|\^/| 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(neg(cos(c(x))));
> end;
exact_soln_y := proc(x) return neg(cos(c(x))) end proc
> exact_soln_yp := proc(x)
> return(sin(c(x)));
> end;
exact_soln_yp := proc(x) return sin(c(x)) end proc
> exact_soln_ypp := proc(x)
> return(cos(c(x)));
> end;
exact_soln_ypp := 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_3,
> array_const_0D0,
> array_const_1,
#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_3, array_const_0D0, array_const_1,
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_3,
> array_const_0D0,
> array_const_1,
#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_3, array_const_0D0, array_const_1,
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_3,
> array_const_0D0,
> array_const_1,
#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_3, array_const_0D0, array_const_1,
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_3,
> array_const_0D0,
> array_const_1,
#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_3, array_const_0D0, array_const_1,
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_3,
> array_const_0D0,
> array_const_1,
#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_3, array_const_0D0, array_const_1,
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_3,
> array_const_0D0,
> array_const_1,
#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_3, array_const_0D0, array_const_1,
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_3,
> array_const_0D0,
> array_const_1,
#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 - 3 - 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 - 3 - 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 - 3 - 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_3, array_const_0D0, array_const_1,
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 - 13;
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 - 13;
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 - 13;
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_3,
> array_const_0D0,
> array_const_1,
#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 = 1
> array_tmp1[1] := array_y_higher[2,1];
> #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[1,4]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[1]) * (expt((glob_h) , c(3))) * c(factorial_3(0,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[3,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[4,1] := 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 = 1
> array_tmp1[2] := array_y_higher[2,2];
> #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[1,5]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[2]) * (expt((glob_h) , c(3))) * c(factorial_3(1,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[3,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[4,2] := 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 = 1
> array_tmp1[3] := array_y_higher[2,3];
> #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[1,6]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[3]) * (expt((glob_h) , c(3))) * c(factorial_3(2,5));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4 order_d = 1
> array_tmp1[4] := array_y_higher[2,4];
> #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[1,7]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[4]) * (expt((glob_h) , c(3))) * c(factorial_3(3,6));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5 order_d = 1
> array_tmp1[5] := array_y_higher[2,5];
> #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[1,8]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[5]) * (expt((glob_h) , c(3))) * c(factorial_3(4,7));
> 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);
> 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[2,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 := 3;
> 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_3, array_const_0D0, array_const_1,
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[2, 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, 4] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[1])*expt(glob_h, c(3))*c(factorial_3(0, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[3, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[4, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_y_higher[2, 2];
array_tmp2[2] := neg(array_tmp1[2]);
array_tmp3[2] := array_tmp2[2];
if not array_y_set_initial[1, 5] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[2])*expt(glob_h, c(3))*c(factorial_3(1, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[3, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[4, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_y_higher[2, 3];
array_tmp2[3] := neg(array_tmp1[3]);
array_tmp3[3] := array_tmp2[3];
if not array_y_set_initial[1, 6] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[3])*expt(glob_h, c(3))*c(factorial_3(2, 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)
end if
end if;
kkk := 4;
array_tmp1[4] := array_y_higher[2, 4];
array_tmp2[4] := neg(array_tmp1[4]);
array_tmp3[4] := array_tmp2[4];
if not array_y_set_initial[1, 7] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[4])*expt(glob_h, c(3))*c(factorial_3(3, 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)
end if
end if;
kkk := 5;
array_tmp1[5] := array_y_higher[2, 5];
array_tmp2[5] := neg(array_tmp1[5]);
array_tmp3[5] := array_tmp2[5];
if not array_y_set_initial[1, 8] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[5])*expt(glob_h, c(3))*c(factorial_3(4, 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)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
if kkk <= ATS_MAX_TERMS then
array_tmp1[kkk] := array_y_higher[2, kkk]
end if;
array_tmp2[kkk] := neg(array_tmp1[kkk]);
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 3;
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_3,
> array_const_0D0,
> array_const_1,
> #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:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(4) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(4) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(4) ,(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 <=4) 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 <=4) 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 <=4) 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_3);
> array_const_3[1] := c(3);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> 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] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/diff2postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -1.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"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,"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(neg(cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"return(sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_ypp := 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 := -1.1 + 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);
> 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 := 3;
> #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 := 4;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #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 := 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 := 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 := 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 , 3 ) = neg ( diff ( y , x , 1 ) ) ; ");
> 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,"2017-11-26T14:43:40-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"diff2")
> ;
> logitem_str(html_log_file,"diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; ")
> ;
> 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,"diff2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"diff2 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_3, array_const_0D0, array_const_1,
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 := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 4, 0 .. 41, []);
array_y_higher_work := Array(0 .. 4, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 4, 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 <= 4 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 <= 4 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 <= 4 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_3);
array_const_3[1] := c(3);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
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] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/diff2postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 3 ) = neg ( diff ( y\
, x , 1 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -1.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "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, "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(neg(cos(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "return(sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_ypp := 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,");
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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, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -1.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
array_y_init[3] := exact_soln_ypp(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 := 3;
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 := 4;
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 := 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 := 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 := 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 , 3 ) = neg ( diff ( \
y , x , 1 ) ) ; ");
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, "2017-11-26T14:43:40-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"diff2");
logitem_str(html_log_file, "diff ( y , x , 3 ) = ne\
g ( diff ( y , x , 1 ) ) ; ");
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,
"diff2 diffeq.mxt");
logitem_str(html_log_file,
"diff2 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=0.08
##############ECHO OF PROBLEM#################
##############temp/diff2postcpx.cpx#################
diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
array_y_init[2 + 1] := exact_soln_ypp(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(neg(cos(c(x))));
end;
exact_soln_yp := proc(x)
return(sin(c(x)));
end;
exact_soln_ypp := 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] = -1.1 0.1
h = 0.0001 0.005
y[1] (numeric) = -0.455865992647 -0.0892693448511
y[1] (closed_form) = -0.455865992647 -0.0892693448511
absolute error = 0
relative error = 0 %
Correct digits = 30
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3587
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0999 0.105
h = 0.0001 0.003
y[1] (numeric) = -0.456140982786 -0.0928480197157
y[1] (closed_form) = -0.456188478361 -0.0937440429529
absolute error = 0.0008973
relative error = 0.1927 %
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 = 0.4829
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0998 0.108
h = 0.001 0.001
y[1] (numeric) = -0.456423344666 -0.0964278542142
y[1] (closed_form) = -0.456423339169 -0.0964277961449
absolute error = 5.833e-08
relative error = 1.250e-05 %
Correct digits = 7
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) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0988 0.109
h = 0.001 0.003
y[1] (numeric) = -0.45671308314 -0.100008882606
y[1] (closed_form) = -0.457368857504 -0.0972745551184
absolute error = 0.002812
relative error = 0.6013 %
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 = 0.5267
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0978 0.112
h = 0.0001 0.004
y[1] (numeric) = -0.457010203998 -0.103591110093
y[1] (closed_form) = -0.458415911571 -0.0999117937484
absolute error = 0.003939
relative error = 0.8395 %
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 = 0.4203
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0977 0.116
h = 0.003 0.006
y[1] (numeric) = -0.457314724974 -0.107174555733
y[1] (closed_form) = -0.458713713382 -0.103490491823
absolute error = 0.003941
relative error = 0.838 %
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 = 0.3064
Order of pole (three term test) = 32.98 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=35.1MB, alloc=40.3MB, time=0.44
x[1] = -1.0947 0.122
h = 0.0001 0.005
y[1] (numeric) = -0.457626700189 -0.110759265376
y[1] (closed_form) = -0.46172812646 -0.108701662058
absolute error = 0.004589
relative error = 0.9673 %
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 = 0.3684
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0946 0.127
h = 0.0001 0.003
y[1] (numeric) = -0.457946312961 -0.114345288456
y[1] (closed_form) = -0.462103758786 -0.113174269605
absolute error = 0.004319
relative error = 0.9079 %
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 = 0.4937
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0945 0.13
h = 0.001 0.001
y[1] (numeric) = -0.458273618164 -0.117932708733
y[1] (closed_form) = -0.462370583784 -0.11585657196
absolute error = 0.004593
relative error = 0.9636 %
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 = 0.7786
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0935 0.131
h = 0.001 0.003
y[1] (numeric) = -0.458608621084 -0.121521560511
y[1] (closed_form) = -0.463326690963 -0.116692556635
absolute error = 0.006751
relative error = 1.413 %
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 = 0.5475
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0925 0.134
h = 0.0001 0.004
y[1] (numeric) = -0.458951327596 -0.125111848938
y[1] (closed_form) = -0.464405823931 -0.119318902776
absolute error = 0.007957
relative error = 1.659 %
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 = 0.4314
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0924 0.138
h = 0.003 0.006
y[1] (numeric) = -0.459301755726 -0.128703592917
y[1] (closed_form) = -0.464746604508 -0.122896545526
absolute error = 0.00796
relative error = 1.656 %
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 = 0.3176
Order of pole (three term test) = 32.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0894 0.144
h = 0.0001 0.005
y[1] (numeric) = -0.45965996035 -0.132296837786
y[1] (closed_form) = -0.467826123802 -0.128075855649
absolute error = 0.009193
relative error = 1.895 %
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 = 0.3786
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0893 0.149
h = 0.0001 0.003
y[1] (numeric) = -0.460026126045 -0.135891630886
y[1] (closed_form) = -0.468256117091 -0.1325483242
absolute error = 0.008883
relative error = 1.825 %
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 = 0.5053
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0892 0.152
h = 0.001 0.001
y[1] (numeric) = -0.460400308922 -0.139488055602
y[1] (closed_form) = -0.46855565349 -0.135230336414
absolute error = 0.0092
relative error = 1.886 %
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 = 0.7863
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0882 0.153
h = 0.001 0.003
y[1] (numeric) = -0.460782514712 -0.143086146298
y[1] (closed_form) = -0.469522980391 -0.136055704953
absolute error = 0.01122
relative error = 2.295 %
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 = 0.57
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=79.2MB, alloc=44.3MB, time=0.96
x[1] = -1.0872 0.156
h = 0.0001 0.004
y[1] (numeric) = -0.461172749377 -0.14668590807
y[1] (closed_form) = -0.470635296771 -0.138672104343
absolute error = 0.0124
relative error = 2.527 %
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 = 0.4431
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0871 0.16
h = 0.003 0.006
y[1] (numeric) = -0.461571031252 -0.15028735967
y[1] (closed_form) = -0.471020045855 -0.142250243422
absolute error = 0.0124
relative error = 2.521 %
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 = 0.3294
Order of pole (three term test) = 32.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0841 0.166
h = 0.0001 0.005
y[1] (numeric) = -0.461977416008 -0.153890545934
y[1] (closed_form) = -0.474167283295 -0.147399336599
absolute error = 0.01381
relative error = 2.781 %
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 = 0.3893
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.084 0.171
h = 0.0001 0.003
y[1] (numeric) = -0.462392089589 -0.157495512079
y[1] (closed_form) = -0.474652876649 -0.151873604973
absolute error = 0.01349
relative error = 2.707 %
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 = 0.5176
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0839 0.174
h = 0.001 0.001
y[1] (numeric) = -0.462815109392 -0.161102341144
y[1] (closed_form) = -0.474985886508 -0.154556479979
absolute error = 0.01382
relative error = 2.767 %
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 = 0.7886
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0829 0.175
h = 0.001 0.003
y[1] (numeric) = -0.463246481609 -0.164711067569
y[1] (closed_form) = -0.475965066647 -0.155371383089
absolute error = 0.01578
relative error = 3.152 %
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 = 0.5941
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0819 0.178
h = 0.0001 0.004
y[1] (numeric) = -0.463686212292 -0.168321696399
y[1] (closed_form) = -0.477111683761 -0.157978769192
absolute error = 0.01695
relative error = 3.372 %
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 = 0.4555
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0818 0.182
h = 0.003 0.006
y[1] (numeric) = -0.464134320098 -0.17193424624
y[1] (closed_form) = -0.477541411253 -0.161558946224
absolute error = 0.01695
relative error = 3.363 %
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 = 0.3418
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0788 0.188
h = 0.0001 0.005
y[1] (numeric) = -0.464590861535 -0.175548761429
y[1] (closed_form) = -0.480759002596 -0.166679436053
absolute error = 0.01844
relative error = 3.624 %
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 = 0.4005
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0787 0.193
h = 0.0001 0.003
y[1] (numeric) = -0.465056024021 -0.179165285038
y[1] (closed_form) = -0.481301460886 -0.171157430921
absolute error = 0.01811
relative error = 3.546 %
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 = 0.5305
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=123.4MB, alloc=44.3MB, time=1.48
x[1] = -1.0786 0.196
h = 0.001 0.001
y[1] (numeric) = -0.465529866295 -0.182783899779
y[1] (closed_form) = -0.481668721726 -0.173842314239
absolute error = 0.01845
relative error = 3.603 %
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 = 0.7856
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0776 0.197
h = 0.0001 0.004
y[1] (numeric) = -0.466012395017 -0.18640464019
y[1] (closed_form) = -0.482660391583 -0.174646895091
absolute error = 0.02038
relative error = 3.971 %
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 = 0.4671
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0775 0.201
h = 0.003 0.006
y[1] (numeric) = -0.466503613874 -0.190027518555
y[1] (closed_form) = -0.4831296106 -0.178230606046
absolute error = 0.02039
relative error = 3.959 %
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 = 0.3533
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0745 0.207
h = 0.0001 0.005
y[1] (numeric) = -0.467003576146 -0.193652576164
y[1] (closed_form) = -0.486410205349 -0.183328625956
absolute error = 0.02198
relative error = 4.229 %
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 = 0.4109
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0744 0.212
h = 0.0001 0.003
y[1] (numeric) = -0.467512470565 -0.197279854271
y[1] (closed_form) = -0.487002568981 -0.187812060825
absolute error = 0.02167
relative error = 4.151 %
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 = 0.5425
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0743 0.215
h = 0.001 0.001
y[1] (numeric) = -0.468030357028 -0.200909435345
y[1] (closed_form) = -0.487399904445 -0.190500005623
absolute error = 0.02199
relative error = 4.202 %
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 = 0.7786
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0733 0.216
h = 0.001 0.003
y[1] (numeric) = -0.468557242601 -0.20454135401
y[1] (closed_form) = -0.488402957992 -0.191295969407
absolute error = 0.02386
relative error = 4.549 %
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 = 0.6443
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0723 0.219
h = 0.0001 0.004
y[1] (numeric) = -0.469093133514 -0.208175615216
y[1] (closed_form) = -0.489616503143 -0.193889467637
absolute error = 0.02501
relative error = 4.749 %
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 = 0.4806
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0722 0.223
h = 0.003 0.006
y[1] (numeric) = -0.469638049058 -0.211812237314
y[1] (closed_form) = -0.49013261813 -0.197478072689
absolute error = 0.02501
relative error = 4.733 %
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 = 0.3666
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0692 0.229
h = 0.0001 0.005
y[1] (numeric) = -0.470192047383 -0.215451263751
y[1] (closed_form) = -0.493488521741 -0.202550445619
absolute error = 0.02663
relative error = 4.992 %
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 = 0.4229
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=167.4MB, alloc=44.3MB, time=2.00
x[1] = -1.0691 0.234
h = 0.0001 0.003
y[1] (numeric) = -0.470755318901 -0.219092733575
y[1] (closed_form) = -0.494140153412 -0.207041177571
absolute error = 0.02631
relative error = 4.91 %
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 = 0.5563
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.069 0.237
h = 0.001 0.001
y[1] (numeric) = -0.471327924949 -0.222736728981
y[1] (closed_form) = -0.494573216476 -0.209733253384
absolute error = 0.02664
relative error = 4.958 %
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 = 0.7672
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.068 0.238
h = 0.001 0.003
y[1] (numeric) = -0.471909873088 -0.226383284719
y[1] (closed_form) = -0.495589951589 -0.210519148653
absolute error = 0.0285
relative error = 5.294 %
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 = 0.6734
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.067 0.241
h = 0.0001 0.004
y[1] (numeric) = -0.472501169655 -0.230032405685
y[1] (closed_form) = -0.496841060483 -0.213106251565
absolute error = 0.02965
relative error = 5.484 %
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) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0669 0.245
h = 0.003 0.006
y[1] (numeric) = -0.473101834304 -0.2336841101
y[1] (closed_form) = -0.497405143677 -0.216701266473
absolute error = 0.02965
relative error = 5.465 %
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 = 0.3804
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0639 0.251
h = 0.0001 0.005
y[1] (numeric) = -0.473711926142 -0.237338440933
y[1] (closed_form) = -0.500839069149 -0.221749522378
absolute error = 0.03129
relative error = 5.712 %
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 = 0.4354
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0638 0.256
h = 0.0001 0.003
y[1] (numeric) = -0.474331637369 -0.240995434991
y[1] (closed_form) = -0.501551313271 -0.226249446869
absolute error = 0.03096
relative error = 5.626 %
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 = 0.5706
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0637 0.259
h = 0.001 0.001
y[1] (numeric) = -0.474961030815 -0.244655174222
y[1] (closed_form) = -0.502020929218 -0.228946780077
absolute error = 0.03129
relative error = 5.671 %
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 = 0.7527
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0627 0.26
h = 0.001 0.003
y[1] (numeric) = -0.475600114552 -0.248317693514
y[1] (closed_form) = -0.503051992735 -0.229722728017
absolute error = 0.03316
relative error = 5.996 %
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 = 0.7042
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0617 0.263
h = 0.0001 0.004
y[1] (numeric) = -0.476248895025 -0.251982997716
y[1] (closed_form) = -0.50434183914 -0.232304323351
absolute error = 0.0343
relative error = 6.177 %
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 = 0.5092
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0616 0.267
h = 0.003 0.006
y[1] (numeric) = -0.476907392269 -0.255651104918
y[1] (closed_form) = -0.504954986139 -0.23590725561
absolute error = 0.0343
relative error = 6.154 %
Correct digits = 1
memory used=211.3MB, alloc=44.3MB, time=2.50
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3946
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0586 0.273
h = 0.0001 0.005
y[1] (numeric) = -0.47757566639 -0.259322057615
y[1] (closed_form) = -0.508469676421 -0.240932895252
absolute error = 0.03595
relative error = 6.39 %
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 = 0.4483
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0585 0.278
h = 0.0001 0.003
y[1] (numeric) = -0.478253911483 -0.262995890344
y[1] (closed_form) = -0.509243907184 -0.245443897791
absolute error = 0.03562
relative error = 6.3 %
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 = 0.5853
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0584 0.281
h = 0.001 0.001
y[1] (numeric) = -0.478942191926 -0.266672684827
y[1] (closed_form) = -0.509750919189 -0.248147608649
absolute error = 0.03595
relative error = 6.341 %
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 = 0.7358
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0574 0.282
h = 0.001 0.003
y[1] (numeric) = -0.479640516316 -0.270352476106
y[1] (closed_form) = -0.510796962159 -0.24891372257
absolute error = 0.03782
relative error = 6.656 %
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 = 0.7369
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0564 0.285
h = 0.0001 0.004
y[1] (numeric) = -0.48034889121 -0.274035268982
y[1] (closed_form) = -0.51212673622 -0.251490686517
absolute error = 0.03896
relative error = 6.829 %
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 = 0.5244
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0563 0.289
h = 0.003 0.006
y[1] (numeric) = -0.481067337042 -0.277721081419
y[1] (closed_form) = -0.512790066839 -0.25510303579
absolute error = 0.03896
relative error = 6.802 %
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 = 0.4093
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0533 0.295
h = 0.0001 0.005
y[1] (numeric) = -0.481795914956 -0.281409955446
y[1] (closed_form) = -0.516388296427 -0.260107530785
absolute error = 0.04063
relative error = 7.026 %
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 = 0.4615
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0532 0.3
h = 0.0001 0.003
y[1] (numeric) = -0.482534821051 -0.285101923288
y[1] (closed_form) = -0.517225918866 -0.264631487478
absolute error = 0.04028
relative error = 6.933 %
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 = 0.6003
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0531 0.303
h = 0.001 0.001
y[1] (numeric) = -0.483284121312 -0.288797066467
y[1] (closed_form) = -0.517771188641 -0.267342690423
absolute error = 0.04062
relative error = 6.97 %
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 = 0.7175
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0521 0.304
h = 0.0001 0.004
y[1] (numeric) = -0.484043824871 -0.292495420196
y[1] (closed_form) = -0.51883286665 -0.268099075659
absolute error = 0.04249
relative error = 7.276 %
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 = 0.5384
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=255.4MB, alloc=44.3MB, time=3.02
x[1] = -1.052 0.308
h = 0.003 0.006
y[1] (numeric) = -0.484813936339 -0.296196996926
y[1] (closed_form) = -0.519540173151 -0.271721342407
absolute error = 0.04248
relative error = 7.246 %
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 = 0.4228
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.049 0.314
h = 0.0001 0.005
y[1] (numeric) = -0.485594513504 -0.299901835832
y[1] (closed_form) = -0.523212786162 -0.276709833698
absolute error = 0.04419
relative error = 7.467 %
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) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0489 0.319
h = 0.0001 0.003
y[1] (numeric) = -0.48638575422 -0.303609967181
y[1] (closed_form) = -0.524105938946 -0.281247214924
absolute error = 0.04385
relative error = 7.372 %
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 = 0.6139
Order of pole (three term test) = 32.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0488 0.322
h = 0.001 0.001
y[1] (numeric) = -0.487187725856 -0.307321472351
y[1] (closed_form) = -0.524684737195 -0.28396622506
absolute error = 0.04418
relative error = 7.405 %
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 = 0.6999
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0478 0.323
h = 0.001 0.003
y[1] (numeric) = -0.488000438002 -0.311036386708
y[1] (closed_form) = -0.525760516333 -0.28471451131
absolute error = 0.04603
relative error = 7.698 %
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 = 0.8038
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0468 0.326
h = 0.0001 0.004
y[1] (numeric) = -0.488823897439 -0.314754714964
y[1] (closed_form) = -0.527167844325 -0.287285660208
absolute error = 0.04717
relative error = 7.857 %
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 = 0.5544
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0467 0.33
h = 0.003 0.006
y[1] (numeric) = -0.489658125367 -0.318476474861
