|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"| ");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(2.0) - sin(c(x)));
> end;
exact_soln_y := proc(x) return c(2.0) - sin(c(x)) end proc
> exact_soln_yp := proc(x)
> return(neg( cos(c(x))));
> end;
exact_soln_yp := proc(x) return neg(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_2,
> array_const_0D0,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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_2,
> array_const_0D0,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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_2,
> array_const_0D0,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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_2,
> array_const_0D0,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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_2,
> array_const_0D0,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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_2,
> array_const_0D0,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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_2,
> array_const_0D0,
#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_g,
> array_tmp1,
> array_tmp2,
> 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 - 2 - 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 - 2 - 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 - 2 - 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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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 - 12;
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 - 12;
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 - 12;
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_2,
> array_const_0D0,
#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_g,
> array_tmp1,
> array_tmp2,
> 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 sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[3,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1);
> array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2);
> array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3);
> array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4);
> array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,7]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6));
> 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);
> 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 sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> 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_tmp2[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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 3] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(2))*c(factorial_3(0, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[3, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1);
array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 4] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(2))*c(factorial_3(1, 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)
end if
end if;
kkk := 3;
array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 5] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(2))*c(factorial_3(2, 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)
end if
end if;
kkk := 4;
array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 6] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(2))*c(factorial_3(3, 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)
end if
end if;
kkk := 5;
array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 7] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(2))*c(factorial_3(4, 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)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 2;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[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_2,
> array_const_0D0,
> #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_g,
> array_tmp1,
> array_tmp2,
> 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_g:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(3) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(3) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(3) ,(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_g[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_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) 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 <=3) 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 <=3) 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_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_2);
> array_const_2[1] := c(2);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := true;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/h2sinpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 2 ) = sin ( x ) ; ");
> 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 := 0.1 + 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,"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(c(2.0) - sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"return(neg( cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> 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 := 2;
> #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 := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #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 := 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 := 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 , 2 ) = sin ( x ) ; ");
> 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,"2017-11-26T14:56:54-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"h2sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 2 ) = sin ( x ) ; ")
> ;
> 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,"h2sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"h2sin 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_2, array_const_0D0, 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_g, array_tmp1, array_tmp2, 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_g := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 3, 0 .. 41, []);
array_y_higher_work := Array(0 .. 3, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 3, 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_g[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_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 3 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 <= 3 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 <= 3 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_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_2);
array_const_2[1] := c(2);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := true;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/h2sinpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 2 ) = sin ( x ) ; ");
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 := 0.1 + 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, "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(c(2.0) - sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "return(neg( 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,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
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 := 2;
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 := 3;
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 := 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 := 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 , 2 ) = sin ( x ) ; ");
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, "2017-11-26T14:56:54-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"h2sin");
logitem_str(html_log_file,
"diff ( y , x , 2 ) = sin ( x ) ; ");
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,
"h2sin diffeq.mxt");
logitem_str(html_log_file,
"h2sin 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/h2sinpostcpx.cpx#################
diff ( y , x , 2 ) = sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
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(c(2.0) - sin(c(x)));
end;
exact_soln_yp := proc(x)
return(neg( cos(c(x))));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 1.89966700016 -0.0996663334921
y[1] (closed_form) = 1.89966700016 -0.0996663334921
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 = 0.1768
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 1.89952569712 -0.103666478625
y[1] (closed_form) = 1.89951569693 -0.104666466122
absolute error = 0.001
relative error = 0.05257 %
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 = 0.08713
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 1.89938260428 -0.1076683
y[1] (closed_form) = 1.8993836282 -0.107667312081
absolute error = 1.423e-06
relative error = 7.479e-05 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06949
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 1.89923891824 -0.111670476005
y[1] (closed_form) = 1.89837190312 -0.108657179181
absolute error = 0.003136
relative error = 0.1649 %
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 = 0.333
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 1.8990943877 -0.115672681358
y[1] (closed_form) = 1.89733726525 -0.111648676907
absolute error = 0.004391
relative error = 0.231 %
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 = 0.1921
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 1.8989482514 -0.119675876471
y[1] (closed_form) = 1.89719049454 -0.115652505773
absolute error = 0.004391
relative error = 0.231 %
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 = 0.2598
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 1.89879774895 -0.123679666692
y[1] (closed_form) = 1.89411132224 -0.121625440337
absolute error = 0.005117
relative error = 0.2696 %
Correct digits = 3
memory used=31.7MB, alloc=40.3MB, time=0.40
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1205
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 1.8986423297 -0.127684693047
y[1] (closed_form) = 1.89394547619 -0.126634997662
absolute error = 0.004813
relative error = 0.2535 %
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 = 0.0994
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1055 0.13
h = 0.001 0.001
y[1] (numeric) = 1.89848498341 -0.13169177979
y[1] (closed_form) = 1.89380452194 -0.129641643138
absolute error = 0.00511
relative error = 0.2692 %
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 = 0.07919
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 1.89832699026 -0.135699312685
y[1] (closed_form) = 1.89278780891 -0.130630663334
absolute error = 0.007508
relative error = 0.3957 %
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 = 0.379
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 1.89816804238 -0.139706940477
y[1] (closed_form) = 1.89174221045 -0.133625537144
absolute error = 0.008847
relative error = 0.4665 %
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 = 0.2183
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 1.89800734691 -0.143715802634
y[1] (closed_form) = 1.89158329247 -0.137637798716
absolute error = 0.008844
relative error = 0.4663 %
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 = 0.2949
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 1.89784176017 -0.147725629219
y[1] (closed_form) = 1.88847900205 -0.143615303875
absolute error = 0.01023
relative error = 0.5399 %
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 = 0.1361
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 1.89767070351 -0.151737159705
y[1] (closed_form) = 1.88829736926 -0.148636531188
absolute error = 0.009873
relative error = 0.5212 %
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 = 0.1122
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 1.89749760619 -0.155751119778
y[1] (closed_form) = 1.88814676402 -0.151650314108
absolute error = 0.01021
relative error = 0.539 %
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 = 0.08927
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 1.89732380798 -0.159765617576
y[1] (closed_form) = 1.88712436884 -0.152638701201
absolute error = 0.01244
relative error = 0.6572 %
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 = 0.4269
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 1.89714894433 -0.163780275644
y[1] (closed_form) = 1.8860666346 -0.155638072673
absolute error = 0.01375
relative error = 0.7267 %
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 = 0.2455
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 1.89697219018 -0.167796412835
y[1] (closed_form) = 1.88589456119 -0.159660559171
absolute error = 0.01374
relative error = 0.7262 %
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 = 0.3312
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 1.89679001719 -0.171813883074
y[1] (closed_form) = 1.88276234326 -0.165644636231
absolute error = 0.01532
relative error = 0.8108 %
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 = 0.1524
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 1.89660181826 -0.175833524481
y[1] (closed_form) = 1.88256366988 -0.170679780464
absolute error = 0.01495
relative error = 0.7911 %
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 = 0.1254
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=75.8MB, alloc=44.3MB, time=0.93
x[1] = 0.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 1.89641146357 -0.179855965306
y[1] (closed_form) = 1.88240264212 -0.173702039755
absolute error = 0.0153
relative error = 0.8094 %
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 = 0.09967
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 1.89622035349 -0.183879035512
y[1] (closed_form) = 1.88137386815 -0.174690005932
absolute error = 0.01746
relative error = 0.9241 %
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 = 0.4762
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 1.89602806676 -0.187902331184
y[1] (closed_form) = 1.88030281638 -0.177694995866
absolute error = 0.01875
relative error = 0.9926 %
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 = 0.2735
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 1.89583374541 -0.191927350971
y[1] (closed_form) = 1.88011657097 -0.181729501103
absolute error = 0.01874
relative error = 0.9919 %
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 = 0.3686
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 1.89563347487 -0.19595407177
y[1] (closed_form) = 1.87695360189 -0.187722147852
absolute error = 0.02041
relative error = 1.082 %
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 = 0.1691
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 1.8954266191 -0.19998343059
y[1] (closed_form) = 1.87673662305 -0.192773458308
absolute error = 0.02003
relative error = 1.062 %
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 = 0.1389
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 1.89521749085 -0.20401595943
y[1] (closed_form) = 1.87656439451 -0.195805534333
absolute error = 0.02038
relative error = 1.08 %
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 = 0.1104
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 1.89500755222 -0.208049209419
y[1] (closed_form) = 1.8755285423 -0.196793290103
absolute error = 0.0225
relative error = 1.193 %
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 = 0.6668
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 1.894796339 -0.212083861926
y[1] (closed_form) = 1.87532944929 -0.200839764217
absolute error = 0.02248
relative error = 1.192 %
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 = 0.4014
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 1.89457872276 -0.216120527275
y[1] (closed_form) = 1.87213787178 -0.206841797121
absolute error = 0.02428
relative error = 1.289 %
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 = 0.1838
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 1.89435404257 -0.220160238948
y[1] (closed_form) = 1.87190434321 -0.211909065234
absolute error = 0.02392
relative error = 1.27 %
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 = 0.1508
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 1.89412699243 -0.224203441792
y[1] (closed_form) = 1.87172198327 -0.214950812089
absolute error = 0.02424
relative error = 1.287 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1198
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 1.89389908524 -0.228247445551
y[1] (closed_form) = 1.8706794767 -0.215938649698
absolute error = 0.02628
relative error = 1.396 %
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 = 0.5716
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 1.89366979359 -0.232291796976
y[1] (closed_form) = 1.86958057139 -0.218957267869
absolute error = 0.02753
relative error = 1.463 %
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 = 0.3277
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=119.9MB, alloc=44.3MB, time=1.45
x[1] = 0.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 1.89343819847 -0.236338331038
y[1] (closed_form) = 1.86936541088 -0.223019117204
absolute error = 0.02751
relative error = 1.461 %
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 = 0.4407
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 1.89319966311 -0.24038725562
y[1] (closed_form) = 1.86613780782 -0.229033462834
absolute error = 0.02935
relative error = 1.561 %
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 = 0.2013
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 1.89295349751 -0.244439692872
y[1] (closed_form) = 1.86588361398 -0.234121106838
absolute error = 0.02897
relative error = 1.541 %
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 = 0.1651
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.131 0.237
h = 0.001 0.001
y[1] (numeric) = 1.89270484181 -0.248495993739
y[1] (closed_form) = 1.86568860092 -0.237175179306
absolute error = 0.02929
relative error = 1.558 %
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 = 0.131
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.132 0.238
h = 0.001 0.003
y[1] (numeric) = 1.89245527305 -0.252553187578
y[1] (closed_form) = 1.8646377083 -0.238163201941
absolute error = 0.03132
relative error = 1.666 %
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 = 0.6248
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 1.89220420674 -0.256610793807
y[1] (closed_form) = 1.86352207458 -0.241190657123
absolute error = 0.03256
relative error = 1.733 %
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 = 0.3579
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 1.89195068872 -0.260670828783
y[1] (closed_form) = 1.86328980118 -0.245269683389
absolute error = 0.03254
relative error = 1.731 %
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 = 0.4809
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 1.89168969033 -0.264733620652
y[1] (closed_form) = 1.86002329837 -0.251298331088
absolute error = 0.0344
relative error = 1.833 %
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 = 0.2193
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 1.89142049108 -0.26880039136
y[1] (closed_form) = 1.85974713684 -0.256408611272
absolute error = 0.03401
relative error = 1.812 %
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 = 0.1796
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 1.89114867958 -0.272871399308
y[1] (closed_form) = 1.85953866949 -0.259476356295
absolute error = 0.03433
relative error = 1.828 %
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 = 0.1425
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 1.89087589836 -0.27694339248
y[1] (closed_form) = 1.85847868128 -0.26046476933
absolute error = 0.03635
relative error = 1.937 %
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 = 0.6793
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 1.89060150574 -0.281015862603
y[1] (closed_form) = 1.85734510443 -0.263502181622
absolute error = 0.03759
relative error = 2.004 %
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 = 0.3888
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 1.89032451147 -0.285091008119
y[1] (closed_form) = 1.85709466095 -0.267600190372
absolute error = 0.03755
relative error = 2.001 %
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 = 0.5221
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 1.89003949265 -0.289169276413
y[1] (closed_form) = 1.85378636314 -0.273645126931
absolute error = 0.03944
relative error = 2.105 %
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 = 0.2377
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=164.0MB, alloc=44.3MB, time=1.98
x[1] = 0.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 1.88974569771 -0.293251989616
y[1] (closed_form) = 1.85348691619 -0.278780308783
absolute error = 0.03904
relative error = 2.083 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1946
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 1.88944916616 -0.297339315007
y[1] (closed_form) = 1.85326418406 -0.281863076396
absolute error = 0.03936
relative error = 2.099 %
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 = 0.1542
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 1.88915160758 -0.301427718096
y[1] (closed_form) = 1.85219438646 -0.282852083264
absolute error = 0.04136
relative error = 2.208 %
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 = 0.7352
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 1.88885232287 -0.305516662541
y[1] (closed_form) = 1.85104164129 -0.285900573122
absolute error = 0.0426
relative error = 2.274 %
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 = 0.4206
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 1.8885502848 -0.309608529637
y[1] (closed_form) = 1.85077195781 -0.290019374322
absolute error = 0.04256
relative error = 2.272 %
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 = 0.5644
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 1.88823967358 -0.313703884949
y[1] (closed_form) = 1.84741894688 -0.296082584212
absolute error = 0.04446
relative error = 2.376 %
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 = 0.2566
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 1.88791970595 -0.31780415122
y[1] (closed_form) = 1.84709488038 -0.301244939142
absolute error = 0.04406
relative error = 2.354 %
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 = 0.2099
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 1.88759687504 -0.32190940609
y[1] (closed_form) = 1.84685706295 -0.304344082905
absolute error = 0.04437
relative error = 2.37 %
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 = 0.1663
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 1.88727295905 -0.326015831386
y[1] (closed_form) = 1.84577673758 -0.305333885021
absolute error = 0.04636
relative error = 2.478 %
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 = 1.003
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.148 0.308
h = 0.003 0.006
y[1] (numeric) = 1.88694737848 -0.330124485328
y[1] (closed_form) = 1.84548990293 -0.309472283621
absolute error = 0.04632
relative error = 2.475 %
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 = 0.6016
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 1.8866127542 -0.334236937311
y[1] (closed_form) = 1.84209629872 -0.315553390472
absolute error = 0.04828
relative error = 2.583 %
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 = 0.2733
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 1.88626827524 -0.338354708457
y[1] (closed_form) = 1.84175031944 -0.320741274242
absolute error = 0.04788
relative error = 2.561 %
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 = 0.2234
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 1.88592082649 -0.342477795036
y[1] (closed_form) = 1.841499069 -0.32385579414
absolute error = 0.04817
relative error = 2.576 %
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 = 0.1769
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 1.88557224321 -0.346602132784
y[1] (closed_form) = 1.84040911529 -0.324846577615
absolute error = 0.05013
relative error = 2.682 %
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 = 0.843
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=208.2MB, alloc=44.3MB, time=2.50
x[1] = 0.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 1.88522171864 -0.350727132707
y[1] (closed_form) = 1.83921756552 -0.327918927857
absolute error = 0.05135
relative error = 2.748 %
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 = 0.4817
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 1.88486815606 -0.354855519135
y[1] (closed_form) = 1.83890948478 -0.332081513707
absolute error = 0.05129
relative error = 2.745 %
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 = 0.6459
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 1.88450499109 -0.358988079385
y[1] (closed_form) = 1.83546569413 -0.338184616598
absolute error = 0.05327
relative error = 2.854 %
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 = 0.2931
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 1.88413138077 -0.363126425086
y[1] (closed_form) = 1.83509259241 -0.343403934662
absolute error = 0.05286
relative error = 2.831 %
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 = 0.2394
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 1.8837546693 -0.367270465767
y[1] (closed_form) = 1.83482471716 -0.346537370287
absolute error = 0.05314
relative error = 2.846 %
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 = 0.1896
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 1.88337676378 -0.371415850899
y[1] (closed_form) = 1.83372288767 -0.347529326872
absolute error = 0.0551
relative error = 2.952 %
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 = 0.9032
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 1.88299679948 -0.375561962182
y[1] (closed_form) = 1.83250861259 -0.350615979092
absolute error = 0.05631
relative error = 3.018 %
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 = 0.5159
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 1.88261363956 -0.379711709436
y[1] (closed_form) = 1.8321781745 -0.35480457816
absolute error = 0.05625
relative error = 3.014 %
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 = 0.6914
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 1.88222031427 -0.383865994944
y[1] (closed_form) = 1.82868120395 -0.360931656483
absolute error = 0.05824
relative error = 3.125 %
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 = 0.3135
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 1.88181594684 -0.388026532392
y[1] (closed_form) = 1.82827959246 -0.366184701432
absolute error = 0.05782
relative error = 3.101 %
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 = 0.256
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 1.88140834414 -0.392193146241
y[1] (closed_form) = 1.82799423948 -0.369338418916
absolute error = 0.0581
relative error = 3.115 %
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 = 0.2026
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 1.88099948705 -0.396361198156
y[1] (closed_form) = 1.82687980053 -0.370331743901
absolute error = 0.06005
relative error = 3.222 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.965
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 1.88058845256 -0.40053004005
y[1] (closed_form) = 1.82564152665 -0.373433822183
absolute error = 0.06126
relative error = 3.288 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5511
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 1.88017406254 -0.404702768293
y[1] (closed_form) = 1.82528760371 -0.377650267082
absolute error = 0.06119
relative error = 3.283 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7383
