|\^/| 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.
| Type ? for help.
#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(1.0)/c(x)/c(x));
> end;
exact_soln_y := proc(x) return c(1.0)/(c(x)*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_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre neg ID_CONST $eq_no = 1
> array_tmp1[1] := neg(array_const_2D0[1]);
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp2[2] := neg(array_tmp2[1])* array_x[2] / array_x[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 3
> #emit pre div CONST - LINEAR $eq_no = 1 i = 4
> #emit pre div CONST - LINEAR $eq_no = 1 i = 5
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> array_tmp2[3] := neg(array_tmp2[2])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> array_tmp2[4] := neg(array_tmp2[3])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> array_tmp2[5] := neg(array_tmp2[4])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit div CONST LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp2[kkk] := array_tmp1[1] * array_x[kkk];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp3[kkk] := neg(ats(kkk,array_x,array_tmp3,2)) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp4[kkk] := neg(ats(kkk,array_x,array_tmp4,2)) / array_x[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := neg(array_const_2D0[1]);
array_tmp2[1] := array_tmp1[1]/array_x[1];
array_tmp3[1] := array_tmp2[1]/array_x[1];
array_tmp4[1] := array_tmp3[1]/array_x[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp2[2] := neg(array_tmp2[1])*array_x[2]/array_x[1];
array_tmp3[2] := (-array_x[2]*array_tmp3[1] + array_tmp2[2])/array_x[1]
;
array_tmp4[2] := (-array_x[2]*array_tmp4[1] + array_tmp3[2])/array_x[1]
;
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp2[3] := neg(array_tmp2[2])*array_x[2]/array_x[1];
array_tmp3[3] := (-array_x[2]*array_tmp3[2] + array_tmp2[3])/array_x[1]
;
array_tmp4[3] := (-array_x[2]*array_tmp4[2] + array_tmp3[3])/array_x[1]
;
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp2[4] := neg(array_tmp2[3])*array_x[2]/array_x[1];
array_tmp3[4] := (-array_x[2]*array_tmp3[3] + array_tmp2[4])/array_x[1]
;
array_tmp4[4] := (-array_x[2]*array_tmp4[3] + array_tmp3[4])/array_x[1]
;
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp2[5] := neg(array_tmp2[4])*array_x[2]/array_x[1];
array_tmp3[5] := (-array_x[2]*array_tmp3[4] + array_tmp2[5])/array_x[1]
;
array_tmp4[5] := (-array_x[2]*array_tmp4[4] + array_tmp3[5])/array_x[1]
;
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp2[kkk] := array_tmp1[1]*array_x[kkk];
array_tmp3[kkk] := neg(ats(kkk, array_x, array_tmp3, 2))/array_x[1]
;
array_tmp4[kkk] := neg(ats(kkk, array_x, array_tmp4, 2))/array_x[1]
;
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 20;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=16;
> max_terms:=20;
> #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..(20),[]);
> array_norms:= Array(0..(20),[]);
> array_fact_1:= Array(0..(20),[]);
> 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..(20),[]);
> array_x:= Array(0..(20),[]);
> array_tmp0:= Array(0..(20),[]);
> array_tmp1:= Array(0..(20),[]);
> array_tmp2:= Array(0..(20),[]);
> array_tmp3:= Array(0..(20),[]);
> array_tmp4:= Array(0..(20),[]);
> array_tmp5:= Array(0..(20),[]);
> array_m1:= Array(0..(20),[]);
> array_y_higher := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..20+ 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..(20) ,(0..20+ 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 <= 20) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) 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 <= 20) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) 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 <= 20) 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 <=20) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 20;
> 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/sing3postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=16;");
> omniout_str(ALWAYS,"max_terms:=20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -2.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.001);");
> omniout_str(ALWAYS,"glob_min_h := c(0.001);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(2.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> 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(1.0)/c(x)/c(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> 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 := -2.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.001);
> glob_min_h := c(0.001);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(0.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(2.0);
> array_given_ord_poles[1,2] := c(0.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 10
> omniout_str(INFO," ");
> fi;# end if 10;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> atomall();
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10
> display_alot(current_iter);
> fi;# end if 10;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (true) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / 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,"2017-11-26T16:23:09-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing3")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / 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,"sing3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing3 maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 20;
Digits := 16;
max_terms := 20;
glob_html_log := true;
array_y_init := Array(0 .. 20, []);
array_norms := Array(0 .. 20, []);
array_fact_1 := Array(0 .. 20, []);
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 .. 20, []);
array_x := Array(0 .. 20, []);
array_tmp0 := Array(0 .. 20, []);
array_tmp1 := Array(0 .. 20, []);
array_tmp2 := Array(0 .. 20, []);
array_tmp3 := Array(0 .. 20, []);
array_tmp4 := Array(0 .. 20, []);
array_tmp5 := Array(0 .. 20, []);
array_m1 := Array(0 .. 20, []);
array_y_higher := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []);
array_y_set_initial := Array(0 .. 2, 0 .. 21, []);
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 .. 20, 0 .. 21, []);
term := 1;
while term <= 20 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 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 <= 20 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 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 <= 20 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 <= 20 do
term := 1;
while term <= 20 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 20;
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/sing3postcpx.cpx#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=16;");
omniout_str(ALWAYS, "max_terms:=20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -2.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.001);");
omniout_str(ALWAYS, "glob_min_h := c(0.001);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(2.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
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(1.0)/c(x)/c(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
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(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -2.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.001);
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(0.);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(2.0);
array_given_ord_poles[1, 2] := c(0.);
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius
;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] :=
array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
atomall();
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = neg ( 2.0 ) /\
x / x / 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, "2017-11-26T16:23:09-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing3");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 2.0 ) / x / x / 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,
"sing3 diffeq.mxt");
logitem_str(html_log_file,
"sing3 maple results")
;
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sing3postcpx.cpx#################
diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=16;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -2.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.001);
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(0.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(2.0);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(1.0)/c(x)/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] = -2.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.225220613829 0.02149833132
y[1] (closed_form) = 0.225220613829 0.02149833132
absolute error = 0
relative error = 0 %
Correct digits = 14
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.628
Order of pole (three term test) = 1.659e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0999 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.225085782276 0.0225661293499
y[1] (closed_form) = 0.225085026309 0.0225659948758
absolute error = 7.678e-07
relative error = 0.0003394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.262
Order of pole (three term test) = 1.613e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0998 0.108
h = 0.001 0.001
y[1] (numeric) = 0.225008386399 0.0232073095974
y[1] (closed_form) = 0.225008538393 0.0232073324723
absolute error = 1.537e-07
relative error = 6.795e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9906
Order of pole (three term test) = 1.487e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0988 0.109
h = 0.001 0.003
y[1] (numeric) = 0.225187427848 0.0234533383001
y[1] (closed_form) = 0.225188050546 0.0234532879043
absolute error = 6.247e-07
relative error = 0.0002759 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.699
Order of pole (three term test) = 8.288e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0978 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.225299641301 0.0241258383941
y[1] (closed_form) = 0.225299296368 0.0241258964346
absolute error = 3.498e-07
relative error = 0.0001544 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.658
Order of pole (three term test) = 1.532e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0977 0.116
h = 0.003 0.006
y[1] (numeric) = 0.225181520437 0.0249813740494
y[1] (closed_form) = 0.225180676702 0.0249807692959
absolute error = 1.038e-06
relative error = 0.0004582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.522
Order of pole (three term test) = 8.590e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0947 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.225602223628 0.0263655513837
y[1] (closed_form) = 0.225600070266 0.0263683481245
absolute error = 3.530e-06
relative error = 0.001554 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.564
Order of pole (three term test) = 1.365e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0946 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.225430530901 0.0274366388602
y[1] (closed_form) = 0.225429624286 0.0274374105929
absolute error = 1.191e-06
relative error = 0.0005243 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.26
Order of pole (three term test) = 1.867e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0945 0.13
h = 0.001 0.001
y[1] (numeric) = 0.225332222888 0.0280787380778
y[1] (closed_form) = 0.225332223719 0.0280797070159
absolute error = 9.689e-07
relative error = 0.0004267 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.099
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9887
Order of pole (three term test) = 1.383e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0935 0.131
h = 0.001 0.003
y[1] (numeric) = 0.225504338388 0.0283317873136
y[1] (closed_form) = 0.225504816255 0.0283327025929
absolute error = 1.033e-06
relative error = 0.0004543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.69
Order of pole (three term test) = 5.692e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0925 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.225595620606 0.0290114188553
y[1] (closed_form) = 0.225595119644 0.0290124019382
absolute error = 1.103e-06
relative error = 0.0004851 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.653
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0924 0.138
h = 0.003 0.006
y[1] (numeric) = 0.225449487563 0.0298676240017
y[1] (closed_form) = 0.225448512806 0.0298679185148
absolute error = 1.018e-06
relative error = 0.0004478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.516
Order of pole (three term test) = 8.533e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0894 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.2258280235 0.0312723803801
y[1] (closed_form) = 0.225825584906 0.0312760427839
absolute error = 4.400e-06
relative error = 0.00193 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.561
Order of pole (three term test) = 8.605e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=39.3MB, alloc=40.3MB, time=0.51
x[1] = -2.0893 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.225621083477 0.0323433448597
y[1] (closed_form) = 0.225619986504 0.0323450225953
absolute error = 2.005e-06
relative error = 0.0008795 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.257
Order of pole (three term test) = 2.898e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0892 0.152
h = 0.001 0.001
y[1] (numeric) = 0.225501685712 0.032985474471
y[1] (closed_form) = 0.225501493529 0.0329873895589
absolute error = 1.925e-06
relative error = 0.0008445 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9869
Order of pole (three term test) = 1.329e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0882 0.153
h = 0.001 0.003
y[1] (numeric) = 0.225666529359 0.0332452940432
y[1] (closed_form) = 0.225666819542 0.0332471755791
absolute error = 1.904e-06
relative error = 0.0008346 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.682
Order of pole (three term test) = 3.595e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0872 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.22573643739 0.0339312077129
y[1] (closed_form) = 0.225735739636 0.033933115498
absolute error = 2.031e-06
relative error = 0.0008899 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.648
Order of pole (three term test) = 4.547e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0871 0.16
h = 0.003 0.006
y[1] (numeric) = 0.225562081606 0.0347868865788
y[1] (closed_form) = 0.225560936642 0.0347880811581
absolute error = 1.655e-06
relative error = 0.000725 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.509
Order of pole (three term test) = 8.090e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0841 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.225897298813 0.0362105471944
y[1] (closed_form) = 0.225894536419 0.0362150675264
absolute error = 5.298e-06
relative error = 0.002316 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.559
Order of pole (three term test) = 1.155e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.084 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.225654896153 0.0372798743272
y[1] (closed_form) = 0.225653568799 0.0372824557342
absolute error = 2.903e-06
relative error = 0.001269 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.255
Order of pole (three term test) = 6.553e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0839 0.174
h = 0.001 0.001
y[1] (numeric) = 0.225514277323 0.0379211293792
y[1] (closed_form) = 0.225513849927 0.0379239884407
absolute error = 2.891e-06
relative error = 0.001264 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9852
Order of pole (three term test) = 4.952e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0829 0.175
h = 0.001 0.003
y[1] (numeric) = 0.225671513989 0.0381874486168
y[1] (closed_form) = 0.225671573249 0.0381902946679
absolute error = 2.847e-06
relative error = 0.001244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.674
Order of pole (three term test) = 6.831e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0819 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.22571964709 0.0388787648096
y[1] (closed_form) = 0.225718711473 0.0388815947598
absolute error = 2.981e-06
relative error = 0.001301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.644
Order of pole (three term test) = 1.729e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0818 0.182
h = 0.003 0.006
y[1] (numeric) = 0.22551692065 0.0397327012789
y[1] (closed_form) = 0.225515565926 0.0397347946393
absolute error = 2.493e-06
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.504
Order of pole (three term test) = 1.088e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0788 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.225807749056 0.0411735170155
y[1] (closed_form) = 0.225804624486 0.0411788854235
absolute error = 6.212e-06
relative error = 0.002706 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 2.608e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0787 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.22552974839 0.0422396698667
y[1] (closed_form) = 0.225528150461 0.042243150447
absolute error = 3.830e-06
relative error = 0.001669 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.253
Order of pole (three term test) = 1.249e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0786 0.196
h = 0.001 0.001
y[1] (numeric) = 0.225367824937 0.0428791318795
y[1] (closed_form) = 0.225367119929 0.0428829304322
absolute error = 3.863e-06
relative error = 0.001684 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9837
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0776 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.225517131686 0.0431516601589
y[1] (closed_form) = 0.225516916545 0.0431554666138
absolute error = 3.813e-06