y[1] (closed_form) = -0.527927467902 -0.290920129144
absolute error = 0.04716
relative error = 7.823 %
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 = 0.4382
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0437 0.336
h = 0.0001 0.005
y[1] (numeric) = -0.490503184954 -0.322201707586
y[1] (closed_form) = -0.531688855678 -0.295890170624
absolute error = 0.04887
relative error = 8.032 %
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 = 0.4878
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0436 0.341
h = 0.0001 0.003
y[1] (numeric) = -0.491359276267 -0.325930441023
y[1] (closed_form) = -0.532648078268 -0.300443991416
absolute error = 0.04852
relative error = 7.934 %
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 = 0.6294
Order of pole (three term test) = 32.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0435 0.344
h = 0.001 0.001
y[1] (numeric) = -0.492226468387 -0.329662756393
y[1] (closed_form) = -0.533266776184 -0.303172563742
absolute error = 0.04885
relative error = 7.963 %
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 = 0.6806
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=299.5MB, alloc=44.3MB, time=3.54
x[1] = -1.0425 0.345
h = 0.001 0.003
y[1] (numeric) = -0.493104771468 -0.333398689263
y[1] (closed_form) = -0.53435942241 -0.303911303664
absolute error = 0.05071
relative error = 8.249 %
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 = 0.842
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0415 0.348
h = 0.0001 0.004
y[1] (numeric) = -0.49399419242 -0.337138244297
y[1] (closed_form) = -0.535810169939 -0.306480279953
absolute error = 0.05185
relative error = 8.4 %
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 = 0.5709
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0414 0.352
h = 0.003 0.006
y[1] (numeric) = -0.494894752882 -0.340881439121
y[1] (closed_form) = -0.536623304546 -0.310128430958
absolute error = 0.05184
relative error = 8.364 %
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 = 0.4538
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0384 0.358
h = 0.0001 0.005
y[1] (numeric) = -0.49580651719 -0.344628314468
y[1] (closed_form) = -0.54047634109 -0.31508141136
absolute error = 0.05356
relative error = 8.561 %
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 = 0.5021
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0383 0.363
h = 0.0001 0.003
y[1] (numeric) = -0.496729687731 -0.348378895797
y[1] (closed_form) = -0.541503132851 -0.319653524201
absolute error = 0.0532
relative error = 8.46 %
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 = 0.6451
Order of pole (three term test) = 32.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0382 0.366
h = 0.001 0.001
y[1] (numeric) = -0.497664335356 -0.352133264196
y[1] (closed_form) = -0.542162648862 -0.322392758442
absolute error = 0.05352
relative error = 8.485 %
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 = 0.6615
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0372 0.367
h = 0.001 0.003
y[1] (numeric) = -0.4986104708 -0.355891455445
y[1] (closed_form) = -0.543272832627 -0.323122034021
absolute error = 0.05539
relative error = 8.764 %
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 = 0.8822
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0362 0.37
h = 0.0001 0.004
y[1] (numeric) = -0.499568101105 -0.359653474163
y[1] (closed_form) = -0.544768260254 -0.325689670617
absolute error = 0.05654
relative error = 8.908 %
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 = 0.588
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0361 0.374
h = 0.003 0.006
y[1] (numeric) = -0.500537248367 -0.363419337863
y[1] (closed_form) = -0.54563612743 -0.329352977328
absolute error = 0.05652
relative error = 8.868 %
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 = 0.4698
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0331 0.38
h = 0.0001 0.005
y[1] (numeric) = -0.501517978132 -0.367189086826
y[1] (closed_form) = -0.549583724552 -0.334290256231
absolute error = 0.05825
relative error = 9.055 %
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 = 0.5168
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=343.5MB, alloc=44.3MB, time=4.05
x[1] = -1.033 0.385
h = 0.0001 0.003
y[1] (numeric) = -0.502510495218 -0.370962744042
y[1] (closed_form) = -0.550679619918 -0.338882506185
absolute error = 0.05787
relative error = 8.951 %
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 = 0.6609
Order of pole (three term test) = 32.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0329 0.388
h = 0.001 0.001
y[1] (numeric) = -0.503514872306 -0.374740390488
y[1] (closed_form) = -0.551380893553 -0.341633497412
absolute error = 0.0582
relative error = 8.973 %
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 = 0.6428
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0319 0.389
h = 0.001 0.003
y[1] (numeric) = -0.504531120725 -0.378522062175
y[1] (closed_form) = -0.552509291092 -0.342353382227
absolute error = 0.06008
relative error = 9.244 %
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 = 0.9243
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0309 0.392
h = 0.0001 0.004
y[1] (numeric) = -0.505559247655 -0.382307763674
y[1] (closed_form) = -0.554050679435 -0.344920501012
absolute error = 0.06123
relative error = 9.382 %
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 = 0.6054
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0308 0.396
h = 0.003 0.006
y[1] (numeric) = -0.506599275665 -0.386097512389
y[1] (closed_form) = -0.554974529209 -0.348600431211
absolute error = 0.06121
relative error = 9.339 %
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 = 0.486
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0278 0.402
h = 0.0001 0.005
y[1] (numeric) = -0.507651271555 -0.38989134815
y[1] (closed_form) = -0.559019638169 -0.353523338985
absolute error = 0.06294
relative error = 9.516 %
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 = 0.5318
Order of pole (three term test) = 32.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0277 0.407
h = 0.0001 0.003
y[1] (numeric) = -0.508715442688 -0.393689291435
y[1] (closed_form) = -0.56018620778 -0.358137564182
absolute error = 0.06256
relative error = 9.408 %
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 = 0.6769
Order of pole (three term test) = 32.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0276 0.41
h = 0.001 0.001
y[1] (numeric) = -0.509791863629 -0.397491423131
y[1] (closed_form) = -0.560930200343 -0.360901403084
absolute error = 0.06288
relative error = 9.427 %
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 = 0.6249
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0266 0.411
h = 0.0001 0.004
y[1] (numeric) = -0.510880546323 -0.401297779492
y[1] (closed_form) = -0.562077494011 -0.361611962183
absolute error = 0.06478
relative error = 9.692 %
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 = 0.6215
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0265 0.415
h = 0.003 0.006
y[1] (numeric) = -0.511981496444 -0.405108373254
y[1] (closed_form) = -0.563050333442 -0.36530806017
absolute error = 0.06475
relative error = 9.647 %
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 = 0.5011
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0235 0.421
h = 0.0001 0.005
y[1] (numeric) = -0.513094777242 -0.408923241573
y[1] (closed_form) = -0.567181922141 -0.370220850877
absolute error = 0.06651
relative error = 9.819 %
Correct digits = 1
memory used=387.6MB, alloc=44.3MB, time=4.56
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5456
Order of pole (three term test) = 32.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0234 0.426
h = 0.0001 0.003
y[1] (numeric) = -0.514220598287 -0.412742402797
y[1] (closed_form) = -0.568410320548 -0.374856326632
absolute error = 0.06612
relative error = 9.711 %
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 = 0.6911
Order of pole (three term test) = 32.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0233 0.429
h = 0.001 0.001
y[1] (numeric) = -0.515359035768 -0.416565937753
y[1] (closed_form) = -0.569191700425 -0.377632619505
absolute error = 0.06644
relative error = 9.726 %
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 = 0.6089
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0223 0.43
h = 0.001 0.003
y[1] (numeric) = -0.516510102149 -0.420393882913
y[1] (closed_form) = -0.570355920761 -0.378335433093
absolute error = 0.06832
relative error = 9.983 %
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 = 1.009
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0213 0.433
h = 0.0001 0.004
y[1] (numeric) = -0.517673804874 -0.424226242765
y[1] (closed_form) = -0.571986295185 -0.380904322843
absolute error = 0.06947
relative error = 10.11 %
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 = 0.6397
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0212 0.437
h = 0.003 0.006
y[1] (numeric) = -0.518850167425 -0.428063034518
y[1] (closed_form) = -0.573017504845 -0.384619776959
absolute error = 0.06944
relative error = 10.06 %
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 = 0.5177
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0182 0.443
h = 0.0001 0.005
y[1] (numeric) = -0.520039259023 -0.431904297182
y[1] (closed_form) = -0.577252192647 -0.389520630338
absolute error = 0.0712
relative error = 10.22 %
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 = 0.5612
Order of pole (three term test) = 32.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0181 0.448
h = 0.0001 0.003
y[1] (numeric) = -0.521241291992 -0.4357500465
y[1] (closed_form) = -0.578554266451 -0.394181504595
absolute error = 0.0708
relative error = 10.11 %
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 = 0.7071
Order of pole (three term test) = 32.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.018 0.451
h = 0.001 0.001
y[1] (numeric) = -0.522456344526 -0.439600363249
y[1] (closed_form) = -0.57938020149 -0.396972676036
absolute error = 0.07112
relative error = 10.13 %
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 = 0.5926
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.017 0.452
h = 0.001 0.003
y[1] (numeric) = -0.523684429732 -0.443455284175
y[1] (closed_form) = -0.580564604514 -0.397666270119
absolute error = 0.07302
relative error = 10.38 %
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 = 1.057
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.016 0.455
h = 0.0001 0.004
y[1] (numeric) = -0.524925555204 -0.44731481372
y[1] (closed_form) = -0.582244711584 -0.400236949124
absolute error = 0.07417
relative error = 10.5 %
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 = 0.6585
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=431.6MB, alloc=44.3MB, time=5.08
x[1] = -1.0159 0.459
h = 0.003 0.006
y[1] (numeric) = -0.526179744945 -0.451178968991
y[1] (closed_form) = -0.583335628135 -0.403973212833
absolute error = 0.07413
relative error = 10.45 %
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 = 0.5344
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0129 0.465
h = 0.0001 0.005
y[1] (numeric) = -0.527447069564 -0.455047788551
y[1] (closed_form) = -0.587676488696 -0.408863375691
absolute error = 0.0759
relative error = 10.6 %
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 = 0.5772
Order of pole (three term test) = 32.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0128 0.47
h = 0.0001 0.003
y[1] (numeric) = -0.528727744253 -0.458921285489
y[1] (closed_form) = -0.589053918541 -0.413551469782
absolute error = 0.07548
relative error = 10.49 %
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 = 0.7232
Order of pole (three term test) = 32.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0127 0.473
h = 0.001 0.001
y[1] (numeric) = -0.530021849271 -0.462799540552
y[1] (closed_form) = -0.589925436256 -0.416358599727
absolute error = 0.0758
relative error = 10.5 %
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 = 0.5773
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0117 0.474
h = 0.001 0.003
y[1] (numeric) = -0.531329398383 -0.466682590774
y[1] (closed_form) = -0.591130723722 -0.417043014306
absolute error = 0.07772
relative error = 10.74 %
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 = 1.107
Order of pole (three term test) = 32.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0107 0.477
h = 0.0001 0.004
y[1] (numeric) = -0.532650399342 -0.470570440551
y[1] (closed_form) = -0.592861928966 -0.419616262768
absolute error = 0.07888
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 = 0.6776
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0106 0.481
h = 0.003 0.006
y[1] (numeric) = -0.533984876687 -0.47446310689
y[1] (closed_form) = -0.594013921143 -0.423374785096
absolute error = 0.07883
relative error = 10.81 %
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 = 0.5513
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0076 0.487
h = 0.0001 0.005
y[1] (numeric) = -0.535332902463 -0.478360627909
y[1] (closed_form) = -0.598464074033 -0.428255474604
absolute error = 0.0806
relative error = 10.95 %
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 = 0.5934
Order of pole (three term test) = 32.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0075 0.492
h = 0.0001 0.003
y[1] (numeric) = -0.536694694841 -0.482263013989
y[1] (closed_form) = -0.599918581268 -0.432972604697
absolute error = 0.08017
relative error = 10.84 %
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 = 0.7392
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0074 0.495
h = 0.001 0.001
y[1] (numeric) = -0.53807033621 -0.486170345863
y[1] (closed_form) = -0.600836733676 -0.435796769727
absolute error = 0.08048
relative error = 10.84 %
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 = 0.5628
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=475.7MB, alloc=44.3MB, time=5.59
x[1] = -1.0064 0.496
h = 0.001 0.003
y[1] (numeric) = -0.539459841013 -0.49008266087
y[1] (closed_form) = -0.60206361472 -0.436472035747
absolute error = 0.08242
relative error = 11.08 %
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 = 1.158
Order of pole (three term test) = 32.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0054 0.499
h = 0.0001 0.004
y[1] (numeric) = -0.540863217162 -0.493999963361
y[1] (closed_form) = -0.603847307559 -0.439048623121
absolute error = 0.08359
relative error = 11.2 %
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 = 0.6972
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0053 0.503
h = 0.003 0.006
y[1] (numeric) = -0.542280489754 -0.497922270245
y[1] (closed_form) = -0.605061777137 -0.442830848999
absolute error = 0.08353
relative error = 11.14 %
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 = 0.5682
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0023 0.509
h = 0.0001 0.005
y[1] (numeric) = -0.543711732313 -0.501849619191
y[1] (closed_form) = -0.609624389546 -0.447703252521
absolute error = 0.0853
relative error = 11.28 %
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 = 0.6099
Order of pole (three term test) = 32.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0022 0.514
h = 0.0001 0.003
y[1] (numeric) = -0.545157166106 -0.50578201782
y[1] (closed_form) = -0.611157737431 -0.452451230046
absolute error = 0.08485
relative error = 11.16 %
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 = 0.7551
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0021 0.517
h = 0.001 0.001
y[1] (numeric) = -0.546616875716 -0.509719546869
y[1] (closed_form) = -0.612123601784 -0.455293503633
absolute error = 0.08517
relative error = 11.16 %
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 = 0.5493
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0011 0.518
h = 0.0001 0.004
y[1] (numeric) = -0.54809087628 -0.513662243996
y[1] (closed_form) = -0.613372793253 -0.455959642834
absolute error = 0.08713
relative error = 11.4 %
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 = 0.715
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.001 0.522
h = 0.003 0.006
y[1] (numeric) = -0.549579174688 -0.517610122339
y[1] (closed_form) = -0.614641884032 -0.459764193702
absolute error = 0.08706
relative error = 11.34 %
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 = 0.5839
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.998 0.528
h = 0.0001 0.005
y[1] (numeric) = -0.551081840664 -0.521563217068
y[1] (closed_form) = -0.619303951685 -0.464631784699
absolute error = 0.08886
relative error = 11.48 %
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 = 0.6251
Order of pole (three term test) = 32.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9979 0.533
h = 0.0001 0.003
y[1] (numeric) = -0.552599098145 -0.525521533456
y[1] (closed_form) = -0.620906211113 -0.469408730432
absolute error = 0.0884
relative error = 11.36 %
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 = 0.7689
Order of pole (three term test) = 32.41 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=519.5MB, alloc=44.3MB, time=6.10
x[1] = -0.9978 0.536
h = 0.001 0.001
y[1] (numeric) = -0.554131033595 -0.529485152261
y[1] (closed_form) = -0.62191379371 -0.472268034959
absolute error = 0.0887
relative error = 11.36 %
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 = 0.5374
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9968 0.537
h = 0.001 0.003
y[1] (numeric) = -0.555677662744 -0.533454111417
y[1] (closed_form) = -0.623182877953 -0.472926605891
absolute error = 0.09067
relative error = 11.59 %
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 = 1.259
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9958 0.54
h = 0.0001 0.004
y[1] (numeric) = -0.557238993816 -0.537428415194
y[1] (closed_form) = -0.62506796029 -0.475512082908
absolute error = 0.09184
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 = 0.7353
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9957 0.544
h = 0.003 0.006
y[1] (numeric) = -0.558815052972 -0.541408080324
y[1] (closed_form) = -0.626402211013 -0.479343033907
absolute error = 0.09176
relative error = 11.63 %
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 = 0.6007
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9927 0.55
h = 0.0001 0.005
y[1] (numeric) = -0.560405916581 -0.545393143653
y[1] (closed_form) = -0.631182750936 -0.484204507441
absolute error = 0.09356
relative error = 11.76 %
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 = 0.6422
Order of pole (three term test) = 32.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9926 0.555
h = 0.0001 0.003
y[1] (numeric) = -0.562011811896 -0.549383607582
y[1] (closed_form) = -0.632867226337 -0.489015682298
absolute error = 0.09308
relative error = 11.64 %
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 = 0.7846
Order of pole (three term test) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9925 0.558
h = 0.001 0.001
y[1] (numeric) = -0.5636328277 -0.553379552907
y[1] (closed_form) = -0.633924582393 -0.491895098973
absolute error = 0.09339
relative error = 11.64 %
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 = 0.5256
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9915 0.559
h = 0.001 0.003
y[1] (numeric) = -0.565268980451 -0.557381017912
y[1] (closed_form) = -0.635217332616 -0.492544567259
absolute error = 0.09538
relative error = 11.87 %
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 = 1.314
Order of pole (three term test) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9905 0.562
h = 0.0001 0.004
y[1] (numeric) = -0.566920278551 -0.56138800682
y[1] (closed_form) = -0.637159007898 -0.495135542852
absolute error = 0.09656
relative error = 11.97 %
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 = 0.756
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9904 0.566
h = 0.003 0.006
y[1] (numeric) = -0.568586748767 -0.565400536269
y[1] (closed_form) = -0.638559920327 -0.49899432943
absolute error = 0.09647
relative error = 11.9 %
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 = 0.6175
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=563.3MB, alloc=44.3MB, time=6.61
x[1] = -0.9874 0.572
h = 0.0001 0.005
y[1] (numeric) = -0.57026846909 -0.569418642655
y[1] (closed_form) = -0.643462245859 -0.503850787051
absolute error = 0.09827
relative error = 12.02 %
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 = 0.6595
Order of pole (three term test) = 32.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9873 0.577
h = 0.0001 0.003
y[1] (numeric) = -0.571965670206 -0.573442325443
y[1] (closed_form) = -0.645230827274 -0.508697991705
absolute error = 0.09777
relative error = 11.9 %
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 = 0.8001
Order of pole (three term test) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9872 0.58
h = 0.001 0.001
y[1] (numeric) = -0.573678443283 -0.577471665487
y[1] (closed_form) = -0.646339110394 -0.511598586727
absolute error = 0.09808
relative error = 11.9 %
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 = 0.5146
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9862 0.581
h = 0.001 0.003
y[1] (numeric) = -0.575406805527 -0.581506701431
y[1] (closed_form) = -0.647656267458 -0.512238946983
absolute error = 0.1001
relative error = 12.12 %
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 = 1.37
Order of pole (three term test) = 32.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9852 0.584
h = 0.0001 0.004
y[1] (numeric) = -0.577150765522 -0.585547437454
y[1] (closed_form) = -0.649656025201 -0.514836149603
absolute error = 0.1013
relative error = 12.22 %
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 = 0.777
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9851 0.588
h = 0.003 0.006
y[1] (numeric) = -0.578910350662 -0.5895938901
y[1] (closed_form) = -0.651125137981 -0.518724204351
absolute error = 0.1012
relative error = 12.15 %
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 = 0.6341
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9821 0.594
h = 0.0001 0.005
y[1] (numeric) = -0.580685640609 -0.593646095311
y[1] (closed_form) = -0.656152616815 -0.523576716918
absolute error = 0.103
relative error = 12.27 %
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 = 0.677
Order of pole (three term test) = 32.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.982 0.599
h = 0.0001 0.003
y[1] (numeric) = -0.582476869597 -0.597704049554
y[1] (closed_form) = -0.658007241035 -0.528461748858
absolute error = 0.1025
relative error = 12.14 %
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 = 0.8154
Order of pole (three term test) = 32.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9819 0.602
h = 0.001 0.001
y[1] (numeric) = -0.584284131251 -0.601767833752
y[1] (closed_form) = -0.65916763298 -0.531384586202
absolute error = 0.1028
relative error = 12.14 %
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 = 0.5044
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9809 0.603
h = 0.001 0.003
y[1] (numeric) = -0.586107443543 -0.605837486929
y[1] (closed_form) = -0.660509946751 -0.532015823198
absolute error = 0.1048
relative error = 12.36 %
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 = 1.427
Order of pole (three term test) = 32.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9799 0.606
h = 0.0001 0.004
y[1] (numeric) = -0.587946815246 -0.609913013219
y[1] (closed_form) = -0.662569304404 -0.534619970591
absolute error = 0.106
relative error = 12.45 %
Correct digits = 1
memory used=607.1MB, alloc=44.3MB, time=7.12
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7984
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9798 0.61
h = 0.003 0.006
y[1] (numeric) = -0.589802274398 -0.613994429071
y[1] (closed_form) = -0.6641081941 -0.538538723537
absolute error = 0.1059
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 = 0.6504
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9768 0.616
h = 0.0001 0.005
y[1] (numeric) = -0.591673902383 -0.61808176997
y[1] (closed_form) = -0.669264250071 -0.543388330926
absolute error = 0.1077
relative error = 12.49 %
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 = 0.6948
Order of pole (three term test) = 32.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9767 0.621
h = 0.0001 0.003
y[1] (numeric) = -0.593561937102 -0.622175029316
y[1] (closed_form) = -0.671206901937 -0.548312984817
absolute error = 0.1072
relative error = 12.36 %
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 = 0.8305
Order of pole (three term test) = 32.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9766 0.624
h = 0.001 0.001
y[1] (numeric) = -0.595466474705 -0.626274288121
y[1] (closed_form) = -0.672420613414 -0.551259126447
absolute error = 0.1075
relative error = 12.36 %
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 = 0.4949
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9756 0.625
h = 0.0001 0.004
y[1] (numeric) = -0.597387533954 -0.6303795858
y[1] (closed_form) = -0.673788843099 -0.551881214928
absolute error = 0.1095
relative error = 12.58 %
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 = 0.8178
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9755 0.629
h = 0.003 0.006
y[1] (numeric) = -0.599325123125 -0.634490936007
y[1] (closed_form) = -0.675388697822 -0.555828392706
absolute error = 0.1094
relative error = 12.51 %
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 = 0.6658
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9725 0.635
h = 0.0001 0.005
y[1] (numeric) = -0.601279319488 -0.638608371895
y[1] (closed_form) = -0.680658232946 -0.560677896405
absolute error = 0.1112
relative error = 12.61 %
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 = 0.7112
Order of pole (three term test) = 32.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9724 0.64
h = 0.0001 0.003
y[1] (numeric) = -0.603250364094 -0.642731884256
y[1] (closed_form) = -0.682677782123 -0.565639172456
absolute error = 0.1107
relative error = 12.49 %
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 = 0.8431
Order of pole (three term test) = 32.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9723 0.643
h = 0.001 0.001
y[1] (numeric) = -0.605238355257 -0.646861554184
y[1] (closed_form) = -0.683938086685 -0.568606877964
absolute error = 0.111
relative error = 12.48 %
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 = 0.4863
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9713 0.644
h = 0.001 0.003
y[1] (numeric) = -0.60724331241 -0.650997421434
y[1] (closed_form) = -0.685329348836 -0.569221384885
absolute error = 0.1131
relative error = 12.69 %
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 = 1.533
Order of pole (three term test) = 32.12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=650.9MB, alloc=44.3MB, time=7.64
x[1] = -0.9703 0.647
h = 0.0001 0.004
y[1] (numeric) = -0.609265244687 -0.655139490055
y[1] (closed_form) = -0.687503643614 -0.571841082383
absolute error = 0.1143
relative error = 12.78 %
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 = 0.8398
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9702 0.651
h = 0.003 0.006
y[1] (numeric) = -0.611304181354 -0.65928777633
y[1] (closed_form) = -0.68917629644 -0.575821633355
absolute error = 0.1142
relative error = 12.71 %
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 = 0.6816
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9672 0.657
h = 0.0001 0.005
y[1] (numeric) = -0.613360207094 -0.663442314891
y[1] (closed_form) = -0.694580923768 -0.580670125683
absolute error = 0.116
relative error = 12.81 %
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 = 0.7294
Order of pole (three term test) = 32.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9671 0.662
h = 0.0001 0.003
y[1] (numeric) = -0.615433566853 -0.667603093329
y[1] (closed_form) = -0.696692305042 -0.585674381898
absolute error = 0.1154
relative error = 12.68 %
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 = 0.8577
Order of pole (three term test) = 32.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.967 0.665
h = 0.001 0.001
y[1] (numeric) = -0.617524361609 -0.671770192855
y[1] (closed_form) = -0.698008249162 -0.588667378364
absolute error = 0.1157
relative error = 12.67 %
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 = 0.4781
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.966 0.666
h = 0.001 0.003
y[1] (numeric) = -0.619632611621 -0.675943653645
y[1] (closed_form) = -0.699426866556 -0.58927267176
absolute error = 0.1178
relative error = 12.88 %
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 = 1.589
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.965 0.669
h = 0.0001 0.004
y[1] (numeric) = -0.621758326226 -0.680123479702
y[1] (closed_form) = -0.701665256182 -0.591901327186
absolute error = 0.119
relative error = 12.97 %
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 = 0.8621
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9649 0.673
h = 0.003 0.006
y[1] (numeric) = -0.623901535392 -0.684309687216
y[1] (closed_form) = -0.703412398046 -0.595916676086
absolute error = 0.1189
relative error = 12.9 %
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 = 0.6971
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9619 0.679
h = 0.0001 0.005
y[1] (numeric) = -0.626062325673 -0.688502310346
y[1] (closed_form) = -0.708955712426 -0.600765107125
absolute error = 0.1207
relative error = 12.99 %
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 = 0.7478
Order of pole (three term test) = 32.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9618 0.684
h = 0.0001 0.003
y[1] (numeric) = -0.628240946035 -0.692701333412
