648 -0.0206103933056
y[1] (closed_form) = 1.36923639943 -0.648450995523
absolute error = 0.721
relative error = 47.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4346
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.546084699139 1.049
h = 0.001 0.003
y[1] (numeric) = 1.014725957 -0.0206104121311
y[1] (closed_form) = 1.3694749081 -0.650352029877
absolute error = 0.7228
relative error = 47.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.663
Order of pole (three term test) = 32.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.547084699139 1.052
h = 0.0001 0.004
y[1] (numeric) = 1.01472596802 -0.0206104318595
y[1] (closed_form) = 1.3718565562 -0.653925695397
absolute error = 0.7271
relative error = 47.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.225
Order of pole (three term test) = 34.78 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.547184699139 1.056
h = 0.00518991310064 0
y[1] (numeric) = 1.01472597958 -0.0206104525878
y[1] (closed_form) = 1.37607807829 -0.65738123907
absolute error = 0.7322
relative error = 48.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4473
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2991.0MB, alloc=44.3MB, time=34.22
x[1] = 0.552374612239 1.056
h = 0.0001 0.005
y[1] (numeric) = 1.01472598893 -0.0206104693799
y[1] (closed_form) = 1.37170855252 -0.662972388448
absolute error = 0.7349
relative error = 48.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.552474612239 1.061
h = 0.0001 0.003
y[1] (numeric) = 1.01472599868 -0.0206104868938
y[1] (closed_form) = 1.37701880909 -0.667316386058
absolute error = 0.7413
relative error = 48.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.161
Order of pole (three term test) = 24.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.552574612239 1.064
h = 0.001 0.001
y[1] (numeric) = 1.01472600885 -0.0206105051973
y[1] (closed_form) = 1.38018710935 -0.669974902213
absolute error = 0.7451
relative error = 48.57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4389
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.553574612239 1.065
h = 0.001 0.003
y[1] (numeric) = 1.01472601948 -0.0206105243706
y[1] (closed_form) = 1.38042181137 -0.67191384878
absolute error = 0.7469
relative error = 48.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.679
Order of pole (three term test) = 32.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.554574612239 1.068
h = 0.0001 0.004
y[1] (numeric) = 1.01472603064 -0.0206105445063
y[1] (closed_form) = 1.38283370528 -0.675567308051
absolute error = 0.7513
relative error = 48.82 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.135
Order of pole (three term test) = 34.69 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3035.1MB, alloc=44.3MB, time=34.72
SETTING H FOR POLE
x[1] = 0.554674612239 1.072
h = 0.00518991310064 0
y[1] (numeric) = 1.01472604236 -0.02061056571
y[1] (closed_form) = 1.38712144654 -0.679108541051
absolute error = 0.7565
relative error = 48.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4455
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.55986452534 1.072
h = 0.0001 0.005
y[1] (numeric) = 1.01472605187 -0.0206105829224
y[1] (closed_form) = 1.38264258046 -0.684788148229
absolute error = 0.7593
relative error = 49.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.038
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.55996452534 1.077
h = 0.0001 0.003
y[1] (numeric) = 1.01472606179 -0.0206106009071
y[1] (closed_form) = 1.38803579165 -0.689239604713
absolute error = 0.7658
relative error = 49.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.668
Order of pole (three term test) = 23.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.56006452534 1.08
h = 0.001 0.001
y[1] (numeric) = 1.01472607216 -0.0206106197367
y[1] (closed_form) = 1.39125313525 -0.691963547145
absolute error = 0.7697
relative error = 49.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4431
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.56106452534 1.081
h = 0.001 0.003
y[1] (numeric) = 1.01472608304 -0.0206106394962
y[1] (closed_form) = 1.39148361279 -0.693940849774
absolute error = 0.7716
relative error = 49.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.694
Order of pole (three term test) = 32.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.56206452534 1.084
h = 0.0001 0.004
y[1] (numeric) = 1.01472609446 -0.0206106602837
y[1] (closed_form) = 1.39392535897 -0.697675411217
absolute error = 0.776
relative error = 49.78 %
Correct digits = 0
memory used=3079.4MB, alloc=44.3MB, time=35.22
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.054
Order of pole (three term test) = 34.61 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.56216452534 1.088
h = 0.00518991310064 0
y[1] (numeric) = 1.0147261065 -0.0206106822104
y[1] (closed_form) = 1.39827932775 -0.701304069144
absolute error = 0.7813
relative error = 49.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4437
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.567354438441 1.088
h = 0.0001 0.005
y[1] (numeric) = 1.01472611627 -0.0206107000348
y[1] (closed_form) = 1.39368886471 -0.707072195955
absolute error = 0.7841
relative error = 50.17 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.016
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.567454438441 1.093
h = 0.0001 0.003
y[1] (numeric) = 1.01472612649 -0.0206107186806
y[1] (closed_form) = 1.39916504168 -0.711633293832
absolute error = 0.7908
relative error = 50.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.78
Order of pole (three term test) = 21.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.567554438441 1.096
h = 0.001 0.001
y[1] (numeric) = 1.01472613719 -0.0206107382235
y[1] (closed_form) = 1.40243141887 -0.714423978206
absolute error = 0.7948
relative error = 50.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4472
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.568554438441 1.097
h = 0.0001 0.004
y[1] (numeric) = 1.01472614842 -0.0206107587522
y[1] (closed_form) = 1.40265724407 -0.716440087402
absolute error = 0.7967
relative error = 50.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.984
Order of pole (three term test) = 34.55 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3123.6MB, alloc=44.3MB, time=35.74
SETTING H FOR POLE
x[1] = 0.568654438441 1.101
h = 0.00518991310064 0
y[1] (numeric) = 1.01472616024 -0.0206107803683
y[1] (closed_form) = 1.40706380529 -0.720143322588
absolute error = 0.802
relative error = 50.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.442
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.573844351541 1.101
h = 0.0001 0.005
y[1] (numeric) = 1.01472616982 -0.0206107979107
y[1] (closed_form) = 1.40237802975 -0.725981893964
absolute error = 0.8049
relative error = 50.97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9978
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.573944351541 1.106
h = 0.0001 0.003
y[1] (numeric) = 1.01472617983 -0.0206108162334
y[1] (closed_form) = 1.4079200891 -0.73063652321
absolute error = 0.8116
relative error = 51.17 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.57
Order of pole (three term test) = 18.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.574044351541 1.109
h = 0.001 0.001
y[1] (numeric) = 1.01472619029 -0.0206108354074
y[1] (closed_form) = 1.41122534987 -0.733484102037
absolute error = 0.8157
relative error = 51.29 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4508
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.575044351541 1.11
h = 0.001 0.003
y[1] (numeric) = 1.01472620126 -0.0206108555169
y[1] (closed_form) = 1.41144620528 -0.735532351722
absolute error = 0.8176
relative error = 51.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.708
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3167.7MB, alloc=44.3MB, time=36.23
x[1] = 0.576044351541 1.113
h = 0.0001 0.004
y[1] (numeric) = 1.01472621279 -0.020610876659
y[1] (closed_form) = 1.41393954609 -0.739418737408
absolute error = 0.8222
relative error = 51.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.917
Order of pole (three term test) = 34.48 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.576144351541 1.117
h = 0.00518991310064 0
y[1] (numeric) = 1.01472622494 -0.0206108989447
y[1] (closed_form) = 1.41841229229 -0.743212645922
absolute error = 0.8277
relative error = 51.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4402
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.581334264642 1.117
h = 0.0001 0.005
y[1] (numeric) = 1.0147262348 -0.0206109170497
y[1] (closed_form) = 1.41361069466 -0.749139777059
absolute error = 0.8306
relative error = 51.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9792
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.581434264642 1.122
h = 0.0001 0.003
y[1] (numeric) = 1.01472624512 -0.0206109359787
y[1] (closed_form) = 1.41923566753 -0.753908132231
absolute error = 0.8375
relative error = 52.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.57
Order of pole (three term test) = 14.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.581534264642 1.125
h = 0.001 0.001
y[1] (numeric) = 1.01472625593 -0.0206109558081
y[1] (closed_form) = 1.4225898995 -0.756824914606
absolute error = 0.8416
relative error = 52.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4548
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.582534264642 1.126
h = 0.001 0.003
y[1] (numeric) = 1.01472626728 -0.0206109766271
y[1] (closed_form) = 1.42280528683 -0.758912799468
absolute error = 0.8436
relative error = 52.31 %
Correct digits = 0
memory used=3212.0MB, alloc=44.3MB, time=36.72
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.718
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.583534264642 1.129
h = 0.0001 0.004
y[1] (numeric) = 1.01472627922 -0.020610998539
y[1] (closed_form) = 1.42532726654 -0.76288409742
absolute error = 0.8483
relative error = 52.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.856
Order of pole (three term test) = 34.42 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.583634264642 1.133
h = 0.00518991310064 0
y[1] (numeric) = 1.01472629182 -0.0206110216605
y[1] (closed_form) = 1.42986618247 -0.766770509714
absolute error = 0.8539
relative error = 52.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4385
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.588824177743 1.133
h = 0.0001 0.005
y[1] (numeric) = 1.01472630208 -0.0206110404617
y[1] (closed_form) = 1.42494638227 -0.772786234572
absolute error = 0.8568
relative error = 52.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9616
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.588924177743 1.138
h = 0.0001 0.003
y[1] (numeric) = 1.01472631281 -0.0206110601338
y[1] (closed_form) = 1.43065425019 -0.777670617086
absolute error = 0.8638
relative error = 53.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.35
Order of pole (three term test) = 6.575 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.589024177743 1.141
h = 0.001 0.001
y[1] (numeric) = 1.01472632406 -0.0206110807564
y[1] (closed_form) = 1.43405742475 -0.780657990033
absolute error = 0.868
relative error = 53.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4588
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3256.0MB, alloc=44.3MB, time=37.21
x[1] = 0.590024177743 1.142
h = 0.001 0.003
y[1] (numeric) = 1.01472633589 -0.0206111024227
y[1] (closed_form) = 1.43426688663 -0.782785979066
absolute error = 0.87
relative error = 53.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.727
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.591024177743 1.145
h = 0.0001 0.004
y[1] (numeric) = 1.01472634834 -0.0206111252399
y[1] (closed_form) = 1.43681705751 -0.786843587626
absolute error = 0.8748
relative error = 53.4 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.591124177743 1.149
h = 0.00518991310064 0
y[1] (numeric) = 1.01472636149 -0.0206111493293
y[1] (closed_form) = 1.44142211898 -0.790824368503
absolute error = 0.8805
relative error = 53.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4369
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.596314090843 1.149
h = 0.0001 0.005
y[1] (numeric) = 1.0147263722 -0.0206111689251
y[1] (closed_form) = 1.43638169086 -0.796928710422
absolute error = 0.8834
relative error = 53.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9451
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.596414090843 1.154
h = 0.0001 0.003
y[1] (numeric) = 1.01472638341 -0.0206111894344
y[1] (closed_form) = 1.44217242413 -0.801931464756
absolute error = 0.8906
relative error = 53.97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.5
Order of pole (three term test) = 24.21 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3300.2MB, alloc=44.3MB, time=37.70
x[1] = 0.596514090843 1.157
h = 0.001 0.001
y[1] (numeric) = 1.01472639516 -0.0206112109393
y[1] (closed_form) = 1.44562450555 -0.80499084114
absolute error = 0.8949
relative error = 54.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4626
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.597514090843 1.158
h = 0.001 0.003
y[1] (numeric) = 1.01472640752 -0.0206112335359
y[1] (closed_form) = 1.44582757379 -0.807159409934
absolute error = 0.8969
relative error = 54.17 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.734
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.598514090843 1.161
h = 0.0001 0.004
y[1] (numeric) = 1.01472642053 -0.0206112573344
y[1] (closed_form) = 1.44840547308 -0.811304751455
absolute error = 0.9018
relative error = 54.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.749
Order of pole (three term test) = 34.32 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.598614090843 1.165
h = 0.00518991310064 0
y[1] (numeric) = 1.01472643428 -0.0206112824597
y[1] (closed_form) = 1.45307664651 -0.815381800438
absolute error = 0.9076
relative error = 54.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4353
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.603804003944 1.165
h = 0.0001 0.005
y[1] (numeric) = 1.01472644546 -0.0206113028966
y[1] (closed_form) = 1.44791311977 -0.821574771556
absolute error = 0.9106
relative error = 54.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9295
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.603904003944 1.17
h = 0.0001 0.003
y[1] (numeric) = 1.01472645717 -0.0206113242837
y[1] (closed_form) = 1.45378667686 -0.826698285713
absolute error = 0.9179
relative error = 54.89 %
Correct digits = 0
memory used=3344.5MB, alloc=44.3MB, time=38.20
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 232.6
Order of pole (three term test) = 217.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.604004003944 1.173
h = 0.001 0.001
y[1] (numeric) = 1.01472646945 -0.0206113467052
y[1] (closed_form) = 1.45728762192 -0.829831104516
absolute error = 0.9223
relative error = 55 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4664
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.605004003944 1.174
h = 0.0001 0.004
y[1] (numeric) = 1.01472648235 -0.0206113702595
y[1] (closed_form) = 1.45748381734 -0.832040735239
absolute error = 0.9244
relative error = 55.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 34.27 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.605104003944 1.178