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=252.3MB, alloc=44.3MB, time=3.02
x[1] = 0.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 1.87974893845 -0.408880398921
y[1] (closed_form) = 1.82173442997 -0.383803298756
absolute error = 0.0632
relative error = 3.395 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3345
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 1.87931216897 -0.413064748253
y[1] (closed_form) = 1.82130290049 -0.389092371911
absolute error = 0.06277
relative error = 3.37 %
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 = 0.273
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 1.87887202721 -0.417255557422
y[1] (closed_form) = 1.82099920419 -0.392267742556
absolute error = 0.06304
relative error = 3.384 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.216
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 1.87843056979 -0.421447898636
y[1] (closed_form) = 1.81987141602 -0.393262628912
absolute error = 0.06499
relative error = 3.491 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 1.87798681519 -0.425641093509
y[1] (closed_form) = 1.81860785533 -0.396381258778
absolute error = 0.0662
relative error = 3.556 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5872
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 1.87753954271 -0.4298384261
y[1] (closed_form) = 1.81822930282 -0.400627389341
absolute error = 0.06611
relative error = 3.551 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7864
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 1.87708096144 -0.434041024936
y[1] (closed_form) = 1.81461687093 -0.40680835101
absolute error = 0.06814
relative error = 3.664 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.356
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 1.87661012462 -0.438250809589
y[1] (closed_form) = 1.81415399321 -0.41213576314
absolute error = 0.0677
relative error = 3.639 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2904
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 1.87613577549 -0.442467439672
y[1] (closed_form) = 1.81383107457 -0.415334163842
absolute error = 0.06796
relative error = 3.652 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2298
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 1.87566004847 -0.446685696173
y[1] (closed_form) = 1.81268919097 -0.416330802141
absolute error = 0.06991
relative error = 3.759 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 1.87518223672 -0.450907022432
y[1] (closed_form) = 1.81228889125 -0.420604276634
absolute error = 0.06981
relative error = 3.752 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.829
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 1.87469262208 -0.45513392353
y[1] (closed_form) = 1.80862334475 -0.426811617548
absolute error = 0.07188
relative error = 3.868 %
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 = 0.3751
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 1.87419022645 -0.459368420238
y[1] (closed_form) = 1.80813281484 -0.43217428577
absolute error = 0.07144
relative error = 3.843 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3059
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 1.87368420004 -0.463610097843
y[1] (closed_form) = 1.80779293236 -0.43539386063
absolute error = 0.07168
relative error = 3.855 %
Correct digits = 1
memory used=296.6MB, alloc=44.3MB, time=3.55
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.242
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 1.87317674251 -0.467853484189
y[1] (closed_form) = 1.80663833704 -0.436392337778
absolute error = 0.0736
relative error = 3.96 %
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 = 1.152
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 1.87266676228 -0.47209784376
y[1] (closed_form) = 1.80532447094 -0.439545105871
absolute error = 0.0748
relative error = 4.026 %
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 = 0.6574
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 1.87215295816 -0.476346813691
y[1] (closed_form) = 1.80489738471 -0.44385172486
absolute error = 0.07469
relative error = 4.019 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8799
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 1.87162676291 -0.480601733355
y[1] (closed_form) = 1.80116682831 -0.450090708459
absolute error = 0.07678
relative error = 4.136 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3979
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 1.87108716271 -0.484864716666
y[1] (closed_form) = 1.80064225388 -0.455496060783
absolute error = 0.07632
relative error = 4.109 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3244
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.182 0.451
h = 0.001 0.001
y[1] (numeric) = 1.87054378563 -0.489135270907
y[1] (closed_form) = 1.80028149182 -0.458741255002
absolute error = 0.07655
relative error = 4.121 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2566
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.183 0.452
h = 0.001 0.003
y[1] (numeric) = 1.8699989133 -0.493407629078
y[1] (closed_form) = 1.79911139626 -0.459741841098
absolute error = 0.07848
relative error = 4.226 %
Correct digits = 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) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 1.86945139472 -0.497681023753
y[1] (closed_form) = 1.79776848418 -0.462914406448
absolute error = 0.07967
relative error = 4.292 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6967
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 1.86889988223 -0.501959283444
y[1] (closed_form) = 1.79731341235 -0.467256033816
absolute error = 0.07955
relative error = 4.284 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9324
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 1.86833538467 -0.506243856218
y[1] (closed_form) = 1.79351469017 -0.473528634562
absolute error = 0.08166
relative error = 4.402 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4215
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 1.86775685021 -0.510536961227
y[1] (closed_form) = 1.79295457142 -0.478979013072
absolute error = 0.08119
relative error = 4.375 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3435
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 1.86717438929 -0.514838029771
y[1] (closed_form) = 1.79257200846 -0.482251222072
absolute error = 0.08141
relative error = 4.386 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2716
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 1.86659036788 -0.519140997906
y[1] (closed_form) = 1.79138564584 -0.483254100418
absolute error = 0.08333
relative error = 4.491 %
Correct digits = 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) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=340.7MB, alloc=44.3MB, time=4.07
x[1] = 0.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 1.86600357523 -0.523445065681
y[1] (closed_form) = 1.79001233563 -0.48644759628
absolute error = 0.08452
relative error = 4.556 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7374
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 1.86541261566 -0.527754254413
y[1] (closed_form) = 1.78952805817 -0.490826105342
absolute error = 0.08439
relative error = 4.548 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9866
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 1.86480806973 -0.53207011943
y[1] (closed_form) = 1.7856579754 -0.497134297128
absolute error = 0.08652
relative error = 4.668 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4458
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 1.86418884654 -0.536394985885
y[1] (closed_form) = 1.78506078584 -0.502632056145
absolute error = 0.08603
relative error = 4.639 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3632
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 1.86356554366 -0.540728211195
y[1] (closed_form) = 1.78465548443 -0.50593268258
absolute error = 0.08624
relative error = 4.649 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2872
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 1.86294061391 -0.545063432261
y[1] (closed_form) = 1.78345207996 -0.506938033732
absolute error = 0.08816
relative error = 4.755 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 1.8623127864 -0.549399815956
y[1] (closed_form) = 1.78204700071 -0.510153595812
absolute error = 0.08935
relative error = 4.82 %
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 = 0.7794
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 1.86168061588 -0.553741577913
y[1] (closed_form) = 1.78153227569 -0.514570869889
absolute error = 0.08921
relative error = 4.811 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.043
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 1.86103424994 -0.558090379231
y[1] (closed_form) = 1.77758759669 -0.520916626191
absolute error = 0.09135
relative error = 4.932 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4709
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 1.86037255759 -0.562448651873
y[1] (closed_form) = 1.77695178187 -0.526464132994
absolute error = 0.09085
relative error = 4.902 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3836
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 1.85970662853 -0.566815681548
y[1] (closed_form) = 1.77652278746 -0.529794587172
absolute error = 0.09105
relative error = 4.911 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3033
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 1.85903900498 -0.571184803674
y[1] (closed_form) = 1.77530155801 -0.530802588836
absolute error = 0.09297
relative error = 5.017 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.826
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.199 0.522
h = 0.003 0.006
y[1] (numeric) = 1.85836883724 -0.575557858445
y[1] (closed_form) = 1.77476010524 -0.535255129962
absolute error = 0.09282
relative error = 5.007 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 1.8576839494 -0.579938260572
y[1] (closed_form) = 1.77074907214 -0.541635742479
absolute error = 0.095
relative error = 5.13 %
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 = 0.4932
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=385.1MB, alloc=44.3MB, time=4.60
x[1] = 0.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 1.85698317465 -0.584328546961
y[1] (closed_form) = 1.77007937418 -0.547228462435
absolute error = 0.09449
relative error = 5.1 %
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 = 0.4018
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 1.85627802963 -0.588727937459
y[1] (closed_form) = 1.76962958603 -0.550586024862
absolute error = 0.09467
relative error = 5.108 %
Correct digits = 1
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) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 1.85557113209 -0.593129504911
y[1] (closed_form) = 1.76839241406 -0.551596673241
absolute error = 0.09657
relative error = 5.213 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.511
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 1.85486109785 -0.597532353365
y[1] (closed_form) = 1.76692479836 -0.554856745278
absolute error = 0.09774
relative error = 5.278 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8615
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 1.85414638733 -0.601941064948
y[1] (closed_form) = 1.76635054802 -0.55935159987
absolute error = 0.09758
relative error = 5.267 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.152
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 1.85341633051 -0.606357498726
y[1] (closed_form) = 1.76225880609 -0.565773488247
absolute error = 0.09978
relative error = 5.391 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.52
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 1.8526697202 -0.610784288201
y[1] (closed_form) = 1.76154754028 -0.571420417242
absolute error = 0.09926
relative error = 5.36 %
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 = 0.4235
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 1.8519185751 -0.615220585721
y[1] (closed_form) = 1.76107225211 -0.574810465358
absolute error = 0.09943
relative error = 5.367 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3347
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 1.85116560751 -0.619659157968
y[1] (closed_form) = 1.75981577641 -0.575824096575
absolute error = 0.1013
relative error = 5.472 %
Correct digits = 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) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 1.85040937195 -0.624099073807
y[1] (closed_form) = 1.75831237199 -0.579109516289
absolute error = 0.1025
relative error = 5.537 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9078
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 1.8496482744 -0.628545114442
y[1] (closed_form) = 1.75770401398 -0.583648599727
absolute error = 0.1023
relative error = 5.525 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.214
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 1.8488711973 -0.632999240223
y[1] (closed_form) = 1.75352820001 -0.590113737583
absolute error = 0.1045
relative error = 5.651 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5477
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 1.84807689018 -0.637464193995
y[1] (closed_form) = 1.7527737251 -0.595817284301
absolute error = 0.104
relative error = 5.618 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.446
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 1.84727787946 -0.641939063025
y[1] (closed_form) = 1.7522719296 -0.59924125286
absolute error = 0.1042
relative error = 5.624 %
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 = 0.3525
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=429.2MB, alloc=44.3MB, time=5.12
x[1] = 0.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 1.8464769749 -0.646416305168
y[1] (closed_form) = 1.75099534091 -0.60025803602
absolute error = 0.1061
relative error = 5.729 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.677
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 1.84567266931 -0.650894953343
y[1] (closed_form) = 1.74945469611 -0.603569950688
absolute error = 0.1072
relative error = 5.794 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9558
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 1.84486331238 -0.655379989641
y[1] (closed_form) = 1.74881089449 -0.608155190564
absolute error = 0.107
relative error = 5.781 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.278
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 1.84403733348 -0.659873473993
y[1] (closed_form) = 1.74454759684 -0.61466555163
absolute error = 0.1093
relative error = 5.908 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5765
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 1.84319343764 -0.664378259549
y[1] (closed_form) = 1.74374823868 -0.62042814049
absolute error = 0.1087
relative error = 5.874 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4693
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 1.84234466493 -0.668893371001
y[1] (closed_form) = 1.74321890854 -0.623887473529
absolute error = 0.1089
relative error = 5.88 %
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 = 0.3709
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 1.84149392563 -0.673410954592
y[1] (closed_form) = 1.7419213877 -0.624907574485
absolute error = 0.1108
relative error = 5.985 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.765
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 1.84063965034 -0.677930006502
y[1] (closed_form) = 1.74034202772 -0.628247134777
absolute error = 0.1119
relative error = 6.049 %
Correct digits = 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) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 1.83978013058 -0.682455711597
y[1] (closed_form) = 1.73966141959 -0.632880471461
absolute error = 0.1117
relative error = 6.035 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.344
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 1.83890333688 -0.686990227628
y[1] (closed_form) = 1.7353071762 -0.639438029682
absolute error = 0.114
relative error = 6.164 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6063
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 1.83800792852 -0.691536519052
y[1] (closed_form) = 1.73446122641 -0.645262101556
absolute error = 0.1134
relative error = 6.129 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4936
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 1.83710746538 -0.696093550579
y[1] (closed_form) = 1.73390331351 -0.648758252816
absolute error = 0.1135
relative error = 6.133 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.39
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 1.83620496143 -0.700653153939
y[1] (closed_form) = 1.73258403105 -0.649781834048
absolute error = 0.1154
relative error = 6.238 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.348
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 1.83529940482 -0.705217581418
y[1] (closed_form) = 1.73187123303 -0.654458595881
absolute error = 0.1152
relative error = 6.223 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.404
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=473.5MB, alloc=44.3MB, time=5.64
x[1] = 0.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 1.83437601167 -0.709791127692
y[1] (closed_form) = 1.72743648846 -0.661059501194
absolute error = 0.1175
relative error = 6.354 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6329
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 1.83343339997 -0.714376866838
y[1] (closed_form) = 1.72654981126 -0.666939046621
absolute error = 0.1169
relative error = 6.318 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5151
Order of pole (three term test) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 1.83248558153 -0.718973707793
y[1] (closed_form) = 1.72596690183 -0.670468419478
absolute error = 0.117
relative error = 6.321 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.407
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 1.83153565834 -0.723573207859
y[1] (closed_form) = 1.72462825931 -0.671495396738
absolute error = 0.1189
relative error = 6.425 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.937
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 1.83058194354 -0.728174293396
y[1] (closed_form) = 1.72297321273 -0.674889977815
absolute error = 0.1201
relative error = 6.489 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.103
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 1.82962261747 -0.732782532626
y[1] (closed_form) = 1.72222102035 -0.679618500022
absolute error = 0.1198
relative error = 6.473 %
Correct digits = 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) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 1.8286447819 -0.737400266064
y[1] (closed_form) = 1.71768877023 -0.686270319178
absolute error = 0.1222
relative error = 6.605 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6648
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 1.82764700882 -0.742030668656
y[1] (closed_form) = 1.71675225632 -0.692215957118
absolute error = 0.1216
relative error = 6.568 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5411
Order of pole (three term test) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.233 0.665
h = 0.001 0.001
y[1] (numeric) = 1.82664384203 -0.74667259436
y[1] (closed_form) = 1.71613877329 -0.695784893628
absolute error = 0.1217
relative error = 6.57 %
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 = 0.4275
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.234 0.666
h = 0.001 0.003
y[1] (numeric) = 1.8256384934 -0.751317280208
y[1] (closed_form) = 1.71477679863 -0.696815654319
absolute error = 0.1235
relative error = 6.674 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.034
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 1.8246292124 -0.755963613387
y[1] (closed_form) = 1.71307869528 -0.700241211747
absolute error = 0.1247
relative error = 6.738 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.159
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 1.82361411534 -0.76061737075
y[1] (closed_form) = 1.71228566282 -0.705023474745
absolute error = 0.1244
relative error = 6.72 %
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 = 1.549
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 1.82257982736 -0.765280985329
y[1] (closed_form) = 1.70765228948 -0.711728183458
absolute error = 0.1268
relative error = 6.853 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.698
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 1.82152487087 -0.76995774647
y[1] (closed_form) = 1.70666412526 -0.717742406252
absolute error = 0.1262
relative error = 6.815 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5681
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=517.8MB, alloc=44.3MB, time=6.17
x[1] = 0.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 1.82046432858 -0.774646456023
y[1] (closed_form) = 1.70601895658 -0.7213523905
absolute error = 0.1262
relative error = 6.816 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4488
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 1.81940152569 -0.7793380275
y[1] (closed_form) = 1.70463278844 -0.722387086932
absolute error = 0.1281
relative error = 6.92 %
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 = 2.135
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 1.81833464751 -0.784031308003
y[1] (closed_form) = 1.70289005521 -0.725844786474
absolute error = 0.1293
relative error = 6.984 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 1.81726174409 -0.78873228521
y[1] (closed_form) = 1.7020547058 -0.730682785655
absolute error = 0.129
relative error = 6.965 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 1.81616895729 -0.79344348266
y[1] (closed_form) = 1.69731653312 -0.73744236017
absolute error = 0.1314
relative error = 7.1 %
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 = 0.7325
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 1.81505475847 -0.798168305253
y[1] (closed_form) = 1.69627486544 -0.743527679381
absolute error = 0.1307
relative error = 7.059 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5961
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 1.81393477644 -0.802905505702
y[1] (closed_form) = 1.69559687505 -0.747180206777
absolute error = 0.1308
relative error = 7.059 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4709
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 1.81281245335 -0.807645670635
y[1] (closed_form) = 1.69418564014 -0.748218987413
absolute error = 0.1327
relative error = 7.164 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.24
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 1.8116859098 -0.812387606115
y[1] (closed_form) = 1.69239667608 -0.751709999076
absolute error = 0.1338
relative error = 7.227 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.276
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 1.81055312728 -0.817137512925
y[1] (closed_form) = 1.69151750056 -0.756605745377
absolute error = 0.1335
relative error = 7.207 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.705
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 1.80939975746 -0.821898003026
y[1] (closed_form) = 1.68667079184 -0.763422162512
absolute error = 0.1359
relative error = 7.343 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7683
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 1.8082242192 -0.826672598069
y[1] (closed_form) = 1.68557372658 -0.769581109641
absolute error = 0.1353
relative error = 7.301 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6252
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 1.80704269478 -0.831460004709
y[1] (closed_form) = 1.68486175354 -0.773277687335
absolute error = 0.1353
relative error = 7.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4939
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 1.80585874708 -0.836250479196
y[1] (closed_form) = 1.68342456618 -0.774320696654
absolute error = 0.1372
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 = 2.973
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=562.2MB, alloc=44.3MB, time=6.70
x[1] = 0.25 0.736
h = 0.003 0.006
y[1] (numeric) = 1.80467117892 -0.841046704719
y[1] (closed_form) = 1.68250715338 -0.779268319478
absolute error = 0.1369
relative error = 7.383 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.776
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 1.80346241519 -0.845853821504
y[1] (closed_form) = 1.67756468953 -0.786136602907
absolute error = 0.1393
relative error = 7.521 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8004
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 1.80223082693 -0.850675466464
y[1] (closed_form) = 1.67641930923 -0.792361660785
absolute error = 0.1387
relative error = 7.478 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6513
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 1.80099307849 -0.855510302433
y[1] (closed_form) = 1.67567768513 -0.796097795764
absolute error = 0.1387
relative error = 7.476 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5144
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 1.79975283579 -0.860348296898
y[1] (closed_form) = 1.6742174924 -0.797144881281
absolute error = 0.1405
relative error = 7.58 %
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 = 2.447
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 1.79850809694 -0.86518817771
y[1] (closed_form) = 1.67233857295 -0.800701605346
absolute error = 0.1417
relative error = 7.642 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.394
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 1.79725671211 -0.870036549403
y[1] (closed_form) = 1.67137446033 -0.805710779413
absolute error = 0.1414
relative error = 7.619 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.111
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 1.79599942345 -0.874897533569
y[1] (closed_form) = 1.67040444842 -0.810732573911
absolute error = 0.141
relative error = 7.596 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.878
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 1.79472010134 -0.879769883405
y[1] (closed_form) = 1.66532826319 -0.817676484628
absolute error = 0.1435
relative error = 7.736 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8461
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 1.79341705435 -0.884657356639
y[1] (closed_form) = 1.66411644872 -0.823996016976
absolute error = 0.1428
relative error = 7.691 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6883
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 1.79210761246 -0.889558548084
y[1] (closed_form) = 1.66333402847 -0.827788691023
absolute error = 0.1428
relative error = 7.687 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5437
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 1.79079557959 -0.894463024445
y[1] (closed_form) = 1.66184150274 -0.828842113114
absolute error = 0.1447
relative error = 7.791 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.586
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 1.7894788742 -0.89936946442
y[1] (closed_form) = 1.65990403339 -0.832443939954
absolute error = 0.1458
relative error = 7.854 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.473
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 1.78815526586 -0.904284733807
y[1] (closed_form) = 1.65888550907 -0.837529762931
absolute error = 0.1455
relative error = 7.829 %
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 = 1.968