y[1] (closed_form) = -0.711161055504 -0.605814132646
absolute error = 0.1201
relative error = 12.86 %
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 = 0.872
Order of pole (three term test) = 32.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=694.8MB, alloc=44.3MB, time=8.15
x[1] = -0.9617 0.687
h = 0.001 0.001
y[1] (numeric) = -0.630437500189 -0.696906837753
y[1] (closed_form) = -0.71253393717 -0.608833477745
absolute error = 0.1204
relative error = 12.85 %
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 = 0.4704
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9607 0.688
h = 0.001 0.003
y[1] (numeric) = -0.632652009245 -0.70111886398
y[1] (closed_form) = -0.713980697753 -0.609429502735
absolute error = 0.1226
relative error = 13.06 %
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 = 1.644
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9597 0.691
h = 0.0001 0.004
y[1] (numeric) = -0.63488448275 -0.705337416049
y[1] (closed_form) = -0.716284815808 -0.612067792523
absolute error = 0.1238
relative error = 13.14 %
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 = 0.8847
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9596 0.695
h = 0.003 0.006
y[1] (numeric) = -0.63713495139 -0.709562510059
y[1] (closed_form) = -0.718108179724 -0.616119362574
absolute error = 0.1236
relative error = 13.07 %
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 = 0.7121
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9566 0.701
h = 0.0001 0.005
y[1] (numeric) = -0.639403503648 -0.71379417969
y[1] (closed_form) = -0.723793839217 -0.620968650035
absolute error = 0.1255
relative error = 13.15 %
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 = 0.7663
Order of pole (three term test) = 32.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9565 0.706
h = 0.0001 0.003
y[1] (numeric) = -0.641690392627 -0.71803240591
y[1] (closed_form) = -0.726095327088 -0.626064232505
absolute error = 0.1248
relative error = 13.02 %
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 = 0.8861
Order of pole (three term test) = 32.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9564 0.709
h = 0.001 0.001
y[1] (numeric) = -0.643995724854 -0.722277270201
y[1] (closed_form) = -0.727526476395 -0.629110982644
absolute error = 0.1251
relative error = 13.01 %
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 = 0.4632
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9554 0.71
h = 0.001 0.003
y[1] (numeric) = -0.646319522305 -0.726528813624
y[1] (closed_form) = -0.729002178781 -0.629697673559
absolute error = 0.1273
relative error = 13.22 %
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 = 1.697
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9544 0.713
h = 0.0001 0.004
y[1] (numeric) = -0.648661794747 -0.730787040086
y[1] (closed_form) = -0.731373691061 -0.632346263203
absolute error = 0.1286
relative error = 13.3 %
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 = 0.9076
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9543 0.717
h = 0.003 0.006
y[1] (numeric) = -0.651022573603 -0.735051965595
y[1] (closed_form) = -0.733275053238 -0.636435476368
absolute error = 0.1284
relative error = 13.23 %
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 = 0.7266
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=738.7MB, alloc=44.3MB, time=8.66
x[1] = -0.9513 0.723
h = 0.0001 0.005
y[1] (numeric) = -0.653401949338 -0.739323623344
y[1] (closed_form) = -0.739106781008 -0.641286505155
absolute error = 0.1302
relative error = 13.31 %
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 = 0.785
Order of pole (three term test) = 32.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9512 0.728
h = 0.0001 0.003
y[1] (numeric) = -0.655800179319 -0.743601990873
y[1] (closed_form) = -0.741506651353 -0.646430431017
absolute error = 0.1296
relative error = 13.17 %
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 = 0.8998
Order of pole (three term test) = 32.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9511 0.731
h = 0.001 0.001
y[1] (numeric) = -0.658217372961 -0.747887149813
y[1] (closed_form) = -0.742997431349 -0.64950564151
absolute error = 0.1299
relative error = 13.16 %
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 = 0.4566
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9501 0.732
h = 0.0001 0.004
y[1] (numeric) = -0.660653553135 -0.752179141693
y[1] (closed_form) = -0.744502885171 -0.650082921676
absolute error = 0.1321
relative error = 13.37 %
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 = 0.9283
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.95 0.736
h = 0.003 0.006
y[1] (numeric) = -0.663108729693 -0.756477980793
y[1] (closed_form) = -0.746472370383 -0.654206633387
absolute error = 0.1319
relative error = 13.29 %
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 = 0.7406
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.947 0.742
h = 0.0001 0.005
y[1] (numeric) = -0.665582988603 -0.760783698143
y[1] (closed_form) = -0.7524328269 -0.659061645829
absolute error = 0.1338
relative error = 13.37 %
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 = 0.8023
Order of pole (three term test) = 32.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9469 0.747
h = 0.0001 0.003
y[1] (numeric) = -0.668076590887 -0.765096268357
y[1] (closed_form) = -0.754918611483 -0.664249823157
absolute error = 0.1331
relative error = 13.24 %
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 = 0.9107
Order of pole (three term test) = 32.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9468 0.75
h = 0.001 0.001
y[1] (numeric) = -0.670589648429 -0.769415773204
y[1] (closed_form) = -0.756461480776 -0.667351108769
absolute error = 0.1334
relative error = 13.22 %
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 = 0.4504
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9458 0.751
h = 0.001 0.003
y[1] (numeric) = -0.673122184864 -0.773742254612
y[1] (closed_form) = -0.757993314198 -0.667920586244
absolute error = 0.1357
relative error = 13.43 %
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 = 1.787
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9448 0.754
h = 0.0001 0.004
y[1] (numeric) = -0.67567421037 -0.778075716398
y[1] (closed_form) = -0.760494638249 -0.670590926147
absolute error = 0.1369
relative error = 13.5 %
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 = 0.9516
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=782.5MB, alloc=44.3MB, time=9.17
x[1] = -0.9447 0.758
h = 0.0001 0.004
y[1] (numeric) = -0.678245757781 -0.7824161744
y[1] (closed_form) = -0.762545528824 -0.674754946773
absolute error = 0.1367
relative error = 13.43 %
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 = 0.9582
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9446 0.762
h = 0.003 0.006
y[1] (numeric) = -0.680836866353 -0.786763688646
y[1] (closed_form) = -0.764609152323 -0.678929146707
absolute error = 0.1366
relative error = 13.35 %
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 = 0.7559
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9416 0.768
h = 0.0001 0.005
y[1] (numeric) = -0.68344763068 -0.791118301962
y[1] (closed_form) = -0.770749503364 -0.683793943564
absolute error = 0.1383
relative error = 13.43 %
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 = 0.8258
Order of pole (three term test) = 32.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9415 0.773
h = 0.0001 0.003
y[1] (numeric) = -0.686078317047 -0.795479984773
y[1] (closed_form) = -0.773353991648 -0.689046800259
absolute error = 0.1376
relative error = 13.29 %
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 = 0.9288
Order of pole (three term test) = 32.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9414 0.776
h = 0.001 0.001
y[1] (numeric) = -0.688729040891 -0.799848819056
y[1] (closed_form) = -0.774968857578 -0.692186238899
absolute error = 0.1379
relative error = 13.28 %
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 = 0.4439
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9404 0.777
h = 0.001 0.003
y[1] (numeric) = -0.691399826939 -0.804224847316
y[1] (closed_form) = -0.776537832535 -0.692745659043
absolute error = 0.1403
relative error = 13.48 %
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 = 1.853
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9394 0.78
h = 0.0001 0.004
y[1] (numeric) = -0.694090685644 -0.808608073313
y[1] (closed_form) = -0.77912371396 -0.695433057187
absolute error = 0.1416
relative error = 13.55 %
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 = 0.9819
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9393 0.784
h = 0.003 0.006
y[1] (numeric) = -0.696801650774 -0.812998512776
y[1] (closed_form) = -0.78127093062 -0.699649303584
absolute error = 0.1414
relative error = 13.48 %
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 = 0.7687
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9363 0.79
h = 0.0001 0.005
y[1] (numeric) = -0.699532819081 -0.817396197393
y[1] (closed_form) = -0.787569025062 -0.704518515155
absolute error = 0.1431
relative error = 13.55 %
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 = 0.8448
Order of pole (three term test) = 32.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9362 0.795
h = 0.0001 0.003
y[1] (numeric) = -0.702284461507 -0.821801093905
y[1] (closed_form) = -0.790278946124 -0.709825250018
absolute error = 0.1424
relative error = 13.41 %
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 = 0.9415
Order of pole (three term test) = 32.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9361 0.798
h = 0.001 0.001
y[1] (numeric) = -0.705056696619 -0.826213284481
y[1] (closed_form) = -0.79195773674 -0.712996418258
absolute error = 0.1427
relative error = 13.39 %
Correct digits = 1
memory used=826.3MB, alloc=44.3MB, time=9.68
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4387
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9351 0.799
h = 0.001 0.003
y[1] (numeric) = -0.707849550109 -0.830632812139
y[1] (closed_form) = -0.793558996047 -0.713546167123
absolute error = 0.1451
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 = 1.895
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9341 0.802
h = 0.0001 0.004
y[1] (numeric) = -0.710663032673 -0.835059680587
y[1] (closed_form) = -0.796219306664 -0.716246525923
absolute error = 0.1464
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 = 1.006
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.934 0.806
h = 0.003 0.006
y[1] (numeric) = -0.713497178902 -0.839493905462
y[1] (closed_form) = -0.798452078755 -0.720506240298
absolute error = 0.1462
relative error = 13.59 %
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 = 0.7809
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.931 0.812
h = 0.0001 0.005
y[1] (numeric) = -0.716352087761 -0.84393551793
y[1] (closed_form) = -0.804911923628 -0.72538061774
absolute error = 0.148
relative error = 13.66 %
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 = 0.8639
Order of pole (three term test) = 32.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9309 0.817
h = 0.0001 0.003
y[1] (numeric) = -0.719228034975 -0.848384480959
y[1] (closed_form) = -0.807729750609 -0.730743018231
absolute error = 0.1472
relative error = 13.52 %
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 = 0.9538
Order of pole (three term test) = 32.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9308 0.82
h = 0.001 0.001
y[1] (numeric) = -0.722125142328 -0.852840876917
y[1] (closed_form) = -0.809473970883 -0.733946970356
absolute error = 0.1475
relative error = 13.5 %
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 = 0.4337
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9298 0.821
h = 0.001 0.003
y[1] (numeric) = -0.7250434365 -0.857304749351
y[1] (closed_form) = -0.8111083728 -0.734486925143
absolute error = 0.15
relative error = 13.71 %
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 = 1.934
Order of pole (three term test) = 31.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9288 0.824
h = 0.0001 0.004
y[1] (numeric) = -0.727982928437 -0.861776101917
y[1] (closed_form) = -0.813844955278 -0.737200855322
absolute error = 0.1513
relative error = 13.78 %
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 = 1.03
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9287 0.828
h = 0.003 0.006
y[1] (numeric) = -0.730943653574 -0.866254950156
y[1] (closed_form) = -0.816165294211 -0.741505459053
absolute error = 0.1511
relative error = 13.7 %
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 = 0.7924
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9257 0.834
h = 0.0001 0.005
y[1] (numeric) = -0.73392571315 -0.870741324701
y[1] (closed_form) = -0.822790971498 -0.746385718155
absolute error = 0.1528
relative error = 13.76 %
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 = 0.883
Order of pole (three term test) = 32.99 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=870.0MB, alloc=44.3MB, time=10.20
x[1] = -0.9256 0.839
h = 0.0001 0.003
y[1] (numeric) = -0.736929387802 -0.875235184652
y[1] (closed_form) = -0.825719239715 -0.751805571949
absolute error = 0.152
relative error = 13.62 %
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 = 0.9659
Order of pole (three term test) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9255 0.842
h = 0.001 0.001
y[1] (numeric) = -0.739954802616 -0.879736612585
y[1] (closed_form) = -0.827530432094 -0.755043361929
absolute error = 0.1524
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 = 0.4291
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9245 0.843
h = 0.001 0.003
y[1] (numeric) = -0.743001985287 -0.884245652588
y[1] (closed_form) = -0.829198847711 -0.755573387645
absolute error = 0.1549
relative error = 13.81 %
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 = 1.969
Order of pole (three term test) = 31.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9235 0.846
h = 0.0001 0.004
y[1] (numeric) = -0.746070947015 -0.888762308265
y[1] (closed_form) = -0.832013582657 -0.758301488327
absolute error = 0.1562
relative error = 13.88 %
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 = 1.054
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9234 0.85
h = 0.003 0.006
y[1] (numeric) = -0.749161724106 -0.893286595059
y[1] (closed_form) = -0.834423550237 -0.762652402836
absolute error = 0.156
relative error = 13.8 %
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 = 0.8033
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9204 0.856
h = 0.0001 0.005
y[1] (numeric) = -0.752274420127 -0.897818543059
y[1] (closed_form) = -0.841219218898 -0.767539223395
absolute error = 0.1577
relative error = 13.85 %
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 = 0.9021
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9203 0.861
h = 0.0001 0.003
y[1] (numeric) = -0.755409320763 -0.902358107396
y[1] (closed_form) = -0.844260527422 -0.773018318601
absolute error = 0.1569
relative error = 13.71 %
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 = 0.9775
Order of pole (three term test) = 32.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9202 0.864
h = 0.001 0.001
y[1] (numeric) = -0.758566554489 -0.906905370862
y[1] (closed_form) = -0.846140272781 -0.776291000217
absolute error = 0.1573
relative error = 13.69 %
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 = 0.4249
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9192 0.865
h = 0.0001 0.004
y[1] (numeric) = -0.761746150039 -0.911460378102
y[1] (closed_form) = -0.847843586376 -0.776810949408
absolute error = 0.1598
relative error = 13.9 %
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 = 1.075
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9191 0.869
h = 0.003 0.006
y[1] (numeric) = -0.764948119518 -0.916023144328
y[1] (closed_form) = -0.850331819061 -0.781203967124
absolute error = 0.1596
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 = 0.8145
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=913.8MB, alloc=44.3MB, time=10.72
x[1] = -0.9161 0.875
h = 0.0001 0.005
y[1] (numeric) = -0.76817256143 -0.920593697679
y[1] (closed_form) = -0.857277112802 -0.786099045781
absolute error = 0.1613
relative error = 13.87 %
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 = 0.9201
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.916 0.88
h = 0.0001 0.003
y[1] (numeric) = -0.771419765774 -0.925171989897
y[1] (closed_form) = -0.860417119095 -0.791631956261
absolute error = 0.1605
relative error = 13.73 %
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 = 0.9861
Order of pole (three term test) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9159 0.883
h = 0.001 0.001
y[1] (numeric) = -0.774689863916 -0.92975810396
y[1] (closed_form) = -0.862356735837 -0.794936358169
absolute error = 0.1608
relative error = 13.71 %
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 = 0.4207
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9149 0.884
h = 0.001 0.003
y[1] (numeric) = -0.777982885482 -0.934352084988
y[1] (closed_form) = -0.86409092956 -0.795447936323
absolute error = 0.1634
relative error = 13.92 %
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 = 2.016
Order of pole (three term test) = 31.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9139 0.887
h = 0.0001 0.004
y[1] (numeric) = -0.781298842156 -0.938953936485
y[1] (closed_form) = -0.867056042333 -0.798204944838
absolute error = 0.1648
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 = 1.1
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9138 0.891
h = 0.003 0.006
y[1] (numeric) = -0.7846377719 -0.94356367371
y[1] (closed_form) = -0.869637861758 -0.802646944987
absolute error = 0.1646
relative error = 13.91 %
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 = 0.8242
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9108 0.897
h = 0.0001 0.005
y[1] (numeric) = -0.787999782719 -0.948181325716
y[1] (closed_form) = -0.876761090612 -0.807549803761
absolute error = 0.1663
relative error = 13.95 %
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 = 0.9392
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9107 0.902
h = 0.0001 0.003
y[1] (numeric) = -0.791385169913 -0.952806840083
y[1] (closed_form) = -0.88001912734 -0.813145317608
absolute error = 0.1654
relative error = 13.81 %
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 = 0.9972
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9106 0.905
h = 0.001 0.001
y[1] (numeric) = -0.794794068407 -0.957440300017
y[1] (closed_form) = -0.882030331741 -0.816486591814
absolute error = 0.1658
relative error = 13.79 %
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 = 0.417
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9096 0.906
h = 0.001 0.003
y[1] (numeric) = -0.798226508918 -0.962081751223
y[1] (closed_form) = -0.883801107378 -0.816987795884
absolute error = 0.1684
relative error = 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 = 2.04
Order of pole (three term test) = 30.97 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=957.7MB, alloc=44.3MB, time=11.23
x[1] = -0.9086 0.909
h = 0.0001 0.004
y[1] (numeric) = -0.801682503406 -0.966731197149
y[1] (closed_form) = -0.886849964437 -0.81976064726
absolute error = 0.1699
relative error = 14.07 %
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 = 1.124
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9085 0.913
h = 0.003 0.006
y[1] (numeric) = -0.805162090768 -0.971388652948
y[1] (closed_form) = -0.889527583664 -0.824253052925
absolute error = 0.1696
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 = 0.8332
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9055 0.919
h = 0.0001 0.005
y[1] (numeric) = -0.808665381522 -0.97605414709
y[1] (closed_form) = -0.896833138708 -0.829164265877
absolute error = 0.1713
relative error = 14.03 %
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 = 0.9582
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9054 0.924
h = 0.0001 0.003
y[1] (numeric) = -0.812192676404 -0.98072762288
y[1] (closed_form) = -0.900211996257 -0.834824174382
absolute error = 0.1704
relative error = 13.88 %
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 = 1.008
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9053 0.927
h = 0.001 0.001
y[1] (numeric) = -0.815744113989 -0.985409163759
y[1] (closed_form) = -0.902296484517 -0.8382033752
absolute error = 0.1708
relative error = 13.87 %
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 = 0.4135
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9043 0.928
h = 0.001 0.003
y[1] (numeric) = -0.819319726115 -0.990098816032
y[1] (closed_form) = -0.904104766295 -0.838694020721
absolute error = 0.1735
relative error = 14.07 %
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 = 2.06
Order of pole (three term test) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9033 0.931
h = 0.0001 0.004
y[1] (numeric) = -0.822919525024 -0.994796583087
y[1] (closed_form) = -0.907239404359 -0.841483268116
absolute error = 0.175
relative error = 14.14 %
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 = 1.149
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9032 0.935
h = 0.003 0.006
y[1] (numeric) = -0.826543550573 -0.999502479971
y[1] (closed_form) = -0.910015091886 -0.846027503019
absolute error = 0.1747
relative error = 14.06 %
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 = 0.8415
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9002 0.941
h = 0.0001 0.005
y[1] (numeric) = -0.830191915855 -1.00421653455
y[1] (closed_form) = -0.917507449269 -0.850947605498
absolute error = 0.1764
relative error = 14.1 %
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 = 0.9772
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9001 0.946
h = 0.0001 0.003
y[1] (numeric) = -0.833864927183 -1.00893868575
y[1] (closed_form) = -0.921009988129 -0.856673701133
absolute error = 0.1754
relative error = 13.95 %
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 = 1.018
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1001.6MB, alloc=44.3MB, time=11.74
x[1] = -0.9 0.949
h = 0.001 0.001
y[1] (numeric) = -0.837562726873 -1.01366901724
y[1] (closed_form) = -0.923169498702 -0.860091883079
absolute error = 0.1758
relative error = 13.94 %
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 = 0.4103
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.899 0.95
h = 0.001 0.003
y[1] (numeric) = -0.841285347915 -1.01840757595
y[1] (closed_form) = -0.925016225485 -0.860571772023
absolute error = 0.1787
relative error = 14.14 %
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 = 2.077
Order of pole (three term test) = 30.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.898 0.953
h = 0.0001 0.004
y[1] (numeric) = -0.845032802839 -1.0231543652
y[1] (closed_form) = -0.92823872421 -0.863377956065
absolute error = 0.1801
relative error = 14.21 %
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 = 1.174
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8979 0.957
h = 0.003 0.006
y[1] (numeric) = -0.848805132487 -1.02790939993
y[1] (closed_form) = -0.931114805333 -0.867975444687
absolute error = 0.1799
relative error = 14.13 %
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 = 0.8492
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8949 0.963
h = 0.0001 0.005
y[1] (numeric) = -0.852602452592 -1.03267270738
y[1] (closed_form) = -0.938798528447 -0.87290493253
absolute error = 0.1815
relative error = 14.16 %
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 = 0.996
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8948 0.968
h = 0.0001 0.003
y[1] (numeric) = -0.856425075183 -1.03744422199
y[1] (closed_form) = -0.942427680931 -0.878699009097
absolute error = 0.1805
relative error = 14.01 %
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 = 1.028
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8947 0.971
h = 0.001 0.001
y[1] (numeric) = -0.860273146414 -1.04222402765
y[1] (closed_form) = -0.944663995568 -0.882157226962
absolute error = 0.181
relative error = 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 = 0.4073
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8937 0.972
h = 0.0001 0.004
y[1] (numeric) = -0.864146700456 -1.04701217193
y[1] (closed_form) = -0.94655012124 -0.882626147432
absolute error = 0.1839
relative error = 14.21 %
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 = 1.195
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8936 0.976
h = 0.003 0.006
y[1] (numeric) = -0.868045751498 -1.05180867091
y[1] (closed_form) = -0.949513866784 -0.887271851087
absolute error = 0.1836
relative error = 14.13 %
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 = 0.8579
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8906 0.982
h = 0.0001 0.005
y[1] (numeric) = -0.871970409675 -1.05661355006
y[1] (closed_form) = -0.957365914525 -0.892212138986
absolute error = 0.1853
relative error = 14.16 %
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 = 1.014
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8905 0.987
h = 0.0001 0.003
y[1] (numeric) = -0.875920991889 -1.06142673995
y[1] (closed_form) = -0.961105617155 -0.89806772594
absolute error = 0.1842
relative error = 14.01 %
Correct digits = 1
memory used=1045.5MB, alloc=44.3MB, time=12.26
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.035
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8904 0.99
h = 0.001 0.001
y[1] (numeric) = -0.879897647573 -1.06624832471
y[1] (closed_form) = -0.963409008772 -0.901562194892
absolute error = 0.1847
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 = 0.4042
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8894 0.991
h = 0.001 0.003
y[1] (numeric) = -0.883900411904 -1.07107835242
y[1] (closed_form) = -0.965329957644 -0.902021978627
absolute error = 0.1876
relative error = 14.2 %
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 = 2.089
Order of pole (three term test) = 30.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8884 0.994
h = 0.0001 0.004
y[1] (numeric) = -0.887929297964 -1.07591682629
y[1] (closed_form) = -0.968721414824 -0.904862179955
absolute error = 0.1892
relative error = 14.27 %
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 = 1.22
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8883 0.998
h = 0.003 0.006
y[1] (numeric) = -0.891984348464 -1.08076376105
y[1] (closed_form) = -0.971790019763 -0.909563819694
absolute error = 0.1889
relative error = 14.19 %
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 = 0.8644
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8853 1.004
h = 0.0001 0.005
y[1] (numeric) = -0.896065684162 -1.08561918276
y[1] (closed_form) = -0.979842159625 -0.914514364444
absolute error = 0.1905
relative error = 14.21 %
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 = 1.033
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8852 1.009
h = 0.0001 0.003
y[1] (numeric) = -0.900173627946 -1.09048301727
y[1] (closed_form) = -0.983714108024 -0.920441311204
absolute error = 0.1895
relative error = 14.06 %
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 = 1.045
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8851 1.012
h = 0.001 0.001
y[1] (numeric) = -0.904308333273 -1.09535534893
y[1] (closed_form) = -0.986097725425 -0.923977802235
absolute error = 0.1899
relative error = 14.05 %
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 = 0.4016
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8841 1.013
h = 0.001 0.003
y[1] (numeric) = -0.90846983656 -1.1002362265
y[1] (closed_form) = -0.988059892367 -0.924426196992
absolute error = 0.193
relative error = 14.26 %
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 = 2.097
Order of pole (three term test) = 30.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8831 1.016
h = 0.0001 0.004
y[1] (numeric) = -0.9126581512 -1.10512565312
y[1] (closed_form) = -0.991545400472 -0.927284836768
absolute error = 0.1946
relative error = 14.33 %
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 = 1.244
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.883 1.02
h = 0.003 0.006
y[1] (numeric) = -0.916873320962 -1.11002364338
y[1] (closed_form) = -0.994721360358 -0.932043840522
absolute error = 0.1943
relative error = 14.25 %
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 = 0.8703
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1089.4MB, alloc=44.3MB, time=12.78
x[1] = -0.88 1.026
h = 0.0001 0.005
y[1] (numeric) = -0.921115469442 -1.11493022269
y[1] (closed_form) = -1.00297841805 -0.937005021287
absolute error = 0.1959
relative error = 14.27 %
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 = 1.051
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8799 1.031
h = 0.0001 0.003
y[1] (numeric) = -0.925384925655 -1.11984531203
y[1] (closed_form) = -1.0069857598 -0.943005127075
absolute error = 0.1948
relative error = 14.12 %
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 = 1.054
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8798 1.034
h = 0.001 0.001
y[1] (numeric) = -0.929681847188 -1.12476899599
y[1] (closed_form) = -1.0094515145 -0.946584696652
absolute error = 0.1952
relative error = 14.11 %
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 = 0.3992
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8788 1.035
h = 0.001 0.003
y[1] (numeric) = -0.934006271729 -1.12970132402
y[1] (closed_form) = -1.01145589868 -0.947021449253
absolute error = 0.1984
relative error = 14.32 %
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 = 2.104
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8778 1.038