relative error = 0.00166 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.905
Order of pole (three term test) = 1.022e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0775 0.201
h = 0.003 0.006
y[1] (numeric) = 0.225291143872 0.0440032125493
y[1] (closed_form) = 0.225289347614 0.0440058223585
absolute error = 3.168e-06
relative error = 0.00138 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.499
Order of pole (three term test) = 5.247e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0745 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.225542798484 0.0454567964025
y[1] (closed_form) = 0.225539103298 0.045462628973
absolute error = 6.905e-06
relative error = 0.003001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.554
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0744 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.225234173502 0.0465185479351
y[1] (closed_form) = 0.225232081381 0.0465225419455
absolute error = 4.509e-06
relative error = 0.00196 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0743 0.215
h = 0.001 0.001
y[1] (numeric) = 0.22505391866 0.0471554687163
y[1] (closed_form) = 0.225052711146 0.0471598151872
absolute error = 4.511e-06
relative error = 0.001962 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9825
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0733 0.216
h = 0.001 0.003
y[1] (numeric) = 0.225196082439 0.047432994598
y[1] (closed_form) = 0.225195366415 0.0474373672382
absolute error = 4.431e-06
relative error = 0.001925 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.661
Order of pole (three term test) = 3.146e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=86.0MB, alloc=44.3MB, time=1.12
x[1] = -2.0723 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.225202746606 0.048131660688
y[1] (closed_form) = 0.225201029311 0.0481359367513
absolute error = 4.608e-06
relative error = 0.002001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.637
Order of pole (three term test) = 8.010e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0722 0.223
h = 0.003 0.006
y[1] (numeric) = 0.224947112999 0.048978725755
y[1] (closed_form) = 0.224945032928 0.0489822257897
absolute error = 4.071e-06
relative error = 0.001769 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.494
Order of pole (three term test) = 2.511e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0692 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.225152645551 0.0504460183107
y[1] (closed_form) = 0.225148517925 0.0504526745457
absolute error = 7.832e-06
relative error = 0.003394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 4.565e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0691 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.22480840916 0.0515016935763
y[1] (closed_form) = 0.224805971802 0.051506572054
absolute error = 5.453e-06
relative error = 0.002365 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.25
Order of pole (three term test) = 2.312e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.069 0.237
h = 0.001 0.001
y[1] (numeric) = 0.224606836632 0.0521350869553
y[1] (closed_form) = 0.224605272706 0.0521403578321
absolute error = 5.498e-06
relative error = 0.002384 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9812
Order of pole (three term test) = 6.562e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.068 0.238
h = 0.001 0.003
y[1] (numeric) = 0.224740510744 0.0524182268021
y[1] (closed_form) = 0.224739439429 0.0524235452566
absolute error = 5.425e-06
relative error = 0.002351 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.655
Order of pole (three term test) = 4.528e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.067 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.224724518132 0.0531196318442
y[1] (closed_form) = 0.22472244516 0.053124809885
absolute error = 5.578e-06
relative error = 0.002415 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.633
Order of pole (three term test) = 7.651e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0669 0.245
h = 0.003 0.006
y[1] (numeric) = 0.224440466945 0.0539613994563
y[1] (closed_form) = 0.224438063215 0.0539657822633
absolute error = 4.999e-06
relative error = 0.002165 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.489
Order of pole (three term test) = 1.365e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0639 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.224599070087 0.0554404674128
y[1] (closed_form) = 0.224594472971 0.0554479314381
absolute error = 8.766e-06
relative error = 0.003789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.55
Order of pole (three term test) = 6.911e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0638 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.224219326126 0.0564884941689
y[1] (closed_form) = 0.224216503642 0.0564942462955
absolute error = 6.407e-06
relative error = 0.002771 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.248
Order of pole (three term test) = 4.450e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0637 0.259
h = 0.001 0.001
y[1] (numeric) = 0.22399649518 0.0571174204616
y[1] (closed_form) = 0.223994532729 0.0571236045272
absolute error = 6.488e-06
relative error = 0.002807 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9799
Order of pole (three term test) = 1.228e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0627 0.26
h = 0.001 0.003
y[1] (numeric) = 0.224121399297 0.0574058306427
y[1] (closed_form) = 0.224119929422 0.0574120838657
absolute error = 6.424e-06
relative error = 0.002777 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.649
Order of pole (three term test) = 1.454e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0617 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.224082532516 0.0581090036058
y[1] (closed_form) = 0.224080062977 0.0581150723326
absolute error = 6.552e-06
relative error = 0.00283 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.63
Order of pole (three term test) = 1.165e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0616 0.267
h = 0.003 0.006
y[1] (numeric) = 0.223770172458 0.05894421779
y[1] (closed_form) = 0.223767405382 0.0589494737201
absolute error = 5.940e-06
relative error = 0.002567 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.485
Order of pole (three term test) = 4.650e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0586 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.223881139493 0.0604330739745
y[1] (closed_form) = 0.22387603656 0.0604413278529
absolute error = 9.704e-06
relative error = 0.004185 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.548
Order of pole (three term test) = 4.715e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0585 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.223466077768 0.0614718777213
y[1] (closed_form) = 0.223462830647 0.0614784904587
absolute error = 7.367e-06
relative error = 0.003179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.247
Order of pole (three term test) = 1.121e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0584 0.281
h = 0.001 0.001
y[1] (numeric) = 0.223222098993 0.0620953958498
y[1] (closed_form) = 0.223219696294 0.06210247952
absolute error = 7.480e-06
relative error = 0.003228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9788
Order of pole (three term test) = 5.085e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0574 0.282
h = 0.001 0.003
y[1] (numeric) = 0.223337970087 0.0623887158425
y[1] (closed_form) = 0.223336058757 0.0623958903465
absolute error = 7.425e-06
relative error = 0.003202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.644
Order of pole (three term test) = 5.616e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0564 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.223276063463 0.0630926691687
y[1] (closed_form) = 0.223273156868 0.0630996150022
absolute error = 7.529e-06
relative error = 0.003245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.627
Order of pole (three term test) = 1.593e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0563 0.289
h = 0.003 0.006
y[1] (numeric) = 0.222935572036 0.0639200738989
y[1] (closed_form) = 0.222932402227 0.0639261911027
absolute error = 6.890e-06
relative error = 0.002971 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.481
Order of pole (three term test) = 1.006e-13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=132.8MB, alloc=44.3MB, time=1.72
x[1] = -2.0533 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.222998300989 0.0654166835325
y[1] (closed_form) = 0.222992656772 0.065425707303
absolute error = 1.064e-05
relative error = 0.00458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.546
Order of pole (three term test) = 1.021e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0532 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.222548197879 0.0664446931187
y[1] (closed_form) = 0.222544487135 0.0664521512211
absolute error = 8.330e-06
relative error = 0.003587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 1.041e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0531 0.303
h = 0.001 0.001
y[1] (numeric) = 0.222283233542 0.067061863954
y[1] (closed_form) = 0.222280349423 0.06706983129
absolute error = 8.473e-06
relative error = 0.003649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9778
Order of pole (three term test) = 2.958e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0521 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.222389827075 0.0673597173867
y[1] (closed_form) = 0.222387431931 0.0673677972533
absolute error = 8.427e-06
relative error = 0.003627 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.869
Order of pole (three term test) = 8.502e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.052 0.308
h = 0.003 0.006
y[1] (numeric) = 0.222026524413 0.0681797623331
y[1] (closed_form) = 0.222022801475 0.0681863060259
absolute error = 7.529e-06
relative error = 0.003242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.479
Order of pole (three term test) = 3.080e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.049 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.222047273603 0.0696808026549
y[1] (closed_form) = 0.222040961769 0.0696901663511
absolute error = 1.129e-05
relative error = 0.004852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.545
Order of pole (three term test) = 3.160e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0489 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.221567449469 0.0706978582804
y[1] (closed_form) = 0.221563133916 0.070705725751
absolute error = 8.973e-06
relative error = 0.003858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 1.020e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0488 0.322
h = 0.001 0.001
y[1] (numeric) = 0.221284681665 0.0713085711498
y[1] (closed_form) = 0.221281175253 0.0713169799086
absolute error = 9.111e-06
relative error = 0.003919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9771
Order of pole (three term test) = 1.933e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0478 0.323
h = 0.001 0.003
y[1] (numeric) = 0.22138306088 0.0716099000541
y[1] (closed_form) = 0.221380040172 0.0716184399289
absolute error = 9.058e-06
relative error = 0.003893 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.636
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0468 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.221278043105 0.0723123576137
y[1] (closed_form) = 0.221274042296 0.0723205870358
absolute error = 9.150e-06
relative error = 0.003931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.622
Order of pole (three term test) = 2.033e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0467 0.33
h = 0.003 0.006
y[1] (numeric) = 0.220886043063 0.073121579501
y[1] (closed_form) = 0.220881845607 0.0731289561387
absolute error = 8.487e-06
relative error = 0.003648 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.476
Order of pole (three term test) = 1.124e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0437 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.220857750059 0.0746264791204
y[1] (closed_form) = 0.220850833985 0.0746365699671
absolute error = 1.223e-05
relative error = 0.005248 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 9.249e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0436 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.220343647891 0.0756298511673
y[1] (closed_form) = 0.220338798308 0.0756385294045
absolute error = 9.941e-06
relative error = 0.004267 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 9.944e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0435 0.344
h = 0.001 0.001
y[1] (numeric) = 0.220040345147 0.0762324894397
y[1] (closed_form) = 0.220036282958 0.0762417455645
absolute error = 1.011e-05
relative error = 0.004341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9763
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0425 0.345
h = 0.001 0.003
y[1] (numeric) = 0.220129049634 0.0765376108875
y[1] (closed_form) = 0.220125468539 0.0765470196421
absolute error = 1.007e-05
relative error = 0.00432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.632
Order of pole (three term test) = 1.302e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0415 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.220000826772 0.0772379625228
y[1] (closed_form) = 0.219996276912 0.0772470172901
absolute error = 1.013e-05
relative error = 0.004346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.62
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0414 0.352
h = 0.003 0.006
y[1] (numeric) = 0.219581599304 0.0780358267505
y[1] (closed_form) = 0.219576889634 0.0780440182721
absolute error = 9.449e-06
relative error = 0.004055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.473
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0384 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.219503980299 0.0795424535978
y[1] (closed_form) = 0.21949642773 0.0795532461721
absolute error = 1.317e-05
relative error = 0.005642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 3.012e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0383 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.218956123383 0.0805306129953
y[1] (closed_form) = 0.218950703113 0.0805400806186
absolute error = 1.091e-05
relative error = 0.004676 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 9.538e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0382 0.366
h = 0.001 0.001
y[1] (numeric) = 0.218632595332 0.0811242624979
y[1] (closed_form) = 0.218627938658 0.0811343435048
absolute error = 1.110e-05
relative error = 0.004762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9756
Order of pole (three term test) = 9.639e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=179.4MB, alloc=44.3MB, time=2.32
x[1] = -2.0372 0.367
h = 0.001 0.003
y[1] (numeric) = 0.218711439477 0.0814327616333
y[1] (closed_form) = 0.218707258102 0.081443016581
absolute error = 1.107e-05
relative error = 0.004745 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.629
Order of pole (three term test) = 1.369e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0362 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.218560055905 0.0821299885339
y[1] (closed_form) = 0.218554919507 0.0821398464815
absolute error = 1.112e-05
relative error = 0.004761 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.619
Order of pole (three term test) = 3.241e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0361 0.374
h = 0.003 0.006
y[1] (numeric) = 0.218114044053 0.0829152821772
y[1] (closed_form) = 0.218108785332 0.0829242684099
absolute error = 1.041e-05
relative error = 0.004462 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.471
Order of pole (three term test) = 5.803e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0331 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.217986931055 0.0844214836796
y[1] (closed_form) = 0.217978711093 0.0844329507856
absolute error = 1.411e-05
relative error = 0.006036 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.542
Order of pole (three term test) = 1.592e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.033 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.21740592747 0.0853929267148
y[1] (closed_form) = 0.217399900938 0.0854031602902
absolute error = 1.188e-05
relative error = 0.005085 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.242
Order of pole (three term test) = 7.648e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0329 0.388
h = 0.001 0.001
y[1] (numeric) = 0.217062534349 0.0859766883442
y[1] (closed_form) = 0.217057245632 0.0859875695592
absolute error = 1.210e-05
relative error = 0.005182 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9751
Order of pole (three term test) = 1.814e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0319 0.389
h = 0.001 0.003
y[1] (numeric) = 0.217131354847 0.0862881393448
y[1] (closed_form) = 0.217126534459 0.0862992155305
absolute error = 1.208e-05
relative error = 0.00517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.626
Order of pole (three term test) = 2.507e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0309 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.216956910756 0.0869812231182
y[1] (closed_form) = 0.216951151462 0.0869918599721
absolute error = 1.210e-05
relative error = 0.005175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.617
Order of pole (three term test) = 6.375e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0308 0.396
h = 0.003 0.006
y[1] (numeric) = 0.216484624742 0.0877527552297
y[1] (closed_form) = 0.216478781135 0.0877625139375
absolute error = 1.137e-05
relative error = 0.004869 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.469