h = 0.00518991310064 0
y[1] (numeric) = 1.01472649593 -0.0206113950595
y[1] (closed_form) = 1.46220726745 -0.836199752753
absolute error = 0.9303
relative error = 55.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4337
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.610293917044 1.178
h = 0.0001 0.005
y[1] (numeric) = 1.01472650696 -0.0206114151816
y[1] (closed_form) = 1.45693880872 -0.842462975017
absolute error = 0.9333
relative error = 55.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9154
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.610393917044 1.183
h = 0.0001 0.003
y[1] (numeric) = 1.01472651847 -0.0206114361925
y[1] (closed_form) = 1.46287785395 -0.847689313119
absolute error = 0.9407
relative error = 55.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 76.26
Order of pole (three term test) = 107 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3388.6MB, alloc=44.3MB, time=38.68
x[1] = 0.610493917044 1.186
h = 0.001 0.001
y[1] (numeric) = 1.01472653051 -0.0206114581707
y[1] (closed_form) = 1.46641737431 -0.850884624307
absolute error = 0.9452
relative error = 55.75 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4697
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.611493917044 1.187
h = 0.001 0.003
y[1] (numeric) = 1.01472654314 -0.0206114812091
y[1] (closed_form) = 1.46660668751 -0.853128226076
absolute error = 0.9472
relative error = 55.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 32.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.612493917044 1.19
h = 0.0001 0.004
y[1] (numeric) = 1.0147265564 -0.0206115054146
y[1] (closed_form) = 1.46923198369 -0.857437722581
absolute error = 0.9523
relative error = 55.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 34.23 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.612593917044 1.194
h = 0.00518991310064 0
y[1] (numeric) = 1.01472657037 -0.0206115309095
y[1] (closed_form) = 1.47402141781 -0.861696558818
absolute error = 0.9583
relative error = 56.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4322
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.617783830145 1.194
h = 0.0001 0.005
y[1] (numeric) = 1.01472658171 -0.0206115516052
y[1] (closed_form) = 1.46862524043 -0.868048348232
absolute error = 0.9613
relative error = 56.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9014
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3432.5MB, alloc=44.3MB, time=39.18
x[1] = 0.617883830145 1.199
h = 0.0001 0.003
y[1] (numeric) = 1.01472659356 -0.0206115732262
y[1] (closed_form) = 1.47464694992 -0.873399909548
absolute error = 0.9689
relative error = 56.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.2
Order of pole (three term test) = 66.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.617983830145 1.202
h = 0.001 0.001
y[1] (numeric) = 1.01472660597 -0.0206115958563
y[1] (closed_form) = 1.47823520366 -0.876671352046
absolute error = 0.9735
relative error = 56.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4734
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.618983830145 1.203
h = 0.001 0.003
y[1] (numeric) = 1.01472661899 -0.0206116195935
y[1] (closed_form) = 1.47841673158 -0.878956900728
absolute error = 0.9756
relative error = 56.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.739
Order of pole (three term test) = 32.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.619983830145 1.206
h = 0.0001 0.004
y[1] (numeric) = 1.01472663267 -0.0206116445511
y[1] (closed_form) = 1.48106833399 -0.883358264674
absolute error = 0.9807
relative error = 56.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.619
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.620083830145 1.21
h = 0.00518991310064 0
y[1] (numeric) = 1.0147266471 -0.0206116708574
y[1] (closed_form) = 1.48592368875 -0.88771891893
absolute error = 0.9869
relative error = 57.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4306
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.625273743246 1.21
h = 0.0001 0.005
y[1] (numeric) = 1.01472665883 -0.0206116922257
y[1] (closed_form) = 1.4803971916 -0.894159251831
memory used=3476.7MB, alloc=44.3MB, time=39.66
absolute error = 0.9899
relative error = 57.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8882
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.625373743246 1.215
h = 0.0001 0.003
y[1] (numeric) = 1.01472667108 -0.0206117145624
y[1] (closed_form) = 1.4865014864 -0.899638549452
absolute error = 0.9976
relative error = 57.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.1
Order of pole (three term test) = 54.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.625473743246 1.218
h = 0.001 0.001
y[1] (numeric) = 1.01472668392 -0.0206117379545
y[1] (closed_form) = 1.4901384067 -0.902987637271
absolute error = 1.002
relative error = 57.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.477
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.626473743246 1.219
h = 0.001 0.003
y[1] (numeric) = 1.0147266974 -0.0206117625041
y[1] (closed_form) = 1.49031163781 -0.905315633257
absolute error = 1.004
relative error = 57.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.742
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.627473743246 1.222
h = 0.0001 0.004
y[1] (numeric) = 1.01472671157 -0.0206117883287
y[1] (closed_form) = 1.49298902158 -0.909810380025
absolute error = 1.01
relative error = 57.75 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.581
Order of pole (three term test) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.627573743246 1.226
h = 0.00518991310064 0
y[1] (numeric) = 1.01472672652 -0.0206118155611
y[1] (closed_form) = 1.49791022237 -0.91427488775
absolute error = 1.016
relative error = 57.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4292
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3520.6MB, alloc=44.3MB, time=40.15
x[1] = 0.632763656346 1.226
h = 0.0001 0.005
y[1] (numeric) = 1.01472673867 -0.0206118376897
y[1] (closed_form) = 1.49225075705 -0.92080372694
absolute error = 1.019
relative error = 58.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8757
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.632863656346 1.231
h = 0.0001 0.003
y[1] (numeric) = 1.01472675138 -0.0206118608273
y[1] (closed_form) = 1.4984375441 -0.926413319285
absolute error = 1.027
relative error = 58.29 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.32
Order of pole (three term test) = 49.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.632963656346 1.234
h = 0.001 0.001
y[1] (numeric) = 1.01472676469 -0.0206118850638
y[1] (closed_form) = 1.50212305525 -0.929841593622
absolute error = 1.032
relative error = 58.4 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4805
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.633963656346 1.235
h = 0.001 0.003
y[1] (numeric) = 1.01472677866 -0.0206119105043
y[1] (closed_form) = 1.5022874662 -0.9322125438
absolute error = 1.034
relative error = 58.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.744
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.634963656346 1.238
h = 0.0001 0.004
y[1] (numeric) = 1.01472679336 -0.0206119372694
y[1] (closed_form) = 1.5049900892 -0.936802213618
absolute error = 1.039
relative error = 58.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.546
Order of pole (three term test) = 34.12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3564.6MB, alloc=44.3MB, time=40.63
SETTING H FOR POLE
x[1] = 0.635063656346 1.242
h = 0.00518991310064 0
y[1] (numeric) = 1.01472680886 -0.0206119654955
y[1] (closed_form) = 1.50997704969 -0.941372646805
absolute error = 1.046
relative error = 58.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4277
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.640253569447 1.242
h = 0.0001 0.005
y[1] (numeric) = 1.01472682146 -0.0206119884318
y[1] (closed_form) = 1.50418192002 -0.947989940906
absolute error = 1.049
relative error = 58.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8639
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.640353569447 1.247
h = 0.0001 0.003
y[1] (numeric) = 1.01472683463 -0.0206120124133
y[1] (closed_form) = 1.51045109152 -0.953732432213
absolute error = 1.057
relative error = 59.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.92
Order of pole (three term test) = 45.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.640453569447 1.25
h = 0.001 0.001
y[1] (numeric) = 1.01472684843 -0.0206120375321
y[1] (closed_form) = 1.51418510854 -0.957241461743
absolute error = 1.061
relative error = 59.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.484
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.641453569447 1.251
h = 0.0001 0.004
y[1] (numeric) = 1.01472686291 -0.0206120638955
y[1] (closed_form) = 1.51434016391 -0.95965587947
absolute error = 1.064
relative error = 59.33 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.514
Order of pole (three term test) = 34.09 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
memory used=3608.9MB, alloc=44.3MB, time=41.13
x[1] = 0.641553569447 1.255
h = 0.00518991310064 0
y[1] (numeric) = 1.01472687813 -0.0206120916272
y[1] (closed_form) = 1.5193788653 -0.964316343147
absolute error = 1.07
relative error = 59.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4263
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.646743482548 1.255
h = 0.0001 0.005
y[1] (numeric) = 1.01472689047 -0.0206121141088
y[1] (closed_form) = 1.51346830687 -0.971003428639
absolute error = 1.073
relative error = 59.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8528
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.646843482548 1.26
h = 0.0001 0.003
y[1] (numeric) = 1.01472690335 -0.0206121375658
y[1] (closed_form) = 1.51980229587 -0.976858877294
absolute error = 1.081
relative error = 59.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.86
Order of pole (three term test) = 43.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.646943482548 1.263
h = 0.001 0.001
y[1] (numeric) = 1.01472691681 -0.020612162084
y[1] (closed_form) = 1.5235744063 -0.980436501278
absolute error = 1.086
relative error = 59.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.487
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.647943482548 1.264
h = 0.001 0.003
y[1] (numeric) = 1.0147269309 -0.0206121877645
y[1] (closed_form) = 1.52372044451 -0.982886838199
absolute error = 1.089
relative error = 60.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.648943482548 1.267
h = 0.0001 0.004
y[1] (numeric) = 1.01472694568 -0.0206122147245
y[1] (closed_form) = 1.52646556252 -0.987654015038
absolute error = 1.094
relative error = 60.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.483
Order of pole (three term test) = 34.06 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3652.9MB, alloc=44.3MB, time=41.62
SETTING H FOR POLE
x[1] = 0.649043482548 1.271
h = 0.00518991310064 0
y[1] (numeric) = 1.01472696124 -0.0206122430972
y[1] (closed_form) = 1.53156978971 -0.992424272622
absolute error = 1.101
relative error = 60.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4249
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.654233395648 1.271
h = 0.0001 0.005
y[1] (numeric) = 1.01472697386 -0.0206122661121
y[1] (closed_form) = 1.5255185311 -0.99919962256
absolute error = 1.104
relative error = 60.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8421
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.654333395648 1.276
h = 0.0001 0.003
y[1] (numeric) = 1.01472698704 -0.0206122901402
y[1] (closed_form) = 1.53193461186 -1.00519283206
absolute error = 1.112
relative error = 60.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.24
Order of pole (three term test) = 42.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.654433395648 1.279
h = 0.001 0.001
y[1] (numeric) = 1.01472700081 -0.0206123152731
y[1] (closed_form) = 1.53575501434 -1.00885413905
absolute error = 1.117
relative error = 60.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4904
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.655433395648 1.28
h = 0.001 0.003
y[1] (numeric) = 1.01472701526 -0.0206123416178
y[1] (closed_form) = 1.53589067864 -1.01134888382
absolute error = 1.119
relative error = 60.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3697.1MB, alloc=44.3MB, time=42.12
x[1] = 0.656433395648 1.283
h = 0.0001 0.004
y[1] (numeric) = 1.01472703043 -0.0206123692978
y[1] (closed_form) = 1.53865937515 -1.0162154536
absolute error = 1.125
relative error = 61.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.454
Order of pole (three term test) = 34.03 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.656533395648 1.287
h = 0.00518991310064 0
y[1] (numeric) = 1.0147270464 -0.0206123984531
y[1] (closed_form) = 1.54382900512 -1.02109768207
absolute error = 1.132
relative error = 61.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4236
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661723308749 1.287
h = 0.0001 0.005
y[1] (numeric) = 1.01472705937 -0.020612422121
y[1] (closed_form) = 1.53763421272 -1.02796120045
absolute error = 1.135
relative error = 61.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8319
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661823308749 1.292
h = 0.0001 0.003
y[1] (numeric) = 1.01472707292 -0.0206124468476
y[1] (closed_form) = 1.54413223135 -1.03409490668
absolute error = 1.143
relative error = 61.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.041
Order of pole (three term test) = 41.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661923308749 1.295
h = 0.001 0.001
y[1] (numeric) = 1.0147270871 -0.0206124727281
y[1] (closed_form) = 1.54800081202 -1.03784154425
absolute error = 1.149
relative error = 61.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4937
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3741.3MB, alloc=44.3MB, time=42.61
x[1] = 0.662923308749 1.296
h = 0.001 0.003
y[1] (numeric) = 1.01472710197 -0.020612499874
y[1] (closed_form) = 1.54812553155 -1.0403812281
absolute error = 1.151
relative error = 61.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.734
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.663923308749 1.299
h = 0.0001 0.004
y[1] (numeric) = 1.01472711761 -0.0206125284131
y[1] (closed_form) = 1.55091719359 -1.04534882726
absolute error = 1.157
relative error = 61.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.428
Order of pole (three term test) = 34.01 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.664023308749 1.303
h = 0.00518991310064 0
y[1] (numeric) = 1.01472713408 -0.0206125584905
y[1] (closed_form) = 1.55615208954 -1.05034524166
absolute error = 1.163
relative error = 61.97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4222
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.66921322185 1.303
h = 0.0001 0.005
y[1] (numeric) = 1.01472714745 -0.0206125829181
y[1] (closed_form) = 1.54981087995 -1.05729681569
absolute error = 1.167
relative error = 62.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8222
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.66931322185 1.308
h = 0.0001 0.003
y[1] (numeric) = 1.01472716144 -0.0206126084479
y[1] (closed_form) = 1.55639066522 -1.06357380225