h = 0.0001 0.004
y[1] (numeric) = -0.938358212987 -1.13464229917
y[1] (closed_form) = -1.01503771352 -0.949899017912
absolute error = 0.2
relative error = 14.39 %
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 = 1.269
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8777 1.042
h = 0.003 0.006
y[1] (numeric) = -0.942737715817 -1.13959193592
y[1] (closed_form) = -1.01832358623 -0.95471681473
absolute error = 0.1997
relative error = 14.31 %
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 = 0.8757
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8747 1.048
h = 0.0001 0.005
y[1] (numeric) = -0.947144906723 -1.14455025898
y[1] (closed_form) = -1.02679048337 -0.959688967733
absolute error = 0.2013
relative error = 14.32 %
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 = 1.069
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8746 1.053
h = 0.0001 0.003
y[1] (numeric) = -0.951580120995 -1.14951718433
y[1] (closed_form) = -1.03093644483 -0.965764033552
absolute error = 0.2002
relative error = 14.17 %
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 = 1.063
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8745 1.056
h = 0.001 0.001
y[1] (numeric) = -0.95604352045 -1.15449279683
y[1] (closed_form) = -1.03348629585 -0.969387738624
absolute error = 0.2007
relative error = 14.16 %
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 = 0.397
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8735 1.057
h = 0.001 0.003
y[1] (numeric) = -0.960535144081 -1.15947714658
y[1] (closed_form) = -1.03553391297 -0.969812580735
absolute error = 0.204
relative error = 14.38 %
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 = 2.107
Order of pole (three term test) = 30.56 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1133.4MB, alloc=44.3MB, time=13.29
x[1] = -0.8725 1.06
h = 0.0001 0.004
y[1] (numeric) = -0.965055005924 -1.16447023659
y[1] (closed_form) = -1.03921433868 -0.972709554885
absolute error = 0.2056
relative error = 14.44 %
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 = 1.293
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8724 1.064
h = 0.003 0.006
y[1] (numeric) = -0.969603151945 -1.1694720812
y[1] (closed_form) = -1.04261274591 -0.977587574986
absolute error = 0.2053
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 = 0.8805
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8694 1.07
h = 0.0001 0.005
y[1] (numeric) = -0.974179711626 -1.17448270439
y[1] (closed_form) = -1.05129450234 -0.982570992515
absolute error = 0.2068
relative error = 14.37 %
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 = 1.087
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8693 1.075
h = 0.0001 0.003
y[1] (numeric) = -0.97878502668 -1.17950201703
y[1] (closed_form) = -1.05558239057 -0.988722821214
absolute error = 0.2057
relative error = 14.22 %
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 = 1.072
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8692 1.078
h = 0.001 0.001
y[1] (numeric) = -0.983419263262 -1.18453010422
y[1] (closed_form) = -1.05821834555 -0.99239171924
absolute error = 0.2062
relative error = 14.21 %
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 = 0.3949
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8682 1.079
h = 0.0001 0.004
y[1] (numeric) = -0.988082461702 -1.18956701675
y[1] (closed_form) = -1.06031022826 -0.992804367017
absolute error = 0.2096
relative error = 14.43 %
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 = 1.315
Order of pole (three term test) = 32.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8681 1.083
h = 0.003 0.006
y[1] (numeric) = -0.992774638555 -1.19461277169
y[1] (closed_form) = -1.06380691011 -0.997736755741
absolute error = 0.2093
relative error = 14.35 %
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 = 0.887
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8651 1.089
h = 0.0001 0.005
y[1] (numeric) = -0.997495917085 -1.19966739142
y[1] (closed_form) = -1.07267756867 -1.00273271179
absolute error = 0.2108
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 = 1.105
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.865 1.094
h = 0.0001 0.003
y[1] (numeric) = -1.00224664447 -1.20473078244
y[1] (closed_form) = -1.07708939029 -1.00895380631
absolute error = 0.2096
relative error = 14.2 %
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 = 1.077
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8649 1.097
h = 0.001 0.001
y[1] (numeric) = -1.00702699058 -1.20980303005
y[1] (closed_form) = -1.07980055086 -1.01266351125
absolute error = 0.2101
relative error = 14.2 %
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 = 0.3925
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1177.3MB, alloc=44.3MB, time=13.80
x[1] = -0.8639 1.098
h = 0.001 0.003
y[1] (numeric) = -1.01183699688 -1.21488418564
y[1] (closed_form) = -1.08193152619 -1.01306596749
absolute error = 0.2136
relative error = 14.41 %
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 = 2.098
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8629 1.101
h = 0.0001 0.004
y[1] (numeric) = -1.01667667802 -1.21997425209
y[1] (closed_form) = -1.0858015027 -1.0160015123
absolute error = 0.2154
relative error = 14.48 %
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 = 1.339
Order of pole (three term test) = 32.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8628 1.105
h = 0.003 0.006
y[1] (numeric) = -1.02154608209 -1.22507324348
y[1] (closed_form) = -1.08941575551 -1.02099682196
absolute error = 0.2151
relative error = 14.4 %
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 = 0.8908
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8598 1.111
h = 0.0001 0.005
y[1] (numeric) = -1.02644534422 -1.23018118242
y[1] (closed_form) = -1.09851088147 -1.02600452855
absolute error = 0.2165
relative error = 14.4 %
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 = 1.122
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8597 1.116
h = 0.0001 0.003
y[1] (numeric) = -1.03137481831 -1.23529796999
y[1] (closed_form) = -1.10307098335 -1.03230578747
absolute error = 0.2153
relative error = 14.25 %
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 = 1.086
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8596 1.119
h = 0.001 0.001
y[1] (numeric) = -1.03633467876 -1.24042369172
y[1] (closed_form) = -1.10587210447 -1.03606267978
absolute error = 0.2159
relative error = 14.25 %
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 = 0.3907
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8586 1.12
h = 0.001 0.003
y[1] (numeric) = -1.04132496845 -1.24555839975
y[1] (closed_form) = -1.10804931716 -1.03645238374
absolute error = 0.2195
relative error = 14.47 %
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 = 2.097
Order of pole (three term test) = 30.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8576 1.123
h = 0.0001 0.004
y[1] (numeric) = -1.04634570238 -1.25070209688
y[1] (closed_form) = -1.11202476836 -1.03940864768
absolute error = 0.2213
relative error = 14.54 %
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 = 1.363
Order of pole (three term test) = 32.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8575 1.127
h = 0.003 0.006
y[1] (numeric) = -1.05139692982 -1.25585479705
y[1] (closed_form) = -1.11575940493 -1.04446831283
absolute error = 0.221
relative error = 14.46 %
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 = 0.8941
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8545 1.133
h = 0.0001 0.005
y[1] (numeric) = -1.05647878911 -1.26101652206
y[1] (closed_form) = -1.12508431285 -1.04948793196
absolute error = 0.2224
relative error = 14.45 %
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 = 1.139
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1221.0MB, alloc=44.3MB, time=14.32
x[1] = -0.8544 1.138
h = 0.0001 0.003
y[1] (numeric) = -1.061591641 -1.26618716745
y[1] (closed_form) = -1.12979624361 -1.05587116466
absolute error = 0.2211
relative error = 14.3 %
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 = 1.094
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8543 1.141
h = 0.001 0.001
y[1] (numeric) = -1.06673566456 -1.271366819
y[1] (closed_form) = -1.13268947855 -1.05967630392
absolute error = 0.2217
relative error = 14.29 %
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 = 0.3891
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8533 1.142
h = 0.001 0.003
y[1] (numeric) = -1.0719109041 -1.27655552958
y[1] (closed_form) = -1.13491401214 -1.06005292553
absolute error = 0.2255
relative error = 14.52 %
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 = 2.096
Order of pole (three term test) = 30.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8523 1.145
h = 0.0001 0.004
y[1] (numeric) = -1.07711737498 -1.28175330191
y[1] (closed_form) = -1.13899743996 -1.06303032926
absolute error = 0.2273
relative error = 14.59 %
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 = 1.387
Order of pole (three term test) = 32.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8522 1.149
h = 0.003 0.006
y[1] (numeric) = -1.0823551277 -1.28696014977
y[1] (closed_form) = -1.14285534301 -1.06815578575
absolute error = 0.227
relative error = 14.51 %
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 = 0.897
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8492 1.155
h = 0.0001 0.005
y[1] (numeric) = -1.08762430386 -1.29217609416
y[1] (closed_form) = -1.15241545499 -1.07318743124
absolute error = 0.2284
relative error = 14.5 %
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 = 1.156
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8491 1.16
h = 0.0001 0.003
y[1] (numeric) = -1.09292527124 -1.29740102492
y[1] (closed_form) = -1.15728285159 -1.07965444907
absolute error = 0.2271
relative error = 14.35 %
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 = 1.102
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.849 1.163
h = 0.001 0.001
y[1] (numeric) = -1.09825821366 -1.30263502804
y[1] (closed_form) = -1.16027040687 -1.08350889539
absolute error = 0.2277
relative error = 14.35 %
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 = 0.3875
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.848 1.164
h = 0.001 0.003
y[1] (numeric) = -1.10362317692 -1.30787815717
y[1] (closed_form) = -1.1625433634 -1.08387208754
absolute error = 0.2316
relative error = 14.57 %
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 = 2.093
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.847 1.167
h = 0.0001 0.004
y[1] (numeric) = -1.10902017676 -1.31313041494
y[1] (closed_form) = -1.16673732397 -1.08687103621
absolute error = 0.2335
relative error = 14.64 %
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 = 1.411
Order of pole (three term test) = 32.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8469 1.171
h = 0.003 0.006
y[1] (numeric) = -1.11444926492 -1.31839181496
y[1] (closed_form) = -1.17072144774 -1.09206372111
absolute error = 0.2332
relative error = 14.57 %
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 = 0.8996
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1264.9MB, alloc=44.3MB, time=14.83
x[1] = -0.8439 1.177
h = 0.0001 0.005
y[1] (numeric) = -1.11991058634 -1.3236623774
y[1] (closed_form) = -1.18052229592 -1.09710745742
absolute error = 0.2345
relative error = 14.55 %
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 = 1.173
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8438 1.182
h = 0.0001 0.003
y[1] (numeric) = -1.12540451598 -1.32894198622
y[1] (closed_form) = -1.18554888574 -1.10366007369
absolute error = 0.2332
relative error = 14.4 %
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 = 1.109
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8437 1.185
h = 0.001 0.001
y[1] (numeric) = -1.13093124257 -1.33423072766
y[1] (closed_form) = -1.18863302238 -1.10756488763
absolute error = 0.2339
relative error = 14.4 %
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 = 0.3861
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8427 1.186
h = 0.0001 0.004
y[1] (numeric) = -1.1364908134 -1.33952865612
y[1] (closed_form) = -1.19095552285 -1.10791428582
absolute error = 0.2379
relative error = 14.63 %
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 = 1.432
Order of pole (three term test) = 32.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8426 1.19
h = 0.003 0.006
y[1] (numeric) = -1.14208324772 -1.34483578972
y[1] (closed_form) = -1.19504989063 -1.11316754319
absolute error = 0.2376
relative error = 14.55 %
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 = 0.9043
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8396 1.196
h = 0.0001 0.005
y[1] (numeric) = -1.14770868355 -1.35015214724
y[1] (closed_form) = -1.20506232825 -1.11822465927
absolute error = 0.2389
relative error = 14.53 %
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 = 1.189
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8395 1.201
h = 0.0001 0.003
y[1] (numeric) = -1.15336750194 -1.35547760768
y[1] (closed_form) = -1.2102279526 -1.12485436777
absolute error = 0.2375
relative error = 14.38 %
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 = 1.113
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8394 1.204
h = 0.001 0.001
y[1] (numeric) = -1.1590598958 -1.36081225741
y[1] (closed_form) = -1.2133964592 -1.12880457427
absolute error = 0.2383
relative error = 14.38 %
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 = 0.3842
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8384 1.205
h = 0.001 0.003
y[1] (numeric) = -1.16478591373 -1.36615615152
y[1] (closed_form) = -1.21576268843 -1.12914240228
absolute error = 0.2424
relative error = 14.61 %
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 = 2.074
Order of pole (three term test) = 30.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8374 1.208
h = 0.0001 0.004
y[1] (numeric) = -1.17054557216 -1.37150929247
y[1] (closed_form) = -1.22016905131 -1.13218385555
absolute error = 0.2444
relative error = 14.68 %
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 = 1.455
Order of pole (three term test) = 32.55 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1309.0MB, alloc=44.3MB, time=15.34
x[1] = -0.8373 1.212
h = 0.003 0.006
y[1] (numeric) = -1.1763389252 -1.37687169357
y[1] (closed_form) = -1.22439531604 -1.13750705588
absolute error = 0.2441
relative error = 14.61 %
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 = 0.906
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8343 1.218
h = 0.0001 0.005
y[1] (numeric) = -1.18216612415 -1.38224337333
y[1] (closed_form) = -1.23465908617 -1.14257631606
absolute error = 0.2453
relative error = 14.58 %
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 = 1.205
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8342 1.223
h = 0.0001 0.003
y[1] (numeric) = -1.18802755757 -1.38762420457
y[1] (closed_form) = -1.23999106582 -1.14929504917
absolute error = 0.2439
relative error = 14.43 %
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 = 1.121
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8341 1.226
h = 0.001 0.001
y[1] (numeric) = -1.19392342345 -1.39301427388
y[1] (closed_form) = -1.24326049782 -1.15329762644
absolute error = 0.2447
relative error = 14.43 %
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 = 0.383
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8331 1.227
h = 0.001 0.003
y[1] (numeric) = -1.199853772 -1.39841363713
y[1] (closed_form) = -1.24567841364 -1.15362094831
absolute error = 0.249
relative error = 14.67 %
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 = 2.07
Order of pole (three term test) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8321 1.23
h = 0.0001 0.004
y[1] (numeric) = -1.20581862003 -1.40382229671
y[1] (closed_form) = -1.25020292798 -1.15668504865
absolute error = 0.2511
relative error = 14.74 %
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 = 1.478
Order of pole (three term test) = 32.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.832 1.234
h = 0.003 0.006
y[1] (numeric) = -1.21181802302 -1.40924026574
y[1] (closed_form) = -1.25456425799 -1.16207963327
absolute error = 0.2508
relative error = 14.67 %
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 = 0.9075
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.829 1.24
h = 0.0001 0.005
y[1] (numeric) = -1.21785213584 -1.41466756179
y[1] (closed_form) = -1.26508522234 -1.16716095506
absolute error = 0.252
relative error = 14.64 %
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 = 1.221
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8289 1.245
h = 0.0001 0.003
y[1] (numeric) = -1.22392135466 -1.42010405134
y[1] (closed_form) = -1.27058755521 -1.17397053248
absolute error = 0.2505
relative error = 14.48 %
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 = 1.128
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8288 1.248
h = 0.001 0.001
y[1] (numeric) = -1.23002588276 -1.42554982117
y[1] (closed_form) = -1.27396033669 -1.17802654291
absolute error = 0.2514
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 = 0.3819
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1352.7MB, alloc=44.3MB, time=15.86
x[1] = -0.8278 1.249
h = 0.001 0.003
y[1] (numeric) = -1.23616577197 -1.43100492798
y[1] (closed_form) = -1.27643111688 -1.17833494214
absolute error = 0.2559
relative error = 14.73 %
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 = 2.066
Order of pole (three term test) = 30.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8268 1.252
h = 0.0001 0.004
y[1] (numeric) = -1.2423410395 -1.43646937405
y[1] (closed_form) = -1.28107656011 -1.18142203135
absolute error = 0.258
relative error = 14.8 %
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 = 1.501
Order of pole (three term test) = 32.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8267 1.256
h = 0.003 0.006
y[1] (numeric) = -1.24855174219 -1.44194317231
y[1] (closed_form) = -1.28557620193 -1.18688944263
absolute error = 0.2577
relative error = 14.73 %
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 = 0.9086
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8237 1.262
h = 0.0001 0.005
y[1] (numeric) = -1.25479803858 -1.44742633937
y[1] (closed_form) = -1.29636034232 -1.19198268904
absolute error = 0.2588
relative error = 14.7 %
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 = 1.236
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8236 1.267
h = 0.0001 0.003
y[1] (numeric) = -1.26108033267 -1.45291873518
y[1] (closed_form) = -1.30203712514 -1.19888493219
absolute error = 0.2573
relative error = 14.54 %
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 = 1.135
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8235 1.27
h = 0.001 0.001
y[1] (numeric) = -1.26739883309 -1.45842044671
y[1] (closed_form) = -1.30551573976 -1.2029954384
absolute error = 0.2583
relative error = 14.55 %
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 = 0.3808
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8225 1.271
h = 0.001 0.003
y[1] (numeric) = -1.27375359335 -1.46393153149
y[1] (closed_form) = -1.30804058274 -1.20328847938
absolute error = 0.2629
relative error = 14.79 %
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 = 2.062
Order of pole (three term test) = 30.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8215 1.274
h = 0.0001 0.004
y[1] (numeric) = -1.28014463108 -1.46945199169
y[1] (closed_form) = -1.31280979279 -1.20639888152
absolute error = 0.2651
relative error = 14.87 %
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 = 1.524
Order of pole (three term test) = 32.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8214 1.278
h = 0.003 0.006
y[1] (numeric) = -1.28657200451 -1.47498184005
y[1] (closed_form) = -1.31745107301 -1.21194056279
absolute error = 0.2648
relative error = 14.8 %
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 = 0.9095
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8184 1.284
h = 0.0001 0.005
y[1] (numeric) = -1.29303587595 -1.48052109217
y[1] (closed_form) = -1.328504494 -1.21704554089
absolute error = 0.2659
relative error = 14.76 %
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 = 1.251
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1396.7MB, alloc=44.3MB, time=16.37
x[1] = -0.8183 1.289
h = 0.0001 0.003
y[1] (numeric) = -1.29953665736 -1.48606960129
y[1] (closed_form) = -1.33435992469 -1.22404227272
absolute error = 0.2643
relative error = 14.6 %
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 = 1.141
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8182 1.292
h = 0.001 0.001
y[1] (numeric) = -1.30607456288 -1.49162745456
y[1] (closed_form) = -1.33794691707 -1.22820833751
absolute error = 0.2653
relative error = 14.61 %
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 = 0.3798
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8172 1.293
h = 0.0001 0.004
y[1] (numeric) = -1.31264964774 -1.49719471034
y[1] (closed_form) = -1.34052704231 -1.228485565
absolute error = 0.2702
relative error = 14.86 %
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 = 1.543
Order of pole (three term test) = 32.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8171 1.297
h = 0.003 0.006
y[1] (numeric) = -1.31926193419 -1.50277138791
y[1] (closed_form) = -1.34529205834 -1.23409407445
absolute error = 0.2699
relative error = 14.79 %
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 = 0.9129
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8141 1.303
h = 0.0001 0.005
y[1] (numeric) = -1.32591157682 -1.50835750177
y[1] (closed_form) = -1.35658211568 -1.23921226144
absolute error = 0.2709
relative error = 14.74 %
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 = 1.266
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.814 1.308
h = 0.0001 0.003
y[1] (numeric) = -1.33259899436 -1.51395289942
y[1] (closed_form) = -1.36259360588 -1.24629398488
absolute error = 0.2693
relative error = 14.59 %
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 = 1.144
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8139 1.311
h = 0.001 0.001
y[1] (numeric) = -1.33932440567 -1.51955766812
y[1] (closed_form) = -1.36627529244 -1.25051005715
absolute error = 0.2704
relative error = 14.6 %
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 = 0.3784
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8129 1.312
h = 0.001 0.003
y[1] (numeric) = -1.34608786742 -1.52517186698
y[1] (closed_form) = -1.36890419187 -1.25077397173
absolute error = 0.2753
relative error = 14.85 %
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 = 2.04
Order of pole (three term test) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8119 1.315
h = 0.0001 0.004
y[1] (numeric) = -1.35288939803 -1.53079549797
y[1] (closed_form) = -1.37391118331 -1.25393011054
absolute error = 0.2777
relative error = 14.93 %
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 = 1.565
Order of pole (three term test) = 32.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8118 1.319
h = 0.003 0.006
y[1] (numeric) = -1.3597290584 -1.53642857343
y[1] (closed_form) = -1.37882422995 -1.25961561972
absolute error = 0.2775
relative error = 14.86 %
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 = 0.9133
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8088 1.325
h = 0.0001 0.005
y[1] (numeric) = -1.36660701795 -1.54207110702
y[1] (closed_form) = -1.39039526718 -1.2647451016
absolute error = 0.2783
relative error = 14.81 %
Correct digits = 1
memory used=1440.6MB, alloc=44.3MB, time=16.89
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.28
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8087 1.33
h = 0.0001 0.003
y[1] (numeric) = -1.37352370372 -1.54772293918
y[1] (closed_form) = -1.39659347205 -1.27192476243
absolute error = 0.2768
relative error = 14.65 %
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 = 1.151
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8086 1.333
h = 0.001 0.001
y[1] (numeric) = -1.38047934031 -1.55338415732
y[1] (closed_form) = -1.40038842576 -1.27619840306
absolute error = 0.2779
relative error = 14.67 %
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 = 0.3775
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8076 1.334
h = 0.001 0.003
y[1] (numeric) = -1.3874739862 -1.5590548214
y[1] (closed_form) = -1.40307494022 -1.27644561831
absolute error = 0.283
relative error = 14.92 %
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 = 2.036
Order of pole (three term test) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8066 1.337
h = 0.0001 0.004
y[1] (numeric) = -1.39450766026 -1.56473493331
y[1] (closed_form) = -1.40821416045 -1.27962593095
absolute error = 0.2854
relative error = 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 = 1.587
Order of pole (three term test) = 32.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8065 1.341
h = 0.003 0.006
y[1] (numeric) = -1.40158042488 -1.57042450514
y[1] (closed_form) = -1.41327880362 -1.28538988622
absolute error = 0.2853
relative error = 14.93 %
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 = 0.9134
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8035 1.347
h = 0.0001 0.005
y[1] (numeric) = -1.40869245349 -1.57612354943
y[1] (closed_form) = -1.42513729253 -1.29053030307
absolute error = 0.2861
relative error = 14.88 %
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 = 1.294
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8034 1.352
h = 0.0001 0.003
y[1] (numeric) = -1.41584418162 -1.58183189938
y[1] (closed_form) = -1.43152671241 -1.29780972913
absolute error = 0.2845
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 = 1.157
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8033 1.355
h = 0.001 0.001
y[1] (numeric) = -1.42303583975 -1.58754964249
y[1] (closed_form) = -1.43543766016 -1.30214200151
absolute error = 0.2857
relative error = 14.74 %
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 = 0.3768
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8023 1.356
h = 0.001 0.003
y[1] (numeric) = -1.43026748822 -1.59327683962
y[1] (closed_form) = -1.43818307215 -1.3023720036
absolute error = 0.291
relative error = 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 = 2.031
Order of pole (three term test) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8013 1.359
h = 0.0001 0.004
y[1] (numeric) = -1.43753914634 -1.59901349255
y[1] (closed_form) = -1.44345760596 -1.30557674149
absolute error = 0.2935
relative error = 15.08 %
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 = 1.609
Order of pole (three term test) = 32.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1484.5MB, alloc=44.3MB, time=17.40
x[1] = -0.8012 1.363
h = 0.003 0.006
y[1] (numeric) = -1.44485087805 -1.60475961312
y[1] (closed_form) = -1.44867749901 -1.31142058959
absolute error = 0.2934
relative error = 15.01 %
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 = 0.9134
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7982 1.369
h = 0.0001 0.005
y[1] (numeric) = -1.45220286089 -1.61051521272
y[1] (closed_form) = -1.46083004498 -1.31657151944
absolute error = 0.2941
relative error = 14.95 %
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 = 1.307
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7981 1.374
h = 0.0001 0.003
y[1] (numeric) = -1.459595539 -1.61628011707
y[1] (closed_form) = -1.46741529064 -1.32395253947
absolute error = 0.2924
relative error = 14.8 %
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 = 1.163
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.798 1.377
h = 0.001 0.001
y[1] (numeric) = -1.46702914894 -1.62205441378
y[1] (closed_form) = -1.47144502589 -1.32834450667
absolute error = 0.2937
relative error = 14.82 %
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 = 0.3761
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.797 1.378
h = 0.001 0.003
y[1] (numeric) = -1.47450375293 -1.62783816461
y[1] (closed_form) = -1.47425064074 -1.32855676019
absolute error = 0.2993
relative error = 15.08 %
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 = 2.027
Order of pole (three term test) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.796 1.381
h = 0.0001 0.004
y[1] (numeric) = -1.48201937074 -1.63363137122
y[1] (closed_form) = -1.47966364032 -1.33178615433
absolute error = 0.3019
relative error = 15.16 %
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 = 1.63
Order of pole (three term test) = 32.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7959 1.385
h = 0.003 0.006
y[1] (numeric) = -1.48957606789 -1.63943404519
y[1] (closed_form) = -1.485042526 -1.33771134224
absolute error = 0.3018
relative error = 15.1 %
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 = 0.9132
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7929 1.391
h = 0.0001 0.005
y[1] (numeric) = -1.49717402611 -1.64524619672
y[1] (closed_form) = -1.49749587096 -1.34287229932
absolute error = 0.3024
relative error = 15.03 %
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 = 1.32
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7928 1.396
h = 0.0001 0.003
y[1] (numeric) = -1.50481369838 -1.65106764383
y[1] (closed_form) = -1.50428166614 -1.35035674269
absolute error = 0.3007
relative error = 14.88 %
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 = 1.169
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7927 1.399
h = 0.001 0.001
y[1] (numeric) = -1.51249532742 -1.65689847423
y[1] (closed_form) = -1.50843305041 -1.35480946731
absolute error = 0.3021
relative error = 14.9 %
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 = 0.3754