Order of pole (three term test) = 8.075e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0278 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.216307967164 0.0892563658669
y[1] (closed_form) = 0.216299050383 0.0892684786239
absolute error = 1.504e-05
relative error = 0.006428 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 8.734e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0277 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.215694508274 0.0902096198037
y[1] (closed_form) = 0.21568784112 0.0902205939108
absolute error = 1.284e-05
relative error = 0.005492 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0276 0.41
h = 0.001 0.001
y[1] (numeric) = 0.215331660018 0.090782612874
y[1] (closed_form) = 0.215325702996 0.0907942675045
absolute error = 1.309e-05
relative error = 0.005601 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9746
Order of pole (three term test) = 8.947e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0266 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.215390316631 0.091096580397
y[1] (closed_form) = 0.21538481981 0.0911084506697
absolute error = 1.308e-05
relative error = 0.005594 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.851
Order of pole (three term test) = 1.592e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0265 0.415
h = 0.003 0.006
y[1] (numeric) = 0.214896992155 0.0918559523072
y[1] (closed_form) = 0.214890508252 0.0918660186504
absolute error = 1.197e-05
relative error = 0.005124 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.468
Order of pole (three term test) = 6.897e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0235 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.214677804195 0.0933550057193
y[1] (closed_form) = 0.214668157852 0.0933673107192
absolute error = 1.564e-05
relative error = 0.006679 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 1.043e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0234 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.214037264504 0.094291077589
y[1] (closed_form) = 0.214029910856 0.09430232872
absolute error = 1.344e-05
relative error = 0.005747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 1.325e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0233 0.429
h = 0.001 0.001
y[1] (numeric) = 0.213658177424 0.0948538884956
y[1] (closed_form) = 0.213651508255 0.0948658469015
absolute error = 1.369e-05
relative error = 0.005857 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9745
Order of pole (three term test) = 1.259e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0223 0.43
h = 0.001 0.003
y[1] (numeric) = 0.213707968323 0.0951695444839
y[1] (closed_form) = 0.213701751207 0.0951817358645
absolute error = 1.369e-05
relative error = 0.00585 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.623
Order of pole (three term test) = 1.740e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0213 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.213491149614 0.0958519558022
y[1] (closed_form) = 0.213484030235 0.0958636316858
absolute error = 1.368e-05
relative error = 0.005844 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.616
Order of pole (three term test) = 2.818e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0212 0.437
h = 0.003 0.006
y[1] (numeric) = 0.212971751856 0.0965945092865
y[1] (closed_form) = 0.212964619837 0.0966053010612
absolute error = 1.294e-05
relative error = 0.005532 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.467
Order of pole (three term test) = 8.879e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=226.1MB, alloc=44.3MB, time=2.92
x[1] = -2.0182 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.212703266491 0.0980869369813
y[1] (closed_form) = 0.212692873245 0.0980998294419
absolute error = 1.656e-05
relative error = 0.00707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 1.721e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0181 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.212031789075 0.0990021910264
y[1] (closed_form) = 0.212023734917 0.099014130003
absolute error = 1.440e-05
relative error = 0.006154 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 1.881e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.018 0.451
h = 0.001 0.001
y[1] (numeric) = 0.211634147604 0.0995526610423
y[1] (closed_form) = 0.211626746963 0.0995653372747
absolute error = 1.468e-05
relative error = 0.006276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9742
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.017 0.452
h = 0.001 0.003
y[1] (numeric) = 0.21167358257 0.099870002343
y[1] (closed_form) = 0.21166662377 0.0998829313393
absolute error = 1.468e-05
relative error = 0.006273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.622
Order of pole (three term test) = 1.222e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.016 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.211434309396 0.100545395701
y[1] (closed_form) = 0.211426470964 0.100557769698
absolute error = 1.465e-05
relative error = 0.006256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.615
Order of pole (three term test) = 1.675e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0159 0.459
h = 0.003 0.006
y[1] (numeric) = 0.210890467602 0.101270949976
y[1] (closed_form) = 0.210882655259 0.101282439432
absolute error = 1.389e-05
relative error = 0.005939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.466
Order of pole (three term test) = 7.895e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0129 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.210572973521 0.10275459352
y[1] (closed_form) = 0.210561808748 0.102768040325
absolute error = 1.748e-05
relative error = 0.007459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 1.142e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0128 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.209871475247 0.10364767642
y[1] (closed_form) = 0.209862690435 0.103660272618
absolute error = 1.536e-05
relative error = 0.006561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 1.855e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0127 0.473
h = 0.001 0.001
y[1] (numeric) = 0.209455823898 0.104184995892
y[1] (closed_form) = 0.209447660017 0.104198357615
absolute error = 1.566e-05
relative error = 0.006693 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9741
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0117 0.474
h = 0.001 0.003
y[1] (numeric) = 0.209484831904 0.104503568701
y[1] (closed_form) = 0.209477098576 0.104517202405
absolute error = 1.567e-05
relative error = 0.006695 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.621
Order of pole (three term test) = 3.287e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0107 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.209223417839 0.105170962347
y[1] (closed_form) = 0.209214829656 0.105184002816
absolute error = 1.561e-05
relative error = 0.006668 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.615
Order of pole (three term test) = 1.118e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0106 0.481
h = 0.003 0.006
y[1] (numeric) = 0.208655885506 0.10587845273
y[1] (closed_form) = 0.208647362136 0.105890610346
absolute error = 1.485e-05
relative error = 0.006346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.466
Order of pole (three term test) = 3.938e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0076 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.208289789345 0.107351170702
y[1] (closed_form) = 0.208277830269 0.107365137469
absolute error = 1.839e-05
relative error = 0.007847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 5.702e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0075 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.207559260517 0.108220780416
y[1] (closed_form) = 0.207549716597 0.10823400158
absolute error = 1.631e-05
relative error = 0.006966 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 2.777e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0074 0.495
h = 0.001 0.001
y[1] (numeric) = 0.207126187628 0.108744170199
y[1] (closed_form) = 0.207117230547 0.10875818334
absolute error = 1.663e-05
relative error = 0.007109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9741
Order of pole (three term test) = 6.163e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0064 0.496
h = 0.001 0.003
y[1] (numeric) = 0.207144722541 0.109063517248
y[1] (closed_form) = 0.207136183684 0.109077820947
absolute error = 1.666e-05
relative error = 0.007116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.622
Order of pole (three term test) = 6.087e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0054 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.206861534611 0.10972194752
y[1] (closed_form) = 0.20685216774 0.109735621151
absolute error = 1.657e-05
relative error = 0.007078 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.615
Order of pole (three term test) = 6.940e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0053 0.503
h = 0.003 0.006
y[1] (numeric) = 0.206271122727 0.110410351696
y[1] (closed_form) = 0.206261859247 0.110423146279
absolute error = 1.580e-05
relative error = 0.006752 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.466
Order of pole (three term test) = 1.183e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0023 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.205856947789 0.111870027411
y[1] (closed_form) = 0.205844173561 0.111884478612
absolute error = 1.929e-05
relative error = 0.008233 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 1.143e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0022 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.205098448654 0.112714917918
y[1] (closed_form) = 0.205088118969 0.11272873027
absolute error = 1.725e-05
relative error = 0.00737 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 9.285e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=272.7MB, alloc=44.3MB, time=3.51
x[1] = -2.0021 0.517
h = 0.001 0.001
y[1] (numeric) = 0.204648584311 0.113223632196
y[1] (closed_form) = 0.204638805985 0.113238261067
absolute error = 1.760e-05
relative error = 0.007524 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9742
Order of pole (three term test) = 8.836e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0011 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.20465662507 0.113543294393
y[1] (closed_form) = 0.20464725165 0.11355823169
absolute error = 1.763e-05
relative error = 0.007535 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.848
Order of pole (three term test) = 3.053e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.001 0.522
h = 0.003 0.006
y[1] (numeric) = 0.204048174342 0.114215328644
y[1] (closed_form) = 0.204038216358 0.114228291511
absolute error = 1.635e-05
relative error = 0.00699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.467
Order of pole (three term test) = 1.590e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.998 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.203593310611 0.115661545429
y[1] (closed_form) = 0.203579785955 0.115676029815
absolute error = 1.982e-05
relative error = 0.008463 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 2.883e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9979 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.202811948678 0.116483891985
y[1] (closed_form) = 0.202800887843 0.116497830771
absolute error = 1.779e-05
relative error = 0.007608 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 9.373e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9978 0.536
h = 0.001 0.001
y[1] (numeric) = 0.202348351785 0.116979215186
y[1] (closed_form) = 0.202337810499 0.116993989576
absolute error = 1.815e-05
relative error = 0.007765 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9745
Order of pole (three term test) = 8.923e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9968 0.537
h = 0.001 0.003
y[1] (numeric) = 0.202347365542 0.117298655967
y[1] (closed_form) = 0.202337216738 0.117313753376
absolute error = 1.819e-05
relative error = 0.007778 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.624
Order of pole (three term test) = 1.234e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9958 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.202024948712 0.117937672386
y[1] (closed_form) = 0.202014027378 0.117952075749
absolute error = 1.808e-05
relative error = 0.007727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.616
Order of pole (three term test) = 6.299e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9957 0.544
h = 0.003 0.006
y[1] (numeric) = 0.201394560356 0.11858775371
y[1] (closed_form) = 0.201383813233 0.118601291131
absolute error = 1.728e-05
relative error = 0.007396 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.468
Order of pole (three term test) = 8.012e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9927 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.200892919445 0.120017090733
y[1] (closed_form) = 0.200878546631 0.120031990664
absolute error = 2.070e-05
relative error = 0.008847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 6.164e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9926 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.200085745887 0.120812578088
y[1] (closed_form) = 0.200073855226 0.120827041323
absolute error = 1.872e-05
relative error = 0.008011 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.242
Order of pole (three term test) = 9.653e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9925 0.558
h = 0.001 0.001
y[1] (numeric) = 0.199606640928 0.121291944232
y[1] (closed_form) = 0.199595232132 0.121307263825
absolute error = 1.910e-05
relative error = 0.008178 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9749
Order of pole (three term test) = 1.275e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9915 0.559
h = 0.001 0.003
y[1] (numeric) = 0.199595193624 0.121610847146
y[1] (closed_form) = 0.199584162287 0.121626506134
absolute error = 1.915e-05
relative error = 0.008195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.625
Order of pole (three term test) = 8.731e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9905 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.199252345949 0.122238280305
y[1] (closed_form) = 0.199240574231 0.122253213156
absolute error = 1.901e-05
relative error = 0.008134 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.617
Order of pole (three term test) = 1.007e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9904 0.566
h = 0.003 0.006
y[1] (numeric) = 0.198601698734 0.12286662851
y[1] (closed_form) = 0.198590138606 0.122880705156
absolute error = 1.822e-05
relative error = 0.0078 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.469
Order of pole (three term test) = 5.731e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9874 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.198054124833 0.124277082493
y[1] (closed_form) = 0.198038888857 0.124292359931
absolute error = 2.158e-05
relative error = 0.009228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.542
Order of pole (three term test) = 8.332e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9873 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.197222376826 0.125044649102
y[1] (closed_form) = 0.197209635331 0.125059599379
absolute error = 1.964e-05
relative error = 0.008412 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.242
Order of pole (three term test) = 1.343e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9872 0.58
h = 0.001 0.001
y[1] (numeric) = 0.196728499517 0.125507422139
y[1] (closed_form) = 0.196716201203 0.1255232474
absolute error = 2.004e-05
relative error = 0.008589 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9753
Order of pole (three term test) = 4.570e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9862 0.581
h = 0.001 0.003
y[1] (numeric) = 0.196706641658 0.125825332263
y[1] (closed_form) = 0.196694704941 0.125841512418
absolute error = 2.011e-05
relative error = 0.008611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.627
Order of pole (three term test) = 1.274e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9852 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.19634392177 0.126440320445
y[1] (closed_form) = 0.196331278455 0.12645574424
absolute error = 1.994e-05
relative error = 0.00854 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.618
Order of pole (three term test) = 9.138e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=319.4MB, alloc=44.3MB, time=4.11
x[1] = -1.9851 0.588
h = 0.003 0.006
y[1] (numeric) = 0.195674018454 0.12704610975
y[1] (closed_form) = 0.19566162344 0.127060689078
absolute error = 1.914e-05
relative error = 0.008202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.471
Order of pole (three term test) = 8.229e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9821 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.195081462008 0.128435730357
y[1] (closed_form) = 0.19506534999 0.12845134664
absolute error = 2.244e-05
relative error = 0.009607 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 1.339e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.982 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.194226430078 0.129174386055
y[1] (closed_form) = 0.194212818851 0.129189784949
absolute error = 2.055e-05
relative error = 0.008811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 1.091e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9819 0.602
h = 0.001 0.001
y[1] (numeric) = 0.193718548003 0.129619972405
y[1] (closed_form) = 0.193705340418 0.129636262727
absolute error = 2.097e-05
relative error = 0.008998 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9759