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=606.5MB, alloc=44.3MB, time=7.23
x[1] = 0.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 1.78680887839 -0.909211724628
y[1] (closed_form) = 1.65368915608 -0.844536711474
absolute error = 0.148
relative error = 7.97 %
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 = 0.8865
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 1.78543796759 -0.914154323305
y[1] (closed_form) = 1.65241606005 -0.850937781192
absolute error = 0.1473
relative error = 7.924 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7212
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 1.78406044123 -0.91911108819
y[1] (closed_form) = 1.65159604997 -0.85477921536
absolute error = 0.1473
relative error = 7.919 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5697
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 1.78268023601 -0.924071244066
y[1] (closed_form) = 1.65007481105 -0.85583732432
absolute error = 0.1491
relative error = 8.023 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.71
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 1.78129520315 -0.929033424451
y[1] (closed_form) = 1.64808440826 -0.859477314253
absolute error = 0.1503
relative error = 8.085 %
Correct digits = 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) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.266 0.806
h = 0.003 0.006
y[1] (numeric) = 1.77990303374 -0.934004718384
y[1] (closed_form) = 1.64701572107 -0.864629246913
absolute error = 0.1499
relative error = 8.059 %
Correct 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) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 1.77848733093 -0.938988097528
y[1] (closed_form) = 1.64169519704 -0.871701216028
absolute error = 0.1524
relative error = 8.201 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9287
Order of pole (three term test) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 1.77704629154 -0.943987570384
y[1] (closed_form) = 1.64035874617 -0.878186444601
absolute error = 0.1517
relative error = 8.153 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7555
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 1.7755984096 -0.949001662358
y[1] (closed_form) = 1.63949987651 -0.882078199046
absolute error = 0.1517
relative error = 8.146 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5967
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 1.7741477589 -0.954019252322
y[1] (closed_form) = 1.63794898405 -0.883141122511
absolute error = 0.1535
relative error = 8.251 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.838
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 1.77269212277 -0.959038927487
y[1] (closed_form) = 1.63590389146 -0.886820470894
absolute error = 0.1547
relative error = 8.313 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.616
Order of pole (three term test) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 1.77122911111 -0.964068002825
y[1] (closed_form) = 1.63478335263 -0.892040612884
absolute error = 0.1543
relative error = 8.285 %
Correct 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) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 1.76974179824 -0.969109527173
y[1] (closed_form) = 1.62933458251 -0.899179586003
absolute error = 0.1569
relative error = 8.429 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9726
Order of pole (three term test) = 33.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 1.76822832023 -0.974167632518
y[1] (closed_form) = 1.627932655 -0.90575161851
absolute error = 0.1561
relative error = 8.379 %
Correct digits = 1
memory used=650.7MB, alloc=44.3MB, time=7.75
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7911
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 1.76670776614 -0.979240814961
y[1] (closed_form) = 1.62703362657 -0.909695267268
absolute error = 0.156
relative error = 8.37 %
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 = 0.6249
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 1.76518435133 -0.984317603341
y[1] (closed_form) = 1.62545212559 -0.910763128154
absolute error = 0.1579
relative error = 8.475 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.972
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 1.76365579053 -0.989396537403
y[1] (closed_form) = 1.62335055269 -0.914483035533
absolute error = 0.1591
relative error = 8.536 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 1.76211960967 -0.994485160827
y[1] (closed_form) = 1.62217643392 -0.919773505505
absolute error = 0.1586
relative error = 8.507 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.261
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 1.76055834582 -0.999586597071
y[1] (closed_form) = 1.61659526856 -0.9269814667
absolute error = 0.1612
relative error = 8.652 %
Correct digits = 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) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 1.75897007245 -1.00470510305
y[1] (closed_form) = 1.61512569252 -0.933642972525
absolute error = 0.1604
relative error = 8.6 %
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 = 0.8283
Order of pole (three term test) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 1.75737448275 -1.00983914934
y[1] (closed_form) = 1.61418517569 -0.937640103926
absolute error = 0.1604
relative error = 8.59 %
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 = 0.6542
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 1.7557759382 -1.01497691048
y[1] (closed_form) = 1.61257209612 -0.938713020261
absolute error = 0.1622
relative error = 8.695 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.937
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 1.75417297593 -1.02012163786
y[1] (closed_form) = 1.61135131484 -0.944066404719
absolute error = 0.1618
relative error = 8.664 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.352
Order of pole (three term test) = 33.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 1.75254425414 -1.02527948657
y[1] (closed_form) = 1.60565366119 -0.951336983551
absolute error = 0.1645
relative error = 8.812 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.059
Order of pole (three term test) = 33.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 1.75088778884 -1.03045483722
y[1] (closed_form) = 1.60412518648 -0.958078503676
absolute error = 0.1636
relative error = 8.758 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8616
Order of pole (three term test) = 33.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 1.74922380045 -1.03564613417
y[1] (closed_form) = 1.60314853226 -0.96212347061
absolute error = 0.1635
relative error = 8.747 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6805
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 1.74755677574 -1.04084124169
y[1] (closed_form) = 1.60150754422 -0.96320122134
absolute error = 0.1654
relative error = 8.851 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.237
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 1.74588429937 -1.04603860882
y[1] (closed_form) = 1.59929650492 -0.967000537974
absolute error = 0.1665
relative error = 8.911 %
Correct digits = 1
memory used=695.0MB, alloc=44.3MB, time=8.28
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.843
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 1.74420373604 -1.0512462136
y[1] (closed_form) = 1.59801884386 -0.972428267003
absolute error = 0.1661
relative error = 8.878 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.462
Order of pole (three term test) = 33.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 1.74249660059 -1.05646731785
y[1] (closed_form) = 1.59218089269 -0.979771578895
absolute error = 0.1688
relative error = 9.027 %
Correct digits = 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) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 1.74076084656 -1.06170641576
y[1] (closed_form) = 1.59058062173 -0.986607633921
absolute error = 0.1679
relative error = 8.971 %
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 = 0.9018
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 1.73901731611 -1.06696193339
y[1] (closed_form) = 1.58955994005 -0.990709095211
absolute error = 0.1678
relative error = 8.958 %
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 = 0.7122
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 1.73727065106 -1.07222137244
y[1] (closed_form) = 1.58788552775 -0.991792119412
absolute error = 0.1697
relative error = 9.062 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.387
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 1.73551836542 -1.07748313096
y[1] (closed_form) = 1.58561270221 -0.995635482114
absolute error = 0.1708
relative error = 9.122 %
Correct digits = 1
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) = 33.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 1.73375773143 -1.08275542414
y[1] (closed_form) = 1.584276313 -1.00113973237
absolute error = 0.1703
relative error = 9.088 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.577
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 1.73196970106 -1.0880415807
y[1] (closed_form) = 1.57829369008 -1.00855776379
absolute error = 0.173
relative error = 9.237 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 33.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 1.73015215981 -1.09334622417
y[1] (closed_form) = 1.57661929897 -1.01549109722
absolute error = 0.1721
relative error = 9.179 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9436
Order of pole (three term test) = 33.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 1.72832658143 -1.09866776646
y[1] (closed_form) = 1.57555316795 -1.01965068477
absolute error = 0.172
relative error = 9.165 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7452
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 1.72649776783 -1.10399334207
y[1] (closed_form) = 1.57384431539 -1.02073908572
absolute error = 0.1739
relative error = 9.269 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.545
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 1.72466316159 -1.10932129675
y[1] (closed_form) = 1.57150777105 -1.0246277167
absolute error = 0.175
relative error = 9.329 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.018
Order of pole (three term test) = 33.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 1.72281993937 -1.11466008596
y[1] (closed_form) = 1.57011076071 -1.03021068602
absolute error = 0.1745
relative error = 9.292 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.696
Order of pole (three term test) = 33.89 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=739.3MB, alloc=44.3MB, time=8.80
x[1] = 0.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 1.72094848078 -1.1200131024
y[1] (closed_form) = 1.56397900841 -1.03770542376
absolute error = 0.1772
relative error = 9.443 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.214
Order of pole (three term test) = 33.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 1.71904660122 -1.12538510055
y[1] (closed_form) = 1.56222811679 -1.04473880616
absolute error = 0.1763
relative error = 9.383 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9873
Order of pole (three term test) = 33.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3 0.949
h = 0.001 0.001
y[1] (numeric) = 1.71713641624 -1.13077448244
y[1] (closed_form) = 1.56111508025 -1.04895816779
absolute error = 0.1762
relative error = 9.367 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7797
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.301 0.95
h = 0.001 0.003
y[1] (numeric) = 1.71522289299 -1.13616801064
y[1] (closed_form) = 1.55937075451 -1.05005204317
absolute error = 0.1781
relative error = 9.472 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.708
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 1.71330340188 -1.14156397724
y[1] (closed_form) = 1.55696851918 -1.05398717043
absolute error = 0.1792
relative error = 9.531 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.111
Order of pole (three term test) = 33.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 1.71137502067 -1.14697108117
y[1] (closed_form) = 1.55550894873 -1.05965107841
absolute error = 0.1787
relative error = 9.492 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.82
Order of pole (three term test) = 33.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 1.70941754693 -1.15239277608
y[1] (closed_form) = 1.54922352354 -1.06722450947
absolute error = 0.1814
relative error = 9.644 %
Correct digits = 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) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 1.70742872383 -1.15783394906
y[1] (closed_form) = 1.54739369282 -1.07436073918
absolute error = 0.1805
relative error = 9.582 %
Correct digits = 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) = 33.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 1.70543131917 -1.16329299669
y[1] (closed_form) = 1.54623225929 -1.07864153901
absolute error = 0.1803
relative error = 9.564 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8157
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 1.70343047072 -1.16875630473
y[1] (closed_form) = 1.54445140997 -1.07974098074
absolute error = 0.1822
relative error = 9.669 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.908
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 1.70142446186 -1.17422761122
y[1] (closed_form) = 1.54293740156 -1.08547712996
absolute error = 0.1816
relative error = 9.629 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.932
Order of pole (three term test) = 33.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 1.69938861894 -1.17971381696
y[1] (closed_form) = 1.53651696372 -1.09312179461
absolute error = 0.1845
relative error = 9.782 %
Correct digits = 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) = 34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 1.69732061841 -1.18521994064
y[1] (closed_form) = 1.53461845737 -1.10034979538
absolute error = 0.1835
relative error = 9.718 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 34.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 1.69524379812 -1.19074436989
y[1] (closed_form) = 1.53341490234 -1.10468542586
absolute error = 0.1833
relative error = 9.698 %
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 = 0.8479
Order of pole (three term test) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=783.5MB, alloc=44.3MB, time=9.33
x[1] = 0.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 1.69316344252 -1.19627315995
y[1] (closed_form) = 1.53160182762 -1.10579018039
absolute error = 0.1852
relative error = 9.802 %
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 = 4.033
Order of pole (three term test) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 1.69107678486 -1.20180450024
y[1] (closed_form) = 1.52907255571 -1.10981595482
absolute error = 0.1863
relative error = 9.86 %
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 = 2.296
Order of pole (three term test) = 34.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 1.6889807129 -1.20734755283
y[1] (closed_form) = 1.52749227906 -1.11563725712
absolute error = 0.1857
relative error = 9.818 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.067
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 1.68685391486 -1.21290588353
y[1] (closed_form) = 1.52090950029 -1.12336436903
absolute error = 0.1886
relative error = 9.973 %
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 = 1.381
Order of pole (three term test) = 34.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 1.68469399539 -1.21848463169
y[1] (closed_form) = 1.51892739036 -1.13070053128
absolute error = 0.1876
relative error = 9.906 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.123
Order of pole (three term test) = 34.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 1.68252496484 -1.22408218799
y[1] (closed_form) = 1.51767258563 -1.13510076014
absolute error = 0.1873
relative error = 9.885 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8868
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 1.68035228864 -1.22968422138
y[1] (closed_form) = 1.51582098556 -1.13621124901
absolute error = 0.1892
relative error = 9.989 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.218
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 1.67817312548 -1.23528886354
y[1] (closed_form) = 1.51322016616 -1.14028709067
absolute error = 0.1904
relative error = 10.05 %
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 = 2.401
Order of pole (three term test) = 34.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.317 1.02
h = 0.003 0.006
y[1] (numeric) = 1.67598425438 -1.24090552966
y[1] (closed_form) = 1.51157154313 -1.14619583156
absolute error = 0.1897
relative error = 10 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.208
Order of pole (three term test) = 34.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 1.67376375208 -1.24653783738
y[1] (closed_form) = 1.5048216201 -1.15400737847
absolute error = 0.1926
relative error = 10.16 %
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 = 1.444
Order of pole (three term test) = 34.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 1.67150914462 -1.25219106365
y[1] (closed_form) = 1.50275329198 -1.16145458467
absolute error = 0.1916
relative error = 10.09 %
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 = 1.174
Order of pole (three term test) = 34.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3202 1.034
h = 0.001 0.001
y[1] (numeric) = 1.66924512624 -1.25786360711
y[1] (closed_form) = 1.50144563924 -1.16592112543
absolute error = 0.1913
relative error = 10.07 %
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 = 0.9274
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3212 1.035
h = 0.001 0.003
y[1] (numeric) = 1.66697734917 -1.26354074511
y[1] (closed_form) = 1.49955441065 -1.1670374231
absolute error = 0.1932
relative error = 10.17 %
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 = 4.411
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = 1.66470289665 -1.26922055009
y[1] (closed_form) = 1.49687990743 -1.1711645837
absolute error = 0.1944
relative error = 10.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.511
Order of pole (three term test) = 34.14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=827.7MB, alloc=44.3MB, time=9.86
x[1] = 0.3223 1.042
h = 0.003 0.006
y[1] (numeric) = 1.66241843535 -1.27491269394
y[1] (closed_form) = 1.49516080836 -1.17716307263
absolute error = 0.1937
relative error = 10.18 %
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 = 3.354
Order of pole (three term test) = 34.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = 1.66010141963 -1.2806208426
y[1] (closed_form) = 1.48823884183 -1.18506104181
absolute error = 0.1966
relative error = 10.34 %
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 = 1.51
Order of pole (three term test) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = 1.65774929461 -1.28635041251
y[1] (closed_form) = 1.4860816157 -1.19262220492
absolute error = 0.1956
relative error = 10.26 %
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 = 1.228
Order of pole (three term test) = 34.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3255 1.056
h = 0.001 0.001
y[1] (numeric) = 1.65538745004 -1.29209981524
y[1] (closed_form) = 1.48471947708 -1.19715678901
absolute error = 0.1953
relative error = 10.24 %
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 = 0.9698
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3265 1.057
h = 0.001 0.003
y[1] (numeric) = 1.65302173094 -1.29785393121
y[1] (closed_form) = 1.48278749739 -1.19827896336
absolute error = 0.1972
relative error = 10.34 %
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 = 4.612
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = 1.65064914426 -1.30361077202
y[1] (closed_form) = 1.48003712845 -1.20245870083
absolute error = 0.1983
relative error = 10.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.626
Order of pole (three term test) = 34.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3276 1.064
h = 0.003 0.006
y[1] (numeric) = 1.6482662405 -1.30938026988
y[1] (closed_form) = 1.47824537061 -1.20854927172
absolute error = 0.1977
relative error = 10.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.507
Order of pole (three term test) = 34.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = 1.64584984052 -1.3151661355
y[1] (closed_form) = 1.47114636275 -1.21653564971
absolute error = 0.2006
relative error = 10.51 %
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 = 1.579
Order of pole (three term test) = 34.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = 1.64339730611 -1.32097392662
y[1] (closed_form) = 1.46889749169 -1.22421371394
absolute error = 0.1995
relative error = 10.43 %
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 = 1.284
Order of pole (three term test) = 34.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3308 1.078
h = 0.001 0.001
y[1] (numeric) = 1.64093473446 -1.32680207299
y[1] (closed_form) = 1.46747918862 -1.22881809111
absolute error = 0.1992
relative error = 10.41 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.014
Order of pole (three term test) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = 1.63846816956 -1.33263505252
y[1] (closed_form) = 1.46550531527 -1.2299462032
absolute error = 0.2011
relative error = 10.51 %
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 = 6.102
Order of pole (three term test) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3319 1.083
h = 0.003 0.006
y[1] (numeric) = 1.63599560209 -1.33847712093
y[1] (closed_form) = 1.46365036085 -1.23611882512
absolute error = 0.2004
relative error = 10.46 %
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 = 3.645
Order of pole (three term test) = 34.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = 1.63348872216 -1.34433586443
y[1] (closed_form) = 1.4563959676 -1.2441850843
absolute error = 0.2035
relative error = 10.62 %
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 = 1.641
Order of pole (three term test) = 34.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.335 1.094
h = 0.0001 0.003
y[1] (numeric) = 1.63094481416 -1.3502169813
y[1] (closed_form) = 1.45406740015 -1.2519672926
absolute error = 0.2023
relative error = 10.54 %
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 = 1.334
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=871.8MB, alloc=44.3MB, time=10.38
x[1] = 0.3351 1.097
h = 0.001 0.001
y[1] (numeric) = 1.62839059434 -1.35611891259
y[1] (closed_form) = 1.45260023657 -1.25663385777
absolute error = 0.202
relative error = 10.52 %
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 = 1.054
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3361 1.098
h = 0.001 0.003
y[1] (numeric) = 1.62583227818 -1.36202578274
y[1] (closed_form) = 1.4505894436 -1.25776764231
absolute error = 0.2039
relative error = 10.62 %
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 = 5.011
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = 1.62326672752 -1.36793548684
y[1] (closed_form) = 1.4476925996 -1.2620495499
absolute error = 0.205
relative error = 10.68 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.853
Order of pole (three term test) = 34.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3372 1.105
h = 0.003 0.006
y[1] (numeric) = 1.62069026944 -1.37385845298
y[1] (closed_form) = 1.44576080685 -1.26831869129
absolute error = 0.2043
relative error = 10.62 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.811
Order of pole (three term test) = 34.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = 1.61807851581 -1.379798473
y[1] (closed_form) = 1.43831982427 -1.27647711538
absolute error = 0.2073
relative error = 10.78 %
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 = 1.715
Order of pole (three term test) = 34.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = 1.61542866833 -1.38576137383
y[1] (closed_form) = 1.4358943512 -1.28438182348
absolute error = 0.2062
relative error = 10.7 %
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 = 1.395
Order of pole (three term test) = 34.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3404 1.119
h = 0.001 0.001
y[1] (numeric) = 1.61276817386 -1.39174562466
y[1] (closed_form) = 1.43436780872 -1.28912150893
absolute error = 0.2058
relative error = 10.67 %
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 = 1.102
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3414 1.12
h = 0.001 0.003
y[1] (numeric) = 1.61010345882 -1.3977349367
y[1] (closed_form) = 1.43231294168 -1.29026134001
absolute error = 0.2077
relative error = 10.78 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.239
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = 1.60743130607 -1.40372713953
y[1] (closed_form) = 1.42933374207 -1.29459948589
absolute error = 0.2089
relative error = 10.83 %
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 = 2.983
Order of pole (three term test) = 34.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3425 1.127
h = 0.003 0.006
y[1] (numeric) = 1.60474791518 -1.40973293251
y[1] (closed_form) = 1.42732276818 -1.30096755446
absolute error = 0.2081
relative error = 10.78 %
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 = 3.984
Order of pole (three term test) = 34.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = 1.60202823092 -1.41575614138
y[1] (closed_form) = 1.41968990107 -1.30922012769
absolute error = 0.2112
relative error = 10.94 %
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 = 1.793
Order of pole (three term test) = 34.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = 1.59926936435 -1.42180274004
y[1] (closed_form) = 1.41716457303 -1.31725037387
absolute error = 0.21
relative error = 10.85 %
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 = 1.458
Order of pole (three term test) = 34.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3457 1.141
h = 0.001 0.001
y[1] (numeric) = 1.59649950578 -1.42787123155
y[1] (closed_form) = 1.41557685029 -1.3220649845
absolute error = 0.2096
relative error = 10.82 %
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 = 1.152
Order of pole (three term test) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3467 1.142
h = 0.001 0.003
y[1] (numeric) = 1.59372529929 -1.43394490793
y[1] (closed_form) = 1.41347670648 -1.32321090258
absolute error = 0.2115
relative error = 10.93 %
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 = 5.477
Order of pole (three term test) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=915.8MB, alloc=44.3MB, time=10.90
x[1] = 0.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = 1.59094344784 -1.44002153152
y[1] (closed_form) = 1.41041278126 -1.32760656979
absolute error = 0.2127
relative error = 10.98 %
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 = 3.118
Order of pole (three term test) = 34.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3478 1.149
h = 0.003 0.006
y[1] (numeric) = 1.58815001921 -1.44611207694
y[1] (closed_form) = 1.40832022421 -1.33407599991
absolute error = 0.2119
relative error = 10.92 %
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 = 4.165
Order of pole (three term test) = 34.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = 1.5853192788 -1.45222039975
y[1] (closed_form) = 1.40049006793 -1.3424247047
absolute error = 0.215
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 = 1.875