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1528.4MB, alloc=44.3MB, time=17.91
x[1] = -0.7917 1.4
h = 0.003 0.006
y[1] (numeric) = -1.52021897742 -1.66273875059
y[1] (closed_form) = -1.51130019678 -1.35500341471
absolute error = 0.3079
relative error = 15.17 %
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 = 0.9168
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7887 1.406
h = 0.0001 0.005
y[1] (numeric) = -1.527984758 -1.66858841584
y[1] (closed_form) = -1.52396467754 -1.36016316999
absolute error = 0.3085
relative error = 15.1 %
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 = 1.327
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7886 1.411
h = 0.0001 0.003
y[1] (numeric) = -1.53579311049 -1.674447264
y[1] (closed_form) = -1.53089388894 -1.36771462154
absolute error = 0.3068
relative error = 14.94 %
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 = 1.167
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7885 1.414
h = 0.001 0.001
y[1] (numeric) = -1.54364428186 -1.6803153828
y[1] (closed_form) = -1.53513221274 -1.3722066043
absolute error = 0.3082
relative error = 14.97 %
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 = 0.3744
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7875 1.415
h = 0.001 0.003
y[1] (numeric) = -1.55153833761 -1.68619283555
y[1] (closed_form) = -1.53804199052 -1.37238603336
absolute error = 0.3141
relative error = 15.24 %
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 = 2.006
Order of pole (three term test) = 30.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7865 1.418
h = 0.0001 0.004
y[1] (numeric) = -1.55947529829 -1.69207962367
y[1] (closed_form) = -1.54369667887 -1.37565384155
absolute error = 0.3168
relative error = 15.32 %
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 = 1.656
Order of pole (three term test) = 32.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7864 1.422
h = 0.003 0.006
y[1] (numeric) = -1.56745523213 -1.69797575831
y[1] (closed_form) = -1.54935479982 -1.38171538418
absolute error = 0.3168
relative error = 15.26 %
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 = 0.9163
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7834 1.428
h = 0.0001 0.005
y[1] (numeric) = -1.57547832807 -1.70388124755
y[1] (closed_form) = -1.56233176116 -1.38688401946
absolute error = 0.3173
relative error = 15.19 %
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 = 1.339
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7833 1.433
h = 0.0001 0.003
y[1] (numeric) = -1.58354505422 -1.70979589607
y[1] (closed_form) = -1.56946980479 -1.3945418574
absolute error = 0.3156
relative error = 15.03 %
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 = 1.173
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7832 1.436
h = 0.001 0.001
y[1] (numeric) = -1.59165566396 -1.71571979165
y[1] (closed_form) = -1.57383479303 -1.39909631352
absolute error = 0.3171
relative error = 15.06 %
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 = 0.3739
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1572.4MB, alloc=44.3MB, time=18.42
x[1] = -0.7822 1.437
h = 0.001 0.003
y[1] (numeric) = -1.59981022484 -1.7216529985
y[1] (closed_form) = -1.57680838381 -1.39925640881
absolute error = 0.3232
relative error = 15.33 %
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 = 2.002
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7812 1.44
h = 0.0001 0.004
y[1] (numeric) = -1.60800875791 -1.72759551795
y[1] (closed_form) = -1.58261036032 -1.40254930291
absolute error = 0.326
relative error = 15.42 %
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 = 1.676
Order of pole (three term test) = 32.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7811 1.444
h = 0.003 0.006
y[1] (numeric) = -1.61625133306 -1.73354736083
y[1] (closed_form) = -1.58843802954 -1.40869597219
absolute error = 0.326
relative error = 15.36 %
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 = 0.9156
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7781 1.45
h = 0.0001 0.005
y[1] (numeric) = -1.6245381437 -1.73950853389
y[1] (closed_form) = -1.60173459335 -1.4138728175
absolute error = 0.3264
relative error = 15.28 %
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 = 1.351
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.778 1.455
h = 0.0001 0.003
y[1] (numeric) = -1.63286966724 -1.7454788335
y[1] (closed_form) = -1.60908650955 -1.42163886851
absolute error = 0.3247
relative error = 15.12 %
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 = 1.179
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7779 1.458
h = 0.001 0.001
y[1] (numeric) = -1.64124616367 -1.75145834744
y[1] (closed_form) = -1.61358121453 -1.42625685648
absolute error = 0.3264
relative error = 15.16 %
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 = 0.3734
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7769 1.459
h = 0.001 0.003
y[1] (numeric) = -1.64966770263 -1.75744714089
y[1] (closed_form) = -1.61662001136 -1.42639699749
absolute error = 0.3327
relative error = 15.43 %
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 = 1.999
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7759 1.462
h = 0.0001 0.004
y[1] (numeric) = -1.65813430567 -1.76344521502
y[1] (closed_form) = -1.62257268925 -1.42971512567
absolute error = 0.3356
relative error = 15.52 %
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 = 1.696
Order of pole (three term test) = 32.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7758 1.466
h = 0.003 0.006
y[1] (numeric) = -1.66664604438 -1.76945258038
y[1] (closed_form) = -1.62857399722 -1.4359483649
absolute error = 0.3357
relative error = 15.46 %
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 = 0.9149
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7728 1.472
h = 0.0001 0.005
y[1] (numeric) = -1.67520311675 -1.77546924231
y[1] (closed_form) = -1.64219743305 -1.4411326795
absolute error = 0.336
relative error = 15.38 %
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 = 1.363
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1616.2MB, alloc=44.3MB, time=18.94
x[1] = -0.7727 1.477
h = 0.0001 0.003
y[1] (numeric) = -1.68380600968 -1.78149498864
y[1] (closed_form) = -1.64976838491 -1.44900876968
absolute error = 0.3342
relative error = 15.22 %
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 = 1.184
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7726 1.48
h = 0.001 0.001
y[1] (numeric) = -1.69245498992 -1.78752990714
y[1] (closed_form) = -1.65439593285 -1.4536913467
absolute error = 0.336
relative error = 15.26 %
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 = 0.3729
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7716 1.481
h = 0.0001 0.004
y[1] (numeric) = -1.70115012925 -1.79357406394
y[1] (closed_form) = -1.65750135388 -1.45381088863
absolute error = 0.3426
relative error = 15.54 %
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 = 1.712
Order of pole (three term test) = 32.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7715 1.485
h = 0.003 0.006
y[1] (numeric) = -1.70989145624 -1.79962748055
y[1] (closed_form) = -1.66365442105 -1.46012193589
absolute error = 0.3426
relative error = 15.48 %
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 = 0.917
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7685 1.491
h = 0.0001 0.005
y[1] (numeric) = -1.71867915949 -1.80569016176
y[1] (closed_form) = -1.67756507809 -1.46531604541
absolute error = 0.3428
relative error = 15.39 %
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 = 1.376
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7684 1.496
h = 0.0001 0.003
y[1] (numeric) = -1.72751373399 -1.81176188806
y[1] (closed_form) = -1.6853274584 -1.47329101046
absolute error = 0.3411
relative error = 15.24 %
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 = 1.186
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7683 1.499
h = 0.001 0.001
y[1] (numeric) = -1.73639545224 -1.81784274717
y[1] (closed_form) = -1.69007112775 -1.4780316635
absolute error = 0.343
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 = 0.3719
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7673 1.5
h = 0.001 0.003
y[1] (numeric) = -1.74532438785 -1.82393280604
y[1] (closed_form) = -1.69323530808 -1.47813375615
absolute error = 0.3497
relative error = 15.56 %
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 = 1.981
Order of pole (three term test) = 30.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7663 1.503
h = 0.0001 0.004
y[1] (numeric) = -1.75430056331 -1.8300320656
y[1] (closed_form) = -1.6994774435 -1.4815010466
absolute error = 0.3528
relative error = 15.65 %
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 = 1.732
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7662 1.507
h = 0.003 0.006
y[1] (numeric) = -1.76332405348 -1.83614053577
y[1] (closed_form) = -1.70581200985 -1.48790139802
absolute error = 0.353
relative error = 15.59 %
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 = 0.916
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7632 1.513
h = 0.0001 0.005
y[1] (numeric) = -1.77239506496 -1.84225821923
y[1] (closed_form) = -1.72006348044 -1.49310149392
absolute error = 0.3531
relative error = 15.5 %
Correct digits = 1
memory used=1660.0MB, alloc=44.3MB, time=19.45
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.386
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7631 1.518
h = 0.0001 0.003
y[1] (numeric) = -1.7815141026 -1.84838488748
y[1] (closed_form) = -1.72805481825 -1.50118995848
absolute error = 0.3513
relative error = 15.35 %
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 = 1.191
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.763 1.521
h = 0.001 0.001
y[1] (numeric) = -1.79068144598 -1.85452062815
y[1] (closed_form) = -1.7329373378 -1.50599720289
absolute error = 0.3533
relative error = 15.39 %
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 = 0.3715
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.762 1.522
h = 0.001 0.003
y[1] (numeric) = -1.79989717094 -1.8606655092
y[1] (closed_form) = -1.736170858 -1.5060774474
absolute error = 0.3603
relative error = 15.67 %
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 = 1.979
Order of pole (three term test) = 30.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.761 1.525
h = 0.0001 0.004
y[1] (numeric) = -1.80916130051 -1.86681953137
y[1] (closed_form) = -1.74257387591 -1.50947030641
absolute error = 0.3635
relative error = 15.77 %
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 = 1.751
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7609 1.529
h = 0.003 0.006
y[1] (numeric) = -1.81847391139 -1.87298270426
y[1] (closed_form) = -1.74909432218 -1.51596140272
absolute error = 0.3637
relative error = 15.71 %
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 = 0.915
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7579 1.535
h = 0.0001 0.005
y[1] (numeric) = -1.82783521503 -1.87915502901
y[1] (closed_form) = -1.76369431667 -1.52116653214
absolute error = 0.3637
relative error = 15.62 %
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 = 1.396
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7578 1.54
h = 0.0001 0.003
y[1] (numeric) = -1.83724572636 -1.88533626783
y[1] (closed_form) = -1.77192014177 -1.52937032021
absolute error = 0.3619
relative error = 15.46 %
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 = 1.197
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7577 1.543
h = 0.001 0.001
y[1] (numeric) = -1.84670573216 -1.89152650826
y[1] (closed_form) = -1.77694485872 -1.53424520903
absolute error = 0.364
relative error = 15.51 %
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 = 0.3712
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7567 1.544
h = 0.001 0.003
y[1] (numeric) = -1.8562153106 -1.89772581925
y[1] (closed_form) = -1.78024921173 -1.53430288788
absolute error = 0.3713
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 = 1.976
Order of pole (three term test) = 30.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7557 1.547
h = 0.0001 0.004
y[1] (numeric) = -1.86577448524 -1.90393420139
y[1] (closed_form) = -1.78681682269 -1.53772136902
absolute error = 0.3746
relative error = 15.89 %
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 = 1.769
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1704.1MB, alloc=44.3MB, time=19.97
x[1] = -0.7556 1.551
h = 0.003 0.006
y[1] (numeric) = -1.87538333465 -1.91015166391
y[1] (closed_form) = -1.79352763554 -1.54430464897
absolute error = 0.3749
relative error = 15.84 %
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 = 0.9139
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7526 1.557
h = 0.0001 0.005
y[1] (numeric) = -1.88504207527 -1.91637820635
y[1] (closed_form) = -1.80848402431 -1.54951378009
absolute error = 0.3748
relative error = 15.74 %
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 = 1.406
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7525 1.562
h = 0.0001 0.003
y[1] (numeric) = -1.89475123227 -1.92261358138
y[1] (closed_form) = -1.81695000032 -1.55783471355
absolute error = 0.373
relative error = 15.58 %
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 = 1.202
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7524 1.565
h = 0.001 0.001
y[1] (numeric) = -1.90451109985 -1.9288578764
y[1] (closed_form) = -1.82212034246 -1.5627782975
absolute error = 0.3752
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 = 0.3709
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7514 1.566
h = 0.001 0.003
y[1] (numeric) = -1.91432175851 -1.93511116139
y[1] (closed_form) = -1.82549704826 -1.56281266634
absolute error = 0.3827
relative error = 15.93 %
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 = 1.974
Order of pole (three term test) = 30.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7504 1.569
h = 0.0001 0.004
y[1] (numeric) = -1.9241832324 -1.94137343676
y[1] (closed_form) = -1.83223304385 -1.56625679651
absolute error = 0.3862
relative error = 16.02 %
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 = 1.787
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7503 1.573
h = 0.003 0.006
y[1] (numeric) = -1.934095602 -1.94764471136
y[1] (closed_form) = -1.83913881823 -1.57293369649
absolute error = 0.3866
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 = 0.9127
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7473 1.579
h = 0.0001 0.005
y[1] (numeric) = -1.94405908882 -1.95392498307
y[1] (closed_form) = -1.85445963511 -1.57814571615
absolute error = 0.3863
relative error = 15.86 %
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 = 1.415
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7472 1.584
h = 0.0001 0.003
y[1] (numeric) = -1.95407422849 -1.96021399476
y[1] (closed_form) = -1.86317156245 -1.5865856143
absolute error = 0.3845
relative error = 15.71 %
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 = 1.207
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7471 1.587
h = 0.001 0.001
y[1] (numeric) = -1.96414132277 -1.96651183363
y[1] (closed_form) = -1.86849103998 -1.59159894146
absolute error = 0.3869
relative error = 15.76 %
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 = 0.3706
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1748.0MB, alloc=44.3MB, time=20.48
x[1] = -0.7461 1.588
h = 0.0001 0.004
y[1] (numeric) = -1.97426045462 -1.9728185707
y[1] (closed_form) = -1.87194164611 -1.59160922846
absolute error = 0.3947
relative error = 16.06 %
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 = 1.802
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.746 1.592
h = 0.003 0.006
y[1] (numeric) = -1.98443165686 -1.97913422886
y[1] (closed_form) = -1.87901786243 -1.59837026047
absolute error = 0.3951
relative error = 16.02 %
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 = 0.9145
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.743 1.598
h = 0.0001 0.005
y[1] (numeric) = -1.99465514054 -1.98545880576
y[1] (closed_form) = -1.89465891261 -1.60358828571
absolute error = 0.3947
relative error = 15.9 %
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 = 1.427
Order of pole (three term test) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7429 1.603
h = 0.0001 0.003
y[1] (numeric) = -2.00493145016 -1.99179203589
y[1] (closed_form) = -1.90358585167 -1.61213506556
absolute error = 0.393
relative error = 15.75 %
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 = 1.208
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7428 1.606
h = 0.001 0.001
y[1] (numeric) = -2.01526089395 -1.99813400627
y[1] (closed_form) = -1.90903572742 -1.61721109731
absolute error = 0.3955
relative error = 15.81 %
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 = 0.3697
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7418 1.607
h = 0.001 0.003
y[1] (numeric) = -2.02564355692 -2.00448478878
y[1] (closed_form) = -1.91255150504 -1.61720092177
absolute error = 0.4035
relative error = 16.11 %
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 = 1.959
Order of pole (three term test) = 30.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7408 1.61
h = 0.0001 0.004
y[1] (numeric) = -2.03607946426 -2.01084438353
y[1] (closed_form) = -1.91961089629 -1.62069487153
absolute error = 0.4072
relative error = 16.21 %
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 = 1.819
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7407 1.614
h = 0.003 0.006
y[1] (numeric) = -2.04656870008 -2.0172127986
y[1] (closed_form) = -1.92689090383 -1.6275522465
absolute error = 0.4076
relative error = 16.16 %
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 = 0.9131
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7377 1.62
h = 0.0001 0.005
y[1] (numeric) = -2.05711149552 -2.02359002865
y[1] (closed_form) = -1.94291179349 -1.63277096488
absolute error = 0.4072
relative error = 16.04 %
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 = 1.435
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7376 1.625
h = 0.0001 0.003
y[1] (numeric) = -2.06770840591 -2.02997579783
y[1] (closed_form) = -1.95209583022 -1.64144015904
absolute error = 0.4054
relative error = 15.89 %
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 = 1.213
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1791.9MB, alloc=44.3MB, time=21.00
x[1] = -0.7375 1.628
h = 0.001 0.001
y[1] (numeric) = -2.07835974741 -2.03637019291
y[1] (closed_form) = -1.95770158635 -1.64658792023
absolute error = 0.408
relative error = 15.95 %
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 = 0.3695
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7365 1.629
h = 0.001 0.003
y[1] (numeric) = -2.08906560757 -2.04277328681
y[1] (closed_form) = -1.96129422902 -1.64655217022
absolute error = 0.4163
relative error = 16.26 %
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 = 1.957
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7355 1.632
h = 0.0001 0.004
y[1] (numeric) = -2.09982601217 -2.04918507946
y[1] (closed_form) = -1.96853331559 -1.65007173905
absolute error = 0.4202
relative error = 16.36 %
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 = 1.836
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7354 1.636
h = 0.003 0.006
y[1] (numeric) = -2.11064104737 -2.05560557851
y[1] (closed_form) = -1.97602203273 -1.65702688558
absolute error = 0.4207
relative error = 16.31 %
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 = 0.9118
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7324 1.642
h = 0.0001 0.005
y[1] (numeric) = -2.12151094971 -2.06203477678
y[1] (closed_form) = -1.99243128326 -1.66224494009
absolute error = 0.4201
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 = 1.443
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7323 1.647
h = 0.0001 0.003
y[1] (numeric) = -2.13243628559 -2.06847238777
y[1] (closed_form) = -2.00187862668 -1.67103835916
absolute error = 0.4183
relative error = 16.04 %
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 = 1.217
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7322 1.65
h = 0.001 0.001
y[1] (numeric) = -2.14341737926 -2.07491849795
y[1] (closed_form) = -2.00764401952 -1.6762588894
absolute error = 0.4211
relative error = 16.1 %
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 = 0.3693
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7312 1.651
h = 0.001 0.003
y[1] (numeric) = -2.15445432088 -2.08137318132
y[1] (closed_form) = -2.01131515688 -1.67619671076
absolute error = 0.4297
relative error = 16.41 %
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 = 1.956
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7302 1.654
h = 0.0001 0.004
y[1] (numeric) = -2.16554713684 -2.0878364376
y[1] (closed_form) = -2.01873806006 -1.67974181503
absolute error = 0.4337
relative error = 16.51 %
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 = 1.852
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7301 1.658
h = 0.003 0.006
y[1] (numeric) = -2.17669591538 -2.09430827401
y[1] (closed_form) = -2.02644052314 -1.68679615763
absolute error = 0.4343
relative error = 16.47 %
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 = 0.9104
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7271 1.664
h = 0.0001 0.005
y[1] (numeric) = -2.18790089859 -2.10078868143
y[1] (closed_form) = -2.04324683283 -1.69201210037
absolute error = 0.4336
relative error = 16.35 %
Correct digits = 1
memory used=1835.9MB, alloc=44.3MB, time=21.51
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.451
Order of pole (three term test) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.727 1.669
h = 0.0001 0.003
y[1] (numeric) = -2.19916266412 -2.10727736243
y[1] (closed_form) = -2.05296384098 -1.70093155018
absolute error = 0.4318
relative error = 16.2 %
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) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7269 1.672
h = 0.001 0.001
y[1] (numeric) = -2.2104815445 -2.11377440312
y[1] (closed_form) = -2.05889271664 -1.70622588505
absolute error = 0.4348
relative error = 16.26 %
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 = 0.3692
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7259 1.673
h = 0.001 0.003
y[1] (numeric) = -2.22185763258 -2.12027987861
y[1] (closed_form) = -2.06264400794 -1.70613639324
absolute error = 0.4437
relative error = 16.58 %
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 = 1.955
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7249 1.676
h = 0.0001 0.004
y[1] (numeric) = -2.23329095536 -2.1267937884
y[1] (closed_form) = -2.07025493877 -1.70970691809
absolute error = 0.4478
relative error = 16.68 %
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 = 1.868
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7248 1.68
h = 0.003 0.006
y[1] (numeric) = -2.24478160323 -2.13331613923
y[1] (closed_form) = -2.07817630472 -1.71686187666
absolute error = 0.4485
relative error = 16.64 %
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 = 0.9091
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7218 1.686
h = 0.0001 0.005
y[1] (numeric) = -2.25632982393 -2.13984692
y[1] (closed_form) = -2.09538855239 -1.72207416616
absolute error = 0.4477
relative error = 16.51 %
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 = 1.458
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7217 1.691
h = 0.0001 0.003
y[1] (numeric) = -2.26793620656 -2.14638582203
y[1] (closed_form) = -2.10538173566 -1.73112144712
absolute error = 0.4459
relative error = 16.36 %
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 = 1.227
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7216 1.694
h = 0.001 0.001
y[1] (numeric) = -2.27960109217 -2.15293293103
y[1] (closed_form) = -2.11147803197 -1.73649061769
absolute error = 0.4491
relative error = 16.43 %
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 = 0.369
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7206 1.695
h = 0.0001 0.004
y[1] (numeric) = -2.29132457632 -2.15948832319
y[1] (closed_form) = -2.11531116665 -1.73637289706
absolute error = 0.4583
relative error = 16.75 %
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 = 1.881
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7205 1.699
h = 0.003 0.006
y[1] (numeric) = -2.30310669665 -2.16605202284
y[1] (closed_form) = -2.123423959 -1.743618289
absolute error = 0.4591
relative error = 16.71 %
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 = 0.9107
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1879.8MB, alloc=44.3MB, time=22.02
x[1] = -0.7175 1.705
h = 0.0001 0.005
y[1] (numeric) = -2.3149476892 -2.17262401911
y[1] (closed_form) = -2.14099294535 -1.74883110896
absolute error = 0.4581
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 = 1.468
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7174 1.71
h = 0.0001 0.003
y[1] (numeric) = -2.32684815281 -2.17920399369
y[1] (closed_form) = -2.1512276313 -1.75799325798
absolute error = 0.4564
relative error = 16.43 %
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 = 1.227
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7173 1.713
h = 0.001 0.001
y[1] (numeric) = -2.33880843575 -2.18579203192
y[1] (closed_form) = -2.15747035453 -1.76342972645
absolute error = 0.4596
relative error = 16.5 %
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 = 0.3683
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7163 1.714
h = 0.001 0.003
y[1] (numeric) = -2.35082863594 -2.19238821091
y[1] (closed_form) = -2.16137566525 -1.76328795264
absolute error = 0.4691
relative error = 16.82 %
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 = 1.942
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7153 1.717
h = 0.0001 0.004
y[1] (numeric) = -2.36290878157 -2.1989925298
y[1] (closed_form) = -2.16934769685 -1.7669077248
absolute error = 0.4735
relative error = 16.92 %
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 = 1.896
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7152 1.721
h = 0.003 0.006
y[1] (numeric) = -2.37504896706 -2.20560499439
y[1] (closed_form) = -2.17768930132 -1.77425642549
absolute error = 0.4744
relative error = 16.89 %
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 = 0.9092
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7122 1.727
h = 0.0001 0.005
y[1] (numeric) = -2.38724945084 -2.21222558972
y[1] (closed_form) = -2.19568126139 -1.77946257634
absolute error = 0.4733
relative error = 16.75 %
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 = 1.475
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7121 1.732
h = 0.0001 0.003
y[1] (numeric) = -2.39951084366 -2.21885398562
y[1] (closed_form) = -2.20620463261 -1.78875597176
absolute error = 0.4715
relative error = 16.6 %
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 = 1.231
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.712 1.735
h = 0.001 0.001
y[1] (numeric) = -2.41183350263 -2.22549026694
y[1] (closed_form) = -2.21262234295 -1.79426923067
absolute error = 0.475
relative error = 16.67 %
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 = 0.3682
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.711 1.736
h = 0.001 0.003
y[1] (numeric) = -2.42421752856 -2.23213451191
y[1] (closed_form) = -2.21661273471 -1.79409745948
absolute error = 0.4847
relative error = 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 = 1.941
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1923.8MB, alloc=44.3MB, time=22.54
x[1] = -0.71 1.739
h = 0.0001 0.004
y[1] (numeric) = -2.43666295028 -2.23878671944
y[1] (closed_form) = -2.22478535629 -1.79774219571
absolute error = 0.4893
relative error = 17.11 %
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 = 1.911
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7099 1.743
h = 0.003 0.006
y[1] (numeric) = -2.44916986452 -2.24544689479
y[1] (closed_form) = -2.23336128985 -1.80519561018
absolute error = 0.4903
relative error = 17.07 %
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 = 0.9077
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7069 1.749
h = 0.0001 0.005
y[1] (numeric) = -2.46173853571 -2.25211502081
y[1] (closed_form) = -2.25178564077 -1.81039326948
absolute error = 0.4891
relative error = 16.93 %
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 = 1.481
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7068 1.754
h = 0.0001 0.003
y[1] (numeric) = -2.47436958669 -2.2587907551
y[1] (closed_form) = -2.26260466247 -1.81981969413
absolute error = 0.4874
relative error = 16.79 %
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 = 1.236
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7067 1.757
h = 0.001 0.001
y[1] (numeric) = -2.48706338367 -2.26547418196
y[1] (closed_form) = -2.26920157171 -1.82541076038
absolute error = 0.491
relative error = 16.86 %
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 = 0.3681
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7057 1.758
h = 0.001 0.003
y[1] (numeric) = -2.49982003039 -2.27216538077
y[1] (closed_form) = -2.27327882376 -1.82520798288
absolute error = 0.5011
relative error = 17.19 %
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 = 1.941
Order of pole (three term test) = 30.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7047 1.761
h = 0.0001 0.004
y[1] (numeric) = -2.51263955637 -2.27886435021
y[1] (closed_form) = -2.28165661142 -1.8288774389
absolute error = 0.5058
relative error = 17.3 %
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 = 1.925
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7046 1.765
h = 0.003 0.006
y[1] (numeric) = -2.52552206064 -2.28557109495