absolute error = 1.175
relative error = 62.34 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.116
Order of pole (three term test) = 40.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.66941322185 1.311
h = 0.001 0.001
y[1] (numeric) = 1.01472717607 -0.0206126351779
y[1] (closed_form) = 1.56030729939 -1.06740744661
absolute error = 1.18
relative error = 62.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4969
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3785.3MB, alloc=44.3MB, time=43.10
x[1] = 0.67041322185 1.312
h = 0.001 0.003
y[1] (numeric) = 1.01472719142 -0.0206126632227
y[1] (closed_form) = 1.56042049037 -1.0699926071
absolute error = 1.183
relative error = 62.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.732
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.67141322185 1.315
h = 0.0001 0.004
y[1] (numeric) = 1.01472720756 -0.0206126927136
y[1] (closed_form) = 1.56323448533 -1.07506289779
absolute error = 1.189
relative error = 62.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.402
Order of pole (three term test) = 33.98 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.67151322185 1.319
h = 0.00518991310064 0
y[1] (numeric) = 1.01472722457 -0.0206127237996
y[1] (closed_form) = 1.56853449616 -1.08017575163
absolute error = 1.196
relative error = 62.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.421
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.67670313495 1.319
h = 0.0001 0.005
y[1] (numeric) = 1.01472723838 -0.020612749049
y[1] (closed_form) = 1.56204393557 -1.08721525104
absolute error = 1.199
relative error = 62.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.813
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.67680313495 1.324
h = 0.0001 0.003
y[1] (numeric) = 1.01472725282 -0.0206127754392
y[1] (closed_form) = 1.56870529829 -1.09363834977
absolute error = 1.208
relative error = 63.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.381
Order of pole (three term test) = 39.59 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3829.3MB, alloc=44.3MB, time=43.59
x[1] = 0.67690313495 1.327
h = 0.001 0.001
y[1] (numeric) = 1.01472726793 -0.0206128030704
y[1] (closed_form) = 1.57266985003 -1.09756070602
absolute error = 1.213
relative error = 63.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5001
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.67790313495 1.328
h = 0.0001 0.004
y[1] (numeric) = 1.01472728378 -0.0206128320598
y[1] (closed_form) = 1.57277091546 -1.10019188706
absolute error = 1.215
relative error = 63.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.378
Order of pole (three term test) = 33.96 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.67800313495 1.332
h = 0.00518991310064 0
y[1] (numeric) = 1.01472730044 -0.0206128625418
y[1] (closed_form) = 1.57812186363 -1.1054035381
absolute error = 1.222
relative error = 63.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4197
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.683193048051 1.332
h = 0.0001 0.005
y[1] (numeric) = 1.01472731394 -0.0206128872447
y[1] (closed_form) = 1.57150445454 -1.11251204173
absolute error = 1.226
relative error = 63.66 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8041
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.683293048051 1.337
h = 0.0001 0.003
y[1] (numeric) = 1.01472732801 -0.0206129130114
y[1] (closed_form) = 1.57822962771 -1.11905911488
absolute error = 1.235
relative error = 63.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.821
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3873.5MB, alloc=44.3MB, time=44.09
x[1] = 0.683393048051 1.34
h = 0.001 0.001
y[1] (numeric) = 1.01472734271 -0.0206129399356
y[1] (closed_form) = 1.58223158084 -1.12305669715
absolute error = 1.24
relative error = 63.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5028
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.684393048051 1.341
h = 0.001 0.003
y[1] (numeric) = 1.0147273581 -0.0206129681273
y[1] (closed_form) = 1.58232125094 -1.12572586009
absolute error = 1.242
relative error = 63.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.717
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.685393048051 1.344
h = 0.0001 0.004
y[1] (numeric) = 1.01472737424 -0.0206129977142
y[1] (closed_form) = 1.58517203733 -1.13098806501
absolute error = 1.248
relative error = 64.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.356
Order of pole (three term test) = 33.94 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.685493048051 1.348
h = 0.00518991310064 0
y[1] (numeric) = 1.01472739121 -0.0206130288413
y[1] (closed_form) = 1.59058773772 -1.13632035824
absolute error = 1.256
relative error = 64.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4184
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.690682961151 1.348
h = 0.0001 0.005
y[1] (numeric) = 1.01472740497 -0.0206130540831
y[1] (closed_form) = 1.58381550392 -1.1435164392
absolute error = 1.259
relative error = 64.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7957
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.690782961151 1.353
h = 0.0001 0.003
y[1] (numeric) = 1.01472741934 -0.0206130804295
y[1] (closed_form) = 1.59062180007 -1.15021490562
absolute error = 1.268
relative error = 64.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.319
Order of pole (three term test) = 38.59 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3917.6MB, alloc=44.3MB, time=44.58
x[1] = 0.690882961151 1.356
h = 0.001 0.001
y[1] (numeric) = 1.01472743435 -0.02061310798
y[1] (closed_form) = 1.59467135596 -1.15430437878
absolute error = 1.273
relative error = 64.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5058
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.691882961151 1.357
h = 0.001 0.003
y[1] (numeric) = 1.01472745008 -0.0206131368513
y[1] (closed_form) = 1.5947477663 -1.15702055649
absolute error = 1.276
relative error = 64.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.714
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.692882961151 1.36
h = 0.0001 0.004
y[1] (numeric) = 1.0147274666 -0.0206131671777
y[1] (closed_form) = 1.59761895358 -1.16239026947
absolute error = 1.282
relative error = 64.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.335
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.692982961151 1.364
h = 0.00518991310064 0
y[1] (numeric) = 1.01472748398 -0.0206131991117
y[1] (closed_form) = 1.60309921071 -1.16784556888
absolute error = 1.289
relative error = 65.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4173
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.698172874252 1.364
h = 0.0001 0.005
y[1] (numeric) = 1.01472749809 -0.0206132250288
y[1] (closed_form) = 1.59616907364 -1.17512904246
absolute error = 1.293
relative error = 65.22 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7877
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3961.6MB, alloc=44.3MB, time=45.07
x[1] = 0.698272874252 1.369
h = 0.0001 0.003
y[1] (numeric) = 1.01472751283 -0.0206132520994
y[1] (closed_form) = 1.60305624783 -1.18198187254
absolute error = 1.302
relative error = 65.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.898
Order of pole (three term test) = 38.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.698372874252 1.372
h = 0.001 0.001
y[1] (numeric) = 1.01472752825 -0.0206132804271
y[1] (closed_form) = 1.60715323579 -1.18616502468
absolute error = 1.307
relative error = 65.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5088
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.699372874252 1.373
h = 0.001 0.003
y[1] (numeric) = 1.01472754441 -0.0206133101331
y[1] (closed_form) = 1.60721575063 -1.18892877845
absolute error = 1.31
relative error = 65.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.711
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.700372874252 1.376
h = 0.0001 0.004
y[1] (numeric) = 1.01472756139 -0.0206133413566
y[1] (closed_form) = 1.61010662571 -1.19440776108
absolute error = 1.316
relative error = 65.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.315
Order of pole (three term test) = 33.9 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.700472874252 1.38
h = 0.00518991310064 0
y[1] (numeric) = 1.01472757928 -0.0206133742554
y[1] (closed_form) = 1.61565122753 -1.19998847072
absolute error = 1.324
relative error = 65.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4161
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4005.8MB, alloc=44.3MB, time=45.56
x[1] = 0.705662787353 1.38
h = 0.0001 0.005
y[1] (numeric) = 1.0147275938 -0.0206134009689
y[1] (closed_form) = 1.60856005611 -1.20735913183
absolute error = 1.327
relative error = 65.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.78
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.705762787353 1.385
h = 0.0001 0.003
y[1] (numeric) = 1.01472760898 -0.0206134288826
y[1] (closed_form) = 1.61552784256 -1.2143693462
absolute error = 1.336
relative error = 66.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.539
Order of pole (three term test) = 37.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.705862787353 1.388
h = 0.001 0.001
y[1] (numeric) = 1.01472762486 -0.020613458103
y[1] (closed_form) = 1.61967207894 -1.21864799553
absolute error = 1.342
relative error = 66.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5118
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.706862787353 1.389
h = 0.001 0.003
y[1] (numeric) = 1.01472764151 -0.0206134887549
y[1] (closed_form) = 1.61972004834 -1.2214598928
absolute error = 1.345
relative error = 66.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.707
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.707862787353 1.392
h = 0.0001 0.004
y[1] (numeric) = 1.01472765901 -0.0206135209812
y[1] (closed_form) = 1.62262987586 -1.22704993322
absolute error = 1.351
relative error = 66.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.296
Order of pole (three term test) = 33.88 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.707962787353 1.396
h = 0.00518991310064 0
y[1] (numeric) = 1.01472767745 -0.0206135549437
y[1] (closed_form) = 1.62823859313 -1.23275849763
absolute error = 1.359
relative error = 66.52 %
Correct digits = 0
memory used=4049.8MB, alloc=44.3MB, time=46.05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.415
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.713152700453 1.396
h = 0.0001 0.005
y[1] (numeric) = 1.01472769242 -0.0206135825248
y[1] (closed_form) = 1.6209832032 -1.24021612003
absolute error = 1.362
relative error = 66.73 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7727
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.713252700453 1.401
h = 0.0001 0.003
y[1] (numeric) = 1.01472770806 -0.0206136113474
y[1] (closed_form) = 1.62803131452 -1.2473867901
absolute error = 1.372
relative error = 66.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.229
Order of pole (three term test) = 37.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.713352700453 1.404
h = 0.001 0.001
y[1] (numeric) = 1.01472772443 -0.0206136415206
y[1] (closed_form) = 1.63222260222 -1.25176278523
absolute error = 1.377
relative error = 66.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5146
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.714352700453 1.405
h = 0.0001 0.004
y[1] (numeric) = 1.01472774159 -0.0206136731719
y[1] (closed_form) = 1.6322553618 -1.2546233996
absolute error = 1.38
relative error = 67.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.278
Order of pole (three term test) = 33.86 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.714452700453 1.409
h = 0.00518991310064 0
y[1] (numeric) = 1.01472775963 -0.0206137064474
y[1] (closed_form) = 1.63791389215 -1.2604402685
absolute error = 1.388
relative error = 67.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4138
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4094.0MB, alloc=44.3MB, time=46.54
x[1] = 0.719642613554 1.409
h = 0.0001 0.005
y[1] (numeric) = 1.01472777424 -0.0206137334102
y[1] (closed_form) = 1.63051926291 -1.26796571276
absolute error = 1.391
relative error = 67.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7654
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.719742613554 1.414
h = 0.0001 0.003
y[1] (numeric) = 1.01472778947 -0.0206137615304
y[1] (closed_form) = 1.6376297747 -1.27527230302
absolute error = 1.401
relative error = 67.49 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.971
Order of pole (three term test) = 37.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.719842613554 1.417
h = 0.001 0.001
y[1] (numeric) = 1.01472780538 -0.0206137909097
y[1] (closed_form) = 1.64185752121 -1.27973071184
absolute error = 1.407
relative error = 67.57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5171
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.720842613554 1.418
h = 0.001 0.003
y[1] (numeric) = 1.01472782202 -0.0206138216679
y[1] (closed_form) = 1.64187624151 -1.2826314815
absolute error = 1.409
relative error = 67.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.689
Order of pole (three term test) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.721842613554 1.421
h = 0.0001 0.004
y[1] (numeric) = 1.01472783947 -0.0206138539437
y[1] (closed_form) = 1.64481624804 -1.28842893277
absolute error = 1.416
relative error = 67.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.261
Order of pole (three term test) = 33.85 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4137.9MB, alloc=44.3MB, time=47.04
SETTING H FOR POLE
x[1] = 0.721942613554 1.425
h = 0.00518991310064 0
y[1] (numeric) = 1.01472785783 -0.0206138878948
y[1] (closed_form) = 1.65053837714 -1.29437821079
absolute error = 1.424
relative error = 67.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4127
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.727132526655 1.425
h = 0.0001 0.005
y[1] (numeric) = 1.0147278727 -0.0206139154229
y[1] (closed_form) = 1.64297359456 -1.30199007834
absolute error = 1.427
relative error = 68.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7587
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.727232526655 1.43
h = 0.0001 0.003
y[1] (numeric) = 1.01472788822 -0.0206139441523
y[1] (closed_form) = 1.65016378323 -1.30946284635
absolute error = 1.437
relative error = 68.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.732
Order of pole (three term test) = 37.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.727332526655 1.433
h = 0.001 0.001
y[1] (numeric) = 1.01472790445 -0.020613974191
y[1] (closed_form) = 1.65443814594 -1.314022044
absolute error = 1.443
relative error = 68.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5199
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.728332526655 1.434
h = 0.001 0.003
y[1] (numeric) = 1.01472792144 -0.0206140056659
y[1] (closed_form) = 1.65444039556 -1.31697257713
absolute error = 1.446
relative error = 68.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.685
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.729332526655 1.437
h = 0.0001 0.004
y[1] (numeric) = 1.01472793928 -0.0206140387229
y[1] (closed_form) = 1.65739711526 -1.32288626066
absolute error = 1.452
relative error = 68.48 %