Order of pole (three term test) = 1.002e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9809 0.603
h = 0.001 0.003
y[1] (numeric) = 0.193686354673 0.129936439304
y[1] (closed_form) = 0.193673492044 0.129953099095
absolute error = 2.105e-05
relative error = 0.009024 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.63
Order of pole (three term test) = 6.437e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9799 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.193304366011 0.130538154539
y[1] (closed_form) = 0.193290832073 0.130554029709
absolute error = 2.086e-05
relative error = 0.008944 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.62
Order of pole (three term test) = 9.305e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9798 0.61
h = 0.003 0.006
y[1] (numeric) = 0.192616250377 0.131120617039
y[1] (closed_form) = 0.192603000655 0.131135661429
absolute error = 2.005e-05
relative error = 0.008604 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.473
Order of pole (three term test) = 4.192e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9768 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.191979764113 0.132487513557
y[1] (closed_form) = 0.191962765321 0.132503429546
absolute error = 2.329e-05
relative error = 0.009984 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 6.107e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9767 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.191102787201 0.133196342681
y[1] (closed_form) = 0.191088289512 0.133212150893
absolute error = 2.145e-05
relative error = 0.009208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 1.408e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9766 0.624
h = 0.001 0.001
y[1] (numeric) = 0.190581696874 0.133624193091
y[1] (closed_form) = 0.190567562577 0.133640906953
absolute error = 2.189e-05
relative error = 0.009404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9766
Order of pole (three term test) = 9.498e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9756 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.19053926731 0.133938772402
y[1] (closed_form) = 0.190525460614 0.133955869331
absolute error = 2.198e-05
relative error = 0.009436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.863
Order of pole (three term test) = 8.574e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9755 0.629
h = 0.003 0.006
y[1] (numeric) = 0.189837096441 0.134501603572
y[1] (closed_form) = 0.189823136032 0.134516667503
absolute error = 2.054e-05
relative error = 0.008828 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.476
Order of pole (three term test) = 4.619e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9725 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.189164014768 0.13584697171
y[1] (closed_form) = 0.189146286985 0.135862763916
absolute error = 2.374e-05
relative error = 0.01019 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.545
Order of pole (three term test) = 9.888e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9724 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.188269622407 0.136529213869
y[1] (closed_form) = 0.188254389931 0.136544992133
absolute error = 2.193e-05
relative error = 0.00943 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9723 0.643
h = 0.001 0.001
y[1] (numeric) = 0.187738039833 0.136941249048
y[1] (closed_form) = 0.187723135517 0.136957942905
absolute error = 2.238e-05
relative error = 0.009631 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9774
Order of pole (three term test) = 9.735e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9713 0.644
h = 0.001 0.003
y[1] (numeric) = 0.187686926317 0.137253733631
y[1] (closed_form) = 0.187672333999 0.137270821236
absolute error = 2.247e-05
relative error = 0.009664 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.637
Order of pole (three term test) = 6.740e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9703 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.187271011848 0.137828463551
y[1] (closed_form) = 0.187255817696 0.137844719926
absolute error = 2.225e-05
relative error = 0.00957 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.624
Order of pole (three term test) = 1.463e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9702 0.651
h = 0.003 0.006
y[1] (numeric) = 0.186552205765 0.138365498401
y[1] (closed_form) = 0.186537359916 0.138380954825
absolute error = 2.143e-05
relative error = 0.009227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.479
Order of pole (three term test) = 8.299e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9672 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.185837430345 0.139684819576
y[1] (closed_form) = 0.185818802058 0.1397008378
absolute error = 2.457e-05
relative error = 0.01057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.546
Order of pole (three term test) = 7.328e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9671 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.184923704274 0.140335755708
y[1] (closed_form) = 0.184907560601 0.140351868204
absolute error = 2.281e-05
relative error = 0.009825 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.246
Order of pole (three term test) = 1.095e-13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=366.2MB, alloc=44.3MB, time=4.72
x[1] = -1.967 0.665
h = 0.001 0.001
y[1] (numeric) = 0.184380467242 0.14072916643
y[1] (closed_form) = 0.184364610587 0.140746204519
absolute error = 2.328e-05
relative error = 0.01003 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9783
Order of pole (three term test) = 1.001e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.966 0.666
h = 0.001 0.003
y[1] (numeric) = 0.184319369557 0.141038959773
y[1] (closed_form) = 0.184303806414 0.141056403291
absolute error = 2.338e-05
relative error = 0.01007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.642
Order of pole (three term test) = 2.772e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.965 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.18388614572 0.141598266913
y[1] (closed_form) = 0.183870019537 0.141614857018
absolute error = 2.314e-05
relative error = 0.009969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.626
Order of pole (three term test) = 7.093e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9649 0.673
h = 0.003 0.006
y[1] (numeric) = 0.183152310137 0.142110131299
y[1] (closed_form) = 0.183136565223 0.142125940318
absolute error = 2.231e-05
relative error = 0.009625 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.482
Order of pole (three term test) = 1.012e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9619 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.18239715924 0.143401720027
y[1] (closed_form) = 0.182377625912 0.143417924564
absolute error = 2.538e-05
relative error = 0.01094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.548
Order of pole (three term test) = 3.308e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9618 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.181465546983 0.144020661589
y[1] (closed_form) = 0.181448481797 0.144037067361
absolute error = 2.367e-05
relative error = 0.01022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.247
Order of pole (three term test) = 1.129e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9617 0.687
h = 0.001 0.001
y[1] (numeric) = 0.180911516969 0.144395033745
y[1] (closed_form) = 0.180894697377 0.144412372825
absolute error = 2.416e-05
relative error = 0.01044 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9793
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9607 0.688
h = 0.001 0.003
y[1] (numeric) = 0.180840599959 0.144701717402
y[1] (closed_form) = 0.180824054878 0.144719472519
absolute error = 2.427e-05
relative error = 0.01048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.646
Order of pole (three term test) = 1.574e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9597 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.180390818124 0.145244928327
y[1] (closed_form) = 0.180373749749 0.145261810084
absolute error = 2.401e-05
relative error = 0.01037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.629
Order of pole (three term test) = 3.661e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9596 0.695
h = 0.003 0.006
y[1] (numeric) = 0.179643115667 0.145731097323
y[1] (closed_form) = 0.179626460293 0.145747218516
absolute error = 2.318e-05
relative error = 0.01002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.486
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9566 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.178848990237 0.146993349892
y[1] (closed_form) = 0.17882854948 0.147009701102
absolute error = 2.618e-05
relative error = 0.01131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.549
Order of pole (three term test) = 4.836e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9565 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.17790096707 0.14757969099
y[1] (closed_form) = 0.177882972326 0.14759634878
absolute error = 2.452e-05
relative error = 0.01061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.248
Order of pole (three term test) = 2.240e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9564 0.709
h = 0.001 0.001
y[1] (numeric) = 0.177337022186 0.147934659648
y[1] (closed_form) = 0.177319231484 0.147952256177
absolute error = 2.502e-05
relative error = 0.01084 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9804
Order of pole (three term test) = 4.274e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9554 0.71
h = 0.001 0.003
y[1] (numeric) = 0.177256472147 0.148237826837
y[1] (closed_form) = 0.177238936518 0.148255848916
absolute error = 2.515e-05
relative error = 0.01088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.652
Order of pole (three term test) = 1.488e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9544 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.176790914989 0.14876431312
y[1] (closed_form) = 0.176772896607 0.14878144417
absolute error = 2.486e-05
relative error = 0.01076 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.632
Order of pole (three term test) = 1.934e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9543 0.717
h = 0.003 0.006
y[1] (numeric) = 0.176030528703 0.149224328018
y[1] (closed_form) = 0.176012953725 0.149240720589
absolute error = 2.403e-05
relative error = 0.01041 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.49
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9513 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.175198906396 0.150455727154
y[1] (closed_form) = 0.175177557943 0.150472185596
absolute error = 2.696e-05
relative error = 0.01167 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.551
Order of pole (three term test) = 7.096e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9512 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.174235969764 0.151008945632
y[1] (closed_form) = 0.174217039697 0.151025814032
absolute error = 2.536e-05
relative error = 0.011 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.25
Order of pole (three term test) = 1.161e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9511 0.731
h = 0.001 0.001
y[1] (numeric) = 0.173663001445 0.151344195687
y[1] (closed_form) = 0.173644233884 0.151362005987
absolute error = 2.587e-05
relative error = 0.01123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9816
Order of pole (three term test) = 2.220e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9501 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.173573025191 0.151643452576
y[1] (closed_form) = 0.1735544929 0.151661696823
absolute error = 2.601e-05
relative error = 0.01128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.893
Order of pole (three term test) = 6.724e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=413.0MB, alloc=44.3MB, time=5.32
x[1] = -1.95 0.736
h = 0.003 0.006
y[1] (numeric) = 0.172803197418 0.152081767171
y[1] (closed_form) = 0.172784934348 0.152098033354
absolute error = 2.446e-05
relative error = 0.01062 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.494
Order of pole (three term test) = 1.050e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.947 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.171940926706 0.15328504139
y[1] (closed_form) = 0.171918909312 0.153301233945
absolute error = 2.733e-05
relative error = 0.01187 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.553
Order of pole (three term test) = 1.106e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9469 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.170966766424 0.153809242247
y[1] (closed_form) = 0.170947138175 0.153825931498
absolute error = 2.576e-05
relative error = 0.0112 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 1.624e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9468 0.75
h = 0.001 0.001
y[1] (numeric) = 0.170386991645 0.154127212345
y[1] (closed_form) = 0.170367490275 0.154144843923
absolute error = 2.629e-05
relative error = 0.01144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.086
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9829
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9458 0.751
h = 0.001 0.003
y[1] (numeric) = 0.170289134839 0.154422690208
y[1] (closed_form) = 0.170269851377 0.154440761819
absolute error = 2.643e-05
relative error = 0.0115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.086
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.664
Order of pole (three term test) = 1.608e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9448 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.169796615232 0.15491637934
y[1] (closed_form) = 0.169776926191 0.154933533708
absolute error = 2.611e-05
relative error = 0.01136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.086
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.639
Order of pole (three term test) = 1.231e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9447 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.169016148736 0.155326619141
y[1] (closed_form) = 0.168996955539 0.155343080256
absolute error = 2.529e-05
relative error = 0.01102 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.087
Order of pole (three term test) = 2.950e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9446 0.762
h = 0.003 0.006
y[1] (numeric) = 0.168235501173 0.155731149641
y[1] (closed_form) = 0.168216307977 0.155747610756
absolute error = 2.529e-05
relative error = 0.01103 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.502
Order of pole (three term test) = 6.853e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9416 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.167334145438 0.156893864916
y[1] (closed_form) = 0.167311237364 0.1569100662
absolute error = 2.806e-05
relative error = 0.01223 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.557
Order of pole (three term test) = 1.194e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9415 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.166347230136 0.157377921597
y[1] (closed_form) = 0.16632666332 0.157394733643
absolute error = 2.656e-05
relative error = 0.0116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.254
Order of pole (three term test) = 1.029e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9414 0.776
h = 0.001 0.001
y[1] (numeric) = 0.165759692629 0.15767197787
y[1] (closed_form) = 0.165739204631 0.157689729344
absolute error = 2.711e-05
relative error = 0.01185 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.985
Order of pole (three term test) = 4.923e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9404 0.777
h = 0.001 0.003
y[1] (numeric) = 0.165651501464 0.157961695797
y[1] (closed_form) = 0.165631207379 0.157979893813
absolute error = 2.726e-05
relative error = 0.01191 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.674
Order of pole (three term test) = 3.413e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9394 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.165144056792 0.158433458914
y[1] (closed_form) = 0.165123406694 0.158450728564
absolute error = 2.692e-05
relative error = 0.01176 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.645
Order of pole (three term test) = 2.769e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9393 0.784
h = 0.003 0.006
y[1] (numeric) = 0.164353904891 0.158811602221
y[1] (closed_form) = 0.16433378013 0.15882821012
absolute error = 2.609e-05
relative error = 0.01142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.092
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.507
Order of pole (three term test) = 1.121e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9363 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.163419996765 0.15993951324
y[1] (closed_form) = 0.163396194603 0.159955705001
absolute error = 2.879e-05
relative error = 0.01259 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.559
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9362 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.162422799992 0.160389455105
y[1] (closed_form) = 0.162401296115 0.16040635283
absolute error = 2.735e-05
relative error = 0.01198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.256
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9361 0.798
h = 0.001 0.001
y[1] (numeric) = 0.16182899749 0.160663189098
y[1] (closed_form) = 0.161807531933 0.16068102273
absolute error = 2.791e-05
relative error = 0.01224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9866
Order of pole (three term test) = 2.583e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9351 0.799
h = 0.001 0.003
y[1] (numeric) = 0.161712138726 0.160947906266
y[1] (closed_form) = 0.161690846686 0.160966191399