Order of pole (three term test) = 34.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = 1.58244824429 -1.45835262286
y[1] (closed_form) = 1.39786186078 -1.35058356117
absolute error = 0.2137
relative error = 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 = 1.525
Order of pole (three term test) = 34.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.351 1.163
h = 0.001 0.001
y[1] (numeric) = 1.57956586265 -1.46450728907
y[1] (closed_form) = 1.39621111105 -1.3554749218
absolute error = 0.2133
relative error = 10.96 %
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 = 1.204
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.352 1.164
h = 0.001 0.003
y[1] (numeric) = 1.57667900256 -1.47066726517
y[1] (closed_form) = 1.39406446572 -1.35662695953
absolute error = 0.2153
relative error = 11.07 %
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 = 5.725
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.353 1.167
h = 0.0001 0.004
y[1] (numeric) = 1.57378428609 -1.47683024447
y[1] (closed_form) = 1.39091339281 -1.36108143761
absolute error = 0.2164
relative error = 11.12 %
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 = 3.26
Order of pole (three term test) = 34.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3531 1.171
h = 0.003 0.006
y[1] (numeric) = 1.57087764486 -1.48300748092
y[1] (closed_form) = 1.3887367898 -1.3676546908
absolute error = 0.2156
relative error = 11.06 %
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 = 4.354
Order of pole (three term test) = 34.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = 1.5679326523 -1.48920285566
y[1] (closed_form) = 1.38070382733 -1.37610150738
absolute error = 0.2187
relative error = 11.22 %
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 = 1.96
Order of pole (three term test) = 34.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = 1.56494622989 -1.49542264271
y[1] (closed_form) = 1.37796964001 -1.38439208101
absolute error = 0.2175
relative error = 11.13 %
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 = 1.594
Order of pole (three term test) = 34.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 1.56194809482 -1.50166543069
y[1] (closed_form) = 1.37625396991 -1.38936203674
absolute error = 0.217
relative error = 11.1 %
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 = 1.258
Order of pole (three term test) = 34.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 1.55894534749 -1.50791365497
y[1] (closed_form) = 1.37405957569 -1.39052021872
absolute error = 0.219
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 = 7.573
Order of pole (three term test) = 34.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 1.55593564086 -1.51417212398
y[1] (closed_form) = 1.37180988599 -1.3971858739
absolute error = 0.2181
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 = 4.523
Order of pole (three term test) = 34.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 1.55288668144 -1.52044903652
y[1] (closed_form) = 1.36359904961 -1.40572123301
absolute error = 0.2213
relative error = 11.3 %
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 = 2.036
Order of pole (three term test) = 34.62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=960.1MB, alloc=44.3MB, time=11.43
x[1] = 0.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 1.54979530104 -1.52675081719
y[1] (closed_form) = 1.3607727146 -1.41412901341
absolute error = 0.22
relative error = 11.21 %
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 = 1.656
Order of pole (three term test) = 34.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 1.54669189154 -1.5330760897
y[1] (closed_form) = 1.35900057703 -1.41916891938
absolute error = 0.2196
relative error = 11.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.307
Order of pole (three term test) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 1.54358375342 -1.53940691008
y[1] (closed_form) = 1.35676413901 -1.42033299292
absolute error = 0.2215
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 = 6.218
Order of pole (three term test) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 1.54046735468 -1.54574083921
y[1] (closed_form) = 1.3534450112 -1.42490146738
absolute error = 0.2227
relative error = 11.33 %
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 = 3.54
Order of pole (three term test) = 34.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 1.53733836505 -1.5520896638
y[1] (closed_form) = 1.35110655513 -1.43167563134
absolute error = 0.2218
relative error = 11.27 %
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 = 4.728
Order of pole (three term test) = 34.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 1.53416903574 -1.55845730936
y[1] (closed_form) = 1.3426823609 -1.44031284887
absolute error = 0.225
relative error = 11.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.128
Order of pole (three term test) = 34.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 1.53095610346 -1.56485033809
y[1] (closed_form) = 1.33974410138 -1.44885826136
absolute error = 0.2236
relative error = 11.33 %
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 = 1.731
Order of pole (three term test) = 34.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 1.5277307565 -1.57126743119
y[1] (closed_form) = 1.33790341433 -1.45398027503
absolute error = 0.2231
relative error = 11.29 %
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 = 1.367
Order of pole (three term test) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 1.52450054076 -1.57769020122
y[1] (closed_form) = 1.33561684418 -1.45515053172
absolute error = 0.2252
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 = 6.499
Order of pole (three term test) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 1.52126184042 -1.58411613465
y[1] (closed_form) = 1.33220335529 -1.459781573
absolute error = 0.2263
relative error = 11.45 %
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 = 3.7
Order of pole (three term test) = 34.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.368 1.234
h = 0.003 0.006
y[1] (numeric) = 1.51801017596 -1.59055730981
y[1] (closed_form) = 1.32977348684 -1.46666678888
absolute error = 0.2253
relative error = 11.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.942
Order of pole (three term test) = 34.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 1.51471706861 -1.59701766496
y[1] (closed_form) = 1.32113007961 -1.47540783806
absolute error = 0.2286
relative error = 11.54 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.224
Order of pole (three term test) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 1.51137915051 -1.60350391969
y[1] (closed_form) = 1.31807656303 -1.48409409343
absolute error = 0.2272
relative error = 11.45 %
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 = 1.809
Order of pole (three term test) = 34.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 1.50802842085 -1.61001481941
y[1] (closed_form) = 1.31616529275 -1.48930012076
absolute error = 0.2267
relative error = 11.41 %
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 = 1.428
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1004.3MB, alloc=44.3MB, time=11.95
x[1] = 0.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 1.50467267873 -1.61653152659
y[1] (closed_form) = 1.31382727505 -1.49047656089
absolute error = 0.2287
relative error = 11.51 %
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 = 6.793
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 1.50130822341 -1.62305145127
y[1] (closed_form) = 1.31031678873 -1.4951714843
absolute error = 0.2298
relative error = 11.56 %
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 = 3.867
Order of pole (three term test) = 34.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 1.49793042129 -1.62958696787
y[1] (closed_form) = 1.30779279432 -1.50217032453
absolute error = 0.2289
relative error = 11.49 %
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 = 5.165
Order of pole (three term test) = 34.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 1.49451004968 -1.63614202256
y[1] (closed_form) = 1.2989241948 -1.51101717482
absolute error = 0.2322
relative error = 11.65 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.325
Order of pole (three term test) = 34.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 1.49104363308 -1.64272349461
y[1] (closed_form) = 1.2957520032 -1.51984752119
absolute error = 0.2307
relative error = 11.55 %
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 = 1.891
Order of pole (three term test) = 34.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 1.48756399645 -1.6493302005
y[1] (closed_form) = 1.29376806415 -1.52513948999
absolute error = 0.2302
relative error = 11.51 %
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 = 1.493
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 1.48407920004 -1.65594284586
y[1] (closed_form) = 1.29137725858 -1.52632210466
absolute error = 0.2322
relative error = 11.62 %
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 = 7.1
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 1.48058545712 -1.66255876227
y[1] (closed_form) = 1.2877670794 -1.53108223201
absolute error = 0.2334
relative error = 11.67 %
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 = 4.042
Order of pole (three term test) = 34.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 1.47707797498 -1.66919062478
y[1] (closed_form) = 1.28514617602 -1.53819729889
absolute error = 0.2324
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 = 5.398
Order of pole (three term test) = 34.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 1.47352677281 -1.67584238246
y[1] (closed_form) = 1.27604627758 -1.54715191543
absolute error = 0.2357
relative error = 11.75 %
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 = 2.43
Order of pole (three term test) = 34.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 1.46992826423 -1.68252107658
y[1] (closed_form) = 1.27275190529 -1.55612963896
absolute error = 0.2342
relative error = 11.65 %
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 = 1.976
Order of pole (three term test) = 34.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 1.46631611525 -1.68922560183
y[1] (closed_form) = 1.27069315877 -1.56150949926
absolute error = 0.2336
relative error = 11.6 %
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 = 1.56
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 1.46269865543 -1.69593620006
y[1] (closed_form) = 1.2682481995 -1.56269827007
absolute error = 0.2357
relative error = 11.71 %
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 = 9.389
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 1.45907314838 -1.70265827151
y[1] (closed_form) = 1.26554302442 -1.56991668882
absolute error = 0.2347
relative error = 11.64 %
Correct digits = 1
memory used=1048.4MB, alloc=44.3MB, time=12.48
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.608
Order of pole (three term test) = 35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 1.45540292323 -1.70940053963
y[1] (closed_form) = 1.2562403574 -1.57896849362
absolute error = 0.2381
relative error = 11.8 %
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 = 2.524
Order of pole (three term test) = 35.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 1.45168428982 -1.71617020749
y[1] (closed_form) = 1.25283974962 -1.58807724939
absolute error = 0.2365
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 = 2.053
Order of pole (three term test) = 35.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 1.44795165164 -1.72296623268
y[1] (closed_form) = 1.25071593606 -1.59353526936
absolute error = 0.2359
relative error = 11.65 %
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 = 1.621
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 1.44421357113 -1.72976844885
y[1] (closed_form) = 1.24822332228 -1.59472998465
absolute error = 0.238
relative error = 11.75 %
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 = 7.708
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 1.44046609761 -1.73657403701
y[1] (closed_form) = 1.24442106916 -1.59961624775
absolute error = 0.2391
relative error = 11.8 %
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 = 4.388
Order of pole (three term test) = 35.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 1.43670413224 -1.74339624617
y[1] (closed_form) = 1.24161364727 -1.60695585189
absolute error = 0.2381
relative error = 11.72 %
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 = 5.861
Order of pole (three term test) = 35.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 1.43289624427 -1.75023902626
y[1] (closed_form) = 1.23206799147 -1.61611914291
absolute error = 0.2415
relative error = 11.88 %
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 = 2.638
Order of pole (three term test) = 35.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 1.42903863427 -1.75710972778
y[1] (closed_form) = 1.22853847844 -1.62538153844
absolute error = 0.2399
relative error = 11.77 %
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 = 2.145
Order of pole (three term test) = 35.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 1.42516657617 -1.7640074002
y[1] (closed_form) = 1.22633575521 -1.63093116603
absolute error = 0.2393
relative error = 11.73 %
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 = 1.694
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 1.42128891747 -1.77091140003
y[1] (closed_form) = 1.22378637572 -1.63213199384
absolute error = 0.2414
relative error = 11.83 %
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 = 8.056
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 1.41740161827 -1.77781882365
y[1] (closed_form) = 1.21987639432 -1.63708731254
absolute error = 0.2425
relative error = 11.88 %
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 = 4.586
Order of pole (three term test) = 35.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 1.41349940558 -1.78474323442
y[1] (closed_form) = 1.21696373392 -1.64455079361
absolute error = 0.2414
relative error = 11.8 %
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 = 6.125
Order of pole (three term test) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 1.40955004778 -1.79168856997
y[1] (closed_form) = 1.20716860022 -1.6538275224
absolute error = 0.2449
relative error = 11.96 %
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 = 2.757
Order of pole (three term test) = 35.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 1.40554962498 -1.79866234978
y[1] (closed_form) = 1.20350641259 -1.66324695748
absolute error = 0.2432
relative error = 11.85 %
Correct digits = 1
memory used=1092.6MB, alloc=44.3MB, time=13.00
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.242
Order of pole (three term test) = 35.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 1.40153429788 -1.805663723
y[1] (closed_form) = 1.20122248115 -1.66889020918
absolute error = 0.2426
relative error = 11.8 %
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 = 1.77
Order of pole (three term test) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 1.39751320788 -1.81267156162
y[1] (closed_form) = 1.19861489358 -1.67009710244
absolute error = 0.2447
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 = 8.419
Order of pole (three term test) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 1.3934822247 -1.81968287517
y[1] (closed_form) = 1.19459424558 -1.67512282409
absolute error = 0.2459
relative error = 11.95 %
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 = 4.793
Order of pole (three term test) = 35.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 1.38943589562 -1.82671154626
y[1] (closed_form) = 1.1915732781 -1.68271290559
absolute error = 0.2447
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 = 6.402
Order of pole (three term test) = 35.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 1.38534117254 -1.83376149455
y[1] (closed_form) = 1.18152203719 -1.69210501722
absolute error = 0.2482
relative error = 12.03 %
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 = 2.881
Order of pole (three term test) = 35.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 1.38119401158 -1.84084041099
y[1] (closed_form) = 1.1777233085 -1.70168493229
absolute error = 0.2465
relative error = 11.91 %
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 = 2.343
Order of pole (three term test) = 35.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.402 1.377
h = 0.001 0.001
y[1] (numeric) = 1.3770314769 -1.84794755243
y[1] (closed_form) = 1.17535581145 -1.70742384834
absolute error = 0.2458
relative error = 11.86 %
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 = 1.85
Order of pole (three term test) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.403 1.378
h = 0.001 0.003
y[1] (numeric) = 1.37286301288 -1.85506129888
y[1] (closed_form) = 1.17268854547 -1.70863674915
absolute error = 0.248
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 = 8.799
Order of pole (three term test) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 1.36868439767 -1.86217857066
y[1] (closed_form) = 1.16855422567 -1.71373422742
absolute error = 0.2492
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.009
Order of pole (three term test) = 35.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 1.36448999313 -1.86931357473
y[1] (closed_form) = 1.16542180365 -1.72145366529
absolute error = 0.248
relative error = 11.93 %
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 = 6.69
Order of pole (three term test) = 35.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 1.36024591865 -1.8764702068
y[1] (closed_form) = 1.15510768252 -1.73096309771
absolute error = 0.2515
relative error = 12.09 %
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 = 3.011
Order of pole (three term test) = 35.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 1.35594800276 -1.8836563319
y[1] (closed_form) = 1.15116844665 -1.74070697454
absolute error = 0.2497
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 = 2.448
Order of pole (three term test) = 35.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 1.35163423013 -1.89087132289
y[1] (closed_form) = 1.14871496617 -1.7465436193
absolute error = 0.249
relative error = 11.91 %
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 = 1.934
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1136.8MB, alloc=44.3MB, time=13.53
x[1] = 0.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 1.34731435747 -1.89809306013
y[1] (closed_form) = 1.14598652284 -1.74776245861
absolute error = 0.2513
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 = 19.51
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 1.34294972587 -1.90532215608
y[1] (closed_form) = 1.13548455052 -1.75734688534
absolute error = 0.2548
relative error = 12.18 %
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 = 3.103
Order of pole (three term test) = 35.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 1.33853033977 -1.91258101676
y[1] (closed_form) = 1.13144207145 -1.76720192988
absolute error = 0.253
relative error = 12.06 %
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 = 2.523
Order of pole (three term test) = 35.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 1.33409474016 -1.91986917707
y[1] (closed_form) = 1.12892548467 -1.77310477112
absolute error = 0.2523
relative error = 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 = 1.992
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 1.32965291699 -1.92716417731
y[1] (closed_form) = 1.12615392618 -1.77432606248
absolute error = 0.2545
relative error = 12.11 %
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 = 9.475
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 1.3252004935 -1.93446277941
y[1] (closed_form) = 1.12181885046 -1.77954471017
absolute error = 0.2557
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 = 5.394
Order of pole (three term test) = 35.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 1.32073149664 -1.94177974451
y[1] (closed_form) = 1.11848752683 -1.78748584172
absolute error = 0.2544
relative error = 12.06 %
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 = 7.205
Order of pole (three term test) = 35.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 1.31621060434 -1.94911889211
y[1] (closed_form) = 1.1077108581 -1.79719066332
absolute error = 0.258
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 = 3.242
Order of pole (three term test) = 35.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 1.31163341666 -1.9564883835
y[1] (closed_form) = 1.10352085401 -1.8072155364
absolute error = 0.2561
relative error = 12.1 %
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 = 2.637
Order of pole (three term test) = 35.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 1.30703950842 -1.96388783113
y[1] (closed_form) = 1.10091400799 -1.81321958215
absolute error = 0.2553
relative error = 12.04 %
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 = 2.082
Order of pole (three term test) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 1.30243919849 -1.97129426261
y[1] (closed_form) = 1.09807867775 -1.81444662962
absolute error = 0.2576
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 = 9.902
Order of pole (three term test) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 1.29782801529 -1.97870434408
y[1] (closed_form) = 1.09362147344 -1.8197406215
absolute error = 0.2588
relative error = 12.19 %
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 = 5.637
Order of pole (three term test) = 35.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 1.29319978404 -1.98613317497
y[1] (closed_form) = 1.09016975582 -1.82781859604
absolute error = 0.2575
relative error = 12.1 %
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 = 7.529
Order of pole (three term test) = 35.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 1.28851830551 -1.99358453347
y[1] (closed_form) = 1.07911121402 -1.83764572385
absolute error = 0.2611
relative error = 12.25 %
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 = 3.388
Order of pole (three term test) = 35.69 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1181.0MB, alloc=44.3MB, time=14.05
x[1] = 0.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 1.2837790418 -2.00106676198
y[1] (closed_form) = 1.07476943661 -1.84784401885
absolute error = 0.2592
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 = 2.755
Order of pole (three term test) = 35.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 1.27902253588 -2.00857961308
y[1] (closed_form) = 1.07206974258 -1.85395139853
absolute error = 0.2583
relative error = 12.06 %
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 = 2.176
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 1.27425944557 -2.01609959364
y[1] (closed_form) = 1.06916906174 -1.85518410029
absolute error = 0.2607
relative error = 12.17 %
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 = 10.35
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 1.26948520326 -2.02362327145
y[1] (closed_form) = 1.06458646204 -1.86055481053
absolute error = 0.2619
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 = 5.891
Order of pole (three term test) = 35.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 1.26469342605 -2.03116608967
y[1] (closed_form) = 1.06101089278 -1.86877250597
absolute error = 0.2605
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 = 7.868
Order of pole (three term test) = 35.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 1.25984702019 -2.03873177848
y[1] (closed_form) = 1.04966314422 -1.87872384136
absolute error = 0.2642
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 = 3.541
Order of pole (three term test) = 35.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 1.25494130582 -2.0463288641
y[1] (closed_form) = 1.04516523554 -1.88909919533
absolute error = 0.2622
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 = 2.879
Order of pole (three term test) = 35.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 1.25001781257 -2.05395724861
y[1] (closed_form) = 1.04237003831 -1.89531206382
absolute error = 0.2613
relative error = 12.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.274
Order of pole (three term test) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 1.24508754759 -2.06159290992
y[1] (closed_form) = 1.03940239688 -1.8965503054
absolute error = 0.2637
relative error = 12.19 %
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 = 13.68
Order of pole (three term test) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 1.24014693647 -2.0692423933
y[1] (closed_form) = 1.03571909519 -1.90489213211
absolute error = 0.2623
relative error = 12.1 %
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 = 8.173
Order of pole (three term test) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 1.23515049793 -2.07691503562
y[1] (closed_form) = 1.02411792193 -1.91495546245
absolute error = 0.266
relative error = 12.25 %
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 = 3.678
Order of pole (three term test) = 35.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 1.23009341841 -2.0846195473
y[1] (closed_form) = 1.01948421406 -1.92548810173
absolute error = 0.264
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 = 2.991
Order of pole (three term test) = 35.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 1.22501809398 -2.09235595475
y[1] (closed_form) = 1.01660592464 -1.93179469868
absolute error = 0.2631
relative error = 12.05 %
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 = 2.362
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 1.21993583452 -2.10009976951
y[1] (closed_form) = 1.01357939616 -1.93303843142
absolute error = 0.2655
relative error = 12.16 %
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 = 11.23
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1225.2MB, alloc=44.3MB, time=14.58
x[1] = 0.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 1.21484188897 -2.10784737047
y[1] (closed_form) = 1.00875546454 -1.93855716263
absolute error = 0.2667
relative error = 12.2 %
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 = 6.394
Order of pole (three term test) = 35.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 1.20972947401 -2.11561485792
y[1] (closed_form) = 1.00494167385 -1.94704420219
absolute error = 0.2652
relative error = 12.11 %
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 = 8.541
Order of pole (three term test) = 36.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 1.20455978298 -2.12340586519
y[1] (closed_form) = 0.993037238865 -1.95723534058
absolute error = 0.269
relative error = 12.26 %
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 = 3.844
Order of pole (three term test) = 36.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 1.19932786304 -2.13122926986
y[1] (closed_form) = 0.988239033628 -1.96795198011
absolute error = 0.2669
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 = 3.126
Order of pole (three term test) = 36.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.437 1.521
h = 0.001 0.001
y[1] (numeric) = 1.19407713266 -2.13908526576
y[1] (closed_form) = 0.985260143997 -1.97436817816
absolute error = 0.266
relative error = 12.05 %
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 = 2.468
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.438 1.522
h = 0.001 0.003
y[1] (numeric) = 1.18881927091 -2.14694881961
y[1] (closed_form) = 0.982163572159 -1.97561722263
absolute error = 0.2684
relative error = 12.17 %