Correct digits = 0
memory used=4182.2MB, alloc=44.3MB, time=47.53
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 33.83 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.729432526655 1.441
h = 0.00518991310064 0
y[1] (numeric) = 1.01472795806 -0.0206140735276
y[1] (closed_form) = 1.66318256102 -1.32897050858
absolute error = 1.46
relative error = 68.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4117
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.734622439755 1.441
h = 0.0001 0.005
y[1] (numeric) = 1.01472797329 -0.0206141017712
y[1] (closed_form) = 1.65544428846 -1.33666850788
absolute error = 1.464
relative error = 68.79 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7523
Order of pole (three term test) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.734722439755 1.446
h = 0.0001 0.003
y[1] (numeric) = 1.0147279892 -0.0206141312687
y[1] (closed_form) = 1.6627138002 -1.34431067082
absolute error = 1.474
relative error = 68.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.521
Order of pole (three term test) = 36.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.734822439755 1.449
h = 0.001 0.001
y[1] (numeric) = 1.01472800584 -0.0206141621326
y[1] (closed_form) = 1.6670345408 -1.34897259319
absolute error = 1.48
relative error = 69.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5226
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.735822439755 1.45
h = 0.001 0.003
y[1] (numeric) = 1.01472802328 -0.0206141944945
y[1] (closed_form) = 1.66701961299 -1.35197348011
absolute error = 1.483
relative error = 69.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.68
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4226.3MB, alloc=44.3MB, time=48.02
x[1] = 0.736822439755 1.453
h = 0.0001 0.004
y[1] (numeric) = 1.0147280416 -0.0206142285057
y[1] (closed_form) = 1.66999221949 -1.35800528675
absolute error = 1.489
relative error = 69.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.229
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.736922439755 1.457
h = 0.00518991310064 0
y[1] (numeric) = 1.0147280609 -0.0206142643375
y[1] (closed_form) = 1.6758406801 -1.36422710748
absolute error = 1.497
relative error = 69.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4107
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.742112352856 1.457
h = 0.0001 0.005
y[1] (numeric) = 1.01472807656 -0.0206142934294
y[1] (closed_form) = 1.66792552558 -1.3720109226
absolute error = 1.501
relative error = 69.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7462
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.742212352856 1.462
h = 0.0001 0.003
y[1] (numeric) = 1.01472809292 -0.0206143238254
y[1] (closed_form) = 1.67527398185 -1.37982575054
absolute error = 1.511
relative error = 69.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.333
Order of pole (three term test) = 36.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.742312352856 1.465
h = 0.001 0.001
y[1] (numeric) = 1.01472811005 -0.0206143556414
y[1] (closed_form) = 1.67964084665 -1.38459236516
absolute error = 1.517
relative error = 69.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5253
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4270.5MB, alloc=44.3MB, time=48.51
x[1] = 0.743312352856 1.466
h = 0.001 0.003
y[1] (numeric) = 1.014728128 -0.0206143890124
y[1] (closed_form) = 1.67960801918 -1.38764420219
absolute error = 1.52
relative error = 69.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.676
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.744312352856 1.469
h = 0.0001 0.004
y[1] (numeric) = 1.01472814686 -0.0206144240939
y[1] (closed_form) = 1.68259566095 -1.39379605018
absolute error = 1.527
relative error = 69.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.215
Order of pole (three term test) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.744412352856 1.473
h = 0.00518991310064 0
y[1] (numeric) = 1.01472816673 -0.0206144610615
y[1] (closed_form) = 1.68850681425 -1.40015808926
absolute error = 1.535
relative error = 69.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4097
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.749602265957 1.473
h = 0.0001 0.005
y[1] (numeric) = 1.01472818285 -0.02061449108
y[1] (closed_form) = 1.68041132987 -1.40802737904
absolute error = 1.539
relative error = 70.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7403
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.749702265957 1.478
h = 0.0001 0.003
y[1] (numeric) = 1.0147281997 -0.0206145224471
y[1] (closed_form) = 1.68783832654 -1.41601819546
absolute error = 1.549
relative error = 70.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.165
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.749802265957 1.481
h = 0.001 0.001
y[1] (numeric) = 1.01472821733 -0.0206145552812
y[1] (closed_form) = 1.69225104598 -1.42089150186
absolute error = 1.556
relative error = 70.4 %
Correct digits = 0
memory used=4314.7MB, alloc=44.3MB, time=49.01
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5279
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.750802265957 1.482
h = 0.0001 0.004
y[1] (numeric) = 1.01472823582 -0.0206145897205
y[1] (closed_form) = 1.69219958079 -1.42399489118
absolute error = 1.558
relative error = 70.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.2
Order of pole (three term test) = 33.79 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.750902265957 1.486
h = 0.00518991310064 0
y[1] (numeric) = 1.01472825524 -0.0206146259236
y[1] (closed_form) = 1.69815904362 -1.43047552001
absolute error = 1.567
relative error = 70.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4086
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.756092179057 1.486
h = 0.0001 0.005
y[1] (numeric) = 1.01472827097 -0.020614655256
y[1] (closed_form) = 1.68991090768 -1.43841097907
absolute error = 1.57
relative error = 70.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7342
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.756192179057 1.491
h = 0.0001 0.003
y[1] (numeric) = 1.01472828736 -0.0206146858453
y[1] (closed_form) = 1.69739841831 -1.44655063715
absolute error = 1.581
relative error = 70.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.017
Order of pole (three term test) = 36.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.756292179057 1.494
h = 0.001 0.001
y[1] (numeric) = 1.01472830448 -0.0206147178016
y[1] (closed_form) = 1.70184635873 -1.45151412879
absolute error = 1.587
relative error = 70.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5301
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4358.7MB, alloc=44.3MB, time=49.50
x[1] = 0.757292179057 1.495
h = 0.001 0.003
y[1] (numeric) = 1.01472832239 -0.0206147512551
y[1] (closed_form) = 1.70177792014 -1.45465995263
absolute error = 1.59
relative error = 71.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.657
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.758292179057 1.498
h = 0.0001 0.004
y[1] (numeric) = 1.01472834117 -0.0206147863561
y[1] (closed_form) = 1.70478810216 -1.46103583159
absolute error = 1.597
relative error = 71.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.187
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.758392179057 1.502
h = 0.00518991310064 0
y[1] (numeric) = 1.01472836092 -0.0206148232756
y[1] (closed_form) = 1.71080955899 -1.46766160277
absolute error = 1.606
relative error = 71.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4077
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.763582092158 1.502
h = 0.0001 0.005
y[1] (numeric) = 1.01472837692 -0.0206148532082
y[1] (closed_form) = 1.70237467298 -1.47568177277
absolute error = 1.609
relative error = 71.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7288
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.763682092158 1.507
h = 0.0001 0.003
y[1] (numeric) = 1.01472839361 -0.0206148844447
y[1] (closed_form) = 1.70993984734 -1.484003605
absolute error = 1.62
relative error = 71.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.879
Order of pole (three term test) = 36.23 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4402.8MB, alloc=44.3MB, time=49.99
x[1] = 0.763782092158 1.51
h = 0.001 0.001
y[1] (numeric) = 1.01472841106 -0.0206149171023
y[1] (closed_form) = 1.71443306565 -1.48907750888
absolute error = 1.627
relative error = 71.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5327
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.764782092158 1.511
h = 0.001 0.003
y[1] (numeric) = 1.01472842933 -0.0206149513186
y[1] (closed_form) = 1.71434459016 -1.49227598123
absolute error = 1.629
relative error = 71.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.652
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.765782092158 1.514
h = 0.0001 0.004
y[1] (numeric) = 1.01472844851 -0.0206149872518
y[1] (closed_form) = 1.71736722156 -1.49877744518
absolute error = 1.637
relative error = 71.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.175
Order of pole (three term test) = 33.77 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.765882092158 1.518
h = 0.00518991310064 0
y[1] (numeric) = 1.0147284687 -0.0206150250816
y[1] (closed_form) = 1.72345028799 -1.50555112645
absolute error = 1.645
relative error = 71.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4068
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.771072005258 1.518
h = 0.0001 0.005
y[1] (numeric) = 1.01472848507 -0.0206150557776
y[1] (closed_form) = 1.71482504345 -1.51365558889
absolute error = 1.649
relative error = 72.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7236
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.771172005258 1.523
h = 0.0001 0.003
y[1] (numeric) = 1.01472850216 -0.0206150878342
y[1] (closed_form) = 1.7224673992 -1.52216307208
memory used=4446.9MB, alloc=44.3MB, time=50.48
absolute error = 1.66
relative error = 72.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.754
Order of pole (three term test) = 36.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.771272005258 1.526
h = 0.001 0.001
y[1] (numeric) = 1.01472852004 -0.0206151213733
y[1] (closed_form) = 1.72700557745 -1.52734947943
absolute error = 1.667
relative error = 72.29 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5351
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.772272005258 1.527
h = 0.001 0.003
y[1] (numeric) = 1.01472853878 -0.0206151565377
y[1] (closed_form) = 1.72689628075 -1.53060121844
absolute error = 1.67
relative error = 72.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.647
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.773272005258 1.53
h = 0.0001 0.004
y[1] (numeric) = 1.01472855847 -0.0206151934912
y[1] (closed_form) = 1.72993040746 -1.5372302915
absolute error = 1.677
relative error = 72.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.163
Order of pole (three term test) = 33.76 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.773372005258 1.534
h = 0.00518991310064 0
y[1] (numeric) = 1.01472857919 -0.0206152324197
y[1] (closed_form) = 1.73607467593 -1.54415469495
absolute error = 1.686
relative error = 72.55 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.406
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.778561918359 1.534
h = 0.0001 0.005
y[1] (numeric) = 1.01472859601 -0.0206152640236
y[1] (closed_form) = 1.72725540616 -1.55234300257
absolute error = 1.689
relative error = 72.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7186
Order of pole (three term test) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4491.1MB, alloc=44.3MB, time=50.98
x[1] = 0.778661918359 1.539
h = 0.0001 0.003
y[1] (numeric) = 1.01472861358 -0.020615297042
y[1] (closed_form) = 1.73497443188 -1.56103966912
absolute error = 1.7
relative error = 72.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.639
Order of pole (three term test) = 36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.778761918359 1.542
h = 0.001 0.001
y[1] (numeric) = 1.01472863197 -0.0206153316005
y[1] (closed_form) = 1.73955723415 -1.56634070443
absolute error = 1.707
relative error = 72.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5375
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.779761918359 1.543
h = 0.001 0.003
y[1] (numeric) = 1.01472865124 -0.0206153678456
y[1] (closed_form) = 1.739426315 -1.56964633393
absolute error = 1.71
relative error = 72.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.642
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.780761918359 1.546
h = 0.0001 0.004
y[1] (numeric) = 1.01472867149 -0.0206154059457
y[1] (closed_form) = 1.74247095464 -1.5764050685
absolute error = 1.718
relative error = 73.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.151
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.780861918359 1.55
h = 0.00518991310064 0
y[1] (numeric) = 1.01472869281 -0.020615446091
y[1] (closed_form) = 1.74867599371 -1.58348305099
absolute error = 1.727
relative error = 73.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4051
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4535.1MB, alloc=44.3MB, time=51.46
x[1] = 0.78605183146 1.55
h = 0.0001 0.005
y[1] (numeric) = 1.01472871012 -0.0206154786877
y[1] (closed_form) = 1.73965897314 -1.59175472679
absolute error = 1.73
relative error = 73.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7138
Order of pole (three term test) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.78615183146 1.555
h = 0.0001 0.003
y[1] (numeric) = 1.0147287282 -0.0206155127468
y[1] (closed_form) = 1.7474541274 -1.60064416529
absolute error = 1.742
relative error = 73.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.534
Order of pole (three term test) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.78625183146 1.558
h = 0.001 0.001
y[1] (numeric) = 1.01472874712 -0.0206155483964
y[1] (closed_form) = 1.75208119921 -1.60606198667
absolute error = 1.749
relative error = 73.57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5399
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.78725183146 1.559
h = 0.0001 0.004
y[1] (numeric) = 1.01472876695 -0.0206155857864
y[1] (closed_form) = 1.75192783912 -1.60942213608
absolute error = 1.752
relative error = 73.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.14
Order of pole (three term test) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.78735183146 1.563
h = 0.00518991310064 0
y[1] (numeric) = 1.01472878778 -0.0206156250886
y[1] (closed_form) = 1.7581792402 -1.61662981043
absolute error = 1.761
relative error = 73.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4041
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.79254174456 1.563
h = 0.0001 0.005
y[1] (numeric) = 1.01472880465 -0.0206156569299
y[1] (closed_form) = 1.74899508197 -1.62496544975
absolute error = 1.764
relative error = 73.91 %
Correct digits = 0
memory used=4579.3MB, alloc=44.3MB, time=51.96
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7087
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.79264174456 1.568
h = 0.0001 0.003
y[1] (numeric) = 1.01472882223 -0.0206156901338
y[1] (closed_form) = 1.75684830592 -1.63401767591
absolute error = 1.776
relative error = 74.02 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.438