absolute error = 2.807e-05
relative error = 0.0123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.681
Order of pole (three term test) = 1.791e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9341 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.161192347473 0.161400939324
y[1] (closed_form) = 0.161170741499 0.161418287811
absolute error = 2.771e-05
relative error = 0.01215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.649
Order of pole (three term test) = 4.597e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.934 0.806
h = 0.003 0.006
y[1] (numeric) = 0.160394407809 0.161751819947
y[1] (closed_form) = 0.160373351353 0.161768533923
absolute error = 2.688e-05
relative error = 0.0118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.513
Order of pole (three term test) = 1.316e-13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=459.8MB, alloc=44.3MB, time=5.92
x[1] = -1.931 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.159429663695 0.162843797368
y[1] (closed_form) = 0.159404975249 0.162859942361
absolute error = 2.950e-05
relative error = 0.01294 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.562
Order of pole (three term test) = 4.329e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9309 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.158423711754 0.163259442241
y[1] (closed_form) = 0.158401273987 0.163276385206
absolute error = 2.812e-05
relative error = 0.01236 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.258
Order of pole (three term test) = 5.682e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9308 0.82
h = 0.001 0.001
y[1] (numeric) = 0.157824553409 0.163512741187
y[1] (closed_form) = 0.157802114044 0.16353061443
absolute error = 2.869e-05
relative error = 0.01262 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9883
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9298 0.821
h = 0.001 0.003
y[1] (numeric) = 0.1576993046 0.16379212795
y[1] (closed_form) = 0.157677018293 0.163810456524
absolute error = 2.886e-05
relative error = 0.01269 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.689
Order of pole (three term test) = 2.109e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9288 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.15716805487 0.164226049163
y[1] (closed_form) = 0.157145496732 0.16424343512
absolute error = 2.848e-05
relative error = 0.01253 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.654
Order of pole (three term test) = 4.844e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9287 0.828
h = 0.003 0.006
y[1] (numeric) = 0.156363542778 0.164549545762
y[1] (closed_form) = 0.156341556664 0.164566325457
absolute error = 2.766e-05
relative error = 0.01218 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.099
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.519
Order of pole (three term test) = 6.207e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9257 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.155369722253 0.165604561986
y[1] (closed_form) = 0.155344157179 0.165620623776
absolute error = 3.019e-05
relative error = 0.0133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.099
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.564
Order of pole (three term test) = 4.568e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9256 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.154356536015 0.165985810247
y[1] (closed_form) = 0.15433316964 0.166002758571
absolute error = 2.887e-05
relative error = 0.01274 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.261
Order of pole (three term test) = 1.756e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9255 0.842
h = 0.001 0.001
y[1] (numeric) = 0.153752927886 0.166218610518
y[1] (closed_form) = 0.153729520699 0.166236481444
absolute error = 2.945e-05
relative error = 0.01301 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9901
Order of pole (three term test) = 1.437e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9245 0.843
h = 0.001 0.003
y[1] (numeric) = 0.153619581217 0.166492355175
y[1] (closed_form) = 0.153596306638 0.166510684146
absolute error = 2.963e-05
relative error = 0.01308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.698
Order of pole (three term test) = 9.965e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9235 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.153077772381 0.166906833492
y[1] (closed_form) = 0.153054267956 0.166924216154
absolute error = 2.923e-05
relative error = 0.01291 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.659
Order of pole (three term test) = 1.054e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9234 0.85
h = 0.003 0.006
y[1] (numeric) = 0.152267897313 0.167202890102
y[1] (closed_form) = 0.152244985693 0.167219695642
absolute error = 2.841e-05
relative error = 0.01256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.525
Order of pole (three term test) = 6.565e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9204 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.151246796166 0.168220020755
y[1] (closed_form) = 0.151220365893 0.168235963824
absolute error = 3.087e-05
relative error = 0.01365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.567
Order of pole (three term test) = 1.104e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9203 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.15022788591 0.168566853966
y[1] (closed_form) = 0.150203598258 0.168583768452
absolute error = 2.960e-05
relative error = 0.01311 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.104
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 6.357e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9202 0.864
h = 0.001 0.001
y[1] (numeric) = 0.149620727904 0.168779140259
y[1] (closed_form) = 0.14959636105 0.168796967696
absolute error = 3.019e-05
relative error = 0.01339 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.106
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9921
Order of pole (three term test) = 1.530e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9192 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.14947958887 0.169046949755
y[1] (closed_form) = 0.149455334251 0.169065236847
absolute error = 3.038e-05
relative error = 0.01346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.956
Order of pole (three term test) = 3.959e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9191 0.869
h = 0.003 0.006
y[1] (numeric) = 0.148666262079 0.169320563073
y[1] (closed_form) = 0.148642739433 0.169337082578
absolute error = 2.874e-05
relative error = 0.01276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.107
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.532
Order of pole (three term test) = 1.250e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9161 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.147623603545 0.170304127085
y[1] (closed_form) = 0.147596621344 0.170319664303
absolute error = 3.114e-05
relative error = 0.01382 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.106
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.57
Order of pole (three term test) = 7.986e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.916 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.146601372657 0.170621338915
y[1] (closed_form) = 0.146576480793 0.170637916781
absolute error = 2.991e-05
relative error = 0.0133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.108
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.266
Order of pole (three term test) = 1.714e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9159 0.883
h = 0.001 0.001
y[1] (numeric) = 0.145992116505 0.170815963483
y[1] (closed_form) = 0.145967113288 0.170833444026
absolute error = 3.051e-05
relative error = 0.01358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9939
Order of pole (three term test) = 6.444e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9149 0.884
h = 0.001 0.003
y[1] (numeric) = 0.145844598956 0.171078356538
y[1] (closed_form) = 0.14581969055 0.171096297015
absolute error = 3.070e-05
relative error = 0.01365 %
Correct digits = 4
memory used=506.7MB, alloc=44.3MB, time=6.52
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.716
Order of pole (three term test) = 3.162e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9139 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.145285799059 0.171455848743
y[1] (closed_form) = 0.145260738114 0.171472842469
absolute error = 3.028e-05
relative error = 0.01347 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.669
Order of pole (three term test) = 1.150e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9138 0.891
h = 0.003 0.006
y[1] (numeric) = 0.144469452306 0.171700885257
y[1] (closed_form) = 0.144445017781 0.171717358244
absolute error = 2.947e-05
relative error = 0.01313 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.111
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.539
Order of pole (three term test) = 7.377e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9108 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.143402935308 0.172645143355
y[1] (closed_form) = 0.143375114008 0.172660498707
absolute error = 3.178e-05
relative error = 0.01416 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.111
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.574
Order of pole (three term test) = 7.701e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9107 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.142377743648 0.172928133171
y[1] (closed_form) = 0.142351949797 0.172944606631
absolute error = 3.061e-05
relative error = 0.01366 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.113
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.268
Order of pole (three term test) = 1.827e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9106 0.905
h = 0.001 0.001
y[1] (numeric) = 0.141766584597 0.173102350663
y[1] (closed_form) = 0.141740642852 0.1731197137
absolute error = 3.122e-05
relative error = 0.01395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.114
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.996
Order of pole (three term test) = 2.097e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9096 0.906
h = 0.001 0.003
y[1] (numeric) = 0.141611876874 0.17335831875
y[1] (closed_form) = 0.141586009906 0.17337614134
absolute error = 3.141e-05
relative error = 0.01403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.114
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.726
Order of pole (three term test) = 4.775e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9086 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.141045125209 0.173715711635
y[1] (closed_form) = 0.141019146554 0.173732590061
absolute error = 3.098e-05
relative error = 0.01385 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.114
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.675
Order of pole (three term test) = 1.371e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9085 0.913
h = 0.003 0.006
y[1] (numeric) = 0.140226805522 0.173933510963
y[1] (closed_form) = 0.140201468984 0.173949899657
absolute error = 3.017e-05
relative error = 0.01351 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.547
Order of pole (three term test) = 1.114e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9055 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.139138289884 0.174837837704
y[1] (closed_form) = 0.139109645506 0.174852978816
absolute error = 3.240e-05
relative error = 0.0145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.577
Order of pole (three term test) = 8.229e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9054 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.138111589829 0.175086808288
y[1] (closed_form) = 0.138084906757 0.175103140765
absolute error = 3.128e-05
relative error = 0.01403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.118
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.271
Order of pole (three term test) = 1.915e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9053 0.927
h = 0.001 0.001
y[1] (numeric) = 0.137499393761 0.175240735134
y[1] (closed_form) = 0.137472527382 0.175257942353
absolute error = 3.190e-05
relative error = 0.01432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.119
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9983
Order of pole (three term test) = 1.837e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9043 0.928
h = 0.001 0.003
y[1] (numeric) = 0.137337831689 0.175490041514
y[1] (closed_form) = 0.137311020318 0.175507706872
absolute error = 3.211e-05
relative error = 0.01441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.118
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.737
Order of pole (three term test) = 1.275e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9033 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.136764039668 0.17582719834
y[1] (closed_form) = 0.136737156824 0.175843924207
absolute error = 3.166e-05
relative error = 0.01421 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.119
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.681
Order of pole (three term test) = 1.313e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9032 0.935
h = 0.003 0.006
y[1] (numeric) = 0.135944896529 0.176017942916
y[1] (closed_form) = 0.135918669703 0.176034210483
absolute error = 3.086e-05
relative error = 0.01388 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.555
Order of pole (three term test) = 9.427e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9002 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.134836251763 0.176881816825
y[1] (closed_form) = 0.134806801757 0.176896712567
absolute error = 3.300e-05
relative error = 0.01484 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.581
Order of pole (three term test) = 6.237e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9001 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.133809467155 0.177097043627
y[1] (closed_form) = 0.133781909371 0.177113199649
absolute error = 3.194e-05
relative error = 0.01439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.274
Order of pole (three term test) = 6.163e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9 0.949
h = 0.001 0.001
y[1] (numeric) = 0.133197083131 0.177230839542
y[1] (closed_form) = 0.133169307841 0.177247853836
absolute error = 3.257e-05
relative error = 0.01469 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.124
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.001
Order of pole (three term test) = 9.855e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.899 0.95
h = 0.001 0.003
y[1] (numeric) = 0.133029010555 0.177473267782
y[1] (closed_form) = 0.13300127083 0.1774907378
absolute error = 3.278e-05
relative error = 0.01478 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.748
Order of pole (three term test) = 5.474e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.898 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.132449085222 0.177790100615
y[1] (closed_form) = 0.132421313483 0.177806637827
absolute error = 3.232e-05
relative error = 0.01458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.124
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.687
Order of pole (three term test) = 7.082e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8979 0.957
h = 0.003 0.006
y[1] (numeric) = 0.131630244174 0.177954029902
y[1] (closed_form) = 0.131603140554 0.177970140556
absolute error = 3.153e-05
relative error = 0.01424 %
Correct digits = 4
memory used=553.6MB, alloc=44.3MB, time=7.12
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.564
Order of pole (three term test) = 9.456e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8949 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.130503342897 0.178777032486
y[1] (closed_form) = 0.130473106044 0.178791653042
absolute error = 3.359e-05
relative error = 0.01517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 1.341e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8948 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.129477864998 0.178958860737
y[1] (closed_form) = 0.129449448652 0.178974806029
absolute error = 3.258e-05
relative error = 0.01475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.128
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 4.941e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8947 0.971
h = 0.001 0.001
y[1] (numeric) = 0.128866122847 0.17907272701
y[1] (closed_form) = 0.128837456094 0.17908951257
absolute error = 3.322e-05
relative error = 0.01506 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.129
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.003
Order of pole (three term test) = 1.544e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8937 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.128691890257 0.179308081158
y[1] (closed_form) = 0.128663240007 0.179325319063
absolute error = 3.344e-05
relative error = 0.01515 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.129
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.022
Order of pole (three term test) = 1.288e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8936 0.976
h = 0.003 0.006
y[1] (numeric) = 0.127874154563 0.179450299461
y[1] (closed_form) = 0.127846530945 0.179466022572
absolute error = 3.178e-05
relative error = 0.01442 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.572
Order of pole (three term test) = 1.130e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8906 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.126733527643 0.180237676645
y[1] (closed_form) = 0.126702853411 0.180251813953
absolute error = 3.378e-05