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 = 11.74
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 1.18354942694 -2.15481620426
y[1] (closed_form) = 0.977204495344 -1.98121667646
absolute error = 0.2697
relative error = 12.21 %
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 = 6.682
Order of pole (three term test) = 36.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 1.17826059026 -2.16270387998
y[1] (closed_form) = 0.973256497529 -1.98985190887
absolute error = 0.2682
relative error = 12.11 %
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 = 8.925
Order of pole (three term test) = 36.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 1.17291300768 -2.17061541179
y[1] (closed_form) = 0.96104099656 -2.00017272536
absolute error = 0.2719
relative error = 12.25 %
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 = 4.017
Order of pole (three term test) = 36.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 1.16750157231 -2.17855986928
y[1] (closed_form) = 0.956073607043 -2.01107713205
absolute error = 0.2697
relative error = 12.11 %
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 = 3.266
Order of pole (three term test) = 36.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 1.16207074479 -2.18653762394
y[1] (closed_form) = 0.95299126268 -2.01760516178
absolute error = 0.2688
relative error = 12.05 %
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 = 2.579
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 1.15663258456 -2.19452308899
y[1] (closed_form) = 0.949822944392 -2.01885936525
absolute error = 0.2713
relative error = 12.16 %
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 = 12.27
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 1.15118213961 -2.20251242838
y[1] (closed_form) = 0.944725155535 -2.02454093809
absolute error = 0.2726
relative error = 12.2 %
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 = 6.983
Order of pole (three term test) = 36.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 1.14571216527 -2.21052246824
y[1] (closed_form) = 0.940639136725 -2.0333273796
absolute error = 0.271
relative error = 12.1 %
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 = 9.326
Order of pole (three term test) = 36.27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1269.5MB, alloc=44.3MB, time=15.10
x[1] = 0.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 1.14018194284 -2.21855669763
y[1] (closed_form) = 0.928104593446 -2.0437797308
absolute error = 0.2748
relative error = 12.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.197
Order of pole (three term test) = 36.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 1.13458620696 -2.22662438111
y[1] (closed_form) = 0.922963211802 -2.05487571776
absolute error = 0.2725
relative error = 12.1 %
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 = 3.413
Order of pole (three term test) = 36.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 1.12897048062 -2.23472607838
y[1] (closed_form) = 0.919774484944 -2.06151783657
absolute error = 0.2716
relative error = 12.03 %
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 = 2.695
Order of pole (three term test) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 1.12334721509 -2.24283564025
y[1] (closed_form) = 0.916532683194 -2.06277703198
absolute error = 0.2742
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 = 12.82
Order of pole (three term test) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 1.11771135581 -2.25094911891
y[1] (closed_form) = 0.911292533053 -2.06854212527
absolute error = 0.2755
relative error = 12.19 %
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 = 7.297
Order of pole (three term test) = 36.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 1.11205541676 -2.25908371233
y[1] (closed_form) = 0.907064581185 -2.07748282889
absolute error = 0.2739
relative error = 12.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.746
Order of pole (three term test) = 36.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 1.10633769431 -2.2672428257
y[1] (closed_form) = 0.894202843139 -2.08806855701
absolute error = 0.2777
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 = 4.386
Order of pole (three term test) = 36.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 1.10055276007 -2.27543592154
y[1] (closed_form) = 0.888882537515 -2.09935998408
absolute error = 0.2753
relative error = 12.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.567
Order of pole (three term test) = 36.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 1.09474722001 -2.28366375861
y[1] (closed_form) = 0.885584425287 -2.1061184766
absolute error = 0.2744
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.817
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 1.088933929 -2.29189961635
y[1] (closed_form) = 0.882267368398 -2.10738248198
absolute error = 0.2771
relative error = 12.13 %
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 = 16.95
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.454 1.592
h = 0.003 0.006
y[1] (numeric) = 1.08310873912 -2.30015076182
y[1] (closed_form) = 0.877915923551 -2.11646019845
absolute error = 0.2754
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 = 10.12
Order of pole (three term test) = 36.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 1.07722043329 -2.30842670403
y[1] (closed_form) = 0.864767499709 -2.12716622938
absolute error = 0.2793
relative error = 12.16 %
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 = 4.556
Order of pole (three term test) = 36.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 1.07126342925 -2.31673710423
y[1] (closed_form) = 0.859291527519 -2.13863122546
absolute error = 0.2769
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.705
Order of pole (three term test) = 36.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 1.06528528456 -2.32508288827
y[1] (closed_form) = 0.855898220433 -2.14549309219
absolute error = 0.2759
relative error = 11.94 %
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 = 2.926
Order of pole (three term test) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1313.7MB, alloc=44.3MB, time=15.63
x[1] = 0.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 1.05929920421 -2.3334368314
y[1] (closed_form) = 0.852514994745 -2.14676200624
absolute error = 0.2786
relative error = 12.06 %
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 = 13.91
Order of pole (three term test) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 1.05329993778 -2.34179477106
y[1] (closed_form) = 0.847000974886 -2.15268806063
absolute error = 0.2799
relative error = 12.1 %
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 = 7.92
Order of pole (three term test) = 36.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 1.04727953472 -2.35017461653
y[1] (closed_form) = 0.842500085038 -2.16192586907
absolute error = 0.2782
relative error = 11.99 %
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 = 10.58
Order of pole (three term test) = 36.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 1.04119440447 -2.35857960729
y[1] (closed_form) = 0.829008835045 -2.17276876495
absolute error = 0.282
relative error = 12.13 %
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 = 4.761
Order of pole (three term test) = 36.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 1.03503880516 -2.36701958444
y[1] (closed_form) = 0.823344468283 -2.18443657237
absolute error = 0.2796
relative error = 11.98 %
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 = 3.872
Order of pole (three term test) = 36.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 1.02886141705 -2.37549569376
y[1] (closed_form) = 0.819836009725 -2.19141917551
absolute error = 0.2785
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 = 3.057
Order of pole (three term test) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 1.02267587139 -2.38398012176
y[1] (closed_form) = 0.816374134711 -2.19269254182
absolute error = 0.2813
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 = 14.54
Order of pole (three term test) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 1.01647681117 -2.39246858538
y[1] (closed_form) = 0.81070685784 -2.19870619901
absolute error = 0.2826
relative error = 12.06 %
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 = 8.277
Order of pole (three term test) = 36.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 1.01025602275 -2.40097938357
y[1] (closed_form) = 0.806052316514 -2.20810726147
absolute error = 0.2809
relative error = 11.95 %
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 = 11.05
Order of pole (three term test) = 36.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 1.00396887273 -2.40951564808
y[1] (closed_form) = 0.792209560646 -2.21908881943
absolute error = 0.2848
relative error = 12.09 %
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 = 4.975
Order of pole (three term test) = 36.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.99760944253 -2.41808742687
y[1] (closed_form) = 0.786351495658 -2.23096343677
absolute error = 0.2822
relative error = 11.93 %
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 = 4.046
Order of pole (three term test) = 36.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 0.991227557007 -2.42669609758
y[1] (closed_form) = 0.782724657575 -2.23806914163
absolute error = 0.2812
relative error = 11.86 %
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 = 3.195
Order of pole (three term test) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 0.984837286378 -2.43531324844
y[1] (closed_form) = 0.779182257917 -2.23934673338
absolute error = 0.2841
relative error = 11.98 %
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 = 15.19
Order of pole (three term test) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.978433165618 -2.44393447268
y[1] (closed_form) = 0.7733577377 -2.24544941343
absolute error = 0.2854
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 = 8.649
Order of pole (three term test) = 36.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1358.2MB, alloc=44.3MB, time=16.16
x[1] = 0.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 0.972006709969 -2.45257846539
y[1] (closed_form) = 0.768545230289 -2.25501693053
absolute error = 0.2836
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 = 11.55
Order of pole (three term test) = 36.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.965512222118 -2.46124824157
y[1] (closed_form) = 0.754342096226 -2.26613892894
absolute error = 0.2875
relative error = 12.04 %
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 = 5.199
Order of pole (three term test) = 37.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.958943601726 -2.46995405927
y[1] (closed_form) = 0.748284892815 -2.27822440391
absolute error = 0.2848
relative error = 11.88 %
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 = 4.228
Order of pole (three term test) = 37.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 0.952351840652 -2.47869754021
y[1] (closed_form) = 0.744536364473 -2.28545560429
absolute error = 0.2838
relative error = 11.81 %
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 = 3.338
Order of pole (three term test) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 0.945751461115 -2.48744966469
y[1] (closed_form) = 0.740911527152 -2.28673717781
absolute error = 0.2868
relative error = 11.93 %
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 = 15.88
Order of pole (three term test) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.939136888607 -2.49620589895
y[1] (closed_form) = 0.734925684806 -2.29293030469
absolute error = 0.2881
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 = 9.038
Order of pole (three term test) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 0.93249935903 -2.50498534073
y[1] (closed_form) = 0.729950785865 -2.30266751613
absolute error = 0.2863
relative error = 11.85 %
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 = 12.07
Order of pole (three term test) = 37.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.925792089615 -2.51379087902
y[1] (closed_form) = 0.715378204225 -2.31393171334
absolute error = 0.2902
relative error = 11.98 %
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 = 5.433
Order of pole (three term test) = 37.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.919008793093 -2.52263298522
y[1] (closed_form) = 0.709116282228 -2.32623214333
absolute error = 0.2875
relative error = 11.82 %
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 = 4.418
Order of pole (three term test) = 37.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 0.9122016512 -2.53151353775
y[1] (closed_form) = 0.705242668144 -2.33359126187
absolute error = 0.2864
relative error = 11.75 %
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 = 3.489
Order of pole (three term test) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.905385651539 -2.54040289913
y[1] (closed_form) = 0.701533441628 -2.3348765561
absolute error = 0.2895
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 = 20.99
Order of pole (three term test) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 0.898555988113 -2.54930911404
y[1] (closed_form) = 0.696417205666 -2.34476446742
absolute error = 0.2876
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 = 12.54
Order of pole (three term test) = 37.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.891655102644 -2.5582416864
y[1] (closed_form) = 0.681520921525 -2.35615700801
absolute error = 0.2915
relative error = 11.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.643
Order of pole (three term test) = 37.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.884676530989 -2.56721130218
y[1] (closed_form) = 0.675080834597 -2.3686483153
absolute error = 0.2887
relative error = 11.72 %
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 = 4.589
Order of pole (three term test) = 37.39 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1402.4MB, alloc=44.3MB, time=16.68
x[1] = 0.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 0.877673501045 -2.57622005665
y[1] (closed_form) = 0.671098329172 -2.37612105044
absolute error = 0.2876
relative error = 11.65 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.624
Order of pole (three term test) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 0.870661404478 -2.58523776677
y[1] (closed_form) = 0.667314910255 -2.37741036215
absolute error = 0.2908
relative error = 11.78 %
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 = 17.23
Order of pole (three term test) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 0.863634457488 -2.59425965485
y[1] (closed_form) = 0.661018821021 -2.3837776324
absolute error = 0.2922
relative error = 11.81 %
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 = 9.81
Order of pole (three term test) = 37.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 0.856583358508 -2.60330558923
y[1] (closed_form) = 0.655731693966 -2.39384142778
absolute error = 0.2902
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 = 13.1
Order of pole (three term test) = 37.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 0.849459244297 -2.61237821224
y[1] (closed_form) = 0.640448566461 -2.40537949502
absolute error = 0.2942
relative error = 11.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.897
Order of pole (three term test) = 37.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 0.842255468146 -2.62148840343
y[1] (closed_form) = 0.633793043223 -2.4180935864
absolute error = 0.2912
relative error = 11.65 %
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 = 4.795
Order of pole (three term test) = 37.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.488 1.735
h = 0.001 0.001
y[1] (numeric) = 0.835026491835 -2.63063853909
y[1] (closed_form) = 0.629678930702 -2.42569886843
absolute error = 0.2901
relative error = 11.58 %
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 = 3.787
Order of pole (three term test) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.489 1.736
h = 0.001 0.003
y[1] (numeric) = 0.827788198163 -2.63979779943
y[1] (closed_form) = 0.625807382264 -2.42699139108
absolute error = 0.2934
relative error = 11.71 %
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 = 18.01
Order of pole (three term test) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 0.820534689507 -2.64896126993
y[1] (closed_form) = 0.619337789196 -2.43345325312
absolute error = 0.2948
relative error = 11.74 %
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 = 10.25
Order of pole (three term test) = 37.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 0.813256360261 -2.65814924109
y[1] (closed_form) = 0.61387501347 -2.44369628781
absolute error = 0.2928
relative error = 11.62 %
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 = 13.69
Order of pole (three term test) = 37.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 0.805903197397 -2.66736420118
y[1] (closed_form) = 0.598195383794 -2.45538157787
absolute error = 0.2968
relative error = 11.74 %
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 = 6.162
Order of pole (three term test) = 37.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 0.798468351754 -2.67661725279
y[1] (closed_form) = 0.59131842469 -2.46832269779
absolute error = 0.2938
relative error = 11.57 %
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 = 5.011
Order of pole (three term test) = 37.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 0.791007543275 -2.68591106695
y[1] (closed_form) = 0.587069055668 -2.47606303465
absolute error = 0.2926
relative error = 11.5 %
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 = 3.957
Order of pole (three term test) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 0.783537160322 -2.69521417682
y[1] (closed_form) = 0.583107311142 -2.47735845462
absolute error = 0.296
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 = 18.82
Order of pole (three term test) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1446.7MB, alloc=44.3MB, time=17.22
x[1] = 0.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 0.776051189907 -2.70452152743
y[1] (closed_form) = 0.576459757585 -2.48391634574
absolute error = 0.2975
relative error = 11.67 %
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 = 10.71
Order of pole (three term test) = 37.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 0.768539713269 -2.71385383843
y[1] (closed_form) = 0.570816453727 -2.49434201576
absolute error = 0.2954
relative error = 11.55 %
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 = 14.31
Order of pole (three term test) = 37.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 0.760951544213 -2.72321343353
y[1] (closed_form) = 0.554730447962 -2.50617619947
absolute error = 0.2994
relative error = 11.66 %
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 = 6.439
Order of pole (three term test) = 37.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 0.753279625417 -2.73261164178
y[1] (closed_form) = 0.547625899531 -2.51934864425
absolute error = 0.2963
relative error = 11.49 %
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 = 5.236
Order of pole (three term test) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 0.745580959765 -2.74205144321
y[1] (closed_form) = 0.543237531441 -2.5272265739
absolute error = 0.2951
relative error = 11.42 %
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 = 4.135
Order of pole (three term test) = 37.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 0.737872455992 -2.75150071338
y[1] (closed_form) = 0.539183482463 -2.52852455786
absolute error = 0.2987
relative error = 11.55 %
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 = 19.66
Order of pole (three term test) = 37.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = 0.730147984182 -2.76095425317
y[1] (closed_form) = 0.532353408229 -2.53517991762
absolute error = 0.3002
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 = 11.19
Order of pole (three term test) = 38.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5007 1.787
h = 0.003 0.006
y[1] (numeric) = 0.722397303068 -2.7704332185
y[1] (closed_form) = 0.526524571877 -2.54579166015
absolute error = 0.298
relative error = 11.46 %
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 = 14.95
Order of pole (three term test) = 38.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = 0.714568029407 -2.77993975766
y[1] (closed_form) = 0.510022096106 -2.55777638144
absolute error = 0.302
relative error = 11.58 %
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 = 6.728
Order of pole (three term test) = 38.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = 0.706652891854 -2.78948542967
y[1] (closed_form) = 0.502683647174 -2.5711844998
absolute error = 0.2988
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 = 5.472
Order of pole (three term test) = 38.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5039 1.801
h = 0.001 0.001
y[1] (numeric) = 0.698710201532 -2.79907353823
y[1] (closed_form) = 0.498152441987 -2.57920259052
absolute error = 0.2976
relative error = 11.33 %
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 = 4.321
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = 0.690757402749 -2.80867129056
y[1] (closed_form) = 0.49400393751 -2.58050278477
absolute error = 0.3013
relative error = 11.47 %
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 = 26
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.505 1.806
h = 0.003 0.006
y[1] (numeric) = 0.682788935525 -2.81828756965
y[1] (closed_form) = 0.488013568962 -2.59127977001
absolute error = 0.2991
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 = 15.53
Order of pole (three term test) = 38.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.508 1.812
h = 0.0001 0.005
y[1] (numeric) = 0.67474022644 -2.82793166236
y[1] (closed_form) = 0.471146174427 -2.60340049252
absolute error = 0.3031
relative error = 11.46 %
Correct digits = 1
memory used=1491.0MB, alloc=44.3MB, time=17.74
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.989
Order of pole (three term test) = 38.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = 0.666603801211 -2.83761535951
y[1] (closed_form) = 0.463604093459 -2.61701788508
absolute error = 0.2998
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 = 5.683
Order of pole (three term test) = 38.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5082 1.82
h = 0.001 0.001
y[1] (numeric) = 0.658439121802 -2.84734223943
y[1] (closed_form) = 0.458948502648 -2.62516046725
absolute error = 0.2986
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 = 4.488
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5092 1.821
h = 0.001 0.003
y[1] (numeric) = 0.650264097864 -2.85707891878
y[1] (closed_form) = 0.454716958483 -2.62646342561
absolute error = 0.3024
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 = 21.34
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = 0.642072375854 -2.86681992146
y[1] (closed_form) = 0.447535955656 -2.63330629674
absolute error = 0.3039
relative error = 11.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.15
Order of pole (three term test) = 38.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5103 1.828
h = 0.003 0.006
y[1] (numeric) = 0.633853094045 -2.87658723875
y[1] (closed_form) = 0.441350441745 -2.64427592448
absolute error = 0.3017
relative error = 11.25 %
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 = 16.23
Order of pole (three term test) = 38.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = 0.625551574065 -2.88638267723
y[1] (closed_form) = 0.424047210841 -2.65655029309
absolute error = 0.3057
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 = 7.303
Order of pole (three term test) = 38.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = 0.617160133049 -2.89621823618
y[1] (closed_form) = 0.416259105901 -2.67041167214
absolute error = 0.3022
relative error = 11.18 %
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 = 5.939
Order of pole (three term test) = 38.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5135 1.842
h = 0.001 0.001
y[1] (numeric) = 0.608739589842 -2.90609784573
y[1] (closed_form) = 0.411453305614 -2.67869932449
absolute error = 0.3011
relative error = 11.11 %
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 = 4.69
Order of pole (three term test) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5145 1.843
h = 0.001 0.003
y[1] (numeric) = 0.600308418896 -2.91598743366
y[1] (closed_form) = 0.407123181852 -2.68000380539
absolute error = 0.305
relative error = 11.25 %
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 = 22.3
Order of pole (three term test) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = 0.591860145113 -2.92588136861
y[1] (closed_form) = 0.399746036373 -2.68694833093
absolute error = 0.3066
relative error = 11.29 %
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 = 12.7
Order of pole (three term test) = 38.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5156 1.85
h = 0.003 0.006
y[1] (numeric) = 0.583383556194 -2.93580209934
y[1] (closed_form) = 0.393359998672 -2.69811415991
absolute error = 0.3043
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 = 16.96
Order of pole (three term test) = 38.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = 0.574822705445 -2.94575122418
y[1] (closed_form) = 0.375610179861 -2.71054373536
absolute error = 0.3082
relative error = 11.26 %
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 = 7.632
Order of pole (three term test) = 38.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = 0.566169678414 -2.95574098283
y[1] (closed_form) = 0.367569267455 -2.72465360429
absolute error = 0.3047
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 = 6.206
Order of pole (three term test) = 38.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5188 1.864
h = 0.001 0.001
y[1] (numeric) = 0.557486677641 -2.96577567321
y[1] (closed_form) = 0.362609133791 -2.73308898455
absolute error = 0.3035
relative error = 11.01 %
Correct digits = 1
memory used=1535.3MB, alloc=44.3MB, time=18.27
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.901
Order of pole (three term test) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5198 1.865
h = 0.001 0.003
y[1] (numeric) = 0.548792758745 -2.97582052298
y[1] (closed_form) = 0.358178152002 -2.73439457288
absolute error = 0.3076
relative error = 11.15 %
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 = 23.31
Order of pole (three term test) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = 0.540081323436 -2.98586974145
y[1] (closed_form) = 0.350599880876 -2.74144219853
absolute error = 0.3093
relative error = 11.19 %
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 = 13.27
Order of pole (three term test) = 38.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5209 1.872
h = 0.003 0.006
y[1] (numeric) = 0.531340798494 -2.9959462425
y[1] (closed_form) = 0.344007803774 -2.75280783015
absolute error = 0.3069
relative error = 11.06 %
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 = 17.72
Order of pole (three term test) = 38.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = 0.522513943026 -3.00605140387
y[1] (closed_form) = 0.325800405713 -2.7653941398
absolute error = 0.3108
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 = 7.975
Order of pole (three term test) = 38.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.524 1.883
h = 0.0001 0.003
y[1] (numeric) = 0.513592604526 -3.01619770942