Order of pole (three term test) = 35.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.79274174456 1.571
h = 0.001 0.001
y[1] (numeric) = 1.01472884059 -0.0206157248195
y[1] (closed_form) = 1.76150901623 -1.63953406675
absolute error = 1.783
relative error = 74.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5419
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.79374174456 1.572
h = 0.001 0.003
y[1] (numeric) = 1.01472885979 -0.020615761128
y[1] (closed_form) = 1.76133543219 -1.64293902974
absolute error = 1.786
relative error = 74.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.623
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.79474174456 1.575
h = 0.0001 0.004
y[1] (numeric) = 1.01472887993 -0.020615799222
y[1] (closed_form) = 1.76439381849 -1.64993957249
absolute error = 1.794
relative error = 74.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.129
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.79484174456 1.579
h = 0.00518991310064 0
y[1] (numeric) = 1.01472890109 -0.0206158392871
y[1] (closed_form) = 1.77070507863 -1.65730613826
absolute error = 1.803
relative error = 74.34 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4033
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4623.3MB, alloc=44.3MB, time=52.45
x[1] = 0.800031657661 1.579
h = 0.0001 0.005
y[1] (numeric) = 1.01472891825 -0.0206158717679
y[1] (closed_form) = 1.76131623875 -1.6657241167
absolute error = 1.807
relative error = 74.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7043
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.800131657661 1.584
h = 0.0001 0.003
y[1] (numeric) = 1.01472893614 -0.0206159056617
y[1] (closed_form) = 1.76924444713 -1.67497578763
absolute error = 1.818
relative error = 74.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.349
Order of pole (three term test) = 35.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.800231657661 1.587
h = 0.001 0.001
y[1] (numeric) = 1.01472895484 -0.0206159410956
y[1] (closed_form) = 1.77394868503 -1.68061297632
absolute error = 1.825
relative error = 74.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5442
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.801231657661 1.588
h = 0.001 0.003
y[1] (numeric) = 1.01472897441 -0.0206159782183
y[1] (closed_form) = 1.77375110995 -1.68407360245
absolute error = 1.828
relative error = 74.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.619
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.802231657661 1.591
h = 0.0001 0.004
y[1] (numeric) = 1.01472899496 -0.0206160172013
y[1] (closed_form) = 1.77681703364 -1.69120973048
absolute error = 1.836
relative error = 74.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.119
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4667.5MB, alloc=44.3MB, time=52.95
SETTING H FOR POLE
x[1] = 0.802331657661 1.595
h = 0.00518991310064 0
y[1] (numeric) = 1.01472901658 -0.0206160582393
y[1] (closed_form) = 1.78318764879 -1.69873817297
absolute error = 1.846
relative error = 74.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4025
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.807521570762 1.595
h = 0.0001 0.005
y[1] (numeric) = 1.01472903412 -0.0206160915365
y[1] (closed_form) = 1.77359023277 -1.70723792292
absolute error = 1.849
relative error = 75.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7001
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.807621570762 1.6
h = 0.0001 0.003
y[1] (numeric) = 1.01472905243 -0.0206161263077
y[1] (closed_form) = 1.78159279295 -1.71669278831
absolute error = 1.861
relative error = 75.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.267
Order of pole (three term test) = 35.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.807721570762 1.603
h = 0.001 0.001
y[1] (numeric) = 1.01472907158 -0.0206161626849
y[1] (closed_form) = 1.78634014766 -1.72245302924
absolute error = 1.869
relative error = 75.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5464
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.808721570762 1.604
h = 0.001 0.003
y[1] (numeric) = 1.01472909165 -0.0206162008227
y[1] (closed_form) = 1.78611771257 -1.72596996295
absolute error = 1.872
relative error = 75.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.614
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4711.7MB, alloc=44.3MB, time=53.44
x[1] = 0.809721570762 1.607
h = 0.0001 0.004
y[1] (numeric) = 1.01472911272 -0.0206162408985
y[1] (closed_form) = 1.7891900761 -1.73324383763
absolute error = 1.88
relative error = 75.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.11
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.809821570762 1.611
h = 0.00518991310064 0
y[1] (numeric) = 1.01472913491 -0.0206162831134
y[1] (closed_form) = 1.7956195153 -1.7409371887
absolute error = 1.889
relative error = 75.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4018
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.815011483862 1.611
h = 0.0001 0.005
y[1] (numeric) = 1.01472915292 -0.0206163173834
y[1] (closed_form) = 1.78580956735 -1.74951810891
absolute error = 1.893
relative error = 75.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.696
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.815111483862 1.616
h = 0.0001 0.003
y[1] (numeric) = 1.01472917173 -0.0206163531853
y[1] (closed_form) = 1.79388581284 -1.75917997687
absolute error = 1.905
relative error = 75.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.191
Order of pole (three term test) = 35.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.815211483862 1.619
h = 0.001 0.001
y[1] (numeric) = 1.0147291914 -0.0206163906552
y[1] (closed_form) = 1.79867585271 -1.76506555939
absolute error = 1.913
relative error = 75.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5486
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.816211483862 1.62
h = 0.001 0.003
y[1] (numeric) = 1.01472921203 -0.0206164299516
y[1] (closed_form) = 1.79842767021 -1.76863945039
absolute error = 1.916
relative error = 75.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4755.8MB, alloc=44.3MB, time=53.94
x[1] = 0.817211483862 1.623
h = 0.0001 0.004
y[1] (numeric) = 1.01472923369 -0.0206164712566
y[1] (closed_form) = 1.80150534431 -1.77605326216
absolute error = 1.924
relative error = 76.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.101
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.817311483862 1.627
h = 0.00518991310064 0
y[1] (numeric) = 1.01472925651 -0.0206165147764
y[1] (closed_form) = 1.80799304881 -1.78391460076
absolute error = 1.934
relative error = 76.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4011
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.822501396963 1.627
h = 0.0001 0.005
y[1] (numeric) = 1.01472927503 -0.0206165501111
y[1] (closed_form) = 1.79796655121 -1.79257605525
absolute error = 1.937
relative error = 76.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6921
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.822601396963 1.632
h = 0.0001 0.003
y[1] (numeric) = 1.01472929437 -0.0206165870291
y[1] (closed_form) = 1.80611578064 -1.80244879295
absolute error = 1.95
relative error = 76.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.12
Order of pole (three term test) = 35.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.822701396963 1.635
h = 0.001 0.001
y[1] (numeric) = 1.0147293146 -0.0206166256692
y[1] (closed_form) = 1.81094805252 -1.80846204169
absolute error = 1.957
relative error = 76.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5507
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4800.0MB, alloc=44.3MB, time=54.43
x[1] = 0.823701396963 1.636
h = 0.0001 0.004
y[1] (numeric) = 1.01472933581 -0.0206166661935
y[1] (closed_form) = 1.81067321637 -1.81209354491
absolute error = 1.96
relative error = 76.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.091
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.823801396963 1.64
h = 0.00518991310064 0
y[1] (numeric) = 1.01472935809 -0.0206167087879
y[1] (closed_form) = 1.81720482007 -1.82009653444
absolute error = 1.97
relative error = 76.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4002
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.828991310064 1.64
h = 0.0001 0.005
y[1] (numeric) = 1.01472937612 -0.0206167432947
y[1] (closed_form) = 1.80699557063 -1.82881910198
absolute error = 1.974
relative error = 76.79 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6876
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.829091310064 1.645
h = 0.0001 0.003
y[1] (numeric) = 1.01472939492 -0.0206167792764
y[1] (closed_form) = 1.81519977809 -1.83886964832
absolute error = 1.987
relative error = 76.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.053
Order of pole (three term test) = 35.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.829191310064 1.648
h = 0.001 0.001
y[1] (numeric) = 1.01472941455 -0.0206168168622
y[1] (closed_form) = 1.82006370702 -1.84499049309
absolute error = 1.994
relative error = 76.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5526
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4844.2MB, alloc=44.3MB, time=54.95
x[1] = 0.830191310064 1.649
h = 0.001 0.003
y[1] (numeric) = 1.01472943508 -0.0206168562044
y[1] (closed_form) = 1.81976505161 -1.84866928146
absolute error = 1.997
relative error = 77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.592
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.831191310064 1.652
h = 0.0001 0.004
y[1] (numeric) = 1.01472945661 -0.0206168974791
y[1] (closed_form) = 1.82284638363 -1.85634386805
absolute error = 2.006
relative error = 77.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.083
Order of pole (three term test) = 33.68 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.831291310064 1.656
h = 0.00518991310064 0
y[1] (numeric) = 1.01472947923 -0.0206169408871
y[1] (closed_form) = 1.82943509418 -1.86452056516
absolute error = 2.016
relative error = 77.17 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3995
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.836481223164 1.656
h = 0.0001 0.005
y[1] (numeric) = 1.01472949756 -0.0206169760761
y[1] (closed_form) = 1.81900182752 -1.87332232894
absolute error = 2.02
relative error = 77.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.684
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.836581223164 1.661
h = 0.0001 0.003
y[1] (numeric) = 1.01472951668 -0.0206170127944
y[1] (closed_form) = 1.82727756464 -1.88359092926
absolute error = 2.032
relative error = 77.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.991
Order of pole (three term test) = 35.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.836681223164 1.664
h = 0.001 0.001
y[1] (numeric) = 1.01472953666 -0.0206170511792
y[1] (closed_form) = 1.83218279247 -1.8898437576
absolute error = 2.04
relative error = 77.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5546
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4888.4MB, alloc=44.3MB, time=55.43
x[1] = 0.837681223164 1.665
h = 0.001 0.003
y[1] (numeric) = 1.01472955757 -0.0206170913915
y[1] (closed_form) = 1.83185576884 -1.89358134502
absolute error = 2.043
relative error = 77.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.838681223164 1.668
h = 0.0001 0.004
y[1] (numeric) = 1.01472957953 -0.0206171336168
y[1] (closed_form) = 1.83493899926 -1.90140218316
absolute error = 2.052
relative error = 77.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.075
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.838781223164 1.672
h = 0.00518991310064 0
y[1] (numeric) = 1.01472960262 -0.0206171780655
y[1] (closed_form) = 1.8415841739 -1.90975580159
absolute error = 2.062
relative error = 77.73 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3988
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.843971136265 1.672
h = 0.0001 0.005
y[1] (numeric) = 1.01472962135 -0.0206172141282
y[1] (closed_form) = 1.83092269478 -1.91863602038
absolute error = 2.066
relative error = 77.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6806
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.844071136265 1.677
h = 0.0001 0.003
y[1] (numeric) = 1.01472964091 -0.0206172517857
y[1] (closed_form) = 1.83926915463 -1.92912671093
absolute error = 2.079
relative error = 78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.934
Order of pole (three term test) = 35.32 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4932.6MB, alloc=44.3MB, time=55.92
x[1] = 0.844171136265 1.68
h = 0.001 0.001
y[1] (numeric) = 1.01472966136 -0.0206172911808
y[1] (closed_form) = 1.84421516321 -1.9355139485
absolute error = 2.087
relative error = 78.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5566
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.845171136265 1.681
h = 0.001 0.003
y[1] (numeric) = 1.01472968279 -0.0206173324804
y[1] (closed_form) = 1.84385881013 -1.93931100374
absolute error = 2.09
relative error = 78.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.583
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.846171136265 1.684
h = 0.0001 0.004
y[1] (numeric) = 1.01472970529 -0.0206173758765
y[1] (closed_form) = 1.84694268075 -1.94728039581
absolute error = 2.099
relative error = 78.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.067
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.846271136265 1.688
h = 0.00518991310064 0
y[1] (numeric) = 1.01472972898 -0.0206174215865
y[1] (closed_form) = 1.85364364563 -1.9558141982
absolute error = 2.109
relative error = 78.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3982
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.851461049365 1.688
h = 0.0001 0.005
y[1] (numeric) = 1.0147297482 -0.0206174586921
y[1] (closed_form) = 1.84274969434 -1.96477209176
absolute error = 2.113
relative error = 78.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6772
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4976.8MB, alloc=44.3MB, time=56.41
x[1] = 0.851561049365 1.693
h = 0.0001 0.003
y[1] (numeric) = 1.01472976828 -0.0206174974547
y[1] (closed_form) = 1.85116603092 -1.97548897015
absolute error = 2.126
relative error = 78.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.88
Order of pole (three term test) = 35.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.851661049365 1.696
h = 0.001 0.001
y[1] (numeric) = 1.01472978928 -0.0206175380213
y[1] (closed_form) = 1.85615227803 -1.98201307924
absolute error = 2.134
relative error = 78.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5586
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.852661049365 1.697
h = 0.001 0.003
y[1] (numeric) = 1.01472981129 -0.0206175805634
y[1] (closed_form) = 1.85576561418 -1.98587027591
absolute error = 2.138
relative error = 78.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.579
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.853661049365 1.7
h = 0.0001 0.004
y[1] (numeric) = 1.01472983441 -0.0206176252778
y[1] (closed_form) = 1.85884883132 -1.99399055415
absolute error = 2.146
relative error = 78.73 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.853761049365 1.704
h = 0.00518991310064 0
y[1] (numeric) = 1.01472985876 -0.0206176723873
y[1] (closed_form) = 1.86560488052 -2.00270785252
absolute error = 2.157