relative error = 0.01533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 7.323e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8905 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.125710651952 0.180391121399
y[1] (closed_form) = 0.125681733939 0.180406634401
absolute error = 3.282e-05
relative error = 0.01493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.133
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.28
Order of pole (three term test) = 2.144e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8904 0.99
h = 0.001 0.001
y[1] (numeric) = 0.125100343871 0.180488045163
y[1] (closed_form) = 0.125071148463 0.180504381413
absolute error = 3.346e-05
relative error = 0.01523 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.005
Order of pole (three term test) = 5.083e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8894 0.991
h = 0.001 0.003
y[1] (numeric) = 0.124921180735 0.180717101354
y[1] (closed_form) = 0.124891985822 0.180733886079
absolute error = 3.368e-05
relative error = 0.01533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.771
Order of pole (three term test) = 7.062e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8884 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.124332472121 0.180995996709
y[1] (closed_form) = 0.124303316097 0.18101186659
absolute error = 3.320e-05
relative error = 0.01512 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.7
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8883 0.998
h = 0.003 0.006
y[1] (numeric) = 0.12351740416 0.181110885588
y[1] (closed_form) = 0.123488933649 0.181126388504
absolute error = 3.242e-05
relative error = 0.01479 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.581
Order of pole (three term test) = 1.127e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8853 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.12236199396 0.181856903671
y[1] (closed_form) = 0.122330571332 0.181870714243
absolute error = 3.432e-05
relative error = 0.01566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.592
Order of pole (three term test) = 7.803e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8852 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.121342908472 0.181977782607
y[1] (closed_form) = 0.121313166355 0.181993024801
absolute error = 3.342e-05
relative error = 0.01528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.138
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.283
Order of pole (three term test) = 1.287e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8851 1.012
h = 0.001 0.001
y[1] (numeric) = 0.120734724179 0.182055264741
y[1] (closed_form) = 0.12070467438 0.182071309619
absolute error = 3.407e-05
relative error = 0.01559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 7.779e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8841 1.013
h = 0.001 0.003
y[1] (numeric) = 0.120550067989 0.182276941221
y[1] (closed_form) = 0.12052000048 0.182293429514
absolute error = 3.429e-05
relative error = 0.01569 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.783
Order of pole (three term test) = 4.173e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8831 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.119957770205 0.18253553089
y[1] (closed_form) = 0.11992777827 0.182551116311
absolute error = 3.380e-05
relative error = 0.01547 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.707
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.883 1.02
h = 0.003 0.006
y[1] (numeric) = 0.119146060011 0.182624594687
y[1] (closed_form) = 0.119116760632 0.182639845124
absolute error = 3.303e-05
relative error = 0.01515 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.142
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.59
Order of pole (three term test) = 1.134e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.88 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.117977712419 0.183329120173
y[1] (closed_form) = 0.117945563394 0.18334257824
absolute error = 3.485e-05
relative error = 0.01599 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.142
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.597
Order of pole (three term test) = 1.191e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8799 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.116963694719 0.183417959659
y[1] (closed_form) = 0.11693314877 0.183432900637
absolute error = 3.400e-05
relative error = 0.01563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.287
Order of pole (three term test) = 2.779e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8798 1.034
h = 0.001 0.001
y[1] (numeric) = 0.116358396847 0.183476309439
y[1] (closed_form) = 0.116327514411 0.18349203131
absolute error = 3.465e-05
relative error = 0.01595 %
Correct digits = 4
memory used=600.3MB, alloc=44.3MB, time=7.72
Radius of convergence (given) for eq 1 = 2.145
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.011
Order of pole (three term test) = 7.552e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8788 1.035
h = 0.001 0.003
y[1] (numeric) = 0.116168609401 0.183690468962
y[1] (closed_form) = 0.116137691572 0.183706628341
absolute error = 3.489e-05
relative error = 0.01605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.145
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.796
Order of pole (three term test) = 7.422e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8778 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.115573585722 0.183928841897
y[1] (closed_form) = 0.11554277901 0.183944112051
absolute error = 3.438e-05
relative error = 0.01583 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.146
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.715
Order of pole (three term test) = 1.353e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8777 1.042
h = 0.003 0.006
y[1] (numeric) = 0.114766238518 0.183992516041
y[1] (closed_form) = 0.114736129691 0.184007483078
absolute error = 3.362e-05
relative error = 0.01551 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.6
Order of pole (three term test) = 1.238e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8747 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.113586779251 0.184655510518
y[1] (closed_form) = 0.113553926759 0.1846685918
absolute error = 3.536e-05
relative error = 0.01631 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.148
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.601
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8746 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.112579061517 0.184712893552
y[1] (closed_form) = 0.112547733251 0.184727504372
absolute error = 3.457e-05
relative error = 0.01598 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.15
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.291
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8745 1.056
h = 0.001 0.001
y[1] (numeric) = 0.111977385836 0.184752454034
y[1] (closed_form) = 0.111945693802 0.184767822839
absolute error = 3.522e-05
relative error = 0.0163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.014
Order of pole (three term test) = 6.498e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8735 1.057
h = 0.001 0.003
y[1] (numeric) = 0.111782830455 0.184958979581
y[1] (closed_form) = 0.11175108591 0.184974779192
absolute error = 3.546e-05
relative error = 0.01641 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.81
Order of pole (three term test) = 4.040e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8725 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.111185926832 0.185177266833
y[1] (closed_form) = 0.111154327725 0.185192192441
absolute error = 3.495e-05
relative error = 0.01618 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.152
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.723
Order of pole (three term test) = 1.165e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8724 1.064
h = 0.003 0.006
y[1] (numeric) = 0.110383910917 0.185216030746
y[1] (closed_form) = 0.110353013344 0.185230684883
absolute error = 3.420e-05
relative error = 0.01586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.154
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.611
Order of pole (three term test) = 6.712e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8694 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.109195140162 0.185837547956
y[1] (closed_form) = 0.109161607953 0.185850229682
absolute error = 3.585e-05
relative error = 0.01663 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.154
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.606
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8693 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.108194906589 0.185864110394
y[1] (closed_form) = 0.108162818647 0.185878363629
absolute error = 3.511e-05
relative error = 0.01633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.156
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.294
Order of pole (three term test) = 7.378e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8692 1.078
h = 0.001 0.001
y[1] (numeric) = 0.107597560469 0.185885256187
y[1] (closed_form) = 0.107565083045 0.185900243492
absolute error = 3.577e-05
relative error = 0.01665 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.158
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.017
Order of pole (three term test) = 4.486e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8682 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.107398600759 0.186084050688
y[1] (closed_form) = 0.107366054304 0.186099461349
absolute error = 3.601e-05
relative error = 0.01676 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.157
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.104
Order of pole (three term test) = 2.207e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8681 1.083
h = 0.003 0.006
y[1] (numeric) = 0.106601674637 0.186102837753
y[1] (closed_form) = 0.106570364326 0.186117032643
absolute error = 3.438e-05
relative error = 0.01603 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.159
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.62
Order of pole (three term test) = 4.362e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8651 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.105406798745 0.186688681417
y[1] (closed_form) = 0.105372950658 0.186700836074
absolute error = 3.596e-05
relative error = 0.01678 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.16
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 1.082e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.865 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.104414273174 0.186689368614
y[1] (closed_form) = 0.104381799443 0.186703126228
absolute error = 3.527e-05
relative error = 0.01649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.162
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.298
Order of pole (three term test) = 2.605e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8649 1.097
h = 0.001 0.001
y[1] (numeric) = 0.103821410299 0.18669504852
y[1] (closed_form) = 0.103788526528 0.186709518621
absolute error = 3.593e-05
relative error = 0.01682 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.164
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.019
Order of pole (three term test) = 1.240e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8639 1.098
h = 0.001 0.003
y[1] (numeric) = 0.10361904329 0.18688707904
y[1] (closed_form) = 0.103586076873 0.186901965336
absolute error = 3.617e-05
relative error = 0.01693 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.163
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.837
Order of pole (three term test) = 1.070e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8629 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.103021058394 0.187068477311
y[1] (closed_form) = 0.102988297568 0.18708252214
absolute error = 3.564e-05
relative error = 0.01669 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.164
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.738
Order of pole (three term test) = 8.648e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8628 1.105
h = 0.003 0.006
y[1] (numeric) = 0.102231686897 0.187062391992
y[1] (closed_form) = 0.102199629727 0.187076223331
absolute error = 3.491e-05
relative error = 0.01638 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.166
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.631
Order of pole (three term test) = 3.185e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=647.2MB, alloc=44.3MB, time=8.32
x[1] = -1.8598 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.101030761218 0.187607112858
y[1] (closed_form) = 0.100996279672 0.187618829972
absolute error = 3.642e-05
relative error = 0.01709 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.166
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.615
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8597 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.10004777924 0.187578302712
y[1] (closed_form) = 0.100014590871 0.187591656156
absolute error = 3.577e-05
relative error = 0.01683 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.302
Order of pole (three term test) = 8.315e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8596 1.119
h = 0.001 0.001
y[1] (numeric) = 0.0994604768811 0.187566348654
y[1] (closed_form) = 0.0994268557506 0.187580389121
absolute error = 3.644e-05
relative error = 0.01716 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.023
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8586 1.12
h = 0.001 0.003
y[1] (numeric) = 0.0992543794403 0.187750523592
y[1] (closed_form) = 0.0992206603542 0.18776497155
absolute error = 3.668e-05
relative error = 0.01727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.852
Order of pole (three term test) = 5.354e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8576 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.0986568169029 0.187912436066
y[1] (closed_form) = 0.0986233338541 0.187926061695
absolute error = 3.615e-05
relative error = 0.01703 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.171
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.747
Order of pole (three term test) = 1.416e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8575 1.127
h = 0.003 0.006
y[1] (numeric) = 0.0978753192276 0.187883037494
y[1] (closed_form) = 0.0978425389594 0.187896480127
absolute error = 3.543e-05
relative error = 0.01672 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.173
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.643
Order of pole (three term test) = 1.120e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8545 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.0966700433019 0.188386933627
y[1] (closed_form) = 0.0966349538126 0.188398194835
absolute error = 3.685e-05
relative error = 0.0174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.173
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.62
Order of pole (three term test) = 2.608e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8544 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.0956976400059 0.188329391028
y[1] (closed_form) = 0.0956637622341 0.188342317401
absolute error = 3.626e-05
relative error = 0.01716 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.176
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.306
Order of pole (three term test) = 9.649e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8543 1.141
h = 0.001 0.001
y[1] (numeric) = 0.0951165172213 0.188300254718
y[1] (closed_form) = 0.0950821855948 0.188313841964
absolute error = 3.692e-05
relative error = 0.0175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.177
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.026
Order of pole (three term test) = 1.432e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8533 1.142
h = 0.001 0.003
y[1] (numeric) = 0.0949070471296 0.188476531786
y[1] (closed_form) = 0.0948726029193 0.188490517218
absolute error = 3.718e-05
relative error = 0.01762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.177
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.868
Order of pole (three term test) = 2.311e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8523 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.0943106664955 0.188619233768
y[1] (closed_form) = 0.0942764873204 0.188632417176
absolute error = 3.663e-05
relative error = 0.01737 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.178
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.755
Order of pole (three term test) = 1.493e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8522 1.149
h = 0.003 0.006
y[1] (numeric) = 0.0935378519554 0.188567141747
y[1] (closed_form) = 0.0935043732114 0.188580172094
absolute error = 3.593e-05
relative error = 0.01707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.18
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.654
Order of pole (three term test) = 1.292e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8492 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.092329882293 0.189030589397
y[1] (closed_form) = 0.0922942108037 0.189041377876
absolute error = 3.727e-05
relative error = 0.01772 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.18
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8491 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.0913690378691 0.188945116878
y[1] (closed_form) = 0.0913344966301 0.188957594897
absolute error = 3.673e-05
relative error = 0.0175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.183
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.31
Order of pole (three term test) = 4.758e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.849 1.163
h = 0.001 0.001
y[1] (numeric) = 0.0907946811884 0.188899272556
y[1] (closed_form) = 0.0907596666342 0.188912384722
absolute error = 3.739e-05