y[1] (closed_form) = -2.2904725223 -1.83643696526
absolute error = 0.5069
relative error = 17.27 %
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 = 0.9063
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7016 1.771
h = 0.0001 0.005
y[1] (numeric) = -2.53846781382 -2.29228559557
y[1] (closed_form) = -2.30933887633 -1.84162420586
absolute error = 0.5056
relative error = 17.12 %
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 = 1.487
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7015 1.776
h = 0.0001 0.003
y[1] (numeric) = -2.55147745105 -2.2990074971
y[1] (closed_form) = -2.32046067957 -1.85118543428
absolute error = 0.5039
relative error = 16.98 %
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 = 1.24
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1967.6MB, alloc=44.3MB, time=23.05
x[1] = -0.7014 1.779
h = 0.001 0.001
y[1] (numeric) = -2.56455134782 -2.30573688326
y[1] (closed_form) = -2.32724109931 -1.85685531844
absolute error = 0.5078
relative error = 17.05 %
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 = 0.3681
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7004 1.78
h = 0.001 0.003
y[1] (numeric) = -2.5776896109 -2.31247383454
y[1] (closed_form) = -2.33140702328 -1.85662049129
absolute error = 0.5181
relative error = 17.38 %
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 = 1.941
Order of pole (three term test) = 30.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6994 1.783
h = 0.0001 0.004
y[1] (numeric) = -2.5908922705 -2.31921834939
y[1] (closed_form) = -2.33999465242 -1.86031438623
absolute error = 0.523
relative error = 17.5 %
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 = 1.939
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6993 1.787
h = 0.003 0.006
y[1] (numeric) = -2.60415942805 -2.3259704319
y[1] (closed_form) = -2.34905632302 -1.86798141503
absolute error = 0.5242
relative error = 17.47 %
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 = 0.9049
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6963 1.793
h = 0.0001 0.005
y[1] (numeric) = -2.61749136041 -2.33273006026
y[1] (closed_form) = -2.3683744915 -1.87315620194
absolute error = 0.5227
relative error = 17.31 %
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 = 1.493
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6962 1.798
h = 0.0001 0.003
y[1] (numeric) = -2.6308887153 -2.3394968666
y[1] (closed_form) = -2.37980637682 -1.8828539995
absolute error = 0.5211
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 = 1.244
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6961 1.801
h = 0.001 0.001
y[1] (numeric) = -2.6443518777 -2.34627093395
y[1] (closed_form) = -2.38677472072 -1.88860370529
absolute error = 0.5252
relative error = 17.25 %
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 = 0.368
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6951 1.802
h = 0.0001 0.004
y[1] (numeric) = -2.65788095748 -2.35305234398
y[1] (closed_form) = -2.39103116119 -1.88833574985
absolute error = 0.5359
relative error = 17.59 %
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 = 1.95
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.695 1.806
h = 0.003 0.006
y[1] (numeric) = -2.67147599767 -2.3598411225
y[1] (closed_form) = -2.4003078056 -1.89609944412
absolute error = 0.5372
relative error = 17.56 %
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 = 0.9064
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.692 1.812
h = 0.0001 0.005
y[1] (numeric) = -2.68513726209 -2.36663724844
y[1] (closed_form) = -2.42002307594 -1.90126734187
absolute error = 0.5356
relative error = 17.4 %
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 = 1.502
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2011.6MB, alloc=44.3MB, time=23.56
x[1] = -0.6919 1.817
h = 0.0001 0.003
y[1] (numeric) = -2.6988654091 -2.37344034288
y[1] (closed_form) = -2.43172619255 -1.91108791487
absolute error = 0.534
relative error = 17.27 %
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 = 1.243
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6918 1.82
h = 0.001 0.001
y[1] (numeric) = -2.71266083177 -2.38025048825
y[1] (closed_form) = -2.43885894227 -1.91690943858
absolute error = 0.5382
relative error = 17.35 %
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 = 0.3674
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6908 1.821
h = 0.001 0.003
y[1] (numeric) = -2.72652364261 -2.38706776718
y[1] (closed_form) = -2.44319521177 -1.91661318482
absolute error = 0.5492
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 = 1.93
Order of pole (three term test) = 30.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6898 1.824
h = 0.0001 0.004
y[1] (numeric) = -2.74045387314 -2.39389217765
y[1] (closed_form) = -2.45218581805 -1.92035431289
absolute error = 0.5544
relative error = 17.8 %
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 = 1.963
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6897 1.828
h = 0.003 0.006
y[1] (numeric) = -2.7544516293 -2.40072372259
y[1] (closed_form) = -2.46171933279 -1.92822814716
absolute error = 0.5558
relative error = 17.78 %
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 = 0.9049
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6867 1.834
h = 0.0001 0.005
y[1] (numeric) = -2.76851719983 -2.4075623756
y[1] (closed_form) = -2.4819052453 -1.93337962916
absolute error = 0.5541
relative error = 17.61 %
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 = 1.507
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6866 1.839
h = 0.0001 0.003
y[1] (numeric) = -2.78265125609 -2.41440774415
y[1] (closed_form) = -2.49393247179 -1.94334012071
absolute error = 0.5525
relative error = 17.48 %
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 = 1.247
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6865 1.842
h = 0.001 0.001
y[1] (numeric) = -2.79685420106 -2.42125990985
y[1] (closed_form) = -2.50126162607 -1.94924336903
absolute error = 0.5569
relative error = 17.56 %
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 = 0.3674
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6855 1.843
h = 0.001 0.003
y[1] (numeric) = -2.8111261505 -2.42811895654
y[1] (closed_form) = -2.505691948 -1.94891190573
absolute error = 0.5683
relative error = 17.9 %
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 = 1.93
Order of pole (three term test) = 30.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6845 1.846
h = 0.0001 0.004
y[1] (numeric) = -2.82546713668 -2.43498488191
y[1] (closed_form) = -2.51490634296 -1.95267651603
absolute error = 0.5736
relative error = 18.02 %
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 = 1.976
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6844 1.85
h = 0.003 0.006
y[1] (numeric) = -2.83987726805 -2.44185768824
y[1] (closed_form) = -2.5247029109 -1.9606618568
absolute error = 0.5752
relative error = 17.99 %
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 = 0.9034
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2055.6MB, alloc=44.3MB, time=24.07
x[1] = -0.6814 1.856
h = 0.0001 0.005
y[1] (numeric) = -2.85435684006 -2.44873734646
y[1] (closed_form) = -2.54536987021 -1.965794564
absolute error = 0.5733
relative error = 17.83 %
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 = 1.512
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6813 1.861
h = 0.0001 0.003
y[1] (numeric) = -2.86890653728 -2.45562345007
y[1] (closed_form) = -2.55772901303 -1.97589671035
absolute error = 0.5718
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 = 1.251
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6812 1.864
h = 0.001 0.001
y[1] (numeric) = -2.88352677283 -2.4625160798
y[1] (closed_form) = -2.56525929015 -1.98188266543
absolute error = 0.5765
relative error = 17.78 %
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 = 0.3674
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6802 1.865
h = 0.001 0.003
y[1] (numeric) = -2.89821766581 -2.46941532069
y[1] (closed_form) = -2.56978560709 -1.98151480823
absolute error = 0.5881
relative error = 18.12 %
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 = 1.931
Order of pole (three term test) = 30.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6792 1.868
h = 0.0001 0.004
y[1] (numeric) = -2.91297924924 -2.47632117014
y[1] (closed_form) = -2.57922886976 -1.98530246818
absolute error = 0.5937
relative error = 18.24 %
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 = 1.988
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6791 1.872
h = 0.003 0.006
y[1] (numeric) = -2.92781163417 -2.48323362973
y[1] (closed_form) = -2.58929481969 -1.9934006714
absolute error = 0.5954
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 = 0.9019
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6761 1.878
h = 0.0001 0.005
y[1] (numeric) = -2.94271512286 -2.49015266768
y[1] (closed_form) = -2.61045344537 -1.99851212403
absolute error = 0.5934
relative error = 18.05 %
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 = 1.516
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.676 1.883
h = 0.0001 0.003
y[1] (numeric) = -2.95769041334 -2.49707786305
y[1] (closed_form) = -2.62315249534 -2.0087576486
absolute error = 0.5919
relative error = 17.92 %
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 = 1.255
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6759 1.886
h = 0.001 0.001
y[1] (numeric) = -2.97273792912 -2.50400929567
y[1] (closed_form) = -2.63088872456 -2.01482728337
absolute error = 0.5968
relative error = 18.01 %
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 = 0.3674
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6749 1.887
h = 0.001 0.003
y[1] (numeric) = -2.98785779272 -2.51094705176
y[1] (closed_form) = -2.63551301436 -2.01442180895
absolute error = 0.6088
relative error = 18.35 %
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 = 1.932
Order of pole (three term test) = 30.54 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2099.5MB, alloc=44.3MB, time=24.59
x[1] = -0.6739 1.89
h = 0.0001 0.004
y[1] (numeric) = -3.00305003792 -2.51789112843
y[1] (closed_form) = -2.64519033349 -2.01823204309
absolute error = 0.6146
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 = 2
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6738 1.894
h = 0.003 0.006
y[1] (numeric) = -3.01831477841 -2.52484152654
y[1] (closed_form) = -2.65553214336 -2.02644445336
absolute error = 0.6165
relative error = 18.45 %
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 = 0.9005
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6708 1.9
h = 0.0001 0.005
y[1] (numeric) = -3.03365232343 -2.53179821147
y[1] (closed_form) = -2.67719327419 -2.03153204728
absolute error = 0.6143
relative error = 18.28 %
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 = 1.52
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6707 1.905
h = 0.0001 0.003
y[1] (numeric) = -3.04906338472 -2.53876074748
y[1] (closed_form) = -2.69024041053 -2.04192265959
absolute error = 0.6129
relative error = 18.15 %
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 = 1.259
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6706 1.908
h = 0.001 0.001
y[1] (numeric) = -3.06454839638 -2.54572921337
y[1] (closed_form) = -2.69818753451 -2.04807693711
absolute error = 0.618
relative error = 18.24 %
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 = 0.3674
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6696 1.909
h = 0.0001 0.004
y[1] (numeric) = -3.08010748445 -2.55270369657
y[1] (closed_form) = -2.70291181094 -2.04763258214
absolute error = 0.6304
relative error = 18.59 %
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 = 2.009
Order of pole (three term test) = 32.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6695 1.913
h = 0.003 0.006
y[1] (numeric) = -3.09574069806 -2.5596842244
y[1] (closed_form) = -2.71349499348 -2.05594775929
absolute error = 0.6323
relative error = 18.57 %
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 = 0.902
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6665 1.919
h = 0.0001 0.005
y[1] (numeric) = -3.11144833187 -2.56667076358
y[1] (closed_form) = -2.73559784277 -2.06101879911
absolute error = 0.63
relative error = 18.39 %
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 = 1.528
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6664 1.924
h = 0.0001 0.003
y[1] (numeric) = -3.12723110921 -2.57366286572
y[1] (closed_form) = -2.74894954113 -2.07153993818
absolute error = 0.6287
relative error = 18.26 %
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 = 1.258
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6663 1.927
h = 0.001 0.001
y[1] (numeric) = -3.14308947325 -2.58066060872
y[1] (closed_form) = -2.75708121899 -2.07777043094
absolute error = 0.634
relative error = 18.36 %
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 = 0.3668
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2143.4MB, alloc=44.3MB, time=25.11
x[1] = -0.6653 1.928
h = 0.001 0.003
y[1] (numeric) = -3.159023553 -2.587664081
y[1] (closed_form) = -2.76189368538 -2.07729279028
absolute error = 0.6467
relative error = 18.71 %
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 = 1.922
Order of pole (three term test) = 30.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6643 1.931
h = 0.0001 0.004
y[1] (numeric) = -3.17503338371 -2.59467327914
y[1] (closed_form) = -2.77202047081 -2.08114655076
absolute error = 0.6528
relative error = 18.83 %
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 = 2.02
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6642 1.935
h = 0.003 0.006
y[1] (numeric) = -3.19111908407 -2.60168820257
y[1] (closed_form) = -2.78289195975 -2.0895784851
absolute error = 0.6549
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 = 0.9006
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6612 1.941
h = 0.0001 0.005
y[1] (numeric) = -3.20728097651 -2.60870881118
y[1] (closed_form) = -2.80551811565 -2.0946206122
absolute error = 0.6525
relative error = 18.64 %
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 = 1.532
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6611 1.946
h = 0.0001 0.003
y[1] (numeric) = -3.22351979853 -2.61573464096
y[1] (closed_form) = -2.81923361574 -2.10529008207
absolute error = 0.6512
relative error = 18.51 %
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 = 1.262
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.661 1.949
h = 0.001 0.001
y[1] (numeric) = -3.23983600437 -2.62276576864
y[1] (closed_form) = -2.82758568475 -2.11160704302
absolute error = 0.6567
relative error = 18.61 %
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 = 0.3669
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.66 1.95
h = 0.001 0.003
y[1] (numeric) = -3.25622972672 -2.62980228387
y[1] (closed_form) = -2.83250199879 -2.11108808601
absolute error = 0.6698
relative error = 18.96 %
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 = 1.923
Order of pole (three term test) = 30.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.659 1.953
h = 0.0001 0.004
y[1] (numeric) = -3.27270100163 -2.63684418292
y[1] (closed_form) = -2.84287831824 -2.11496287722
absolute error = 0.6761
relative error = 19.08 %
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 = 2.031
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6589 1.957
h = 0.003 0.006
y[1] (numeric) = -3.28924995065 -2.64389146438
y[1] (closed_form) = -2.85404503662 -2.12351287763
absolute error = 0.6784
relative error = 19.07 %
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 = 0.8991
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6559 1.963
h = 0.0001 0.005
y[1] (numeric) = -3.30587690357 -2.65094408502
y[1] (closed_form) = -2.87720599081 -2.12852311403
absolute error = 0.6758
relative error = 18.88 %
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 = 1.535
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2187.3MB, alloc=44.3MB, time=25.62
x[1] = -0.6558 1.968
h = 0.0001 0.003
y[1] (numeric) = -3.32258261234 -2.65800156475
y[1] (closed_form) = -2.89129403417 -2.13934258044
absolute error = 0.6745
relative error = 18.75 %
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 = 1.265
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6557 1.971
h = 0.001 0.001
y[1] (numeric) = -3.33936754251 -2.66506397906
y[1] (closed_form) = -2.89987177544 -2.14574694179
absolute error = 0.6803
relative error = 18.86 %
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 = 0.3669
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6547 1.972
h = 0.001 0.003
y[1] (numeric) = -3.35623183055 -2.67213141885
y[1] (closed_form) = -2.90489405756 -2.14518528525
absolute error = 0.6938
relative error = 19.21 %
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 = 1.924
Order of pole (three term test) = 30.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6537 1.975
h = 0.0001 0.004
y[1] (numeric) = -3.37317551335 -2.67920388003
y[1] (closed_form) = -2.91552554551 -2.14908045386
absolute error = 0.7003
relative error = 19.34 %
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 = 2.041
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6536 1.979
h = 0.003 0.006
y[1] (numeric) = -3.39019871532 -2.68628136035
y[1] (closed_form) = -2.92699457848 -2.15774981421
absolute error = 0.7028
relative error = 19.33 %
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 = 0.8977
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6506 1.985
h = 0.0001 0.005
y[1] (numeric) = -3.40730177384 -2.69336381331
y[1] (closed_form) = -2.95070205907 -2.16272504263
absolute error = 0.7
relative error = 19.14 %
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 = 1.538
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6505 1.99
h = 0.0001 0.003
y[1] (numeric) = -3.4244854555 -2.70045074233
y[1] (closed_form) = -2.96517159203 -2.17369615285
absolute error = 0.6989
relative error = 19.01 %
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 = 1.268
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6504 1.993
h = 0.001 0.001
y[1] (numeric) = -3.44175023746 -2.70754222155
y[1] (closed_form) = -2.97398040997 -2.18018883401
absolute error = 0.7049
relative error = 19.12 %
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 = 0.367
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6494 1.994
h = 0.001 0.003
y[1] (numeric) = -3.45909626005 -2.7146383431
y[1] (closed_form) = -2.97911081896 -2.17958305058
absolute error = 0.7188
relative error = 19.47 %
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 = 1.926
Order of pole (three term test) = 30.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6484 1.997
h = 0.0001 0.004
y[1] (numeric) = -3.47652356099 -2.72173910256
y[1] (closed_form) = -2.99000323095 -2.18349789304
absolute error = 0.7255
relative error = 19.6 %
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 = 2.052
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6483 2.001
h = 0.003 0.006
y[1] (numeric) = -3.49403226767 -2.72884449679
y[1] (closed_form) = -3.00178182938 -2.1922878911
absolute error = 0.7282
relative error = 19.59 %
Correct digits = 1
memory used=2231.1MB, alloc=44.3MB, time=26.14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8964
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6453 2.007
h = 0.0001 0.005
y[1] (numeric) = -3.51162272517 -2.73595447591
y[1] (closed_form) = -3.02604780545 -2.19722485086
absolute error = 0.7253
relative error = 19.39 %
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 = 1.541
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6452 2.012
h = 0.0001 0.003
y[1] (numeric) = -3.52929571499 -2.74306852636
y[1] (closed_form) = -3.04090798366 -2.20834923232
absolute error = 0.7242
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 = 1.272
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6451 2.015
h = 0.001 0.001
y[1] (numeric) = -3.54705172616 -2.75018672085
y[1] (closed_form) = -3.04995340861 -2.21493113907
absolute error = 0.7305
relative error = 19.38 %
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 = 0.367
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6441 2.016
h = 0.0001 0.004
y[1] (numeric) = -3.56489090297 -2.75730915275
y[1] (closed_form) = -3.05519414226 -2.21427975606
absolute error = 0.7448
relative error = 19.74 %
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 = 2.059
Order of pole (three term test) = 32.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.644 2.02
h = 0.003 0.006
y[1] (numeric) = -3.58281330142 -2.76443585092
y[1] (closed_form) = -3.06724368229 -2.22317841338
absolute error = 0.7475
relative error = 19.73 %
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 = 0.8979
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.641 2.026
h = 0.0001 0.005
y[1] (numeric) = -3.60081925035 -2.77156676756
y[1] (closed_form) = -3.09200067612 -2.22808656042
absolute error = 0.7445
relative error = 19.53 %
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 = 1.548
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6409 2.031
h = 0.0001 0.003
y[1] (numeric) = -3.61890954389 -2.77870137458
y[1] (closed_form) = -3.10720275174 -2.23934896543
absolute error = 0.7435
relative error = 19.41 %
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 = 1.27
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6408 2.034
h = 0.001 0.001
y[1] (numeric) = -3.63708468116 -2.78583974341
y[1] (closed_form) = -3.11645528959 -2.24601129939
absolute error = 0.75
relative error = 19.52 %
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 = 0.3665
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6398 2.035
h = 0.001 0.003
y[1] (numeric) = -3.65534480984 -2.79298196849
y[1] (closed_form) = -3.12179334514 -2.24532080155
absolute error = 0.7646
relative error = 19.88 %
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 = 1.917
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6388 2.038
h = 0.0001 0.004
y[1] (numeric) = -3.67368996926 -2.80012804473
y[1] (closed_form) = -3.13318680747 -2.24927347673
absolute error = 0.7717
relative error = 20.01 %
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 = 2.068
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2275.1MB, alloc=44.3MB, time=26.66
x[1] = -0.6387 2.042
h = 0.003 0.006
y[1] (numeric) = -3.69212029236 -2.80727796725
y[1] (closed_form) = -3.14555984369 -2.25829519397
absolute error = 0.7747
relative error = 20.01 %
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 = 0.8965
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6357 2.048
h = 0.0001 0.005
y[1] (numeric) = -3.71063613884 -2.81443167966
y[1] (closed_form) = -3.17089830536 -2.26315875808
absolute error = 0.7715
relative error = 19.8 %
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 = 1.551
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6356 2.053
h = 0.0001 0.003
y[1] (numeric) = -3.72923831824 -2.82158863599
y[1] (closed_form) = -3.18650861672 -2.27457752016
absolute error = 0.7706
relative error = 19.68 %
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 = 1.274
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6355 2.056
h = 0.001 0.001
y[1] (numeric) = -3.74792734206 -2.82874890602
y[1] (closed_form) = -3.19600838652 -2.28133079543
absolute error = 0.7774
relative error = 19.8 %
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 = 0.3666
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6345 2.057
h = 0.001 0.003
y[1] (numeric) = -3.76670336211 -2.83591258547
y[1] (closed_form) = -3.20146098125 -2.28059186024
absolute error = 0.7924
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 = 1.919
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6335 2.06
h = 0.0001 0.004
y[1] (numeric) = -3.78556641864 -2.84307966886
y[1] (closed_form) = -3.21313253438 -2.28456197776
absolute error = 0.7998
relative error = 20.29 %
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 = 2.077
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6334 2.064
h = 0.003 0.006
y[1] (numeric) = -3.80451664773 -2.85025015032
y[1] (closed_form) = -3.22583681196 -2.2937079825
absolute error = 0.8029
relative error = 20.28 %
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 = 0.8951
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6304 2.07
h = 0.0001 0.005
y[1] (numeric) = -3.82355441727 -2.85742396972
y[1] (closed_form) = -3.25176942812 -2.29852327173
absolute error = 0.7996
relative error = 20.08 %
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 = 1.553
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6303 2.075
h = 0.0001 0.003
y[1] (numeric) = -3.84268055247 -2.86460056268
y[1] (closed_form) = -3.26779775537 -2.31009995633
absolute error = 0.7987
relative error = 19.96 %
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 = 1.277
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6302 2.078
h = 0.001 0.001
y[1] (numeric) = -3.86189557749 -2.87177999727
y[1] (closed_form) = -3.27755066328 -2.31694503638
absolute error = 0.8058
relative error = 20.08 %
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 = 0.3667
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2319.0MB, alloc=44.3MB, time=27.18
x[1] = -0.6292 2.079
h = 0.001 0.003
y[1] (numeric) = -3.8811996484 -2.87896237048
y[1] (closed_form) = -3.28312011082 -2.3161560553
absolute error = 0.8212
relative error = 20.44 %
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 = 1.921
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6282 2.082
h = 0.0001 0.004
y[1] (numeric) = -3.90059280636 -2.88614767642
y[1] (closed_form) = -3.29507600197 -2.32014270321
absolute error = 0.8289
relative error = 20.57 %
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 = 2.086
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6281 2.086
h = 0.003 0.006
y[1] (numeric) = -3.92007519066 -2.89333590818
y[1] (closed_form) = -3.3081194461 -2.32941420247
absolute error = 0.8322
relative error = 20.57 %
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 = 0.8938
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6251 2.092
h = 0.0001 0.005
y[1] (numeric) = -3.93964717757 -2.90052700178
y[1] (closed_form) = -3.33465916303 -2.33417736426
absolute error = 0.8287
relative error = 20.36 %
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 = 1.555
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.625 2.097
h = 0.0001 0.003
y[1] (numeric) = -3.95930960822 -2.90772037391
y[1] (closed_form) = -3.35111551373 -2.34591351139
absolute error = 0.828
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 = 1.28
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6249 2.1
h = 0.001 0.001
y[1] (numeric) = -3.97906301972 -2.9149160908
y[1] (closed_form) = -3.36112760271 -2.35285124248
absolute error = 0.8353
relative error = 20.36 %
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 = 0.3668
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6239 2.101
h = 0.001 0.003
y[1] (numeric) = -3.9989075725 -2.92211425071
y[1] (closed_form) = -3.36681625831 -2.3520105569
absolute error = 0.8512
relative error = 20.73 %
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 = 1.922
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6229 2.104
h = 0.0001 0.004
y[1] (numeric) = -4.01884330866 -2.92931484736
y[1] (closed_form) = -3.3790628682 -2.35601276448
absolute error = 0.8591
relative error = 20.85 %
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 = 2.094
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6228 2.108
h = 0.003 0.006
y[1] (numeric) = -4.03887037077 -2.93651787274
y[1] (closed_form) = -3.39245358795 -2.36541094338
absolute error = 0.8626
relative error = 20.86 %
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 = 0.8925
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6198 2.114
h = 0.0001 0.005
y[1] (numeric) = -4.05898914363 -2.94372325886
y[1] (closed_form) = -3.41961361658 -2.37011795984
absolute error = 0.859
relative error = 20.64 %
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 = 1.557
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2362.9MB, alloc=44.3MB, time=27.69
x[1] = -0.6197 2.119
h = 0.0001 0.003
y[1] (numeric) = -4.07920048458 -2.95093040299
y[1] (closed_form) = -3.43650823063 -2.38201508235
absolute error = 0.8583
relative error = 20.53 %
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 = 1.283
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6196 2.122
h = 0.001 0.001
y[1] (numeric) = -4.09950494397 -2.95813936938
y[1] (closed_form) = -3.44678568342 -2.38904629257
absolute error = 0.866
relative error = 20.65 %
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 = 0.3669
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6186 2.123
h = 0.0001 0.004
y[1] (numeric) = -4.11990268668 -2.96535025757
y[1] (closed_form) = -3.45259594459 -2.3881521925
absolute error = 0.8823
relative error = 21.02 %
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 = 2.1
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6185 2.127
h = 0.003 0.006
y[1] (numeric) = -4.14039377648 -2.97256309792
y[1] (closed_form) = -3.46629069671 -2.39766461602
absolute error = 0.886
relative error = 21.02 %
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 = 0.8941
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6155 2.133
h = 0.0001 0.005
y[1] (numeric) = -4.16097858003 -2.97977782537
y[1] (closed_form) = -3.49399619081 -2.40232756546
absolute error = 0.8822
relative error = 20.81 %
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 = 1.564
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6154 2.138
h = 0.0001 0.003
y[1] (numeric) = -4.1816579684 -2.98699382054