relative error = 78.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3975
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.858950962466 1.704
h = 0.0001 0.005
y[1] (numeric) = 1.01472987851 -0.0206177106349
y[1] (closed_form) = 1.8544741323 -2.01174260041
absolute error = 2.161
relative error = 78.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.674
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5020.9MB, alloc=44.3MB, time=56.90
x[1] = 0.859050962466 1.709
h = 0.0001 0.003
y[1] (numeric) = 1.01472989915 -0.0206177505945
y[1] (closed_form) = 1.86295945935 -2.02268982622
absolute error = 2.174
relative error = 79.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.83
Order of pole (three term test) = 35.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.859150962466 1.712
h = 0.001 0.001
y[1] (numeric) = 1.01472992073 -0.0206177924164
y[1] (closed_form) = 1.867985378 -2.02935330612
absolute error = 2.182
relative error = 79.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5605
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.860150962466 1.713
h = 0.0001 0.004
y[1] (numeric) = 1.01472994336 -0.0206178362756
y[1] (closed_form) = 1.86756740157 -2.0332713226
absolute error = 2.186
relative error = 79.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.052
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.860250962466 1.717
h = 0.00518991310064 0
y[1] (numeric) = 1.01472996712 -0.0206178823732
y[1] (closed_form) = 1.87436429332 -2.04214312911
absolute error = 2.197
relative error = 79.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3967
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.865440875567 1.717
h = 0.0001 0.005
y[1] (numeric) = 1.01472998636 -0.0206179197163
y[1] (closed_form) = 1.86303399521 -2.05123539406
absolute error = 2.201
relative error = 79.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6701
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5065.1MB, alloc=44.3MB, time=57.38
x[1] = 0.865540875567 1.722
h = 0.0001 0.003
y[1] (numeric) = 1.0147300064 -0.0206179586541
y[1] (closed_form) = 1.87157046267 -2.06237657618
absolute error = 2.214
relative error = 79.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.779
Order of pole (three term test) = 35.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.865640875567 1.725
h = 0.001 0.001
y[1] (numeric) = 1.01473002733 -0.020617999326
y[1] (closed_form) = 1.8766255981 -2.0691573514
absolute error = 2.222
relative error = 79.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5621
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.866640875567 1.726
h = 0.001 0.003
y[1] (numeric) = 1.01473004923 -0.0206180418967
y[1] (closed_form) = 1.8761798319 -2.07312520827
absolute error = 2.226
relative error = 79.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.562
Order of pole (three term test) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.867640875567 1.729
h = 0.0001 0.004
y[1] (numeric) = 1.01473007217 -0.0206180865566
y[1] (closed_form) = 1.87925517016 -2.08152644798
absolute error = 2.235
relative error = 79.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.045
Order of pole (three term test) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.867740875567 1.733
h = 0.00518991310064 0
y[1] (numeric) = 1.01473009629 -0.0206181335224
y[1] (closed_form) = 1.88610570342 -2.09058789802
absolute error = 2.246
relative error = 79.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3961
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5109.3MB, alloc=44.3MB, time=57.87
x[1] = 0.872930788667 1.733
h = 0.0001 0.005
y[1] (numeric) = 1.01473011583 -0.020618171594
y[1] (closed_form) = 1.87453057726 -2.09975532217
absolute error = 2.25
relative error = 79.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6672
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.873030788667 1.738
h = 0.0001 0.003
y[1] (numeric) = 1.01473013621 -0.0206182113186
y[1] (closed_form) = 1.88313422366 -2.11113457223
absolute error = 2.264
relative error = 80.02 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.735
Order of pole (three term test) = 35.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.873130788667 1.741
h = 0.001 0.001
y[1] (numeric) = 1.0147301575 -0.0206182528445
y[1] (closed_form) = 1.88822787784 -2.11805935583
absolute error = 2.272
relative error = 80.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.564
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.874130788667 1.742
h = 0.001 0.003
y[1] (numeric) = 1.01473017979 -0.0206182963456
y[1] (closed_form) = 1.88774890545 -2.12208925876
absolute error = 2.276
relative error = 80.12 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.559
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.875130788667 1.745
h = 0.0001 0.004
y[1] (numeric) = 1.01473020319 -0.0206183420223
y[1] (closed_form) = 1.89081969028 -2.13064809963
absolute error = 2.285
relative error = 80.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.039
Order of pole (three term test) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.875230788667 1.749
h = 0.00518991310064 0
y[1] (numeric) = 1.0147302278 -0.0206183901018
y[1] (closed_form) = 1.89772306257 -2.13990264655
absolute error = 2.296
relative error = 80.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3955
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5153.2MB, alloc=44.3MB, time=58.35
x[1] = 0.880420701768 1.749
h = 0.0001 0.005
y[1] (numeric) = 1.01473024776 -0.0206184291088
y[1] (closed_form) = 1.8858985972 -2.14914428807
absolute error = 2.3
relative error = 80.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6643
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.880520701768 1.754
h = 0.0001 0.003
y[1] (numeric) = 1.01473026859 -0.0206184698392
y[1] (closed_form) = 1.89456841497 -2.16076594296
absolute error = 2.314
relative error = 80.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.693
Order of pole (three term test) = 35.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.880620701768 1.757
h = 0.001 0.001
y[1] (numeric) = 1.01473029038 -0.0206185124473
y[1] (closed_form) = 1.89969994637 -2.16783734008
absolute error = 2.322
relative error = 80.57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5658
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.881620701768 1.758
h = 0.001 0.003
y[1] (numeric) = 1.0147303132 -0.0206185571133
y[1] (closed_form) = 1.89918670613 -2.17192997982
absolute error = 2.326
relative error = 80.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.555
Order of pole (three term test) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.882620701768 1.761
h = 0.0001 0.004
y[1] (numeric) = 1.01473033717 -0.0206186040447
y[1] (closed_form) = 1.90225149995 -2.18064886879
absolute error = 2.335
relative error = 80.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.033
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5197.3MB, alloc=44.3MB, time=58.84
SETTING H FOR POLE
x[1] = 0.882720701768 1.765
h = 0.00518991310064 0
y[1] (numeric) = 1.0147303624 -0.0206186534763
y[1] (closed_form) = 1.90920687308 -2.19010001721
absolute error = 2.347
relative error = 80.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.395
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.887910614869 1.765
h = 0.0001 0.005
y[1] (numeric) = 1.01473038287 -0.0206186936013
y[1] (closed_form) = 1.8971284897 -2.19941488936
absolute error = 2.351
relative error = 80.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6615
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.888010614869 1.77
h = 0.0001 0.003
y[1] (numeric) = 1.01473040425 -0.0206187355166
y[1] (closed_form) = 1.90586342641 -2.21128335026
absolute error = 2.365
relative error = 81.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.654
Order of pole (three term test) = 35.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.888110614869 1.773
h = 0.001 0.001
y[1] (numeric) = 1.01473042661 -0.0206187793809
y[1] (closed_form) = 1.91103216589 -2.21850400442
absolute error = 2.374
relative error = 81.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5675
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.889110614869 1.774
h = 0.001 0.003
y[1] (numeric) = 1.01473045005 -0.0206188253794
y[1] (closed_form) = 1.91048357426 -2.22266007609
absolute error = 2.377
relative error = 81.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5241.4MB, alloc=44.3MB, time=59.33
x[1] = 0.890110614869 1.777
h = 0.0001 0.004
y[1] (numeric) = 1.01473047466 -0.0206188737247
y[1] (closed_form) = 1.91354089994 -2.23154149065
absolute error = 2.387
relative error = 81.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.027
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.890210614869 1.781
h = 0.00518991310064 0
y[1] (numeric) = 1.01473050058 -0.0206189246573
y[1] (closed_form) = 1.92054739898 -2.24119279695
absolute error = 2.398
relative error = 81.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3945
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.895400527969 1.781
h = 0.0001 0.005
y[1] (numeric) = 1.01473052161 -0.0206189660072
y[1] (closed_form) = 1.9082104505 -2.25057986675
absolute error = 2.402
relative error = 81.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6589
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.895500527969 1.786
h = 0.0001 0.003
y[1] (numeric) = 1.01473054357 -0.0206190092066
y[1] (closed_form) = 1.91700940755 -2.26269959981
absolute error = 2.417
relative error = 81.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.616
Order of pole (three term test) = 35.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.895600527969 1.789
h = 0.001 0.001
y[1] (numeric) = 1.01473056654 -0.0206190544174
y[1] (closed_form) = 1.92221465767 -2.27007219328
absolute error = 2.426
relative error = 81.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5692
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.896600527969 1.79
h = 0.0001 0.004
y[1] (numeric) = 1.01473059062 -0.0206191018288
y[1] (closed_form) = 1.92162960883 -2.27429239619
absolute error = 2.429
relative error = 81.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.019
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5285.4MB, alloc=44.3MB, time=59.81
SETTING H FOR POLE
x[1] = 0.896700527969 1.794
h = 0.00518991310064 0
y[1] (numeric) = 1.0147306159 -0.0206191516578
y[1] (closed_form) = 1.92867321369 -2.28411200793
absolute error = 2.441
relative error = 81.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3937
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.90189044107 1.794
h = 0.0001 0.005
y[1] (numeric) = 1.01473063637 -0.0206191920222
y[1] (closed_form) = 1.91611867632 -2.2935521424
absolute error = 2.445
relative error = 81.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6555
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.90199044107 1.799
h = 0.0001 0.003
y[1] (numeric) = 1.0147306577 -0.0206192341089
y[1] (closed_form) = 1.9249640818 -2.30588315882
absolute error = 2.46
relative error = 81.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.577
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.90209044107 1.802
h = 0.001 0.001
y[1] (numeric) = 1.01473067997 -0.0206192780684
y[1] (closed_form) = 1.9301955839 -2.31338345054
absolute error = 2.469
relative error = 81.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5707
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.90309044107 1.803
h = 0.001 0.003
y[1] (numeric) = 1.01473070326 -0.0206193240785
y[1] (closed_form) = 1.92957836701 -2.31765612223
absolute error = 2.473
relative error = 81.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.536
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5329.5MB, alloc=44.3MB, time=60.30
x[1] = 0.90409044107 1.806
h = 0.0001 0.004
y[1] (numeric) = 1.01473072767 -0.0206193723447
y[1] (closed_form) = 1.93261466244 -2.32683993294
absolute error = 2.482
relative error = 82.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.014
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.90419044107 1.81
h = 0.00518991310064 0
y[1] (numeric) = 1.01473075332 -0.0206194231008
y[1] (closed_form) = 1.93970762485 -2.33686629777
absolute error = 2.494
relative error = 82.12 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3932
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.909380354171 1.81
h = 0.0001 0.005
y[1] (numeric) = 1.0147307741 -0.0206194642436
y[1] (closed_form) = 1.92688590028 -2.34637652475
absolute error = 2.498
relative error = 82.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.653
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.909480354171 1.815
h = 0.0001 0.003
y[1] (numeric) = 1.01473079577 -0.0206195071712
y[1] (closed_form) = 1.93579310564 -2.35896709549
absolute error = 2.513
relative error = 82.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.544
Order of pole (three term test) = 34.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.909580354171 1.818
h = 0.001 0.001
y[1] (numeric) = 1.01473081842 -0.0206195520438
y[1] (closed_form) = 1.94105971455 -2.36662429914
absolute error = 2.522
relative error = 82.4 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5724
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5373.7MB, alloc=44.3MB, time=60.79
x[1] = 0.910580354171 1.819
h = 0.001 0.003
y[1] (numeric) = 1.01473084212 -0.020619599049
y[1] (closed_form) = 1.94040395221 -2.37096236272
absolute error = 2.526
relative error = 82.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.533
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.911580354171 1.822
h = 0.0001 0.004
y[1] (numeric) = 1.01473086699 -0.0206196484032
y[1] (closed_form) = 1.94342833611 -2.38031582354
absolute error = 2.536
relative error = 82.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.009
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.911680354171 1.826
h = 0.00518991310064 0
y[1] (numeric) = 1.01473089316 -0.0206197003516
y[1] (closed_form) = 1.9505696708 -2.39055264579
absolute error = 2.548
relative error = 82.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3927
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.916870267271 1.826
h = 0.0001 0.005
y[1] (numeric) = 1.01473091438 -0.0206197424959
y[1] (closed_form) = 1.93747591651 -2.40013179321
absolute error = 2.552
relative error = 82.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6507
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.916970267271 1.831
h = 0.0001 0.003
y[1] (numeric) = 1.01473093652 -0.0206197865008
y[1] (closed_form) = 1.94644368452 -2.41298657004
absolute error = 2.567
relative error = 82.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.512
Order of pole (three term test) = 34.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.917070267271 1.834
h = 0.001 0.001
y[1] (numeric) = 1.01473095968 -0.0206198325328
y[1] (closed_form) = 1.95174461771 -2.42080347863
absolute error = 2.577
relative error = 82.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.574
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5417.9MB, alloc=44.3MB, time=61.28
x[1] = 0.918070267271 1.835
h = 0.001 0.003
y[1] (numeric) = 1.01473098394 -0.0206198807863
y[1] (closed_form) = 1.95104913907 -2.42520764411
absolute error = 2.58