relative error = 0.01784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 1.651e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.848 1.164
h = 0.001 0.003
y[1] (numeric) = 0.0905821922074 0.189067627623
y[1] (closed_form) = 0.0905470511451 0.18908112812
absolute error = 3.765e-05
relative error = 0.01796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.884
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.847 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.0899877266715 0.189191426763
y[1] (closed_form) = 0.0899528781558 0.189204146598
absolute error = 3.710e-05
relative error = 0.01771 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.185
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.764
Order of pole (three term test) = 4.942e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8469 1.171
h = 0.003 0.006
y[1] (numeric) = 0.0892243605625 0.189117289912
y[1] (closed_form) = 0.0891902087167 0.189129885991
absolute error = 3.640e-05
relative error = 0.01741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.187
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.666
Order of pole (three term test) = 8.764e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8439 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.0880153069698 0.189540739391
y[1] (closed_form) = 0.0879790797553 0.189551039851
absolute error = 3.766e-05
relative error = 0.01802 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.188
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.631
Order of pole (three term test) = 3.176e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8438 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.0870669456606 0.189428173151
y[1] (closed_form) = 0.0870317674797 0.18944018316
absolute error = 3.717e-05
relative error = 0.01783 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.315
Order of pole (three term test) = 7.438e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=693.9MB, alloc=44.3MB, time=8.91
x[1] = -1.8437 1.185
h = 0.001 0.001
y[1] (numeric) = 0.0864999084515 0.189366115227
y[1] (closed_form) = 0.0864642391273 0.189378732187
absolute error = 3.784e-05
relative error = 0.01817 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.192
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.033
Order of pole (three term test) = 7.161e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8427 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.0862847493537 0.189526541705
y[1] (closed_form) = 0.0862489403177 0.189539536642
absolute error = 3.809e-05
relative error = 0.01829 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.2
Order of pole (three term test) = 5.922e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8426 1.19
h = 0.003 0.006
y[1] (numeric) = 0.0855296803877 0.189434892327
y[1] (closed_form) = 0.0854952293915 0.189446988365
absolute error = 3.651e-05
relative error = 0.01757 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.193
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.677
Order of pole (three term test) = 8.146e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8396 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.0843214126318 0.189824338966
y[1] (closed_form) = 0.0842849882454 0.189834099813
absolute error = 3.771e-05
relative error = 0.01816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.194
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 3.480e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8395 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.0833848018356 0.189689306371
y[1] (closed_form) = 0.0833493567935 0.189700789617
absolute error = 3.726e-05
relative error = 0.01798 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.197
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.319
Order of pole (three term test) = 1.730e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8394 1.204
h = 0.001 0.001
y[1] (numeric) = 0.0828246672382 0.189613797433
y[1] (closed_form) = 0.0827887173376 0.189625863739
absolute error = 3.792e-05
relative error = 0.01833 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.198
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.036
Order of pole (three term test) = 5.552e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8384 1.205
h = 0.001 0.003
y[1] (numeric) = 0.0826075788406 0.189767380612
y[1] (closed_form) = 0.0825714785804 0.189779815478
absolute error = 3.818e-05
relative error = 0.01845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.198
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.915
Order of pole (three term test) = 7.728e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8374 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.0820187477887 0.189856968484
y[1] (closed_form) = 0.0819829869362 0.189868665171
absolute error = 3.763e-05
relative error = 0.01819 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.199
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.782
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8373 1.212
h = 0.003 0.006
y[1] (numeric) = 0.0812750893816 0.1897437552
y[1] (closed_form) = 0.0812400143454 0.189755380664
absolute error = 3.695e-05
relative error = 0.0179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.201
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.69
Order of pole (three term test) = 5.163e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8343 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.0800685905698 0.190094241734
y[1] (closed_form) = 0.0800316600524 0.19010349045
absolute error = 3.807e-05
relative error = 0.01846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.202
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.641
Order of pole (three term test) = 1.941e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8342 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.0791460206774 0.189933756893
y[1] (closed_form) = 0.0791099894478 0.189944740199
absolute error = 3.767e-05
relative error = 0.01831 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.205
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.323
Order of pole (three term test) = 4.482e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8341 1.226
h = 0.001 0.001
y[1] (numeric) = 0.0785941391922 0.189843005649
y[1] (closed_form) = 0.0785575882885 0.189854544239
absolute error = 3.833e-05
relative error = 0.01865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.039
Order of pole (three term test) = 6.167e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8331 1.227
h = 0.001 0.003
y[1] (numeric) = 0.0783750129491 0.189988696339
y[1] (closed_form) = 0.0783382998595 0.190000592356
absolute error = 3.859e-05
relative error = 0.01878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.932
Order of pole (three term test) = 8.586e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8321 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.0777900330877 0.1900604278
y[1] (closed_form) = 0.0777536825196 0.190071609414
absolute error = 3.803e-05
relative error = 0.01852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.207
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.792
Order of pole (three term test) = 6.285e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.832 1.234
h = 0.003 0.006
y[1] (numeric) = 0.077057755026 0.189927163518
y[1] (closed_form) = 0.0770220828619 0.189938301035
absolute error = 3.737e-05
relative error = 0.01823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.209
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.703
Order of pole (three term test) = 5.740e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.829 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.0758544836569 0.190239327538
y[1] (closed_form) = 0.0758170737079 0.190248053111
absolute error = 3.841e-05
relative error = 0.01876 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.21
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.647
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8289 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.0749467154013 0.190054300628
y[1] (closed_form) = 0.0749101256002 0.190064768964
absolute error = 3.806e-05
relative error = 0.01863 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.212
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.328
Order of pole (three term test) = 2.138e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8288 1.248
h = 0.001 0.001
y[1] (numeric) = 0.0744035434307 0.189948845945
y[1] (closed_form) = 0.07436642073 0.189959841609
absolute error = 3.872e-05
relative error = 0.01898 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.214
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.043
Order of pole (three term test) = 1.375e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8278 1.249
h = 0.001 0.003
y[1] (numeric) = 0.0741827088942 0.190086683844
y[1] (closed_form) = 0.0741454129286 0.190098025451
absolute error = 3.898e-05
relative error = 0.0191 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.214
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.95
Order of pole (three term test) = 1.167e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8268 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.0736022005708 0.190140970098
y[1] (closed_form) = 0.0735652886835 0.190151621726
absolute error = 3.842e-05
relative error = 0.01884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.215
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.802
Order of pole (three term test) = 7.002e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=740.7MB, alloc=44.3MB, time=9.51
x[1] = -1.8267 1.256
h = 0.003 0.006
y[1] (numeric) = 0.072881893043 0.189988384818
y[1] (closed_form) = 0.0728456510075 0.189999018612
absolute error = 3.777e-05
relative error = 0.01856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.217
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.717
Order of pole (three term test) = 1.865e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8237 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.0716832502332 0.190262920956
y[1] (closed_form) = 0.0716453875415 0.190271113817
absolute error = 3.874e-05
relative error = 0.01905 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.218
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.653
Order of pole (three term test) = 7.192e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8236 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.070790987051 0.190054280902
y[1] (closed_form) = 0.0707538664898 0.190064220825
absolute error = 3.843e-05
relative error = 0.01895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.221
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.333
Order of pole (three term test) = 7.954e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8235 1.27
h = 0.001 0.001
y[1] (numeric) = 0.0702569470039 0.189934672967
y[1] (closed_form) = 0.0702192818812 0.189945112174
absolute error = 3.909e-05
relative error = 0.0193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.222
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.047
Order of pole (three term test) = 7.703e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8225 1.271
h = 0.001 0.003
y[1] (numeric) = 0.0700347256274 0.190064712532
y[1] (closed_form) = 0.0699968769109 0.190075485899
absolute error = 3.935e-05
relative error = 0.01943 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.222
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.968
Order of pole (three term test) = 3.203e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8215 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.069459278087 0.1901019862
y[1] (closed_form) = 0.0694218334483 0.190112094553
absolute error = 3.879e-05
relative error = 0.01916 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.223
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.813
Order of pole (three term test) = 6.182e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8214 1.278
h = 0.003 0.006
y[1] (numeric) = 0.0687514857503 0.189930823792
y[1] (closed_form) = 0.0687147013456 0.189940939672
absolute error = 3.815e-05
relative error = 0.01889 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.225
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.73
Order of pole (three term test) = 1.288e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8184 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.0675588133342 0.190168479187
y[1] (closed_form) = 0.0675205244996 0.190176131178
absolute error = 3.905e-05
relative error = 0.01935 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.226
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 8.041e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8183 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.0666827016337 0.189937170011
y[1] (closed_form) = 0.0666450782254 0.189946569638
absolute error = 3.878e-05
relative error = 0.01926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.229
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 8.896e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8182 1.292
h = 0.001 0.001
y[1] (numeric) = 0.0661581820756 0.189803968163
y[1] (closed_form) = 0.0661200039762 0.189813839033
absolute error = 3.943e-05
relative error = 0.01962 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 8.574e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8172 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.0659348865746 0.189926277811
y[1] (closed_form) = 0.0658965153015 0.189936470806
absolute error = 3.970e-05
relative error = 0.01975 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.31
Order of pole (three term test) = 7.461e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8171 1.297
h = 0.003 0.006
y[1] (numeric) = 0.0652377296038 0.189740503631
y[1] (closed_form) = 0.0652007571136 0.189750107512
absolute error = 3.820e-05
relative error = 0.01904 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.233
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.743
Order of pole (three term test) = 8.835e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8141 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.0640516507164 0.189947140084
y[1] (closed_form) = 0.0640132730563 0.189954266363
absolute error = 3.903e-05
relative error = 0.01947 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.234
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 1.069e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.814 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.0631901706394 0.189697284766
y[1] (closed_form) = 0.0631523936175 0.18970615543
absolute error = 3.880e-05
relative error = 0.01941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.236
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.342
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8139 1.311
h = 0.001 0.001
y[1] (numeric) = 0.0626742842567 0.189552954156
y[1] (closed_form) = 0.062635945356 0.189562271896
absolute error = 3.945e-05
relative error = 0.01976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.238
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.054
Order of pole (three term test) = 1.342e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8129 1.312
h = 0.001 0.003
y[1] (numeric) = 0.0624503982308 0.189668667097
y[1] (closed_form) = 0.0624118586542 0.189678296335
absolute error = 3.972e-05
relative error = 0.01989 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.238
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.004
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8119 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.0618860171471 0.189675575176
y[1] (closed_form) = 0.0618479144348 0.189684587158
absolute error = 3.915e-05
relative error = 0.01962 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.239
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.833
Order of pole (three term test) = 4.847e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8118 1.319
h = 0.003 0.006
y[1] (numeric) = 0.0612030075499 0.189472022842
y[1] (closed_form) = 0.0611655443233 0.189481086866
absolute error = 3.854e-05
relative error = 0.01936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.241
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.757
Order of pole (three term test) = 1.675e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8088 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.0600252228806 0.189643307289
y[1] (closed_form) = 0.0599864681447 0.189649881436
absolute error = 3.931e-05
relative error = 0.01976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.242
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.672
Order of pole (three term test) = 3.722e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8087 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.0591809356738 0.189372573736
y[1] (closed_form) = 0.0591427078107 0.189380886372
absolute error = 3.912e-05
relative error = 0.01972 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.245
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.348
Order of pole (three term test) = 1.106e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=787.7MB, alloc=44.3MB, time=10.12
x[1] = -1.8086 1.333
h = 0.001 0.001
y[1] (numeric) = 0.0586751969876 0.189215710935
y[1] (closed_form) = 0.058636399864 0.189224442847
absolute error = 3.977e-05
relative error = 0.02007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.247
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.059
Order of pole (three term test) = 1.066e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8076 1.334
h = 0.001 0.003
y[1] (numeric) = 0.0584507923977 0.189323859082
y[1] (closed_form) = 0.0584117864017 0.189332890124
absolute error = 4.004e-05
relative error = 0.02021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.247