y[1] (closed_form) = 0.317499729135 -2.77975705634
absolute error = 0.3072
relative error = 10.98 %
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 = 6.485
Order of pole (three term test) = 39.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5241 1.886
h = 0.001 0.001
y[1] (numeric) = 0.504640396589 -3.02638984133
y[1] (closed_form) = 0.312381033376 -2.78834285361
absolute error = 0.306
relative error = 10.91 %
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 = 5.121
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5251 1.887
h = 0.001 0.003
y[1] (numeric) = 0.495676972799 -3.03659231572
y[1] (closed_form) = 0.307846868888 -2.78964911122
absolute error = 0.3103
relative error = 11.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.35
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = 0.486695610014 -3.0467991784
y[1] (closed_form) = 0.300062373376 -2.79680128276
absolute error = 0.312
relative error = 11.09 %
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 = 13.86
Order of pole (three term test) = 39.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5262 1.894
h = 0.003 0.006
y[1] (numeric) = 0.477684363475 -3.05703381611
y[1] (closed_form) = 0.29325860073 -2.8083703615
absolute error = 0.3096
relative error = 10.96 %
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 = 18.52
Order of pole (three term test) = 39.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = 0.468584671668 -3.06729737328
y[1] (closed_form) = 0.274582386899 -2.82111489744
absolute error = 0.3134
relative error = 11.06 %
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 = 8.333
Order of pole (three term test) = 39.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = 0.459388137409 -3.07760258172
y[1] (closed_form) = 0.266014811995 -2.8357354741
absolute error = 0.3097
relative error = 10.87 %
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 = 6.777
Order of pole (three term test) = 39.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5294 1.908
h = 0.001 0.001
y[1] (numeric) = 0.450159813254 -3.08795452485
y[1] (closed_form) = 0.26073321805 -2.84447440907
absolute error = 0.3085
relative error = 10.8 %
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 = 5.351
Order of pole (three term test) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = 0.440919967991 -3.09831699564
y[1] (closed_form) = 0.256093498992 -2.84578087407
absolute error = 0.3129
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 = 32.2
Order of pole (three term test) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5305 1.913
h = 0.003 0.006
y[1] (numeric) = 0.431662179018 -3.10869978096
y[1] (closed_form) = 0.249105350105 -2.85753064089
absolute error = 0.3105
relative error = 10.83 %
Correct digits = 1
memory used=1579.7MB, alloc=44.3MB, time=18.80
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.23
Order of pole (three term test) = 39.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = 0.42231410922 -3.11911169795
y[1] (closed_form) = 0.230018314447 -2.87041831057
absolute error = 0.3144
relative error = 10.92 %
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 = 8.656
Order of pole (three term test) = 39.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = 0.41286712895 -3.12956572883
y[1] (closed_form) = 0.221218295889 -2.88526770653
absolute error = 0.3105
relative error = 10.73 %
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 = 7.039
Order of pole (three term test) = 39.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5337 1.927
h = 0.001 0.001
y[1] (numeric) = 0.403387557221 -3.14006729874
y[1] (closed_form) = 0.215794797357 -2.89414267305
absolute error = 0.3093
relative error = 10.66 %
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 = 5.559
Order of pole (three term test) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5347 1.928
h = 0.001 0.003
y[1] (numeric) = 0.393896197704 -3.15057956118
y[1] (closed_form) = 0.211062278885 -2.8954502247
absolute error = 0.3139
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 = 26.43
Order of pole (three term test) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = 0.384386088391 -3.16109624779
y[1] (closed_form) = 0.202881355853 -2.90280338338
absolute error = 0.3157
relative error = 10.85 %
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 = 15.05
Order of pole (three term test) = 39.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5358 1.935
h = 0.003 0.006
y[1] (numeric) = 0.374844569801 -3.17164165097
y[1] (closed_form) = 0.195670645454 -2.91476356601
absolute error = 0.3132
relative error = 10.72 %
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 = 20.1
Order of pole (three term test) = 39.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = 0.365210547703 -3.18221646224
y[1] (closed_form) = 0.176093230822 -2.9278122789
absolute error = 0.317
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 = 9.045
Order of pole (three term test) = 39.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = 0.355475154455 -3.19283388819
y[1] (closed_form) = 0.167012608267 -2.94292815528
absolute error = 0.313
relative error = 10.62 %
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 = 7.356
Order of pole (three term test) = 39.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.539 1.949
h = 0.001 0.001
y[1] (numeric) = 0.345706201692 -3.20349978781
y[1] (closed_form) = 0.161417881644 -2.95196146174
absolute error = 0.3118
relative error = 10.55 %
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 = 5.809
Order of pole (three term test) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.54 1.95
h = 0.001 0.003
y[1] (numeric) = 0.335925141418 -3.21417656921
y[1] (closed_form) = 0.156575259926 -2.95326832507
absolute error = 0.3166
relative error = 10.71 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.62
Order of pole (three term test) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.541 1.953
h = 0.0001 0.004
y[1] (numeric) = 0.326124881875 -3.22485778797
y[1] (closed_form) = 0.148172880182 -2.96073022699
absolute error = 0.3185
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 = 15.72
Order of pole (three term test) = 39.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5411 1.957
h = 0.003 0.006
y[1] (numeric) = 0.31629236019 -3.23556823241
y[1] (closed_form) = 0.140733531417 -2.97290459669
absolute error = 0.3159
relative error = 10.62 %
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 = 21
Order of pole (three term test) = 39.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = 0.306365082707 -3.24630832231
y[1] (closed_form) = 0.120653768831 -2.98611573619
absolute error = 0.3197
relative error = 10.7 %
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 = 9.452
Order of pole (three term test) = 39.99 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1623.8MB, alloc=44.3MB, time=19.32
x[1] = 0.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = 0.296333917242 -3.2570915235
y[1] (closed_form) = 0.111284876926 -3.00150286692
absolute error = 0.3155
relative error = 10.51 %
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 = 7.686
Order of pole (three term test) = 40.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5443 1.971
h = 0.001 0.001
y[1] (numeric) = 0.2862681976 -3.26792414726
y[1] (closed_form) = 0.105514264721 -3.01069732701
absolute error = 0.3144
relative error = 10.44 %
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 = 6.07
Order of pole (three term test) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5453 1.972
h = 0.001 0.003
y[1] (numeric) = 0.276190042667 -3.27876784418
y[1] (closed_form) = 0.100559027113 -3.01200296845
absolute error = 0.3194
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 = 28.87
Order of pole (three term test) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = 0.266092229203 -3.28961598921
y[1] (closed_form) = 0.0919296195718 -3.01957505609
absolute error = 0.3213
relative error = 10.64 %
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 = 16.43
Order of pole (three term test) = 40.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5464 1.979
h = 0.003 0.006
y[1] (numeric) = 0.255961279206 -3.30049387482
y[1] (closed_form) = 0.0842554013939 -3.03196742845
absolute error = 0.3187
relative error = 10.51 %
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 = 21.95
Order of pole (three term test) = 40.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = 0.245733271007 -3.31140163469
y[1] (closed_form) = 0.0636610549598 -3.04534233485
absolute error = 0.3224
relative error = 10.58 %
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 = 9.877
Order of pole (three term test) = 40.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = 0.235398800575 -3.32235299786
y[1] (closed_form) = 0.0539960336626 -3.06100555027
absolute error = 0.3181
relative error = 10.39 %
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 = 8.032
Order of pole (three term test) = 40.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5496 1.993
h = 0.001 0.001
y[1] (numeric) = 0.225028754023 -3.33335474701
y[1] (closed_form) = 0.0480447606112 -3.07036401017
absolute error = 0.317
relative error = 10.32 %
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 = 6.343
Order of pole (three term test) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5506 1.994
h = 0.001 0.003
y[1] (numeric) = 0.214645936148 -3.34436776282
y[1] (closed_form) = 0.0429743434074 -3.07166786934
absolute error = 0.3222
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 = 30.16
Order of pole (three term test) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = 0.204242990481 -3.35538523495
y[1] (closed_form) = 0.0341122077812 -3.07935158244
absolute error = 0.3243
relative error = 10.53 %
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 = 17.17
Order of pole (three term test) = 40.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5517 2.001
h = 0.003 0.006
y[1] (numeric) = 0.193806011846 -3.36643296838
y[1] (closed_form) = 0.0261967312184 -3.09196581766
absolute error = 0.3216
relative error = 10.4 %
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 = 22.93
Order of pole (three term test) = 40.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = 0.183269621386 -3.37751079586
y[1] (closed_form) = 0.00507529223977 -3.10550578593
absolute error = 0.3252
relative error = 10.47 %
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 = 10.32
Order of pole (three term test) = 40.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = 0.172624135735 -3.38863271371
y[1] (closed_form) = -0.00489391789308 -3.12144997321
absolute error = 0.3208
relative error = 10.28 %
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 = 8.393
Order of pole (three term test) = 40.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5549 2.015
h = 0.001 0.001
y[1] (numeric) = 0.16194202405 -3.3998059956
y[1] (closed_form) = -0.0110307476703 -3.13097531169
absolute error = 0.3197
relative error = 10.21 %
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 = 6.628
Order of pole (three term test) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1668.1MB, alloc=44.3MB, time=19.84
x[1] = 0.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = 0.15124679656 -3.41099073984
y[1] (closed_form) = -0.0162189602713 -3.13227680055
absolute error = 0.3252
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 = 39.88
Order of pole (three term test) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.556 2.02
h = 0.003 0.006
y[1] (numeric) = 0.140531045134 -3.42219770778
y[1] (closed_form) = -0.0243446372769 -3.14508811377
absolute error = 0.3224
relative error = 10.25 %
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 = 23.82
Order of pole (three term test) = 40.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.559 2.026
h = 0.0001 0.005
y[1] (numeric) = 0.12971383909 -3.4334349467
y[1] (closed_form) = -0.0459280229704 -3.1587776491
absolute error = 0.326
relative error = 10.32 %
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 = 10.72
Order of pole (three term test) = 40.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = 0.118785229191 -3.44471672332
y[1] (closed_form) = -0.0561622510723 -3.17497140266
absolute error = 0.3215
relative error = 10.12 %
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 = 8.718
Order of pole (three term test) = 40.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5592 2.034
h = 0.001 0.001
y[1] (numeric) = 0.107819078483 -3.45605073075
y[1] (closed_form) = -0.0624607814819 -3.18464500699
absolute error = 0.3204
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 = 6.885
Order of pole (three term test) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5602 2.035
h = 0.001 0.003
y[1] (numeric) = 0.096839510895 -3.46739637493
y[1] (closed_form) = -0.0677525619512 -3.18594540945
absolute error = 0.326
relative error = 10.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.74
Order of pole (three term test) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = 0.0858389149906 -3.4787464894
y[1] (closed_form) = -0.0770620065764 -3.19384359015
absolute error = 0.3282
relative error = 10.27 %
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 = 18.64
Order of pole (three term test) = 41.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5613 2.042
h = 0.003 0.006
y[1] (numeric) = 0.0748025639362 -3.49012786105
y[1] (closed_form) = -0.0854412165474 -3.20688414955
absolute error = 0.3254
relative error = 10.14 %
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 = 24.89
Order of pole (three term test) = 41.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = 0.0636622836731 -3.50153973972
y[1] (closed_form) = -0.107575703243 -3.2207411846
absolute error = 0.3289
relative error = 10.21 %
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 = 11.2
Order of pole (three term test) = 41.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = 0.0524078537663 -3.51299663362
y[1] (closed_form) = -0.118129604372 -3.2372252581
absolute error = 0.3242
relative error = 10.01 %
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 = 9.11
Order of pole (three term test) = 41.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5645 2.056
h = 0.001 0.001
y[1] (numeric) = 0.041114779378 -3.5245067646
y[1] (closed_form) = -0.124623097394 -3.24707124707
absolute error = 0.3232
relative error = 9.945 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.194
Order of pole (three term test) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5655 2.057
h = 0.001 0.003
y[1] (numeric) = 0.0298079273849 -3.53602873215
y[1] (closed_form) = -0.130037690769 -3.24836814098
absolute error = 0.3291
relative error = 10.12 %
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 = 34.21
Order of pole (three term test) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = 0.0184795479655 -3.54755517041
y[1] (closed_form) = -0.139596893706 -3.25638211815
absolute error = 0.3313
relative error = 10.17 %
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 = 19.48
Order of pole (three term test) = 41.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5666 2.064
h = 0.003 0.006
y[1] (numeric) = 0.0071144510021 -3.55911340367
y[1] (closed_form) = -0.148236498204 -3.26965591504
absolute error = 0.3285
relative error = 10.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.01
Order of pole (three term test) = 41.52 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1712.4MB, alloc=44.3MB, time=20.38
x[1] = 0.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = -0.00435708172517 -3.57070233609
y[1] (closed_form) = -0.170935409225 -3.2836816054
absolute error = 0.3319
relative error = 10.09 %
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 = 11.71
Order of pole (three term test) = 41.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = -0.0159455724259 -3.58233675518
y[1] (closed_form) = -0.181817639524 -3.30046105296
absolute error = 0.3271
relative error = 9.894 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.52
Order of pole (three term test) = 41.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5698 2.078
h = 0.001 0.001
y[1] (numeric) = -0.0275738413165 -3.59402543287
y[1] (closed_form) = -0.188511351947 -3.31048240117
absolute error = 0.326
relative error = 9.833 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.518
Order of pole (three term test) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5708 2.079
h = 0.001 0.003
y[1] (numeric) = -0.0392162575776 -3.60572614914
y[1] (closed_form) = -0.194051529323 -3.31177511504
absolute error = 0.3322
relative error = 10.01 %
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 = 35.75
Order of pole (three term test) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = -0.050880711233 -3.61743133354
y[1] (closed_form) = -0.203866717832 -3.31990631307
absolute error = 0.3346
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 = 20.35
Order of pole (three term test) = 41.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5719 2.086
h = 0.003 0.006
y[1] (numeric) = -0.0625828689818 -3.62916885672
y[1] (closed_form) = -0.212773751535 -3.33341738436
absolute error = 0.3317
relative error = 9.931 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.18
Order of pole (three term test) = 41.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = -0.0743940247357 -3.64093726035
y[1] (closed_form) = -0.236050706872 -3.34761283087
absolute error = 0.3349
relative error = 9.98 %
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 = 12.23
Order of pole (three term test) = 41.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.575 2.097
h = 0.0001 0.003
y[1] (numeric) = -0.0863250107249 -3.65275161556
y[1] (closed_form) = -0.247270141062 -3.36469276468
absolute error = 0.33
relative error = 9.781 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.948
Order of pole (three term test) = 42.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5751 2.1
h = 0.001 0.001
y[1] (numeric) = -0.0982969394023 -3.66462126634
y[1] (closed_form) = -0.254169461859 -3.37489248002
absolute error = 0.329
relative error = 9.721 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.856
Order of pole (three term test) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5761 2.101
h = 0.001 0.003
y[1] (numeric) = -0.110283394474 -3.67650315991
y[1] (closed_form) = -0.259838050613 -3.37618031115
absolute error = 0.3355
relative error = 9.908 %
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 = 37.36
Order of pole (three term test) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = -0.122292407997 -3.68838951594
y[1] (closed_form) = -0.269915596001 -3.38443014816
absolute error = 0.3379
relative error = 9.953 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.27
Order of pole (three term test) = 42.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5772 2.108
h = 0.003 0.006
y[1] (numeric) = -0.134340136894 -3.70030876047
y[1] (closed_form) = -0.27909727085 -3.39818257659
absolute error = 0.335
relative error = 9.826 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.41
Order of pole (three term test) = 42.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = -0.146499482935 -3.7122590554
y[1] (closed_form) = -0.302966193626 -3.41254882267
absolute error = 0.3381
relative error = 9.869 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.78
Order of pole (three term test) = 42.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = -0.158781596823 -3.72425575981
y[1] (closed_form) = -0.314531930246 -3.4299344133
absolute error = 0.333
relative error = 9.668 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.4
Order of pole (three term test) = 42.49 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1756.8MB, alloc=44.3MB, time=20.91
x[1] = 0.5804 2.122
h = 0.001 0.001
y[1] (numeric) = -0.17110584946 -3.73630881245
y[1] (closed_form) = -0.321642383729 -3.440315537
absolute error = 0.3321
relative error = 9.611 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.209
Order of pole (three term test) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = -0.183445016993 -3.74837431426
y[1] (closed_form) = -0.327442268645 -3.44159775053
absolute error = 0.3389
relative error = 9.803 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.4
Order of pole (three term test) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5815 2.127
h = 0.003 0.006
y[1] (numeric) = -0.19580763196 -3.7604640769
y[1] (closed_form) = -0.336863316953 -3.45556462738
absolute error = 0.3359
relative error = 9.676 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.51
Order of pole (three term test) = 42.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = -0.208284137143 -3.77258502231
y[1] (closed_form) = -0.361251120779 -3.47008596468
absolute error = 0.339
relative error = 9.716 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.28
Order of pole (three term test) = 42.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = -0.220885986873 -3.78475280147
y[1] (closed_form) = -0.373118677799 -3.48774311659
absolute error = 0.3338
relative error = 9.515 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 42.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5847 2.141
h = 0.001 0.001
y[1] (numeric) = -0.233531017963 -3.7969778624
y[1] (closed_form) = -0.380413185838 -3.49828545858
absolute error = 0.3329
relative error = 9.459 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.527
Order of pole (three term test) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5857 2.142
h = 0.001 0.003
y[1] (numeric) = -0.246191303625 -3.8092155567
y[1] (closed_form) = -0.38632852029 -3.49956383476
absolute error = 0.3399
relative error = 9.654 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.55
Order of pole (three term test) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = -0.258875147793 -3.82145770076
y[1] (closed_form) = -0.396910262228 -3.50804149198
absolute error = 0.3425
relative error = 9.7 %
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 = 23.08
Order of pole (three term test) = 42.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5868 2.149
h = 0.003 0.006
y[1] (numeric) = -0.271599650231 -3.83373378488
y[1] (closed_form) = -0.406619807879 -3.52225753658
absolute error = 0.3395
relative error = 9.575 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.83
Order of pole (three term test) = 43.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = -0.284440797413 -3.84604123647
y[1] (closed_form) = -0.431626305617 -3.53695162734
absolute error = 0.3423
relative error = 9.608 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.88
Order of pole (three term test) = 43.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = -0.297410352322 -3.85839596625
y[1] (closed_form) = -0.443857646206 -3.55492432831
absolute error = 0.337
relative error = 9.406 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.28
Order of pole (three term test) = 43.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.59 2.163
h = 0.001 0.001
y[1] (numeric) = -0.310424345309 -3.87080906051
y[1] (closed_form) = -0.451373900538 -3.5656538966
absolute error = 0.3361
relative error = 9.352 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.911
Order of pole (three term test) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.591 2.164
h = 0.001 0.003
y[1] (numeric) = -0.323453999584 -3.88323499874
y[1] (closed_form) = -0.45742606549 -3.56692523469
absolute error = 0.3435
relative error = 9.552 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.37
Order of pole (three term test) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.592 2.167
h = 0.0001 0.004
y[1] (numeric) = -0.336507766508 -3.89566537163
y[1] (closed_form) = -0.468289199263 -3.57552562754
absolute error = 0.3462
relative error = 9.601 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.12
Order of pole (three term test) = 43.44 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1801.1MB, alloc=44.3MB, time=21.44
x[1] = 0.5921 2.171
h = 0.003 0.006
y[1] (numeric) = -0.349603276965 -3.90813025172
y[1] (closed_form) = -0.478294984492 -3.58999505687
absolute error = 0.3432
relative error = 9.476 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.22
Order of pole (three term test) = 43.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = -0.362818221122 -3.9206266345
y[1] (closed_form) = -0.503935004098 -3.60486276852
absolute error = 0.3459
relative error = 9.502 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.5
Order of pole (three term test) = 43.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = -0.376164705758 -3.9331707315
y[1] (closed_form) = -0.516539896356 -3.62315636013
absolute error = 0.3403
relative error = 9.299 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.79
Order of pole (three term test) = 43.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5953 2.185
h = 0.001 0.001
y[1] (numeric) = -0.389556919062 -3.94577429196
y[1] (closed_form) = -0.524283826137 -3.63407629366
absolute error = 0.3396
relative error = 9.248 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.311
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5963 2.186
h = 0.001 0.003
y[1] (numeric) = -0.402965210505 -3.95839090919
y[1] (closed_form) = -0.530475877407 -3.63533976182
absolute error = 0.3473
relative error = 9.453 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.28
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = -0.416398180768 -3.97101194237
y[1] (closed_form) = -0.54162736153 -3.64406427794
absolute error = 0.3501
relative error = 9.503 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.21
Order of pole (three term test) = 43.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5974 2.193
h = 0.003 0.006
y[1] (numeric) = -0.429874006905 -3.98366805588
y[1] (closed_form) = -0.55193732273 -3.65879135542
absolute error = 0.3471
relative error = 9.379 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.67
Order of pole (three term test) = 44.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = -0.443472117499 -3.99635579383
y[1] (closed_form) = -0.578226021486 -3.67383348676
absolute error = 0.3495
relative error = 9.399 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.15
Order of pole (three term test) = 44.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = -0.457204972425 -4.0090916731
y[1] (closed_form) = -0.59121447866 -3.69245336982
absolute error = 0.3438
relative error = 9.195 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.32
Order of pole (three term test) = 44.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6006 2.207
h = 0.001 0.001
y[1] (numeric) = -0.470984881324 -4.02188813124
y[1] (closed_form) = -0.599192161246 -3.7035668412
absolute error = 0.3432
relative error = 9.147 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.73
Order of pole (three term test) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6016 2.208
h = 0.001 0.003
y[1] (numeric) = -0.484781295589 -4.03469786116
y[1] (closed_form) = -0.605527216595 -3.70482157139
absolute error = 0.3513
relative error = 9.358 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.27
Order of pole (three term test) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = -0.498602967127 -4.04751198458
y[1] (closed_form) = -0.616974169996 -3.71367158775
absolute error = 0.3542
relative error = 9.409 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.34
Order of pole (three term test) = 44.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6027 2.215