relative error = 82.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.53
Order of pole (three term test) = 33.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.919070267271 1.838
h = 0.0001 0.004
y[1] (numeric) = 1.01473100941 -0.0206199314854
y[1] (closed_form) = 1.95405997413 -2.43473334968
absolute error = 2.59
relative error = 82.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.004
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.919170267271 1.842
h = 0.00518991310064 0
y[1] (numeric) = 1.01473103622 -0.0206199848832
y[1] (closed_form) = 1.96124865503 -2.44518438738
absolute error = 2.603
relative error = 83.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3922
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.924360180372 1.842
h = 0.0001 0.005
y[1] (numeric) = 1.01473105798 -0.020620028226
y[1] (closed_form) = 1.9478779576 -2.45483123172
absolute error = 2.607
relative error = 83.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6484
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.924460180372 1.847
h = 0.0001 0.003
y[1] (numeric) = 1.01473108069 -0.0206200735014
y[1] (closed_form) = 1.95690499982 -2.46795493374
absolute error = 2.622
relative error = 83.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.482
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5462.1MB, alloc=44.3MB, time=61.77
x[1] = 0.924560180372 1.85
h = 0.001 0.001
y[1] (numeric) = 1.01473110445 -0.0206201208805
y[1] (closed_form) = 1.96223944334 -2.47593438042
absolute error = 2.632
relative error = 83.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5756
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.925560180372 1.851
h = 0.001 0.003
y[1] (numeric) = 1.01473112935 -0.020620170563
y[1] (closed_form) = 1.96150305376 -2.48040536149
absolute error = 2.636
relative error = 83.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.527
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.926560180372 1.854
h = 0.0001 0.004
y[1] (numeric) = 1.0147311555 -0.0206202227784
y[1] (closed_form) = 1.96449865868 -2.49010593766
absolute error = 2.646
relative error = 83.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.999
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.926660180372 1.858
h = 0.00518991310064 0
y[1] (numeric) = 1.01473118303 -0.0206202777862
y[1] (closed_form) = 1.97173361784 -2.50077500298
absolute error = 2.658
relative error = 83.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3918
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.931850093472 1.858
h = 0.0001 0.005
y[1] (numeric) = 1.01473120537 -0.020620322443
y[1] (closed_form) = 1.95808099227 -2.51048826788
absolute error = 2.663
relative error = 83.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6462
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5506.3MB, alloc=44.3MB, time=62.26
x[1] = 0.931950093472 1.863
h = 0.0001 0.003
y[1] (numeric) = 1.01473122869 -0.0206203690957
y[1] (closed_form) = 1.96716596764 -2.52388568217
absolute error = 2.678
relative error = 83.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.454
Order of pole (three term test) = 34.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.932050093472 1.866
h = 0.001 0.001
y[1] (numeric) = 1.01473125309 -0.0206204179191
y[1] (closed_form) = 1.9725330753 -2.53203054063
absolute error = 2.688
relative error = 83.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5771
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.933050093472 1.867
h = 0.0001 0.004
y[1] (numeric) = 1.01473127866 -0.0206204691172
y[1] (closed_form) = 1.97175455595 -2.53656905453
absolute error = 2.692
relative error = 83.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9928
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.933150093472 1.871
h = 0.00518991310064 0
y[1] (numeric) = 1.01473130551 -0.0206205229241
y[1] (closed_form) = 1.9790221094 -2.54742120519
absolute error = 2.705
relative error = 83.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3911
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.938340006573 1.871
h = 0.0001 0.005
y[1] (numeric) = 1.01473132724 -0.0206205665094
y[1] (closed_form) = 1.96513255703 -2.55718210411
absolute error = 2.709
relative error = 83.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6432
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.938440006573 1.876
h = 0.0001 0.003
y[1] (numeric) = 1.01473134989 -0.0206206119531
y[1] (closed_form) = 1.97425831562 -2.57080936156
absolute error = 2.725
relative error = 84.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.423
Order of pole (three term test) = 34.84 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5550.4MB, alloc=44.3MB, time=62.75
x[1] = 0.938540006573 1.879
h = 0.001 0.001
y[1] (numeric) = 1.01473137353 -0.0206206594176
y[1] (closed_form) = 1.97964811387 -2.57909305602
absolute error = 2.734
relative error = 84.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5785
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.939540006573 1.88
h = 0.001 0.003
y[1] (numeric) = 1.01473139825 -0.0206207090945
y[1] (closed_form) = 1.97883260545 -2.58368672772
absolute error = 2.738
relative error = 84.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.512
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.940540006573 1.883
h = 0.0001 0.004
y[1] (numeric) = 1.01473142417 -0.0206207612056
y[1] (closed_form) = 1.9817922333 -2.59371240748
absolute error = 2.749
relative error = 84.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9883
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.940640006573 1.887
h = 0.00518991310064 0
y[1] (numeric) = 1.01473145139 -0.0206208160031
y[1] (closed_form) = 1.98910392594 -2.60478964901
absolute error = 2.762
relative error = 84.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3907
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.945829919674 1.887
h = 0.0001 0.005
y[1] (numeric) = 1.01473147345 -0.0206208604202
y[1] (closed_form) = 1.97492320453 -2.61461439523
absolute error = 2.766
relative error = 84.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6411
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5594.5MB, alloc=44.3MB, time=63.24
x[1] = 0.945929919674 1.892
h = 0.0001 0.003
y[1] (numeric) = 1.01473149645 -0.020620906763
y[1] (closed_form) = 1.98410421013 -2.62852423436
absolute error = 2.782
relative error = 84.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.397
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.946029919674 1.895
h = 0.001 0.001
y[1] (numeric) = 1.01473152048 -0.0206209552041
y[1] (closed_form) = 1.98952498325 -2.63697866326
absolute error = 2.792
relative error = 84.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5799
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.947029919674 1.896
h = 0.001 0.003
y[1] (numeric) = 1.01473154564 -0.0206210059458
y[1] (closed_form) = 1.9886650455 -2.64164115694
absolute error = 2.796
relative error = 84.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.51
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.948029919674 1.899
h = 0.0001 0.004
y[1] (numeric) = 1.01473157203 -0.0206210592213
y[1] (closed_form) = 1.99160439591 -2.65184924914
absolute error = 2.807
relative error = 84.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9841
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.948129919674 1.903
h = 0.00518991310064 0
y[1] (numeric) = 1.01473159979 -0.0206211152953
y[1] (closed_form) = 1.99895903431 -2.6631555484
absolute error = 2.82
relative error = 84.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3902
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5638.7MB, alloc=44.3MB, time=63.72
x[1] = 0.953319832774 1.903
h = 0.0001 0.005
y[1] (numeric) = 1.01473162231 -0.0206211607852
y[1] (closed_form) = 1.98448195429 -2.67304270698
absolute error = 2.824
relative error = 84.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6392
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.953419832774 1.908
h = 0.0001 0.003
y[1] (numeric) = 1.0147316458 -0.020621208282
y[1] (closed_form) = 1.99371670819 -2.68724010891
absolute error = 2.841
relative error = 84.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.373
Order of pole (three term test) = 34.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.953519832774 1.911
h = 0.001 0.001
y[1] (numeric) = 1.01473167037 -0.0206212579653
y[1] (closed_form) = 1.99916751339 -2.69586826156
absolute error = 2.851
relative error = 84.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5814
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.954519832774 1.912
h = 0.001 0.003
y[1] (numeric) = 1.0147316961 -0.0206213100447
y[1] (closed_form) = 1.99826185688 -2.70060030314
absolute error = 2.855
relative error = 84.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.508
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.955519832774 1.915
h = 0.0001 0.004
y[1] (numeric) = 1.01473172312 -0.0206213647618
y[1] (closed_form) = 2.00117907071 -2.7109935529
absolute error = 2.866
relative error = 85.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.98
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.955619832774 1.919
h = 0.00518991310064 0
y[1] (numeric) = 1.01473175156 -0.0206214223895
y[1] (closed_form) = 2.0085754151 -2.7225329328
absolute error = 2.879
relative error = 85.09 %
Correct digits = 0
memory used=5682.7MB, alloc=44.3MB, time=64.21
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3899
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.960809745875 1.919
h = 0.0001 0.005
y[1] (numeric) = 1.01473177463 -0.0206214691644
y[1] (closed_form) = 1.9937967127 -2.73248101024
absolute error = 2.883
relative error = 85.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6373
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.960909745875 1.924
h = 0.0001 0.003
y[1] (numeric) = 1.01473179872 -0.0206215180235
y[1] (closed_form) = 2.00308365802 -2.74697102646
absolute error = 2.9
relative error = 85.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.35
Order of pole (three term test) = 34.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.961009745875 1.927
h = 0.001 0.001
y[1] (numeric) = 1.01473182391 -0.0206215691513
y[1] (closed_form) = 2.00856351687 -2.75577593411
absolute error = 2.91
relative error = 85.34 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5828
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.962009745875 1.928
h = 0.001 0.003
y[1] (numeric) = 1.01473185031 -0.0206216227632
y[1] (closed_form) = 2.00761082637 -2.76057825245
absolute error = 2.914
relative error = 85.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.505
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.963009745875 1.931
h = 0.0001 0.004
y[1] (numeric) = 1.01473187804 -0.0206216791065
y[1] (closed_form) = 2.01050399565 -2.7711594366
absolute error = 2.925
relative error = 85.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.976
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5726.9MB, alloc=44.3MB, time=64.70
SETTING H FOR POLE
x[1] = 0.963109745875 1.935
h = 0.00518991310064 0
y[1] (numeric) = 1.01473190722 -0.020621738461
y[1] (closed_form) = 2.01794075873 -2.78293597666
absolute error = 2.939
relative error = 85.49 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3895
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.968299658976 1.935
h = 0.0001 0.005
y[1] (numeric) = 1.01473193091 -0.0206217866452
y[1] (closed_form) = 2.00285509529 -2.79294341934
absolute error = 2.943
relative error = 85.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6354
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.968399658976 1.94
h = 0.0001 0.003
y[1] (numeric) = 1.01473195563 -0.0206218369815
y[1] (closed_form) = 2.01219261545 -2.80773117234
absolute error = 2.96
relative error = 85.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.327
Order of pole (three term test) = 34.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.968499658976 1.943
h = 0.001 0.001
y[1] (numeric) = 1.0147319815 -0.0206218896585
y[1] (closed_form) = 2.01770051297 -2.81671590853
absolute error = 2.971
relative error = 85.73 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5842
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.969499658976 1.944
h = 0.0001 0.004
y[1] (numeric) = 1.01473200859 -0.020621944896
y[1] (closed_form) = 2.01669944698 -2.82158923526
absolute error = 2.975
relative error = 85.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9705
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
memory used=5771.2MB, alloc=44.3MB, time=65.19
x[1] = 0.969599658976 1.948
h = 0.00518991310064 0
y[1] (numeric) = 1.01473203705 -0.0206220029463
y[1] (closed_form) = 2.02416341425 -2.83356466576
absolute error = 2.989
relative error = 85.82 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3888
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.974789572076 1.948
h = 0.0001 0.005
y[1] (numeric) = 1.01473206009 -0.0206220499677
y[1] (closed_form) = 2.00882012875 -2.84361319996
absolute error = 2.993
relative error = 85.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6327
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.974889572076 1.953
h = 0.0001 0.003
y[1] (numeric) = 1.01473208409 -0.0206220989926
y[1] (closed_form) = 2.01819166336 -2.8586506422
absolute error = 3.01
relative error = 86.02 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.302
Order of pole (three term test) = 34.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.974989572076 1.956
h = 0.001 0.001
y[1] (numeric) = 1.01473210914 -0.0206221501962
y[1] (closed_form) = 2.02371801452 -2.86778611819
absolute error = 3.021
relative error = 86.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5854
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.975989572076 1.957
h = 0.001 0.003
y[1] (numeric) = 1.01473213534 -0.0206222037851
y[1] (closed_form) = 2.02267465846 -2.87271733766
absolute error = 3.025
relative error = 86.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.492
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.976989572076 1.96
h = 0.0001 0.004
y[1] (numeric) = 1.01473216279 -0.0206222599981
y[1] (closed_form) = 2.0255149121 -2.88364762606
absolute error = 3.036
relative error = 86.16 %
Correct digits = 0
memory used=5815.3MB, alloc=44.3MB, time=65.69
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9669
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.977089572076 1.964
h = 0.00518991310064 0
y[1] (numeric) = 1.01473219164 -0.0206223191072
y[1] (closed_form) = 2.03301673877 -2.89586776851
absolute error = 3.05
relative error = 86.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3884
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.982279485177 1.964
h = 0.0001 0.005
y[1] (numeric) = 1.014732215 -0.0206223670178
y[1] (closed_form) = 2.01735660447 -2.90597256281
absolute error = 3.055
relative error = 86.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.631
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.982379485177 1.969
h = 0.0001 0.003
y[1] (numeric) = 1.01473223937 -0.0206224170044
y[1] (closed_form) = 2.02677549991 -2.9213172242
absolute error = 3.072
relative error = 86.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.282