y[1] (closed_form) = -3.51127448675 -2.41436983071
absolute error = 0.8817
relative error = 20.69 %
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 = 1.281
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6153 2.141
h = 0.001 0.001
y[1] (numeric) = -4.20243250319 -2.99421114597
y[1] (closed_form) = -3.5217842892 -2.42148541695
absolute error = 0.8895
relative error = 20.81 %
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 = 0.3664
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6143 2.142
h = 0.001 0.003
y[1] (numeric) = -4.22330235312 -3.00142990228
y[1] (closed_form) = -3.52770184203 -2.42054541818
absolute error = 0.9062
relative error = 21.18 %
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 = 1.915
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6133 2.145
h = 0.0001 0.004
y[1] (numeric) = -4.24426756206 -3.0086500824
y[1] (closed_form) = -3.54050670746 -2.42457743456
absolute error = 0.9146
relative error = 21.31 %
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 = 2.108
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6132 2.149
h = 0.003 0.006
y[1] (numeric) = -4.26532827879 -3.01587167621
y[1] (closed_form) = -3.554564314 -2.43421878201
absolute error = 0.9184
relative error = 21.32 %
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 = 0.8928
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2406.8MB, alloc=44.3MB, time=28.21
x[1] = -0.6102 2.155
h = 0.0001 0.005
y[1] (numeric) = -4.28648490425 -3.02309460799
y[1] (closed_form) = -3.58291547678 -2.43881781777
absolute error = 0.9145
relative error = 21.1 %
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 = 1.565
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6101 2.16
h = 0.0001 0.003
y[1] (numeric) = -4.30773832622 -3.03031823788
y[1] (closed_form) = -3.60065170861 -2.45102392419
absolute error = 0.9141
relative error = 20.99 %
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 = 1.284
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.61 2.163
h = 0.001 0.001
y[1] (numeric) = -4.32908912011 -3.03754262624
y[1] (closed_form) = -3.61143875258 -2.45823455599
absolute error = 0.9223
relative error = 21.11 %
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 = 0.3665
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.609 2.164
h = 0.001 0.003
y[1] (numeric) = -4.35053745933 -3.04476787496
y[1] (closed_form) = -3.61748250905 -2.4572378493
absolute error = 0.9394
relative error = 21.48 %
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 = 1.917
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.608 2.167
h = 0.0001 0.004
y[1] (numeric) = -4.37208338876 -3.05199397653
y[1] (closed_form) = -3.63059712244 -2.46128238782
absolute error = 0.948
relative error = 21.61 %
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 = 2.116
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6079 2.171
h = 0.003 0.006
y[1] (numeric) = -4.39372706063 -3.05922091961
y[1] (closed_form) = -3.64502624112 -2.47105377643
absolute error = 0.9521
relative error = 21.62 %
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 = 0.8915
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6049 2.177
h = 0.0001 0.005
y[1] (numeric) = -4.41546888498 -3.06644862406
y[1] (closed_form) = -3.6740370711 -2.47558438333
absolute error = 0.9481
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 = 1.567
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6048 2.182
h = 0.0001 0.003
y[1] (numeric) = -4.43730976657 -3.07367642896
y[1] (closed_form) = -3.69224217185 -2.48795575955
absolute error = 0.9477
relative error = 21.29 %
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 = 1.287
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6047 2.185
h = 0.001 0.001
y[1] (numeric) = -4.45925029493 -3.08090439234
y[1] (closed_form) = -3.70331305706 -2.49526220868
absolute error = 0.9563
relative error = 21.41 %
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 = 0.3666
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6037 2.186
h = 0.001 0.003
y[1] (numeric) = -4.48129064828 -3.08813261741
y[1] (closed_form) = -3.70948554019 -2.49420693014
absolute error = 0.9739
relative error = 21.79 %
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 = 1.919
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6027 2.189
h = 0.0001 0.004
y[1] (numeric) = -4.5034308725 -3.09536109616
y[1] (closed_form) = -3.72291682405 -2.49826277624
absolute error = 0.9827
relative error = 21.92 %
Correct digits = 1
memory used=2450.7MB, alloc=44.3MB, time=28.73
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.123
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6026 2.193
h = 0.003 0.006
y[1] (numeric) = -4.52567112341 -3.10258981602
y[1] (closed_form) = -3.73772631229 -2.50816529587
absolute error = 0.987
relative error = 21.93 %
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 = 0.8903
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5996 2.199
h = 0.0001 0.005
y[1] (numeric) = -4.54801182027 -3.10981869224
y[1] (closed_form) = -3.76741109279 -2.51262277367
absolute error = 0.9828
relative error = 21.7 %
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 = 1.568
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5995 2.204
h = 0.0001 0.003
y[1] (numeric) = -4.57045388513 -3.11704704227
y[1] (closed_form) = -3.78609624781 -2.52516081434
absolute error = 0.9826
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 = 1.29
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5994 2.207
h = 0.001 0.001
y[1] (numeric) = -4.59299792197 -3.12427492167
y[1] (closed_form) = -3.79745772571 -2.53256383005
absolute error = 0.9915
relative error = 21.72 %
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 = 0.3667
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5984 2.208
h = 0.001 0.003
y[1] (numeric) = -4.6156441139 -3.13150243497
y[1] (closed_form) = -3.80376150357 -2.53144805899
absolute error = 1.01
relative error = 22.1 %
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 = 1.921
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5974 2.211
h = 0.0001 0.004
y[1] (numeric) = -4.63839250787 -3.13872957366
y[1] (closed_form) = -3.81751652744 -2.53551392941
absolute error = 1.019
relative error = 22.23 %
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 = 2.13
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5973 2.215
h = 0.003 0.006
y[1] (numeric) = -4.66124326331 -3.14595632386
y[1] (closed_form) = -3.83271544667 -2.54554864102
absolute error = 1.023
relative error = 22.24 %
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 = 0.8891
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5943 2.221
h = 0.0001 0.005
y[1] (numeric) = -4.68419680894 -3.15318259609
y[1] (closed_form) = -3.86308875122 -2.54992809897
absolute error = 1.019
relative error = 22.01 %
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 = 1.569
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5942 2.226
h = 0.0001 0.003
y[1] (numeric) = -4.70725408437 -3.16040768552
y[1] (closed_form) = -3.88226540358 -2.56263416276
absolute error = 1.019
relative error = 21.9 %
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 = 1.292
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5941 2.229
h = 0.001 0.001
y[1] (numeric) = -4.73041570831 -3.16763164515
y[1] (closed_form) = -3.89392438065 -2.57013447055
absolute error = 1.028
relative error = 22.03 %
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 = 0.3668
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2494.7MB, alloc=44.3MB, time=29.24
x[1] = -0.5931 2.23
h = 0.0001 0.004
y[1] (numeric) = -4.75368186894 -3.17485458079
y[1] (closed_form) = -3.90036206706 -2.56895622811
absolute error = 1.047
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 = 2.134
Order of pole (three term test) = 32.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.593 2.234
h = 0.003 0.006
y[1] (numeric) = -4.77705263871 -3.18207652423
y[1] (closed_form) = -3.91590201934 -2.57911034213
absolute error = 1.051
relative error = 22.42 %
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 = 0.8907
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.59 2.24
h = 0.0001 0.005
y[1] (numeric) = -4.80052842615 -3.18929738995
y[1] (closed_form) = -3.94688089046 -2.58342702062
absolute error = 1.047
relative error = 22.19 %
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 = 1.575
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5899 2.245
h = 0.0001 0.003
y[1] (numeric) = -4.82411018571 -3.19651645411
y[1] (closed_form) = -3.96648794873 -2.59628481723
absolute error = 1.047
relative error = 22.08 %
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 = 1.29
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5898 2.248
h = 0.001 0.001
y[1] (numeric) = -4.84779854869 -3.2037337674
y[1] (closed_form) = -3.97840748424 -2.6038730914
absolute error = 1.056
relative error = 22.21 %
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 = 0.3663
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5888 2.249
h = 0.001 0.003
y[1] (numeric) = -4.87159370755 -3.21094943673
y[1] (closed_form) = -3.98496334056 -2.60264108387
absolute error = 1.075
relative error = 22.59 %
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 = 1.914
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5878 2.252
h = 0.0001 0.004
y[1] (numeric) = -4.89549571121 -3.21816345267
y[1] (closed_form) = -3.99934002062 -2.60672600938
absolute error = 1.085
relative error = 22.73 %
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 = 2.141
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5877 2.256
h = 0.003 0.006
y[1] (numeric) = -4.91950472598 -3.22537579878
y[1] (closed_form) = -4.01528681136 -2.61701432083
absolute error = 1.09
relative error = 22.74 %
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 = 0.8895
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5847 2.262
h = 0.0001 0.005
y[1] (numeric) = -4.9436211984 -3.23258637645
y[1] (closed_form) = -4.04698217968 -2.62124353448
absolute error = 1.085
relative error = 22.51 %
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 = 1.576
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5846 2.267
h = 0.0001 0.003
y[1] (numeric) = -4.96784610105 -3.23979443837
y[1] (closed_form) = -4.06710271814 -2.63427192337
absolute error = 1.085
relative error = 22.4 %
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 = 1.293
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2538.7MB, alloc=44.3MB, time=29.76
x[1] = -0.5845 2.27
h = 0.001 0.001
y[1] (numeric) = -4.99218008061 -3.24700003239
y[1] (closed_form) = -4.07933302021 -2.6419588588
absolute error = 1.095
relative error = 22.53 %
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 = 0.3665
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5835 2.271
h = 0.001 0.003
y[1] (numeric) = -5.01662333482 -3.25420326673
y[1] (closed_form) = -4.08602779834 -2.64066057005
absolute error = 1.115
relative error = 22.91 %
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 = 1.916
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5825 2.274
h = 0.0001 0.004
y[1] (numeric) = -5.0411759137 -3.2614041314
y[1] (closed_form) = -4.10074929912 -2.64475153948
absolute error = 1.125
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 = 2.147
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5824 2.278
h = 0.003 0.006
y[1] (numeric) = -5.06583798744 -3.26860260851
y[1] (closed_form) = -4.11711259825 -2.65517501996
absolute error = 1.13
relative error = 23.06 %
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 = 0.8883
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5794 2.284
h = 0.0001 0.005
y[1] (numeric) = -5.09061001259 -3.2757985942
y[1] (closed_form) = -4.14953990075 -2.65931130504
absolute error = 1.125
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 = 1.577
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5793 2.289
h = 0.0001 0.003
y[1] (numeric) = -5.11549298011 -3.2829913171
y[1] (closed_form) = -4.17018613126 -2.67251153369
absolute error = 1.125
relative error = 22.72 %
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 = 1.296
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5792 2.292
h = 0.001 0.001
y[1] (numeric) = -5.14048755243 -3.29018082201
y[1] (closed_form) = -4.18273456869 -2.68029778269
absolute error = 1.135
relative error = 22.86 %
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 = 0.3666
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5782 2.293
h = 0.001 0.003
y[1] (numeric) = -5.1655939327 -3.29736721847
y[1] (closed_form) = -4.18957101815 -2.67893105946
absolute error = 1.155
relative error = 23.24 %
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 = 1.919
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5772 2.296
h = 0.0001 0.004
y[1] (numeric) = -5.19081217207 -3.30455049593
y[1] (closed_form) = -4.20464500562 -2.68302650468
absolute error = 1.166
relative error = 23.37 %
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 = 2.153
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5771 2.3
h = 0.003 0.006
y[1] (numeric) = -5.21614244465 -3.31173063497
y[1] (closed_form) = -4.22143470446 -2.69358609028
absolute error = 1.171
relative error = 23.39 %
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 = 0.8872
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2582.5MB, alloc=44.3MB, time=30.26
x[1] = -0.5741 2.306
h = 0.0001 0.005
y[1] (numeric) = -5.24158521725 -3.31890752635
y[1] (closed_form) = -4.25460969014 -2.69762376999
absolute error = 1.166
relative error = 23.15 %
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 = 1.578
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.574 2.311
h = 0.0001 0.003
y[1] (numeric) = -5.2671414995 -3.32608037389
y[1] (closed_form) = -4.27579410431 -2.71099704162
absolute error = 1.167
relative error = 23.04 %
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 = 1.298
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5739 2.314
h = 0.001 0.001
y[1] (numeric) = -5.2928119699 -3.33324921924
y[1] (closed_form) = -4.28866821412 -2.71888322761
absolute error = 1.177
relative error = 23.18 %
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 = 0.3668
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5729 2.315
h = 0.001 0.003
y[1] (numeric) = -5.31859683715 -3.34041417323
y[1] (closed_form) = -4.29564913306 -2.7174458524
absolute error = 1.198
relative error = 23.56 %
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 = 1.921
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5719 2.318
h = 0.0001 0.004
y[1] (numeric) = -5.34449615357 -3.34757522475
y[1] (closed_form) = -4.31108343491 -2.72154412508
absolute error = 1.208
relative error = 23.7 %
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 = 2.159
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5718 2.322
h = 0.003 0.006
y[1] (numeric) = -5.37051009729 -3.35473235279
y[1] (closed_form) = -4.32830965097 -2.7322407145
absolute error = 1.214
relative error = 23.72 %
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 = 0.8861
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5688 2.328
h = 0.0001 0.005
y[1] (numeric) = -5.39663914554 -3.3618854425
y[1] (closed_form) = -4.36224838671 -2.73617389273
absolute error = 1.209
relative error = 23.48 %
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 = 1.578
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5687 2.333
h = 0.0001 0.003
y[1] (numeric) = -5.42288432692 -3.36903367227
y[1] (closed_form) = -4.38398376189 -2.74972136393
absolute error = 1.209
relative error = 23.37 %
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 = 1.301
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5686 2.336
h = 0.001 0.001
y[1] (numeric) = -5.44924633639 -3.3761770804
y[1] (closed_form) = -4.39719125287 -2.75770807993
absolute error = 1.22
relative error = 23.51 %
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 = 0.3669
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5676 2.337
h = 0.0001 0.004
y[1] (numeric) = -5.47572538833 -3.38331577902
y[1] (closed_form) = -4.40431948882 -2.75619776934
absolute error = 1.241
relative error = 23.89 %
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 = 2.162
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5675 2.341
h = 0.003 0.006
y[1] (numeric) = -5.50232156501 -3.39044980127
y[1] (closed_form) = -4.42192807656 -2.76701834484
absolute error = 1.247
relative error = 23.91 %
Correct digits = 1
memory used=2626.5MB, alloc=44.3MB, time=30.78
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8878
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5645 2.347
h = 0.0001 0.005
y[1] (numeric) = -5.52903532117 -3.39757903747
y[1] (closed_form) = -4.45653868052 -2.77086604226
absolute error = 1.242
relative error = 23.67 %
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 = 1.584
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5644 2.352
h = 0.0001 0.003
y[1] (numeric) = -5.55586770148 -3.40470264424
y[1] (closed_form) = -4.47875666607 -2.78457112302
absolute error = 1.243
relative error = 23.57 %
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 = 1.298
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5643 2.355
h = 0.001 0.001
y[1] (numeric) = -5.58281941486 -3.41182065693
y[1] (closed_form) = -4.49225622077 -2.7926489219
absolute error = 1.254
relative error = 23.71 %
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 = 0.3664
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5633 2.356
h = 0.001 0.003
y[1] (numeric) = -5.60989068058 -3.41893318877
y[1] (closed_form) = -4.49951448789 -2.79107575282
absolute error = 1.276
relative error = 24.09 %
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 = 1.914
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5623 2.359
h = 0.0001 0.004
y[1] (numeric) = -5.63708155311 -3.42604022752
y[1] (closed_form) = -4.51564066838 -2.79517913429
absolute error = 1.287
relative error = 24.23 %
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 = 2.168
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5622 2.363
h = 0.003 0.006
y[1] (numeric) = -5.6643922182 -3.43314174914
y[1] (closed_form) = -4.53370520855 -2.80613840676
absolute error = 1.293
relative error = 24.25 %
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 = 0.8866
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5592 2.369
h = 0.0001 0.005
y[1] (numeric) = -5.69182317277 -3.44023762798
y[1] (closed_form) = -4.56911040253 -2.80987022605
absolute error = 1.288
relative error = 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 = 1.584
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5591 2.374
h = 0.0001 0.003
y[1] (numeric) = -5.71937548104 -3.44732699389
y[1] (closed_form) = -4.59190389383 -2.82375168652
absolute error = 1.288
relative error = 23.9 %
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 = 1.301
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.559 2.377
h = 0.001 0.001
y[1] (numeric) = -5.74704986907 -3.45440987852
y[1] (closed_form) = -4.60575163763 -2.83193112957
absolute error = 1.3
relative error = 24.04 %
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 = 0.3665
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.558 2.378
h = 0.001 0.003
y[1] (numeric) = -5.77484656208 -3.46148639641
y[1] (closed_form) = -4.61316268358 -2.83028063028
absolute error = 1.322
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 = 1.917
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2670.3MB, alloc=44.3MB, time=31.29
x[1] = -0.557 2.381
h = 0.0001 0.004
y[1] (numeric) = -5.80276561576 -3.46855653469
y[1] (closed_form) = -4.62967251673 -2.8343817577
absolute error = 1.334
relative error = 24.57 %
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 = 2.173
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5569 2.385
h = 0.003 0.006
y[1] (numeric) = -5.83080722015 -3.47562026755
y[1] (closed_form) = -4.64820380125 -2.84548051073
absolute error = 1.34
relative error = 24.59 %
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 = 0.8855
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5539 2.391
h = 0.0001 0.005
y[1] (numeric) = -5.85897188322 -3.48267746318
y[1] (closed_form) = -4.68442059763 -2.84908989621
absolute error = 1.335
relative error = 24.34 %
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 = 1.584
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5538 2.396
h = 0.0001 0.003
y[1] (numeric) = -5.88726068903 -3.48972722389
y[1] (closed_form) = -4.70780322415 -2.86314874942
absolute error = 1.336
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 = 1.303
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5537 2.399
h = 0.001 0.001
y[1] (numeric) = -5.91567438118 -3.49676957747
y[1] (closed_form) = -4.72200737813 -2.87143033628
absolute error = 1.348
relative error = 24.38 %
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 = 0.3667
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5527 2.4
h = 0.001 0.003
y[1] (numeric) = -5.94421319098 -3.50380463975
y[1] (closed_form) = -4.72957419687 -2.86970002589
absolute error = 1.37
relative error = 24.77 %
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 = 1.92
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5517 2.403
h = 0.0001 0.004
y[1] (numeric) = -5.97287717537 -3.51083239721
y[1] (closed_form) = -4.74647616634 -2.87379691867
absolute error = 1.382
relative error = 24.91 %
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 = 2.177
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5516 2.407
h = 0.003 0.006
y[1] (numeric) = -6.00166652876 -3.51785282219
y[1] (closed_form) = -4.76548523248 -2.88503589062
absolute error = 1.389
relative error = 24.93 %
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 = 0.8845
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5486 2.413
h = 0.0001 0.005
y[1] (numeric) = -6.03058177039 -3.52486577654
y[1] (closed_form) = -4.80253098508 -2.88851604148
absolute error = 1.383
relative error = 24.68 %
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 = 1.584
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5485 2.418
h = 0.0001 0.003
y[1] (numeric) = -6.05962400448 -3.53187033426
y[1] (closed_form) = -4.82651668627 -2.90275324395
absolute error = 1.384
relative error = 24.58 %
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 = 1.305
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2714.1MB, alloc=44.3MB, time=31.80
x[1] = -0.5484 2.421
h = 0.001 0.001
y[1] (numeric) = -6.08879399253 -3.53886651907
y[1] (closed_form) = -4.84108565786 -2.91113743773
absolute error = 1.397
relative error = 24.73 %
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 = 0.3668
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5474 2.422
h = 0.001 0.003
y[1] (numeric) = -6.1180919721 -3.54585444811
y[1] (closed_form) = -4.84881129571 -2.90932476264
absolute error = 1.42
relative error = 25.11 %
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 = 1.922
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5464 2.425
h = 0.0001 0.004
y[1] (numeric) = -6.14751800141 -3.55283410716
y[1] (closed_form) = -4.86611406297 -2.91341534681
absolute error = 1.432
relative error = 25.25 %
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 = 2.182
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5463 2.429
h = 0.003 0.006
y[1] (numeric) = -6.17707227932 -3.55980546669
y[1] (closed_form) = -4.88561219852 -2.92479522852
absolute error = 1.439
relative error = 25.27 %
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 = 0.8835
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5433 2.435
h = 0.0001 0.005
y[1] (numeric) = -6.2067553366 -3.56676838194
y[1] (closed_form) = -4.92350460898 -2.92813909172
absolute error = 1.433
relative error = 25.02 %
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 = 1.585
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5432 2.44
h = 0.0001 0.003
y[1] (numeric) = -6.23656829789 -3.57372189783
y[1] (closed_form) = -4.94810764084 -2.94255554062
absolute error = 1.435
relative error = 24.92 %
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 = 1.307
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5431 2.443
h = 0.001 0.001
y[1] (numeric) = -6.26651194302 -3.58066603385
y[1] (closed_form) = -4.96305002769 -2.95104276611
absolute error = 1.448
relative error = 25.07 %
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 = 0.367
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5421 2.444
h = 0.0001 0.004
y[1] (numeric) = -6.29658651595 -3.58760090839
y[1] (closed_form) = -4.97093758421 -2.94914509813
absolute error = 1.471
relative error = 25.46 %
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 = 2.185
Order of pole (three term test) = 32.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.542 2.448
h = 0.003 0.006
y[1] (numeric) = -6.32679210994 -3.59452655585
y[1] (closed_form) = -4.99086423979 -2.96065279904
absolute error = 1.479
relative error = 25.48 %
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 = 0.8852
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.539 2.454
h = 0.0001 0.005
y[1] (numeric) = -6.35712923077 -3.60144283801
y[1] (closed_form) = -5.02950161301 -2.96388388338
absolute error = 1.473
relative error = 25.23 %
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 = 1.59
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2758.1MB, alloc=44.3MB, time=32.32
x[1] = -0.5389 2.459
h = 0.0001 0.003
y[1] (numeric) = -6.38759902036 -3.60834877494
y[1] (closed_form) = -5.05464553641 -2.97846288335
absolute error = 1.474
relative error = 25.13 %
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 = 1.305
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5388 2.462
h = 0.001 0.001
y[1] (numeric) = -6.41820227413 -3.61524438239
y[1] (closed_form) = -5.06991514623 -2.98704369581
absolute error = 1.487
relative error = 25.28 %
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 = 0.3665
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5378 2.463
h = 0.001 0.003
y[1] (numeric) = -6.44893924151 -3.62212977985
y[1] (closed_form) = -5.07794565665 -2.98507268584
absolute error = 1.512
relative error = 25.67 %
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 = 1.915
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5368 2.466
h = 0.0001 0.004
y[1] (numeric) = -6.4798099831 -3.62900495178
y[1] (closed_form) = -5.09601802934 -2.98915070535
absolute error = 1.525
relative error = 25.81 %
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 = 2.189
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5367 2.47
h = 0.003 0.006
y[1] (numeric) = -6.51081470621 -3.63586986499
y[1] (closed_form) = -5.11645543656 -3.00080060889
absolute error = 1.532
relative error = 25.83 %
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 = 0.8842
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5337 2.476
h = 0.0001 0.005
y[1] (numeric) = -6.54195396331 -3.64272436206
y[1] (closed_form) = -5.15597344547 -3.00388180577
absolute error = 1.526
relative error = 25.58 %
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 = 1.59
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5336 2.481
h = 0.0001 0.003
y[1] (numeric) = -6.57322891739 -3.64956743242
y[1] (closed_form) = -5.18176208332 -3.01864173265
absolute error = 1.528
relative error = 25.48 %
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 = 1.307
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5335 2.484
h = 0.001 0.001
y[1] (numeric) = -6.60464038293 -3.6563990872
y[1] (closed_form) = -5.19742162297 -3.02732636705
absolute error = 1.541
relative error = 25.63 %
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 = 0.3667
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5325 2.485
h = 0.001 0.003
y[1] (numeric) = -6.63618861608 -3.66321944714
y[1] (closed_form) = -5.20561999743 -3.02526530704
absolute error = 1.566
relative error = 26.02 %
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 = 1.918
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5315 2.488
h = 0.0001 0.004
y[1] (numeric) = -6.66787367879 -3.67002849596
y[1] (closed_form) = -5.22411898814 -3.02933065279
absolute error = 1.58
relative error = 26.16 %
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 = 2.193
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2802.0MB, alloc=44.3MB, time=32.83
x[1] = -0.5314 2.492
h = 0.003 0.006
y[1] (numeric) = -6.6996957831 -3.67682619836
y[1] (closed_form) = -5.24507918184 -3.04112330404
absolute error = 1.587
relative error = 26.18 %
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 = 0.8831
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5284 2.498
h = 0.0001 0.005
y[1] (numeric) = -6.73165549366 -3.68361238967
y[1] (closed_form) = -5.2854965622 -3.04404680195
absolute error = 1.581
relative error = 25.93 %
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 = 1.59
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5283 2.503
h = 0.0001 0.003
y[1] (numeric) = -6.76375399484 -3.6903860279
y[1] (closed_form) = -5.3119451144 -3.05898837076
absolute error = 1.583
relative error = 25.83 %
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 = 1.309
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5282 2.506
h = 0.001 0.001
y[1] (numeric) = -6.79599212061 -3.69714711929
y[1] (closed_form) = -5.32800374884 -3.06777713455
absolute error = 1.597
relative error = 25.98 %
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 = 0.3668
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5272 2.507
h = 0.001 0.003
y[1] (numeric) = -6.82837013398 -3.70389578583
y[1] (closed_form) = -5.33637324448 -3.0656231728
absolute error = 1.623