h = 0.003 0.006
y[1] (numeric) = -0.5124686346 -4.06036176746
y[1] (closed_form) = -0.627596442328 -3.72866062332
absolute error = 0.3511
relative error = 9.286 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.18
Order of pole (three term test) = 44.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = -0.526459500416 -4.07324328242
y[1] (closed_form) = -0.654549313944 -3.74387790143
absolute error = 0.3534
relative error = 9.298 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.83
Order of pole (three term test) = 44.64 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1845.4MB, alloc=44.3MB, time=21.98
x[1] = 0.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = -0.540588387075 -4.08617335633
y[1] (closed_form) = -0.667931600253 -3.76282953601
absolute error = 0.3475
relative error = 9.093 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.88
Order of pole (three term test) = 44.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6059 2.229
h = 0.001 0.001
y[1] (numeric) = -0.554765688595 -4.09916514118
y[1] (closed_form) = -0.676149264711 -3.77413975159
absolute error = 0.347
relative error = 9.049 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.17
Order of pole (three term test) = 44.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = -0.568959933327 -4.11217041501
y[1] (closed_form) = -0.68263050506 -3.77538483842
absolute error = 0.3555
relative error = 9.265 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.18
Order of pole (three term test) = 44.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.607 2.234
h = 0.003 0.006
y[1] (numeric) = -0.583180934997 -4.12520212079
y[1] (closed_form) = -0.693525082888 -3.79060670154
absolute error = 0.3523
relative error = 9.143 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.54
Order of pole (three term test) = 45.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.61 2.24
h = 0.0001 0.005
y[1] (numeric) = -0.597529663646 -4.13826563546
y[1] (closed_form) = -0.721060224765 -3.80598343431
absolute error = 0.3545
relative error = 9.152 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.45
Order of pole (three term test) = 45.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = -0.612019288038 -4.15137810078
y[1] (closed_form) = -0.734785879953 -3.82522990964
absolute error = 0.3485
relative error = 8.947 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.37
Order of pole (three term test) = 45.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6102 2.248
h = 0.001 0.001
y[1] (numeric) = -0.626558514108 -4.16455328176
y[1] (closed_form) = -0.743212823133 -3.83671503191
absolute error = 0.348
relative error = 8.904 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.56
Order of pole (three term test) = 45.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6112 2.249
h = 0.001 0.003
y[1] (numeric) = -0.641115066346 -4.17774214584
y[1] (closed_form) = -0.749822621255 -3.8379528578
absolute error = 0.3568
relative error = 9.123 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.23
Order of pole (three term test) = 45.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = -0.655697986179 -4.19093535845
y[1] (closed_form) = -0.761837352553 -3.84704375246
absolute error = 0.3599
relative error = 9.177 %
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 = 28.59
Order of pole (three term test) = 45.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6123 2.256
h = 0.003 0.006
y[1] (numeric) = -0.670327092301 -4.20416533849
y[1] (closed_form) = -0.773059871753 -3.86253582025
absolute error = 0.3567
relative error = 9.056 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.19
Order of pole (three term test) = 45.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = -0.685086990642 -4.21742724773
y[1] (closed_form) = -0.801288930465 -3.87808904471
absolute error = 0.3587
relative error = 9.058 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.19
Order of pole (three term test) = 45.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = -0.69999120083 -4.230738507
y[1] (closed_form) = -0.815428135857 -3.89767771929
absolute error = 0.3525
relative error = 8.852 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.98
Order of pole (three term test) = 45.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6155 2.27
h = 0.001 0.001
y[1] (numeric) = -0.714946441956 -4.24411364593
y[1] (closed_form) = -0.824107028731 -3.90936572043
absolute error = 0.3521
relative error = 8.813 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.04
Order of pole (three term test) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6165 2.271
h = 0.001 0.003
y[1] (numeric) = -0.729919467505 -4.2575026894
y[1] (closed_form) = -0.83086911506 -3.91059215462
absolute error = 0.3613
relative error = 9.037 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.48
Order of pole (three term test) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1889.7MB, alloc=44.3MB, time=22.51
x[1] = 0.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = -0.74491947573 -4.27089604758
y[1] (closed_form) = -0.843200583407 -3.91981251202
absolute error = 0.3646
relative error = 9.093 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.88
Order of pole (three term test) = 46.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6176 2.278
h = 0.003 0.006
y[1] (numeric) = -0.759966893202 -4.28432676981
y[1] (closed_form) = -0.854759773608 -3.93557923036
absolute error = 0.3614
relative error = 8.974 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.91
Order of pole (three term test) = 46.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = -0.775148205128 -4.2977894858
y[1] (closed_form) = -0.883699246714 -3.95130945406
absolute error = 0.3631
relative error = 8.967 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.96
Order of pole (three term test) = 46.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = -0.790477322311 -4.31130194002
y[1] (closed_form) = -0.898263017121 -3.9712459613
absolute error = 0.3567
relative error = 8.761 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.6
Order of pole (three term test) = 46.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6208 2.292
h = 0.001 0.001
y[1] (numeric) = -0.805858937859 -4.32487945514
y[1] (closed_form) = -0.907200542444 -3.98314014607
absolute error = 0.3564
relative error = 8.725 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.53
Order of pole (three term test) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6218 2.293
h = 0.001 0.003
y[1] (numeric) = -0.821258807433 -4.33847109841
y[1] (closed_form) = -0.914118285995 -3.98435417068
absolute error = 0.3661
relative error = 8.956 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.84
Order of pole (three term test) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = -0.836686288073 -4.35206701826
y[1] (closed_form) = -0.92677426394 -3.99370531867
absolute error = 0.3695
relative error = 9.013 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.22
Order of pole (three term test) = 46.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6229 2.3
h = 0.003 0.006
y[1] (numeric) = -0.852162431246 -4.36570090477
y[1] (closed_form) = -0.938679072317 -4.00975118017
absolute error = 0.3663
relative error = 8.895 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.7
Order of pole (three term test) = 46.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = -0.867775639619 -4.37936683294
y[1] (closed_form) = -0.968345822549 -4.02565882568
absolute error = 0.3677
relative error = 8.881 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.77
Order of pole (three term test) = 46.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.626 2.311
h = 0.0001 0.003
y[1] (numeric) = -0.883540225643 -4.39308287577
y[1] (closed_form) = -0.983345447473 -4.04594885855
absolute error = 0.3612
relative error = 8.675 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.26
Order of pole (three term test) = 47.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6261 2.314
h = 0.001 0.001
y[1] (numeric) = -0.899358816567 -4.40686517814
y[1] (closed_form) = -0.992548454001 -4.0580525654
absolute error = 0.361
relative error = 8.642 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.05
Order of pole (three term test) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6271 2.315
h = 0.001 0.003
y[1] (numeric) = -0.915196142739 -4.42066183447
y[1] (closed_form) = -0.999625291863 -4.05925312059
absolute error = 0.3711
relative error = 8.878 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.31
Order of pole (three term test) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = -0.931061721953 -4.43446272475
y[1] (closed_form) = -1.01261373041 -4.06873637096
absolute error = 0.3747
relative error = 8.937 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.63
Order of pole (three term test) = 47.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6282 2.322
h = 0.003 0.006
y[1] (numeric) = -0.946977248027 -4.44830219026
y[1] (closed_form) = -1.02487332681 -4.08506591489
absolute error = 0.3715
relative error = 8.821 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.58
Order of pole (three term test) = 47.48 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1933.8MB, alloc=44.3MB, time=23.03
x[1] = 0.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = -0.963033080008 -4.46217372797
y[1] (closed_form) = -1.05528458987 -4.10115131606
absolute error = 0.3726
relative error = 8.799 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.61
Order of pole (three term test) = 47.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = -0.979243942742 -4.47609574431
y[1] (closed_form) = -1.07073163997 -4.12180062707
absolute error = 0.3659
relative error = 8.592 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.95
Order of pole (three term test) = 47.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6314 2.336
h = 0.001 0.001
y[1] (numeric) = -0.995510356984 -4.49008523646
y[1] (closed_form) = -1.08020714636 -4.13411722804
absolute error = 0.3659
relative error = 8.563 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.59
Order of pole (three term test) = 47.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = -1.01179599959 -4.50408931054
y[1] (closed_form) = -1.08744658502 -4.13530321073
absolute error = 0.3765
relative error = 8.804 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.78
Order of pole (three term test) = 47.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6325 2.341
h = 0.003 0.006
y[1] (numeric) = -1.02811214226 -4.51812212704
y[1] (closed_form) = -1.10001563431 -4.15188498863
absolute error = 0.3732
relative error = 8.69 %
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 = 45.26
Order of pole (three term test) = 48.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = -1.04457140279 -4.53218702402
y[1] (closed_form) = -1.13107972055 -4.1681327478
absolute error = 0.3742
relative error = 8.664 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.37
Order of pole (three term test) = 48.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = -1.06118890038 -4.54630274726
y[1] (closed_form) = -1.1469170103 -4.18910148795
absolute error = 0.3673
relative error = 8.458 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.57
Order of pole (three term test) = 48.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6357 2.355
h = 0.001 0.001
y[1] (numeric) = -1.07786329881 -4.56048702658
y[1] (closed_form) = -1.15663023723 -4.20160742994
absolute error = 0.3674
relative error = 8.431 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.08
Order of pole (three term test) = 48.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6367 2.356
h = 0.001 0.003
y[1] (numeric) = -1.09455735704 -4.57468609187
y[1] (closed_form) = -1.16401269139 -4.20278194686
absolute error = 0.3783
relative error = 8.675 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.21
Order of pole (three term test) = 48.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = -1.11128090065 -4.58888930731
y[1] (closed_form) = -1.17763994142 -4.21251863259
absolute error = 0.3822
relative error = 8.737 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.41
Order of pole (three term test) = 48.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6378 2.363
h = 0.003 0.006
y[1] (numeric) = -1.12805685867 -4.60313226236
y[1] (closed_form) = -1.19058139701 -4.2293927791
absolute error = 0.3789
relative error = 8.624 %
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 = 47.3
Order of pole (three term test) = 48.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = -1.14497934426 -4.61740733835
y[1] (closed_form) = -1.22242308632 -4.24581888182
absolute error = 0.3796
relative error = 8.591 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.29
Order of pole (three term test) = 49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = -1.16206387504 -4.63173358057
y[1] (closed_form) = -1.23873003246 -4.2671579084
absolute error = 0.3725
relative error = 8.384 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.31
Order of pole (three term test) = 49.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.641 2.377
h = 0.001 0.001
y[1] (numeric) = -1.17920693028 -4.64612962892
y[1] (closed_form) = -1.24872924415 -4.27988319678
absolute error = 0.3728
relative error = 8.362 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.67
Order of pole (three term test) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1978.2MB, alloc=44.3MB, time=23.56
x[1] = 0.642 2.378
h = 0.001 0.003
y[1] (numeric) = -1.19637016127 -4.6605406954
y[1] (closed_form) = -1.25628102758 -4.28104101275
absolute error = 0.3842
relative error = 8.611 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65.01
Order of pole (three term test) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.643 2.381
h = 0.0001 0.004
y[1] (numeric) = -1.21356356013 -4.67495585576
y[1] (closed_form) = -1.27026449028 -4.29091355576
absolute error = 0.3882
relative error = 8.675 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.01
Order of pole (three term test) = 49.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6431 2.385
h = 0.003 0.006
y[1] (numeric) = -1.23081075051 -4.68941138162
y[1] (closed_form) = -1.28358818782 -4.30808474599
absolute error = 0.385
relative error = 8.564 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.43
Order of pole (three term test) = 49.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = -1.24820791786 -4.70389900603
y[1] (closed_form) = -1.3162258284 -4.32468925527
absolute error = 0.3853
relative error = 8.522 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.24
Order of pole (three term test) = 49.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = -1.26577102435 -4.71843812215
y[1] (closed_form) = -1.33301484229 -4.34640449415
absolute error = 0.3781
relative error = 8.316 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.09
Order of pole (three term test) = 50.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6463 2.399
h = 0.001 0.001
y[1] (numeric) = -1.28339432186 -4.73304831264
y[1] (closed_form) = -1.34330756538 -4.35935259868
absolute error = 0.3785
relative error = 8.297 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.28
Order of pole (three term test) = 50.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6473 2.4
h = 0.001 0.003
y[1] (numeric) = -1.30103832378 -4.74767375555
y[1] (closed_form) = -1.35103239112 -4.36049248037
absolute error = 0.3904
relative error = 8.552 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.93
Order of pole (three term test) = 50.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = -1.31871319076 -4.76230323093
y[1] (closed_form) = -1.36538074432 -4.37050212057
absolute error = 0.3946
relative error = 8.617 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.67
Order of pole (three term test) = 50.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6484 2.407
h = 0.003 0.006
y[1] (numeric) = -1.33644326033 -4.77697370353
y[1] (closed_form) = -1.37909676302 -4.38797507595
absolute error = 0.3913
relative error = 8.508 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.65
Order of pole (three term test) = 50.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = -1.35432683214 -4.79167623196
y[1] (closed_form) = -1.41254910758 -4.40475795047
absolute error = 0.3913
relative error = 8.459 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.24
Order of pole (three term test) = 50.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = -1.37238032467 -4.80643056235
y[1] (closed_form) = -1.42983290809 -4.42685538664
absolute error = 0.3839
relative error = 8.252 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.9
Order of pole (three term test) = 50.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6516 2.421
h = 0.001 0.001
y[1] (numeric) = -1.39049571883 -4.82125725373
y[1] (closed_form) = -1.44042685499 -4.44002981021
absolute error = 0.3845
relative error = 8.237 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.93
Order of pole (three term test) = 51.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6526 2.422
h = 0.001 0.003
y[1] (numeric) = -1.40863235904 -4.83609943393
y[1] (closed_form) = -1.44832851081 -4.44115047575
absolute error = 0.3969
relative error = 8.497 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.99
Order of pole (three term test) = 51.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = -1.42680057652 -4.85094557982
y[1] (closed_form) = -1.46305063068 -4.45129843048
absolute error = 0.4013
relative error = 8.564 %
Correct digits = 1
memory used=2022.6MB, alloc=44.3MB, time=24.09
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.41
Order of pole (three term test) = 51.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6537 2.429
h = 0.003 0.006
y[1] (numeric) = -1.44502544238 -4.8658333605
y[1] (closed_form) = -1.47716929898 -4.46907791851
absolute error = 0.3981
relative error = 8.457 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 53.97
Order of pole (three term test) = 51.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = -1.4634074132 -4.88075313307
y[1] (closed_form) = -1.51145551328 -4.48603900829
absolute error = 0.3976
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 = 24.29
Order of pole (three term test) = 51.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = -1.4819633759 -4.89572500187
y[1] (closed_form) = -1.529247134 -4.50852468558
absolute error = 0.3901
relative error = 8.193 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.75
Order of pole (three term test) = 51.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6569 2.443
h = 0.001 0.001
y[1] (numeric) = -1.50058299592 -4.91077053682
y[1] (closed_form) = -1.54015020724 -4.52192896401
absolute error = 0.3908
relative error = 8.182 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.6
Order of pole (three term test) = 51.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = -1.51922441694 -4.9258317991
y[1] (closed_form) = -1.54823255705 -4.52302908153
absolute error = 0.4038
relative error = 8.447 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 93.86
Order of pole (three term test) = 51.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.658 2.448
h = 0.003 0.006
y[1] (numeric) = -1.53790056789 -4.94092425812
y[1] (closed_form) = -1.56270254849 -4.54108124387
absolute error = 0.4006
relative error = 8.342 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.06
Order of pole (three term test) = 52.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661 2.454
h = 0.0001 0.005
y[1] (numeric) = -1.55673694947 -4.95604863346
y[1] (closed_form) = -1.59772008088 -4.55820578055
absolute error = 0.3999
relative error = 8.28 %
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 = 25.23
Order of pole (three term test) = 52.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = -1.5757508972 -4.97122539485
y[1] (closed_form) = -1.61595477519 -4.58103679374
absolute error = 0.3923
relative error = 8.075 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.52
Order of pole (three term test) = 52.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6612 2.462
h = 0.001 0.001
y[1] (numeric) = -1.5948300346 -4.98647698248
y[1] (closed_form) = -1.62712761469 -4.59464559397
absolute error = 0.3932
relative error = 8.066 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.2
Order of pole (three term test) = 52.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6622 2.463
h = 0.001 0.003
y[1] (numeric) = -1.61393145869 -5.00174451128
y[1] (closed_form) = -1.63536892048 -4.59572913514
absolute error = 0.4066
relative error = 8.335 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 77.05
Order of pole (three term test) = 52.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = -1.63306582726 -5.01701587548
y[1] (closed_form) = -1.65080917389 -4.60614232864
absolute error = 0.4113
relative error = 8.405 %
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 = 43.86
Order of pole (three term test) = 52.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6633 2.47
h = 0.003 0.006
y[1] (numeric) = -1.65225962198 -5.03233009436
y[1] (closed_form) = -1.6657016591 -4.62451014697
absolute error = 0.408
relative error = 8.301 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 58.58
Order of pole (three term test) = 53.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = -1.67161743862 -5.04767617198
y[1] (closed_form) = -1.70158985853 -4.64181255524
absolute error = 0.407
relative error = 8.232 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.37
Order of pole (three term test) = 53.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = -1.69115706456 -5.06307489905
y[1] (closed_form) = -1.72035741483 -4.66504337581
absolute error = 0.3991
relative error = 8.027 %
Correct digits = 1
memory used=2066.9MB, alloc=44.3MB, time=24.62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.44
Order of pole (three term test) = 53.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6665 2.484
h = 0.001 0.001
y[1] (numeric) = -1.71076372251 -5.07854979311
y[1] (closed_form) = -1.73185456364 -4.67888879678
absolute error = 0.4002
relative error = 8.022 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.93
Order of pole (three term test) = 53.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6675 2.485
h = 0.001 0.003
y[1] (numeric) = -1.73039324766 -5.09404087088
y[1] (closed_form) = -1.74028397821 -4.67994922159
absolute error = 0.4142
relative error = 8.296 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 80.52
Order of pole (three term test) = 53.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = -1.75005647424 -5.10953570103
y[1] (closed_form) = -1.75612451186 -4.69050418762
absolute error = 0.4191
relative error = 8.367 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.84
Order of pole (three term test) = 53.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6686 2.492
h = 0.003 0.006
y[1] (numeric) = -1.76978067657 -5.12507404022
y[1] (closed_form) = -1.77145056436 -4.70919256305
absolute error = 0.4159
relative error = 8.266 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.22
Order of pole (three term test) = 54.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = -1.78967273452 -5.14064410973
y[1] (closed_form) = -1.80822982829 -4.7266723617
absolute error = 0.4144
relative error = 8.188 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.55
Order of pole (three term test) = 54.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = -1.80975094009 -5.15626707367
y[1] (closed_form) = -1.82754422098 -4.7503092042
absolute error = 0.4063
relative error = 7.984 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.4
Order of pole (three term test) = 54.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6718 2.506
h = 0.001 0.001
y[1] (numeric) = -1.82989806835 -5.17196756444
y[1] (closed_form) = -1.8393741499 -4.76439487701
absolute error = 0.4077
relative error = 7.983 %
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 = 17.69
Order of pole (three term test) = 54.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6728 2.507
h = 0.001 0.003
y[1] (numeric) = -1.8500686585 -5.18768448352
y[1] (closed_form) = -1.84799576374 -4.76543070305
absolute error = 0.4223
relative error = 8.261 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 84.14
Order of pole (three term test) = 54.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = -1.87027372327 -5.2034050658
y[1] (closed_form) = -1.86424626128 -4.77612855955
absolute error = 0.4273
relative error = 8.335 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.9
Order of pole (three term test) = 55.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6739 2.514
h = 0.003 0.006
y[1] (numeric) = -1.89054135133 -5.21916981711
y[1] (closed_form) = -1.88001722702 -4.79514243824
absolute error = 0.4242
relative error = 8.235 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.97
Order of pole (three term test) = 55.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = -1.91098075266 -5.23496614562
y[1] (closed_form) = -1.91770840057 -4.81279901914
absolute error = 0.4222
relative error = 8.15 %
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 = 28.79
Order of pole (three term test) = 55.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.677 2.525
h = 0.0001 0.003
y[1] (numeric) = -1.93161073713 -5.25081559426
y[1] (closed_form) = -1.93758394804 -4.83684815568
absolute error = 0.414
relative error = 7.946 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.41
Order of pole (three term test) = 55.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6771 2.528
h = 0.001 0.001
y[1] (numeric) = -1.95231158446 -5.26674394885
y[1] (closed_form) = -1.94975533565 -4.85117774336
absolute error = 0.4156
relative error = 7.948 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.49
Order of pole (three term test) = 56.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6781 2.529
h = 0.001 0.003
y[1] (numeric) = -1.97303650291 -5.28268897835
y[1] (closed_form) = -1.95857332111 -4.85218743216
absolute error = 0.4307
relative error = 8.232 %
Correct digits = 1
memory used=2111.3MB, alloc=44.3MB, time=25.15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 87.92
Order of pole (three term test) = 56.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = -1.99379668574 -5.29863757551
y[1] (closed_form) = -1.97524368644 -4.86302926663
absolute error = 0.436
relative error = 8.307 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.05
Order of pole (three term test) = 56.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6792 2.536
h = 0.003 0.006
y[1] (numeric) = -2.01462105825 -5.31463100723
y[1] (closed_form) = -1.99147119016 -4.88237363938
absolute error = 0.4329
relative error = 8.209 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 66.85
Order of pole (three term test) = 56.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = -2.03562120731 -5.33065583736
y[1] (closed_form) = -2.03009557541 -4.9002062623
absolute error = 0.4305
relative error = 8.116 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.09
Order of pole (three term test) = 56.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = -2.05681647435 -5.3467339931
y[1] (closed_form) = -2.05054694806 -4.9246740221
absolute error = 0.4221
relative error = 7.913 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.47