Order of pole (three term test) = 34.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.982479485177 1.972
h = 0.001 0.001
y[1] (numeric) = 1.01473226483 -0.0206224692528
y[1] (closed_form) = 2.03232787737 -2.93063821643
absolute error = 3.083
relative error = 86.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5867
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.983479485177 1.973
h = 0.001 0.003
y[1] (numeric) = 1.01473229147 -0.0206225239811
y[1] (closed_form) = 2.03123361714 -2.93564175493
absolute error = 3.087
relative error = 86.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.49
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5859.4MB, alloc=44.3MB, time=66.18
x[1] = 0.984479485177 1.976
h = 0.0001 0.004
y[1] (numeric) = 1.01473231943 -0.0206225814407
y[1] (closed_form) = 2.03404410947 -2.94676794324
absolute error = 3.099
relative error = 86.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9634
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.984579485177 1.98
h = 0.00518991310064 0
y[1] (numeric) = 1.01473234883 -0.0206226419168
y[1] (closed_form) = 2.04158236616 -2.95923703852
absolute error = 3.113
relative error = 86.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3881
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.989769398278 1.98
h = 0.0001 0.005
y[1] (numeric) = 1.01473237267 -0.0206226909765
y[1] (closed_form) = 2.02559983064 -2.96939635936
absolute error = 3.117
relative error = 86.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6294
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.989869398278 1.985
h = 0.0001 0.003
y[1] (numeric) = 1.01473239755 -0.0206227421994
y[1] (closed_form) = 2.03506429185 -2.98505356486
absolute error = 3.135
relative error = 86.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.263
Order of pole (three term test) = 34.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.989969398278 1.988
h = 0.001 0.001
y[1] (numeric) = 1.01473242357 -0.0206227957788
y[1] (closed_form) = 2.04064157143 -2.99456326743
absolute error = 3.146
relative error = 86.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.588
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5903.7MB, alloc=44.3MB, time=66.66
x[1] = 0.990969398278 1.989
h = 0.001 0.003
y[1] (numeric) = 1.01473245081 -0.0206228519409
y[1] (closed_form) = 2.03949498901 -2.99963986289
absolute error = 3.15
relative error = 86.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.488
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.991969398278 1.992
h = 0.0001 0.004
y[1] (numeric) = 1.01473247942 -0.0206229109456
y[1] (closed_form) = 2.04227361505 -3.01096484885
absolute error = 3.162
relative error = 86.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.96
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.992069398278 1.996
h = 0.00518991310064 0
y[1] (numeric) = 1.01473250953 -0.0206229730873
y[1] (closed_form) = 2.04984682 -3.02368719634
absolute error = 3.176
relative error = 86.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3878
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.997259311378 1.996
h = 0.0001 0.005
y[1] (numeric) = 1.01473253395 -0.0206230235247
y[1] (closed_form) = 2.03353625331 -3.0338992438
absolute error = 3.181
relative error = 87.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6278
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.997359311378 2.001
h = 0.0001 0.003
y[1] (numeric) = 1.01473255945 -0.0206230762082
y[1] (closed_form) = 2.04304441946 -3.04987439177
absolute error = 3.199
relative error = 87.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.244
Order of pole (three term test) = 34.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.997459311378 2.004
h = 0.001 0.001
y[1] (numeric) = 1.01473258612 -0.0206231313367
y[1] (closed_form) = 2.04864543671 -3.05957604245
absolute error = 3.21
relative error = 87.18 %
Correct digits = 0
memory used=5947.7MB, alloc=44.3MB, time=67.15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5892
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.998459311378 2.005
h = 0.001 0.003
y[1] (numeric) = 1.01473261407 -0.0206231891421
y[1] (closed_form) = 2.04744508611 -3.06472643487
absolute error = 3.215
relative error = 87.22 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.486
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.999459311378 2.008
h = 0.0001 0.004
y[1] (numeric) = 1.01473264341 -0.0206232498909
y[1] (closed_form) = 2.05018968689 -3.07625314834
absolute error = 3.226
relative error = 87.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9567
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 0.999559311378 2.012
h = 0.00518991310064 0
y[1] (numeric) = 1.0147326743 -0.0206233138844
y[1] (closed_form) = 2.05779630462 -3.08923310642
absolute error = 3.241
relative error = 87.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3875
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.00474922448 2.012
h = 0.0001 0.005
y[1] (numeric) = 1.01473269936 -0.0206233658333
y[1] (closed_form) = 2.04115199861 -3.09949601248
absolute error = 3.245
relative error = 87.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6263
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.00484922448 2.017
h = 0.0001 0.003
y[1] (numeric) = 1.01473272553 -0.0206234201012
y[1] (closed_form) = 2.05070194135 -3.11579457532
absolute error = 3.264
relative error = 87.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.227
Order of pole (three term test) = 34.64 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5991.8MB, alloc=44.3MB, time=67.64
x[1] = 1.00494922448 2.02
h = 0.001 0.001
y[1] (numeric) = 1.0147327529 -0.0206234768912
y[1] (closed_form) = 2.05632549058 -3.12569145594
absolute error = 3.275
relative error = 87.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5905
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.00594922448 2.021
h = 0.0001 0.004
y[1] (numeric) = 1.01473278157 -0.0206235364401
y[1] (closed_form) = 2.05506989738 -3.13091638717
absolute error = 3.28
relative error = 87.57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9519
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 1.00604922448 2.025
h = 0.00518991310064 0
y[1] (numeric) = 1.01473281168 -0.0206235990196
y[1] (closed_form) = 2.06269733706 -3.14411210842
absolute error = 3.295
relative error = 87.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3868
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01123913758 2.025
h = 0.0001 0.005
y[1] (numeric) = 1.01473283605 -0.0206236497085
y[1] (closed_form) = 2.04577329795 -3.15440830531
absolute error = 3.299
relative error = 87.75 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6239
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01133913758 2.03
h = 0.0001 0.003
y[1] (numeric) = 1.01473286144 -0.020623702556
y[1] (closed_form) = 2.05534924017 -3.17097774299
absolute error = 3.318
relative error = 87.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.206
Order of pole (three term test) = 34.63 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6036.0MB, alloc=44.3MB, time=68.14
x[1] = 1.01143913758 2.033
h = 0.001 0.001
y[1] (numeric) = 1.01473288794 -0.0206237577508
y[1] (closed_form) = 2.06098624418 -3.18103806423
absolute error = 3.329
relative error = 87.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5916
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01243913758 2.034
h = 0.001 0.003
y[1] (numeric) = 1.01473291565 -0.0206238155153
y[1] (closed_form) = 2.05968254019 -3.18632365184
absolute error = 3.334
relative error = 87.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.474
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01343913758 2.037
h = 0.0001 0.004
y[1] (numeric) = 1.01473294469 -0.0206238761069
y[1] (closed_form) = 2.06235508226 -3.1982247787
absolute error = 3.346
relative error = 87.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9489
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 1.01353913758 2.041
h = 0.00518991310064 0
y[1] (numeric) = 1.0147329752 -0.0206239398185
y[1] (closed_form) = 2.07001290099 -3.21168617122
absolute error = 3.361
relative error = 87.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3865
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01872905068 2.041
h = 0.0001 0.005
y[1] (numeric) = 1.01473299992 -0.0206239914584
y[1] (closed_form) = 2.05274455992 -3.22202951987
absolute error = 3.365
relative error = 88.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6225
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01882905068 2.046
h = 0.0001 0.003
y[1] (numeric) = 1.01473302569 -0.0206240453346
y[1] (closed_form) = 2.06235846882 -3.23893249331
absolute error = 3.385
relative error = 88.14 %
Correct digits = 0
memory used=6080.0MB, alloc=44.3MB, time=68.63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.19
Order of pole (three term test) = 34.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01892905068 2.049
h = 0.001 0.001
y[1] (numeric) = 1.01473305261 -0.0206241016475
y[1] (closed_form) = 2.06801562813 -3.24919411209
absolute error = 3.396
relative error = 88.17 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5927
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01992905068 2.05
h = 0.001 0.003
y[1] (numeric) = 1.01473308079 -0.0206241606317
y[1] (closed_form) = 2.06665390473 -3.25455556247
absolute error = 3.401
relative error = 88.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.472
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.02092905068 2.053
h = 0.0001 0.004
y[1] (numeric) = 1.01473311034 -0.020624222558
y[1] (closed_form) = 2.06928596423 -3.26666681056
absolute error = 3.413
relative error = 88.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.946
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 1.02102905068 2.057
h = 0.00518991310064 0
y[1] (numeric) = 1.01473314143 -0.0206242877335
y[1] (closed_form) = 2.07697246632 -3.28039840073
absolute error = 3.428
relative error = 88.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3862
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.02621896378 2.057
h = 0.0001 0.005
y[1] (numeric) = 1.01473316664 -0.0206243406043
y[1] (closed_form) = 2.0593538922 -3.29078682982
absolute error = 3.433
relative error = 88.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6211
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6124.3MB, alloc=44.3MB, time=69.12
x[1] = 1.02631896378 2.062
h = 0.0001 0.003
y[1] (numeric) = 1.01473319294 -0.0206243958051
y[1] (closed_form) = 2.06900363821 -3.30802902221
absolute error = 3.452
relative error = 88.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.175
Order of pole (three term test) = 34.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.02641896378 2.065
h = 0.001 0.001
y[1] (numeric) = 1.01473322044 -0.0206244535442
y[1] (closed_form) = 2.07467962412 -3.31849534578
absolute error = 3.464
relative error = 88.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5939
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.02741896378 2.066
h = 0.001 0.003
y[1] (numeric) = 1.01473324924 -0.020624514065
y[1] (closed_form) = 2.07325832404 -3.32393340429
absolute error = 3.469
relative error = 88.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.471
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.02841896378 2.069
h = 0.0001 0.004
y[1] (numeric) = 1.01473327948 -0.0206245776475
y[1] (closed_form) = 2.07584752424 -3.3362578255
absolute error = 3.481
relative error = 88.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9432
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 1.02851896378 2.073
h = 0.00518991310064 0
y[1] (numeric) = 1.01473331131 -0.0206246446087
y[1] (closed_form) = 2.08356095495 -3.35026420062
absolute error = 3.497
relative error = 88.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.386
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6168.4MB, alloc=44.3MB, time=69.61
x[1] = 1.03370887688 2.073
h = 0.0001 0.005
y[1] (numeric) = 1.01473333712 -0.0206246989565
y[1] (closed_form) = 2.06558613588 -3.36069556387
absolute error = 3.501
relative error = 88.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6198
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.03380887688 2.078
h = 0.0001 0.003
y[1] (numeric) = 1.01473336407 -0.0206247557235
y[1] (closed_form) = 2.07526951528 -3.37828273482
absolute error = 3.521
relative error = 88.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.16
Order of pole (three term test) = 34.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.03390887688 2.081
h = 0.001 0.001
y[1] (numeric) = 1.01473339226 -0.0206248151236
y[1] (closed_form) = 2.0809629538 -3.38895721584
absolute error = 3.533
relative error = 88.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.595
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.03490887688 2.082
h = 0.001 0.003
y[1] (numeric) = 1.01473342179 -0.0206248774066
y[1] (closed_form) = 2.07948048949 -3.39447262889
absolute error = 3.538
relative error = 88.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.47
Order of pole (three term test) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.03590887688 2.085
h = 0.0001 0.004
y[1] (numeric) = 1.0147334528 -0.0206249428594
y[1] (closed_form) = 2.082024394 -3.40701330747
absolute error = 3.551
relative error = 88.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9405
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
x[1] = 1.03600887688 2.089
h = 0.00518991310064 0
y[1] (numeric) = 1.01473348543 -0.0206250118064
y[1] (closed_form) = 2.08976293812 -3.42129911619
memory used=6212.4MB, alloc=44.3MB, time=70.10
absolute error = 3.567
relative error = 88.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3857
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.04119878998 2.089
h = 0.0001 0.005
y[1] (numeric) = 1.01473351191 -0.0206250677752
y[1] (closed_form) = 2.0714257807 -3.43177119054
absolute error = 3.571
relative error = 89.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6186
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.04129878998 2.094
h = 0.0001 0.003
y[1] (numeric) = 1.01473353956 -0.0206251262413
y[1] (closed_form) = 2.08114051382 -3.44970917669
absolute error = 3.591
relative error = 89.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.146
Order of pole (three term test) = 34.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.04139878998 2.097
h = 0.001 0.001
y[1] (numeric) = 1.01473356847 -0.0206251874233
y[1] (closed_form) = 2.08684998455 -3.46059531362
absolute error = 3.603
relative error = 89.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5961
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.04239878998 2.098
h = 0.001 0.003
y[1] (numeric) = 1.01473359876 -0.0206252515761
y[1] (closed_form) = 2.0853047377 -3.46618882841
absolute error = 3.608
relative error = 89.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.468
Order of pole (three term test) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 5 ) = neg ( diff ( y , x , 3 ) ) ;
Iterations = 754
Total Elapsed Time = 1 Minutes 10 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 1 Minutes 10 Seconds
> quit
memory used=6256.6MB, alloc=44.3MB, time=70.58