relative error = 26.37 %
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 = 1.921
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5262 2.51
h = 0.0001 0.004
y[1] (numeric) = -6.8608880983 -3.71063201048
y[1] (closed_form) = -5.35530823542 -3.06967338399
absolute error = 1.636
relative error = 26.51 %
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 = 2.197
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5261 2.514
h = 0.003 0.006
y[1] (numeric) = -6.89354623041 -3.71735575575
y[1] (closed_form) = -5.37680352209 -3.08160927121
absolute error = 1.645
relative error = 26.54 %
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 = 0.8822
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5231 2.52
h = 0.0001 0.005
y[1] (numeric) = -6.92634510742 -3.72406684951
y[1] (closed_form) = -5.41813938292 -3.08436697698
absolute error = 1.638
relative error = 26.28 %
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 = 1.589
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.523 2.525
h = 0.0001 0.003
y[1] (numeric) = -6.95928593535 -3.73076421743
y[1] (closed_form) = -5.44526339261 -3.09949083166
absolute error = 1.64
relative error = 26.18 %
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 = 1.311
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5229 2.528
h = 0.001 0.001
y[1] (numeric) = -6.99236956812 -3.73744786066
y[1] (closed_form) = -5.46173049302 -3.10838398667
absolute error = 1.655
relative error = 26.33 %
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 = 0.367
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5219 2.529
h = 0.001 0.003
y[1] (numeric) = -7.02559627576 -3.74411790245
y[1] (closed_form) = -5.47027442335 -3.10613418924
absolute error = 1.681
relative error = 26.72 %
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 = 1.924
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2845.9MB, alloc=44.3MB, time=33.34
x[1] = -0.5209 2.532
h = 0.0001 0.004
y[1] (numeric) = -7.05896612303 -3.75077432495
y[1] (closed_form) = -5.489654992 -3.11016669647
absolute error = 1.695
relative error = 26.86 %
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 = 2.201
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5208 2.536
h = 0.003 0.006
y[1] (numeric) = -7.09247933171 -3.75741708841
y[1] (closed_form) = -5.51169795549 -3.12224624841
absolute error = 1.704
relative error = 26.89 %
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 = 0.8812
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5178 2.542
h = 0.0001 0.005
y[1] (numeric) = -7.12613649157 -3.76404601297
y[1] (closed_form) = -5.55397178589 -3.1248297791
absolute error = 1.697
relative error = 26.63 %
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 = 1.589
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5177 2.547
h = 0.0001 0.003
y[1] (numeric) = -7.15993883063 -3.7706599911
y[1] (closed_form) = -5.58178714668 -3.14013648915
absolute error = 1.699
relative error = 26.54 %
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 = 1.313
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5176 2.55
h = 0.001 0.001
y[1] (numeric) = -7.19388722317 -3.77725901862
y[1] (closed_form) = -5.59867229483 -3.14913424955
absolute error = 1.714
relative error = 26.69 %
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 = 0.3671
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5166 2.551
h = 0.0001 0.004
y[1] (numeric) = -7.22798194644 -3.78384322003
y[1] (closed_form) = -5.60739403053 -3.14678559811
absolute error = 1.741
relative error = 27.08 %
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 = 2.202
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5165 2.555
h = 0.003 0.006
y[1] (numeric) = -7.26222310607 -3.79041263071
y[1] (closed_form) = -5.62991699173 -3.15899584093
absolute error = 1.75
relative error = 27.11 %
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 = 0.883
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5135 2.561
h = 0.0001 0.005
y[1] (numeric) = -7.29661126404 -3.796967079
y[1] (closed_form) = -5.67301631294 -3.16143400344
absolute error = 1.744
relative error = 26.85 %
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 = 1.594
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5134 2.566
h = 0.0001 0.003
y[1] (numeric) = -7.33114766697 -3.80350542902
y[1] (closed_form) = -5.70143757995 -3.17690700564
absolute error = 1.746
relative error = 26.75 %
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 = 1.31
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5133 2.569
h = 0.001 0.001
y[1] (numeric) = -7.36583320644 -3.8100276719
y[1] (closed_form) = -5.71868915791 -3.18600007952
absolute error = 1.761
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 = 0.3666
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2889.7MB, alloc=44.3MB, time=33.86
x[1] = -0.5123 2.57
h = 0.001 0.003
y[1] (numeric) = -7.40066816587 -3.81653393319
y[1] (closed_form) = -5.72756791406 -3.18356602855
absolute error = 1.789
relative error = 27.3 %
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 = 1.917
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5113 2.573
h = 0.0001 0.004
y[1] (numeric) = -7.43565261264 -3.82302419346
y[1] (closed_form) = -5.7478040626 -3.18756395459
absolute error = 1.804
relative error = 27.44 %
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 = 2.206
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5112 2.577
h = 0.003 0.006
y[1] (numeric) = -7.47078677787 -3.82949840862
y[1] (closed_form) = -5.77089887122 -3.19991865015
absolute error = 1.813
relative error = 27.47 %
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 = 0.882
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5082 2.583
h = 0.0001 0.005
y[1] (numeric) = -7.50607127524 -3.83595638393
y[1] (closed_form) = -5.81497357053 -3.2021664819
absolute error = 1.806
relative error = 27.2 %
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 = 1.594
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5081 2.588
h = 0.0001 0.003
y[1] (numeric) = -7.54150737398 -3.84239694858
y[1] (closed_form) = -5.84411671657 -3.21782338876
absolute error = 1.809
relative error = 27.11 %
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 = 1.312
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.508 2.591
h = 0.001 0.001
y[1] (numeric) = -7.57709598689 -3.8488200879
y[1] (closed_form) = -5.86180474625 -3.22702145259
absolute error = 1.825
relative error = 27.27 %
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 = 0.3668
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.507 2.592
h = 0.001 0.003
y[1] (numeric) = -7.61283740492 -3.85522592866
y[1] (closed_form) = -5.87086777328 -3.22448274098
absolute error = 1.853
relative error = 27.66 %
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 = 1.92
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.506 2.595
h = 0.0001 0.004
y[1] (numeric) = -7.64873169695 -3.86161445054
y[1] (closed_form) = -5.89157804593 -3.22845510437
absolute error = 1.868
relative error = 27.8 %
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 = 2.209
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5059 2.599
h = 0.003 0.006
y[1] (numeric) = -7.68477909934 -3.86798560694
y[1] (closed_form) = -5.91525811276 -3.24095449934
absolute error = 1.877
relative error = 27.83 %
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 = 0.8811
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5029 2.605
h = 0.0001 0.005
y[1] (numeric) = -7.72098023918 -3.87433919465
y[1] (closed_form) = -5.96032880906 -3.24300274616
absolute error = 1.87
relative error = 27.57 %
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 = 1.593
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2933.7MB, alloc=44.3MB, time=34.38
x[1] = -0.5028 2.61
h = 0.0001 0.003
y[1] (numeric) = -7.75733640862 -3.88067400696
y[1] (closed_form) = -5.99021077262 -3.25884389932
absolute error = 1.873
relative error = 27.47 %
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 = 1.314
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5027 2.613
h = 0.001 0.001
y[1] (numeric) = -7.79384854215 -3.88699002316
y[1] (closed_form) = -6.00834546354 -3.26814702154
absolute error = 1.89
relative error = 27.63 %
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 = 0.3669
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5017 2.614
h = 0.001 0.003
y[1] (numeric) = -7.83051693845 -3.89328737119
y[1] (closed_form) = -6.01759630142 -3.26550037818
absolute error = 1.919
relative error = 28.02 %
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 = 1.923
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5007 2.617
h = 0.0001 0.004
y[1] (numeric) = -7.86734166793 -3.89956602983
y[1] (closed_form) = -6.0387910669 -3.26944416
absolute error = 1.934
relative error = 28.16 %
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 = 2.212
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5006 2.621
h = 0.003 0.006
y[1] (numeric) = -7.90432297226 -3.90582594991
y[1] (closed_form) = -6.0630701033 -3.28208843052
absolute error = 1.944
relative error = 28.2 %
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 = 0.8802
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4976 2.627
h = 0.0001 0.005
y[1] (numeric) = -7.94146149223 -3.91206691941
y[1] (closed_form) = -6.10915782303 -3.28392751498
absolute error = 1.937
relative error = 27.93 %
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 = 1.593
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4975 2.632
h = 0.0001 0.003
y[1] (numeric) = -7.97875854325 -3.91828769479
y[1] (closed_form) = -6.13979592241 -3.29995316778
absolute error = 1.94
relative error = 27.83 %
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 = 1.316
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4974 2.635
h = 0.001 0.001
y[1] (numeric) = -8.01621508194 -3.924488249
y[1] (closed_form) = -6.15838771225 -3.30936136057
absolute error = 1.957
relative error = 27.99 %
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 = 0.3671
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4964 2.636
h = 0.001 0.003
y[1] (numeric) = -8.05383141491 -3.93066871117
y[1] (closed_form) = -6.16782996141 -3.30660342133
absolute error = 1.987
relative error = 28.39 %
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 = 1.925
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4954 2.639
h = 0.0001 0.004
y[1] (numeric) = -8.09160761411 -3.93682905912
y[1] (closed_form) = -6.18951980264 -3.31051547665
absolute error = 2.003
relative error = 28.53 %
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 = 2.215
Order of pole (three term test) = 32.47 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2977.7MB, alloc=44.3MB, time=34.89
x[1] = -0.4953 2.643
h = 0.003 0.006
y[1] (numeric) = -8.12954392667 -3.94296924099
y[1] (closed_form) = -6.21441182685 -3.32330472524
absolute error = 2.013
relative error = 28.56 %
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 = 0.8793
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4923 2.649
h = 0.0001 0.005
y[1] (numeric) = -8.16764100732 -3.94908903574
y[1] (closed_form) = -6.26153801136 -3.32492473733
absolute error = 2.006
relative error = 28.29 %
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 = 1.592
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4922 2.654
h = 0.0001 0.003
y[1] (numeric) = -8.20590019505 -3.95518716195
y[1] (closed_form) = -6.29294995264 -3.34113505089
absolute error = 2.009
relative error = 28.2 %
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 = 1.318
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4921 2.657
h = 0.001 0.001
y[1] (numeric) = -8.24432246912 -3.96126358596
y[1] (closed_form) = -6.31200951198 -3.35064826771
absolute error = 2.026
relative error = 28.36 %
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 = 0.3672
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4911 2.658
h = 0.0001 0.004
y[1] (numeric) = -8.28290814424 -3.96731843806
y[1] (closed_form) = -6.32164683415 -3.34777557309
absolute error = 2.057
relative error = 28.75 %
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 = 2.217
Order of pole (three term test) = 32.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.491 2.662
h = 0.003 0.006
y[1] (numeric) = -8.32165733992 -3.97335175439
y[1] (closed_form) = -6.34707623507 -3.36069717243
absolute error = 2.067
relative error = 28.79 %
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 = 0.8812
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.488 2.668
h = 0.0001 0.005
y[1] (numeric) = -8.36057068003 -3.97936332402
y[1] (closed_form) = -6.39511656399 -3.36213314336
absolute error = 2.06
relative error = 28.51 %
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 = 1.597
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4879 2.673
h = 0.0001 0.003
y[1] (numeric) = -8.39964952349 -3.98535183323
y[1] (closed_form) = -6.42720688267 -3.37851197472
absolute error = 2.064
relative error = 28.42 %
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 = 1.315
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4878 2.676
h = 0.001 0.001
y[1] (numeric) = -8.43889486878 -3.99131724256
y[1] (closed_form) = -6.44667655936 -3.38812125828
absolute error = 2.082
relative error = 28.58 %
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 = 0.3668
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4868 2.677
h = 0.001 0.003
y[1] (numeric) = -8.47830703756 -3.99725968327
y[1] (closed_form) = -6.45648619841 -3.38514932537
absolute error = 2.112
relative error = 28.98 %
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 = 1.919
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4858 2.68
h = 0.0001 0.004
y[1] (numeric) = -8.51788610468 -4.00317913137
y[1] (closed_form) = -6.47912665034 -3.38899973197
absolute error = 2.129
relative error = 29.12 %
Correct digits = 1
memory used=3021.6MB, alloc=44.3MB, time=35.40
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.219
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4857 2.684
h = 0.003 0.006
y[1] (numeric) = -8.55763232757 -4.00907552983
y[1] (closed_form) = -6.50519596354 -3.40206646893
absolute error = 2.14
relative error = 29.16 %
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 = 0.8802
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4827 2.69
h = 0.0001 0.005
y[1] (numeric) = -8.59754638728 -4.0149486402
y[1] (closed_form) = -6.55431591237 -3.40326427686
absolute error = 2.133
relative error = 28.88 %
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 = 1.597
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4826 2.695
h = 0.0001 0.003
y[1] (numeric) = -8.63762966692 -4.02079710889
y[1] (closed_form) = -6.58721408065 -3.41982803151
absolute error = 2.137
relative error = 28.79 %
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 = 1.317
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4825 2.698
h = 0.001 0.001
y[1] (numeric) = -8.67788318856 -4.02662088933
y[1] (closed_form) = -6.60717202119 -3.42954222153
absolute error = 2.155
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 = 0.3669
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4815 2.699
h = 0.001 0.003
y[1] (numeric) = -8.71830728233 -4.03242011388
y[1] (closed_form) = -6.61718375705 -3.42644887905
absolute error = 2.187
relative error = 29.35 %
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 = 1.922
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4805 2.702
h = 0.0001 0.004
y[1] (numeric) = -8.75890202472 -4.03819475751
y[1] (closed_form) = -6.64035082281 -3.43025796592
absolute error = 2.204
relative error = 29.49 %
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 = 2.222
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4804 2.706
h = 0.003 0.006
y[1] (numeric) = -8.79966767896 -4.04394476022
y[1] (closed_form) = -6.66707498129 -3.44346971809
absolute error = 2.216
relative error = 29.53 %
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 = 0.8794
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4774 2.712
h = 0.0001 0.005
y[1] (numeric) = -8.84060494083 -4.04966987363
y[1] (closed_form) = -6.71729722428 -3.44441845349
absolute error = 2.208
relative error = 29.25 %
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 = 1.596
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4773 2.717
h = 0.0001 0.003
y[1] (numeric) = -8.88171521799 -4.05536870329
y[1] (closed_form) = -6.75102210413 -3.46116701079
absolute error = 2.212
relative error = 29.16 %
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 = 1.319
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4772 2.72
h = 0.001 0.001
y[1] (numeric) = -8.9229995566 -4.06104119511
y[1] (closed_form) = -6.77147967334 -3.47098588165
absolute error = 2.231
relative error = 29.32 %
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 = 0.3671
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3065.6MB, alloc=44.3MB, time=35.92
x[1] = -0.4762 2.721
h = 0.001 0.003
y[1] (numeric) = -8.96445829546 -4.06668748258
y[1] (closed_form) = -6.78169734915 -3.46776738436
absolute error = 2.263
relative error = 29.72 %
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 = 1.925
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4752 2.724
h = 0.0001 0.004
y[1] (numeric) = -9.00609151275 -4.07230753958
y[1] (closed_form) = -6.80540247949 -3.47153148516
absolute error = 2.281
relative error = 29.86 %
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 = 2.225
Order of pole (three term test) = 32.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4751 2.728
h = 0.003 0.006
y[1] (numeric) = -9.04789947758 -4.07790130306
y[1] (closed_form) = -6.83279674861 -3.48488804355
absolute error = 2.293
relative error = 29.9 %
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 = 0.8785
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4721 2.734
h = 0.0001 0.005
y[1] (numeric) = -9.08988290079 -4.08346851437
y[1] (closed_form) = -6.8841444045 -3.48557642624
absolute error = 2.285
relative error = 29.62 %
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 = 1.595
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.472 2.739
h = 0.0001 0.003
y[1] (numeric) = -9.1320432149 -4.08900773708
y[1] (closed_form) = -6.91871527793 -3.502509557
absolute error = 2.29
relative error = 29.53 %
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 = 1.32
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4719 2.742
h = 0.001 0.001
y[1] (numeric) = -9.17438149066 -4.09451890931
y[1] (closed_form) = -6.9396840928 -3.51243281429
absolute error = 2.309
relative error = 29.69 %
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 = 0.3672
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4709 2.743
h = 0.001 0.003
y[1] (numeric) = -9.21689807579 -4.10000216559
y[1] (closed_form) = -6.95011161643 -3.50908531185
absolute error = 2.343
relative error = 30.09 %
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 = 1.927
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4699 2.746
h = 0.0001 0.004
y[1] (numeric) = -9.25959305015 -4.10545747873
y[1] (closed_form) = -6.97436649691 -3.51280061428
absolute error = 2.361
relative error = 30.23 %
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 = 2.227
Order of pole (three term test) = 32.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4698 2.75
h = 0.003 0.006
y[1] (numeric) = -9.30246668889 -4.11088478249
y[1] (closed_form) = -7.00244648133 -3.5263016796
absolute error = 2.373
relative error = 30.27 %
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 = 0.8777
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4668 2.756
h = 0.0001 0.005
y[1] (numeric) = -9.34551971817 -4.11628380764
y[1] (closed_form) = -7.05494312123 -3.52671804826
absolute error = 2.365
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 = 1.595
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3109.5MB, alloc=44.3MB, time=36.43
x[1] = -0.4667 2.761
h = 0.0001 0.003
y[1] (numeric) = -9.3887535957 -4.12165307462
y[1] (closed_form) = -7.09037969899 -3.54383541014
absolute error = 2.37
relative error = 29.9 %
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 = 1.322
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4666 2.764
h = 0.001 0.001
y[1] (numeric) = -9.43216941737 -4.12699251343
y[1] (closed_form) = -7.11187163396 -3.55386268778
absolute error = 2.39
relative error = 30.06 %
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 = 0.3674
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4656 2.765
h = 0.0001 0.004
y[1] (numeric) = -9.47576754001 -4.13230225966
y[1] (closed_form) = -7.12251297886 -3.55038222212
absolute error = 2.424
relative error = 30.46 %
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 = 2.228
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4655 2.769
h = 0.003 0.006
y[1] (numeric) = -9.5195480987 -4.13758234986
y[1] (closed_form) = -7.15119424942 -3.56401579048
absolute error = 2.437
relative error = 30.5 %
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 = 0.8796
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4625 2.775
h = 0.0001 0.005
y[1] (numeric) = -9.56351178536 -4.14283252722
y[1] (closed_form) = -7.20470255942 -3.56420245878
absolute error = 2.429
relative error = 30.22 %
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 = 1.599
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4624 2.78
h = 0.0001 0.003
y[1] (numeric) = -9.60766007901 -4.14805127529
y[1] (closed_form) = -7.24089823757 -3.58148867655
absolute error = 2.434
relative error = 30.13 %
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 = 1.319
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4623 2.783
h = 0.001 0.001
y[1] (numeric) = -9.65199409686 -4.15323851705
y[1] (closed_form) = -7.26284893433 -3.59161157024
absolute error = 2.454
relative error = 30.29 %
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 = 0.3669
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4613 2.784
h = 0.001 0.003
y[1] (numeric) = -9.69651420356 -4.15839438893
y[1] (closed_form) = -7.27367921209 -3.58801601313
absolute error = 2.489
relative error = 30.69 %
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 = 1.921
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4603 2.787
h = 0.0001 0.004
y[1] (numeric) = -9.74122048216 -4.16351886158
y[1] (closed_form) = -7.29898966933 -3.59163673632
absolute error = 2.508
relative error = 30.83 %
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 = 2.23
Order of pole (three term test) = 32.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4602 2.791
h = 0.003 0.006
y[1] (numeric) = -9.78611321918 -4.16861186266
y[1] (closed_form) = -7.32838662536 -3.60541419725
absolute error = 2.521
relative error = 30.87 %
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 = 0.8787
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3153.3MB, alloc=44.3MB, time=36.94
x[1] = -0.4572 2.797
h = 0.0001 0.005
y[1] (numeric) = -9.83119316968 -4.17367310263
y[1] (closed_form) = -7.38308916145 -3.60530639463
absolute error = 2.513
relative error = 30.59 %
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 = 1.598
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4571 2.802
h = 0.0001 0.003
y[1] (numeric) = -9.8764618385 -4.17870101973
y[1] (closed_form) = -7.42018840031 -3.62277613623
absolute error = 2.518
relative error = 30.5 %
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 = 1.32
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.457 2.805
h = 0.001 0.001
y[1] (numeric) = -9.92192036905 -4.18369552813
y[1] (closed_form) = -7.44268502275 -3.63300231726
absolute error = 2.54
relative error = 30.66 %
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 = 0.3671
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.456 2.806
h = 0.001 0.003
y[1] (numeric) = -9.96756913548 -4.18865676527
y[1] (closed_form) = -7.45373674335 -3.62926618486
absolute error = 2.575
relative error = 31.06 %
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 = 1.924
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.455 2.809
h = 0.0001 0.004
y[1] (numeric) = -10.0134082227 -4.19358470059
y[1] (closed_form) = -7.47963176885 -3.63282650582
absolute error = 2.595
relative error = 31.21 %
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 = 2.232
Order of pole (three term test) = 32.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4549 2.813
h = 0.003 0.006
y[1] (numeric) = -10.0594379235 -4.19847925822
y[1] (closed_form) = -7.50976102624 -3.64674728489
absolute error = 2.609
relative error = 31.25 %
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 = 0.8779
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4519 2.819
h = 0.0001 0.005
y[1] (numeric) = -10.1056590093 -4.20334013707
y[1] (closed_form) = -7.56568270341 -3.6463322046
absolute error = 2.6
relative error = 30.96 %
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 = 1.598
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4518 2.824
h = 0.0001 0.003
y[1] (numeric) = -10.1520730109 -4.20816572879
y[1] (closed_form) = -7.60370649163 -3.66398478268
absolute error = 2.606
relative error = 30.87 %
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 = 1.322
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4517 2.827
h = 0.001 0.001
y[1] (numeric) = -10.1986810987 -4.21295593844
y[1] (closed_form) = -7.62676168139 -3.6743136668
absolute error = 2.628
relative error = 31.04 %
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 = 0.3672
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4507 2.828
h = 0.001 0.003
y[1] (numeric) = -10.2454836564 -4.21771090439
y[1] (closed_form) = -7.63803901225 -3.67043267827
absolute error = 2.664
relative error = 31.44 %
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 = 1.927
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3197.2MB, alloc=44.3MB, time=37.45
x[1] = -0.4497 2.831
h = 0.0001 0.004
y[1] (numeric) = -10.2924807708 -4.22243059485
y[1] (closed_form) = -7.66453124247 -3.67392818105
absolute error = 2.685
relative error = 31.58 %
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 = 2.234
Order of pole (three term test) = 32.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4496 2.835
h = 0.003 0.006
y[1] (numeric) = -10.3396727413 -4.22711493032
y[1] (closed_form) = -7.69540978441 -3.68799159838
absolute error = 2.699
relative error = 31.62 %
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 = 0.8771
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4466 2.841
h = 0.0001 0.005
y[1] (numeric) = -10.3870603557 -4.23176359774
y[1] (closed_form) = -7.75257600183 -3.68725600925
absolute error = 2.69
relative error = 31.34 %
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 = 1.597
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4465 2.846
h = 0.0001 0.003
y[1] (numeric) = -10.4346451715 -4.23637494098
y[1] (closed_form) = -7.7915457922 -3.7050906042
absolute error = 2.696
relative error = 31.25 %
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 = 1.324
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4464 2.849
h = 0.001 0.001
y[1] (numeric) = -10.4824283861 -4.24094885558
y[1] (closed_form) = -7.81517246956 -3.7155215237
absolute error = 2.719
relative error = 31.42 %
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 = 0.3674
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4454 2.85
h = 0.001 0.003
y[1] (numeric) = -10.5304103934 -4.24548548082
y[1] (closed_form) = -7.82667964714 -3.71149127954
absolute error = 2.756
relative error = 31.82 %
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 = 1.929
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4444 2.853
h = 0.0001 0.004
y[1] (numeric) = -10.5785912821 -4.24998478363
y[1] (closed_form) = -7.85378197571 -3.71491737937
absolute error = 2.777
relative error = 31.96 %
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 = 2.236
Order of pole (three term test) = 32.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4443 2.857
h = 0.003 0.006
y[1] (numeric) = -10.6269713581 -4.25444668075
y[1] (closed_form) = -7.88542716026 -3.72912264536
absolute error = 2.791
relative error = 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 = 0.8764
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4413 2.863
h = 0.0001 0.005
y[1] (numeric) = -10.6755514261 -4.2588708468
y[1] (closed_form) = -7.94386380975 -3.72805287985
absolute error = 2.783
relative error = 31.71 %
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 = 1.596
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4412 2.868
h = 0.0001 0.003
y[1] (numeric) = -10.7243330704 -4.26325557656
y[1] (closed_form) = -7.98380152885 -3.74606853442
absolute error = 2.789
relative error = 31.62 %
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 = 1.325
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4411 2.871
h = 0.001 0.001
y[1] (numeric) = -10.7733175164 -4.26760075567
y[1] (closed_form) = -8.00801289841 -3.75660073484
absolute error = 2.812
relative error = 31.79 %
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 = 0.3675
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3241.1MB, alloc=44.3MB, time=37.96
x[1] = -0.4401 2.872
h = 0.001 0.003
y[1] (numeric) = -10.8225051681 -4.2719065243
y[1] (closed_form) = -8.01975422918 -3.75241671389
absolute error = 2.85
relative error = 32.19 %
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 = 1.932
Order of pole (three term test) = 30.59 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ;
Iterations = 754
Total Elapsed Time = 37 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 37 Seconds
> quit
memory used=3250.2MB, alloc=44.3MB, time=38.07