Order of pole (three term test) = 57.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6824 2.55
h = 0.001 0.001
y[1] (numeric) = -2.07808459511 -5.36289245335
y[1] (closed_form) = -2.06306868549 -4.93925121926
absolute error = 0.4239
relative error = 7.919 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.32
Order of pole (three term test) = 57.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = -2.09937741109 -5.37906783712
y[1] (closed_form) = -2.07208729836 -4.94023317466
absolute error = 0.4397
relative error = 8.207 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 116.3
Order of pole (three term test) = 57.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6835 2.555
h = 0.003 0.006
y[1] (numeric) = -2.12070973268 -5.39527701917
y[1] (closed_form) = -2.08871328253 -4.95987168794
absolute error = 0.4366
relative error = 8.112 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 69.44
Order of pole (three term test) = 57.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = -2.14222130361 -5.41151742233
y[1] (closed_form) = -2.12815627694 -4.97786661488
absolute error = 0.4339
relative error = 8.014 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.25
Order of pole (three term test) = 57.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = -2.16393197494 -5.42781136669
y[1] (closed_form) = -2.14911023287 -5.00270692683
absolute error = 0.4254
relative error = 7.812 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.41
Order of pole (three term test) = 58.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6867 2.569
h = 0.001 0.001
y[1] (numeric) = -2.18571723826 -5.44418685966
y[1] (closed_form) = -2.16193781543 -5.01750456186
absolute error = 0.4273
relative error = 7.822 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.07
Order of pole (three term test) = 58.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6877 2.57
h = 0.001 0.003
y[1] (numeric) = -2.20752774316 -5.46057949939
y[1] (closed_form) = -2.17113295182 -5.01846378221
absolute error = 0.4436
relative error = 8.113 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 95.44
Order of pole (three term test) = 58.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = -2.22937502859 -5.47697552112
y[1] (closed_form) = -2.18860998293 -5.02958159913
absolute error = 0.4492
relative error = 8.19 %
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 = 54.33
Order of pole (three term test) = 58.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6888 2.577
h = 0.003 0.006
y[1] (numeric) = -2.25128962836 -5.49341765083
y[1] (closed_form) = -2.20571483943 -5.04956015707
absolute error = 0.4462
relative error = 8.097 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 72.56
Order of pole (three term test) = 58.9 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2155.6MB, alloc=44.3MB, time=25.67
x[1] = 0.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = -2.27338769097 -5.50989082466
y[1] (closed_form) = -2.24613194566 -5.06772964592
absolute error = 0.443
relative error = 7.992 %
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 = 32.66
Order of pole (three term test) = 59.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = -2.29568957945 -5.52641770616
y[1] (closed_form) = -2.26768991294 -5.09300069347
absolute error = 0.4343
relative error = 7.79 %
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 = 26.56
Order of pole (three term test) = 59.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.692 2.591
h = 0.001 0.001
y[1] (numeric) = -2.31806814824 -5.54302757213
y[1] (closed_form) = -2.28088492741 -5.10805300755
absolute error = 0.4366
relative error = 7.804 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.97
Order of pole (three term test) = 59.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.693 2.592
h = 0.001 0.003
y[1] (numeric) = -2.34047261125 -5.55965483726
y[1] (closed_form) = -2.29028885844 -5.10898141798
absolute error = 0.4535
relative error = 8.099 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 99.73
Order of pole (three term test) = 59.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.694 2.595
h = 0.0001 0.004
y[1] (numeric) = -2.36291469393 -5.57628536955
y[1] (closed_form) = -2.30821533779 -5.12024626641
absolute error = 0.4593
relative error = 8.178 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.77
Order of pole (three term test) = 59.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6941 2.599
h = 0.003 0.006
y[1] (numeric) = -2.38542583335 -5.59296269127
y[1] (closed_form) = -2.32581152448 -5.14056998853
absolute error = 0.4563
relative error = 8.087 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.83
Order of pole (three term test) = 60.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = -2.40812469435 -5.6096708003
y[1] (closed_form) = -2.36722540705 -5.15891289718
absolute error = 0.4526
relative error = 7.974 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.13
Order of pole (three term test) = 60.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = -2.43103221215 -5.62643276042
y[1] (closed_form) = -2.38940310811 -5.18462117427
absolute error = 0.4438
relative error = 7.774 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.75
Order of pole (three term test) = 61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6973 2.613
h = 0.001 0.001
y[1] (numeric) = -2.45401855288 -5.64327916081
y[1] (closed_form) = -2.40297508086 -5.19993195279
absolute error = 0.4463
relative error = 7.791 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.91
Order of pole (three term test) = 61.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6983 2.614
h = 0.001 0.003
y[1] (numeric) = -2.47703145633 -5.66014321465
y[1] (closed_form) = -2.41259231051 -5.20082778343
absolute error = 0.4638
relative error = 8.09 %
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 = 104.2
Order of pole (three term test) = 61.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = -2.50008283652 -5.67701041354
y[1] (closed_form) = -2.43097903838 -5.21224061848
absolute error = 0.4699
relative error = 8.17 %
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 = 59.33
Order of pole (three term test) = 61.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6994 2.621
h = 0.003 0.006
y[1] (numeric) = -2.52320505824 -5.69392508854
y[1] (closed_form) = -2.4490793176 -5.23291466709
absolute error = 0.4669
relative error = 8.082 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 79.24
Order of pole (three term test) = 61.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = -2.54651935304 -5.71087026428
y[1] (closed_form) = -2.49151313593 -5.25142970004
absolute error = 0.4627
relative error = 7.961 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.66
Order of pole (three term test) = 62.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = -2.57004724326 -5.72786941044
y[1] (closed_form) = -2.51432667772 -5.27758175544
absolute error = 0.4537
relative error = 7.761 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29
Order of pole (three term test) = 62.52 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2200.0MB, alloc=44.3MB, time=26.20
x[1] = 0.7026 2.635
h = 0.001 0.001
y[1] (numeric) = -2.59365615466 -5.74495447278
y[1] (closed_form) = -2.52828536726 -5.29315481371
absolute error = 0.4565
relative error = 7.782 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.9
Order of pole (three term test) = 62.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7036 2.636
h = 0.001 0.003
y[1] (numeric) = -2.61729231352 -5.76205744471
y[1] (closed_form) = -2.53812048918 -5.29401623007
absolute error = 0.4747
relative error = 8.085 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 108.9
Order of pole (three term test) = 62.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = -2.64096782446 -5.77916343204
y[1] (closed_form) = -2.55697851016 -5.30557796701
absolute error = 0.481
relative error = 8.167 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.99
Order of pole (three term test) = 63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7047 2.643
h = 0.003 0.006
y[1] (numeric) = -2.66471600509 -5.79631758728
y[1] (closed_form) = -2.5755959558 -5.32660754657
absolute error = 0.4781
relative error = 8.08 %
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 = 82.8
Order of pole (three term test) = 63.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = -2.68866070498 -5.8135019258
y[1] (closed_form) = -2.61907337448 -5.34529324893
absolute error = 0.4734
relative error = 7.952 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.26
Order of pole (three term test) = 63.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = -2.71282404888 -5.83074032886
y[1] (closed_form) = -2.64253925732 -5.37189568543
absolute error = 0.4642
relative error = 7.754 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.3
Order of pole (three term test) = 64.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7079 2.657
h = 0.001 0.001
y[1] (numeric) = -2.7370706692 -5.84806614428
y[1] (closed_form) = -2.65689465966 -5.38773486814
absolute error = 0.4673
relative error = 7.778 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.93
Order of pole (three term test) = 64.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = -2.76134523831 -5.86541012727
y[1] (closed_form) = -2.66695235879 -5.38855996923
absolute error = 0.4861
relative error = 8.085 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 144
Order of pole (three term test) = 64.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.709 2.662
h = 0.003 0.006
y[1] (numeric) = -2.78566470038 -5.88279065936
y[1] (closed_form) = -2.6860213562 -5.40990615561
absolute error = 0.4833
relative error = 8.001 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 86.01
Order of pole (three term test) = 64.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.712 2.668
h = 0.0001 0.005
y[1] (numeric) = -2.81018453816 -5.90020107479
y[1] (closed_form) = -2.73041440826 -5.42875029776
absolute error = 0.4782
relative error = 7.869 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.71
Order of pole (three term test) = 65.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = -2.83492745475 -5.91766567668
y[1] (closed_form) = -2.75444985165 -5.45575378092
absolute error = 0.4689
relative error = 7.672 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.48
Order of pole (three term test) = 65.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7122 2.676
h = 0.001 0.001
y[1] (numeric) = -2.85975561752 -5.93521902298
y[1] (closed_form) = -2.76915168808 -5.47183002762
absolute error = 0.4722
relative error = 7.699 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.86
Order of pole (three term test) = 65.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7132 2.677
h = 0.001 0.003
y[1] (numeric) = -2.88461234323 -5.95279076893
y[1] (closed_form) = -2.77940526148 -5.47262502427
absolute error = 0.4916
relative error = 8.008 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 118.2
Order of pole (three term test) = 65.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = -2.90951010149 -5.97036527897
y[1] (closed_form) = -2.79916870601 -5.48447205971
absolute error = 0.4983
relative error = 8.092 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.29
Order of pole (three term test) = 66.14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2244.1MB, alloc=44.3MB, time=26.73
x[1] = 0.7143 2.684
h = 0.003 0.006
y[1] (numeric) = -2.93448404172 -5.98798928051
y[1] (closed_form) = -2.81877998797 -5.50618373601
absolute error = 0.4955
relative error = 8.01 %
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 = 89.88
Order of pole (three term test) = 66.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = -2.95966303794 -6.00564284406
y[1] (closed_form) = -2.86426207717 -5.5251956914
absolute error = 0.4898
relative error = 7.871 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.45
Order of pole (three term test) = 66.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = -2.98507037274 -6.02335063961
y[1] (closed_form) = -2.88898156298 -5.55266219087
absolute error = 0.4804
relative error = 7.675 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.89
Order of pole (three term test) = 67.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7175 2.698
h = 0.001 0.001
y[1] (numeric) = -3.01056531841 -6.04114871461
y[1] (closed_form) = -2.90409931665 -5.56901191832
absolute error = 0.484
relative error = 7.706 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.97
Order of pole (three term test) = 67.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7185 2.699
h = 0.001 0.003
y[1] (numeric) = -3.03608956025 -6.05896545067
y[1] (closed_form) = -2.91458445834 -5.56976693711
absolute error = 0.5041
relative error = 8.018 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 123.5
Order of pole (three term test) = 67.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = -3.0616557644 -6.07678479835
y[1] (closed_form) = -2.93485217969 -5.5817653948
absolute error = 0.511
relative error = 8.103 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.32
Order of pole (three term test) = 67.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7196 2.706
h = 0.003 0.006
y[1] (numeric) = -3.08730010829 -6.09465434391
y[1] (closed_form) = -2.95501975098 -5.60384788617
absolute error = 0.5083
relative error = 8.024 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 93.92
Order of pole (three term test) = 68.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = -3.11315423654 -6.11255304021
y[1] (closed_form) = -3.00161604755 -5.62302571555
absolute error = 0.5021
relative error = 7.877 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.27
Order of pole (three term test) = 68.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = -3.13924207989 -6.13050598551
y[1] (closed_form) = -3.02703725163 -5.65096198892
absolute error = 0.4925
relative error = 7.682 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.37
Order of pole (three term test) = 69.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7228 2.72
h = 0.001 0.001
y[1] (numeric) = -3.16541995981 -6.14855076605
y[1] (closed_form) = -3.04258162813 -5.6675891256
absolute error = 0.4964
relative error = 7.717 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.14
Order of pole (three term test) = 69.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7238 2.721
h = 0.001 0.003
y[1] (numeric) = -3.19162788682 -6.16661447074
y[1] (closed_form) = -3.05330329461 -5.66830206545
absolute error = 0.5172
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 = 129.1
Order of pole (three term test) = 69.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = -3.21787872567 -6.18468062596
y[1] (closed_form) = -3.07408733153 -5.68045268896
absolute error = 0.5243
relative error = 8.118 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 73.48
Order of pole (three term test) = 69.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7249 2.728
h = 0.003 0.006
y[1] (numeric) = -3.24420970933 -6.20279769012
y[1] (closed_form) = -3.09482553705 -5.70291135989
absolute error = 0.5217
relative error = 8.041 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 98.15
Order of pole (three term test) = 70.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = -3.27075530818 -6.22094345812
y[1] (closed_form) = -3.14256175792 -5.72225293979
absolute error = 0.5149
relative error = 7.887 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.17
Order of pole (three term test) = 70.77 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2288.5MB, alloc=44.3MB, time=27.25
x[1] = 0.728 2.739
h = 0.0001 0.003
y[1] (numeric) = -3.29754011787 -6.23914346234
y[1] (closed_form) = -3.1687027856 -5.75066579516
absolute error = 0.5052
relative error = 7.694 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.92
Order of pole (three term test) = 71.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7281 2.742
h = 0.001 0.001
y[1] (numeric) = -3.32441745228 -6.25743687846
y[1] (closed_form) = -3.1846847497 -5.76757429654
absolute error = 0.5094
relative error = 7.732 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.36
Order of pole (three term test) = 71.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7291 2.743
h = 0.001 0.003
y[1] (numeric) = -3.35132560282 -6.27574948343
y[1] (closed_form) = -3.19564799549 -5.768242982
absolute error = 0.5308
relative error = 8.05 %
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 = 134.9
Order of pole (three term test) = 71.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = -3.37827763485 -6.29406436897
y[1] (closed_form) = -3.21696065765 -5.78054646388
absolute error = 0.5383
relative error = 8.136 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 76.79
Order of pole (three term test) = 71.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7302 2.75
h = 0.003 0.006
y[1] (numeric) = -3.4053118652 -6.31243087901
y[1] (closed_form) = -3.23828419016 -5.80338671727
absolute error = 0.5357
relative error = 8.062 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 102.6
Order of pole (three term test) = 72.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = -3.43256564609 -6.33082560902
y[1] (closed_form) = -3.28718661017 -5.82288973302
absolute error = 0.5283
relative error = 7.901 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.16
Order of pole (three term test) = 72.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = -3.46006425527 -6.34927453144
y[1] (closed_form) = -3.31406600613 -5.8517860279
absolute error = 0.5185
relative error = 7.71 %
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 = 37.53
Order of pole (three term test) = 73.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7334 2.764
h = 0.001 0.001
y[1] (numeric) = -3.4876579413 -6.3678184634
y[1] (closed_form) = -3.33049678774 -5.86897987568
absolute error = 0.523
relative error = 7.75 %
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 = 29.64
Order of pole (three term test) = 73.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = -3.51528323103 -6.38638185049
y[1] (closed_form) = -3.34170676718 -5.8696020548
absolute error = 0.5452
relative error = 8.071 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 178.4
Order of pole (three term test) = 73.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7345 2.769
h = 0.003 0.006
y[1] (numeric) = -3.542959486 -6.40498468703
y[1] (closed_form) = -3.36354153305 -5.89278233398
absolute error = 0.5427
relative error = 7.999 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 106.5
Order of pole (three term test) = 74.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = -3.57085957166 -6.42361529665
y[1] (closed_form) = -3.41346737115 -5.91243663179
absolute error = 0.5349
relative error = 7.834 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.94
Order of pole (three term test) = 74.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = -3.59900942137 -6.44230010398
y[1] (closed_form) = -3.44099165205 -5.94176368786
absolute error = 0.5249
relative error = 7.644 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.99
Order of pole (three term test) = 75.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7377 2.783
h = 0.001 0.001
y[1] (numeric) = -3.62725657775 -6.46108134447
y[1] (closed_form) = -3.45781449624 -5.95921189356
absolute error = 0.5297
relative error = 7.688 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.79
Order of pole (three term test) = 75.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7387 2.784
h = 0.001 0.003
y[1] (numeric) = -3.6555360277 -6.47988228018
y[1] (closed_form) = -3.46924165275 -5.95979520273
absolute error = 0.5524
relative error = 8.011 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 146.4
Order of pole (three term test) = 75.77 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2332.8MB, alloc=44.3MB, time=27.78
x[1] = 0.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = -3.68386122069 -6.49868516762
y[1] (closed_form) = -3.49156983992 -5.97239143227
absolute error = 0.5603
relative error = 8.099 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 83.35
Order of pole (three term test) = 76.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7398 2.791
h = 0.003 0.006
y[1] (numeric) = -3.71227255709 -6.51754104842
y[1] (closed_form) = -3.51401816056 -5.99596363155
absolute error = 0.558
relative error = 8.029 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 111.3
Order of pole (three term test) = 76.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = -3.74091292005 -6.53642420755
y[1] (closed_form) = -3.56516064664 -6.01577485375
absolute error = 0.5495
relative error = 7.858 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.1
Order of pole (three term test) = 77.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = -3.76980889822 -6.55536146074
y[1] (closed_form) = -3.593458924 -6.04559847064
absolute error = 0.5394
relative error = 7.67 %
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 = 40.74
Order of pole (three term test) = 77.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.743 2.805
h = 0.001 0.001
y[1] (numeric) = -3.79880485808 -6.57439678498
y[1] (closed_form) = -3.61075216025 -6.06333964027
absolute error = 0.5446
relative error = 7.717 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.17
Order of pole (three term test) = 78.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.744 2.806
h = 0.001 0.003
y[1] (numeric) = -3.82783393465 -6.59345207369
y[1] (closed_form) = -3.62243594247 -6.0638721057
absolute error = 0.568
relative error = 8.042 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 153
Order of pole (three term test) = 78.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.745 2.809
h = 0.0001 0.004
y[1] (numeric) = -3.85690978389 -6.61250911727
y[1] (closed_form) = -3.64532951202 -6.0766230277
absolute error = 0.5761
relative error = 8.131 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 87.1
Order of pole (three term test) = 78.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7451 2.813
h = 0.003 0.006
y[1] (numeric) = -3.88607397466 -6.63161988246
y[1] (closed_form) = -3.66840711958 -6.10059265885
absolute error = 0.5739
relative error = 8.062 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 116.3
Order of pole (three term test) = 78.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = -3.91547243886 -6.65075732998
y[1] (closed_form) = -3.72079419099 -6.12055791047
absolute error = 0.5648
relative error = 7.885 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.35
Order of pole (three term test) = 79.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = -3.94513249858 -6.66994873292
y[1] (closed_form) = -3.74988632203 -6.1508850858
absolute error = 0.5546
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 = 42.57
Order of pole (three term test) = 80.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7483 2.827
h = 0.001 0.001
y[1] (numeric) = -3.97489528347 -6.68923986623
y[1] (closed_form) = -3.76766197228 -6.16892327487
absolute error = 0.5601
relative error = 7.748 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.62
Order of pole (three term test) = 80.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7493 2.828
h = 0.001 0.003
y[1] (numeric) = -4.00469202797 -6.70855123462
y[1] (closed_form) = -3.7796078313 -6.16940241445
absolute error = 0.5842
relative error = 8.075 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 159.9
Order of pole (three term test) = 80.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = -4.0345365965 -6.72786415093
y[1] (closed_form) = -3.80308019466 -6.18230850318
absolute error = 0.5926
relative error = 8.165 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 91.02
Order of pole (three term test) = 80.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7504 2.835
h = 0.003 0.006
y[1] (numeric) = -4.06447175749 -6.74723152097
y[1] (closed_form) = -3.8268032009 -6.20668111238
absolute error = 0.5905
relative error = 8.098 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 121.6
Order of pole (three term test) = 81.51 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2377.1MB, alloc=44.3MB, time=28.30
x[1] = 0.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = -4.09464655181 -6.76662493486
y[1] (closed_form) = -3.88046339835 -6.22679727845
absolute error = 0.5808
relative error = 7.916 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.71
Order of pole (three term test) = 82.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = -4.12508905381 -6.78607212915
y[1] (closed_form) = -3.91036971968 -6.25763505427
absolute error = 0.5704
relative error = 7.73 %
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 = 44.49
Order of pole (three term test) = 82.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7536 2.849
h = 0.001 0.001
y[1] (numeric) = -4.15563709455 -6.80562073461
y[1] (closed_form) = -3.92864009507 -6.2759743412
absolute error = 0.5762
relative error = 7.783 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.13
Order of pole (three term test) = 83.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7546 2.85
h = 0.001 0.003
y[1] (numeric) = -4.186219958 -6.82518984709
y[1] (closed_form) = -3.94085358901 -6.27639758741
absolute error = 0.6011
relative error = 8.112 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 167.1
Order of pole (three term test) = 83.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = -4.21685171901 -6.84476029007
y[1] (closed_form) = -3.9649184577 -6.28945925286
absolute error = 0.6098
relative error = 8.202 %
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 = 95.11
Order of pole (three term test) = 83.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7557 2.857
h = 0.003 0.006
y[1] (numeric) = -4.24757637741 -6.86438592262
y[1] (closed_form) = -3.9893033626 -6.31424041951
absolute error = 0.6078
relative error = 8.137 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 127
Order of pole (three term test) = 84.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = -4.27854614437 -6.88403691654
y[1] (closed_form) = -4.04426584244 -6.33450415695
absolute error = 0.5974
relative error = 7.949 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.17
Order of pole (three term test) = 84.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = -4.30978986576 -6.90374147789
y[1] (closed_form) = -4.07500718095 -6.36585961822
absolute error = 0.5869
relative error = 7.765 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.49
Order of pole (three term test) = 85.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7589 2.871
h = 0.001 0.001
y[1] (numeric) = -4.34114201124 -6.92354915287
y[1] (closed_form) = -4.09378488842 -6.38450410333
absolute error = 0.5931
relative error = 7.82 %
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 = 36.71
Order of pole (three term test) = 86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7599 2.872
h = 0.001 0.003
y[1] (numeric) = -4.3725298632 -6.94337760801
y[1] (closed_form) = -4.1062716844 -6.38486880073
absolute error = 0.6187
relative error = 8.15 %
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 = 174.6
Order of pole (three term test) = 86.09 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 2 ) = sin ( x ) ;
Iterations = 754
Total Elapsed Time = 28 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 28 Seconds
> quit
memory used=2411.5MB, alloc=44.3MB, time=28.69