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.023
Order of pole (three term test) = 1.515e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8066 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.0578929765713 0.189315096312
y[1] (closed_form) = 0.0578544230358 0.189323536062
absolute error = 3.947e-05
relative error = 0.01994 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.248
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.844
Order of pole (three term test) = 3.852e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8065 1.341
h = 0.003 0.006
y[1] (numeric) = 0.0572237829405 0.189095150932
y[1] (closed_form) = 0.0571858566547 0.189103665296
absolute error = 3.887e-05
relative error = 0.01968 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.25
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.772
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8035 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.0560554568547 0.18923195503
y[1] (closed_form) = 0.0560163509776 0.189237972681
absolute error = 3.957e-05
relative error = 0.02005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.251
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.678
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8034 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.0552288492087 0.188941310728
y[1] (closed_form) = 0.0551901982117 0.18894905773
absolute error = 3.942e-05
relative error = 0.02003 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.254
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.353
Order of pole (three term test) = 1.244e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8033 1.355
h = 0.001 0.001
y[1] (numeric) = 0.0547335519505 0.188772489551
y[1] (closed_form) = 0.0546943257269 0.188780628263
absolute error = 4.006e-05
relative error = 0.02038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.256
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.063
Order of pole (three term test) = 1.224e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8023 1.356
h = 0.001 0.003
y[1] (numeric) = 0.0545089134639 0.188873176597
y[1] (closed_form) = 0.0544694709014 0.188881601951
absolute error = 4.033e-05
relative error = 0.02052 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.255
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.043
Order of pole (three term test) = 1.673e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8013 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.0539581288001 0.188849237205
y[1] (closed_form) = 0.0539191527945 0.188857097407
absolute error = 3.976e-05
relative error = 0.02024 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.256
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.855
Order of pole (three term test) = 9.699e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8012 1.363
h = 0.003 0.006
y[1] (numeric) = 0.0533031241639 0.188613669674
y[1] (closed_form) = 0.0532647623983 0.188621626043
absolute error = 3.918e-05
relative error = 0.01999 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.259
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.787
Order of pole (three term test) = 5.613e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7982 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.0521453576145 0.188716900286
y[1] (closed_form) = 0.0521059261808 0.188722358319
absolute error = 3.981e-05
relative error = 0.02033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.26
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.685
Order of pole (three term test) = 1.791e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7981 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.0513368622778 0.188407314943
y[1] (closed_form) = 0.0512978156358 0.188414490122
absolute error = 3.970e-05
relative error = 0.02033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.263
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.358
Order of pole (three term test) = 5.613e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.798 1.377
h = 0.001 0.001
y[1] (numeric) = 0.0508522681336 0.188227110713
y[1] (closed_form) = 0.0508126416668 0.188234650338
absolute error = 4.034e-05
relative error = 0.02069 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.265
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.067
Order of pole (three term test) = 3.385e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.797 1.378
h = 0.001 0.003
y[1] (numeric) = 0.0506276698603 0.188320451105
y[1] (closed_form) = 0.0505878203062 0.188328264805
absolute error = 4.061e-05
relative error = 0.02082 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.265
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.064
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.796 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.0500843502715 0.188281840227
y[1] (closed_form) = 0.0500449798988 0.188289115007
absolute error = 4.004e-05
relative error = 0.02055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.266
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.867
Order of pole (three term test) = 9.791e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7959 1.385
h = 0.003 0.006
y[1] (numeric) = 0.0494438650795 0.188031422363
y[1] (closed_form) = 0.0494050952381 0.18803881383
absolute error = 3.947e-05
relative error = 0.0203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.268
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.802
Order of pole (three term test) = 2.004e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7929 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.0482976952776 0.188102017256
y[1] (closed_form) = 0.0482579634652 0.188106913736
absolute error = 4.003e-05
relative error = 0.02061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.269
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 6.746e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7928 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.0475076922871 0.187774459827
y[1] (closed_form) = 0.0474682771996 0.187781058363
absolute error = 3.996e-05
relative error = 0.02063 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.272
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.364
Order of pole (three term test) = 4.758e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7927 1.399
h = 0.001 0.001
y[1] (numeric) = 0.04703403162 0.187583447606
y[1] (closed_form) = 0.0469940334262 0.187590383692
absolute error = 4.060e-05
relative error = 0.02099 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.274
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.071
Order of pole (three term test) = 1.560e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7917 1.4
h = 0.003 0.006
y[1] (numeric) = 0.0468097367979 0.187669565704
y[1] (closed_form) = 0.0467695094727 0.187676763263
absolute error = 4.087e-05
relative error = 0.02113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.274
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.79
Order of pole (three term test) = 4.741e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=834.7MB, alloc=44.3MB, time=10.72
x[1] = -1.7887 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.0456694563088 0.187719387954
y[1] (closed_form) = 0.0456302032977 0.187722652908
absolute error = 3.939e-05
relative error = 0.02039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.275
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.696
Order of pole (three term test) = 7.295e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7886 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.0448919438816 0.187379552646
y[1] (closed_form) = 0.0448529615388 0.187384509347
absolute error = 3.930e-05
relative error = 0.02039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.278
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 1.249e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7885 1.414
h = 0.001 0.001
y[1] (numeric) = 0.0444256668646 0.187181157125
y[1] (closed_form) = 0.04438609923 0.187186433164
absolute error = 3.992e-05
relative error = 0.02075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.28
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 1.655e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7875 1.415
h = 0.001 0.003
y[1] (numeric) = 0.0442015498192 0.187262368843
y[1] (closed_form) = 0.0441617489785 0.187267897816
absolute error = 4.018e-05
relative error = 0.02088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.28
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.098
Order of pole (three term test) = 2.308e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7865 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.0436713851284 0.187199954558
y[1] (closed_form) = 0.0436320821908 0.187204988633
absolute error = 3.962e-05
relative error = 0.02061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.281
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.886
Order of pole (three term test) = 5.990e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7864 1.422
h = 0.003 0.006
y[1] (numeric) = 0.0430557095629 0.186925836264
y[1] (closed_form) = 0.0430169830944 0.186931019659
absolute error = 3.907e-05
relative error = 0.02037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.283
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.828
Order of pole (three term test) = 2.373e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7834 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.04193052027 0.186943201403
y[1] (closed_form) = 0.0418910083266 0.186945903482
absolute error = 3.960e-05
relative error = 0.02067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.285
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 8.268e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7833 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.0411720501362 0.186587013258
y[1] (closed_form) = 0.0411327443679 0.18659138748
absolute error = 3.955e-05
relative error = 0.0207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.288
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 9.724e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7832 1.436
h = 0.001 0.001
y[1] (numeric) = 0.0407170410077 0.186378771044
y[1] (closed_form) = 0.0406771487793 0.186383438435
absolute error = 4.016e-05
relative error = 0.02105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.29
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.079
Order of pole (three term test) = 7.964e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7822 1.437
h = 0.001 0.003
y[1] (numeric) = 0.0404936500015 0.186452984535
y[1] (closed_form) = 0.0404535196751 0.186457892263
absolute error = 4.043e-05
relative error = 0.02119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.289
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.119
Order of pole (three term test) = 1.888e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7812 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.0399719734677 0.186377286936
y[1] (closed_form) = 0.0399323498803 0.186381725891
absolute error = 3.987e-05
relative error = 0.02092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.29
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.898
Order of pole (three term test) = 1.359e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7811 1.444
h = 0.003 0.006
y[1] (numeric) = 0.0393715219738 0.186090374886
y[1] (closed_form) = 0.0393324595997 0.186094980867
absolute error = 3.933e-05
relative error = 0.02068 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.293
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.844
Order of pole (three term test) = 9.841e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7781 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.0382604273045 0.186077724877
y[1] (closed_form) = 0.0382206802976 0.186079865097
absolute error = 3.980e-05
relative error = 0.02095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.294
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.71
Order of pole (three term test) = 6.673e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.778 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.0375212447937 0.185706138608
y[1] (closed_form) = 0.0374816417369 0.185709928968
absolute error = 3.978e-05
relative error = 0.021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.297
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.379
Order of pole (three term test) = 1.250e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7779 1.458
h = 0.001 0.001
y[1] (numeric) = 0.0370776538259 0.185488616796
y[1] (closed_form) = 0.0370374643109 0.185492674676
absolute error = 4.039e-05
relative error = 0.02135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.299
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.083
Order of pole (three term test) = 8.793e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7769 1.459
h = 0.001 0.003
y[1] (numeric) = 0.0368552219686 0.185555979256
y[1] (closed_form) = 0.0368147901213 0.18556026494
absolute error = 4.066e-05
relative error = 0.02149 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.299
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.141
Order of pole (three term test) = 4.207e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7759 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.0363423523475 0.185467527787
y[1] (closed_form) = 0.0363024347399 0.185471370633
absolute error = 4.010e-05
relative error = 0.02122 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.3
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.911
Order of pole (three term test) = 4.635e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7758 1.466
h = 0.003 0.006
y[1] (numeric) = 0.0357573078326 0.185168579195
y[1] (closed_form) = 0.0357179357451 0.18517260572
absolute error = 3.958e-05
relative error = 0.02099 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.303
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.861
Order of pole (three term test) = 1.001e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7728 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.0346611118205 0.185126931988
y[1] (closed_form) = 0.0346211530441 0.185128512354
absolute error = 3.999e-05
relative error = 0.02123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.304
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.718
Order of pole (three term test) = 3.021e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7727 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.0339414151963 0.184740892012
y[1] (closed_form) = 0.0339015404781 0.1847440983
absolute error = 4.000e-05
relative error = 0.0213 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.307
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.385
Order of pole (three term test) = 1.813e-13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=881.5MB, alloc=44.3MB, time=11.32
x[1] = -1.7726 1.48
h = 0.001 0.001
y[1] (numeric) = 0.0335093646585 0.184514651759
y[1] (closed_form) = 0.0334689045958 0.184518100487
absolute error = 4.061e-05
relative error = 0.02165 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.309
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.088
Order of pole (three term test) = 6.866e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7716 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.0332881135208 0.184575317288
y[1] (closed_form) = 0.0332474075285 0.18457898138
absolute error = 4.087e-05
relative error = 0.02179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.309
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.533
Order of pole (three term test) = 9.460e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7715 1.485
h = 0.003 0.006
y[1] (numeric) = 0.0327157962193 0.184267105723
y[1] (closed_form) = 0.0326764058492 0.184270654606
absolute error = 3.955e-05
relative error = 0.02113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.312
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.875
Order of pole (three term test) = 1.145e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7685 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.0316333496934 0.184201512705
y[1] (closed_form) = 0.0315934542246 0.184202636463
absolute error = 3.991e-05
relative error = 0.02136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.313
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.724
Order of pole (three term test) = 8.479e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7684 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.030930707116 0.183804012752
y[1] (closed_form) = 0.0308908463819 0.183806739275
absolute error = 3.995e-05
relative error = 0.02144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.316
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.39
Order of pole (three term test) = 3.445e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7683 1.499
h = 0.001 0.001
y[1] (numeric) = 0.0305087623958 0.18357085078
y[1] (closed_form) = 0.0304683184098 0.183573798671
absolute error = 4.055e-05
relative error = 0.02179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.318
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 8.361e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7673 1.5
h = 0.001 0.003
y[1] (numeric) = 0.0302887733259 0.183625897345
y[1] (closed_form) = 0.030248080953 0.183629049959
absolute error = 4.081e-05
relative error = 0.02193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.318
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.183
Order of pole (three term test) = 1.545e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7663 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.0297931741689 0.183515241844
y[1] (closed_form) = 0.0297530062949 0.183517999223
absolute error = 4.026e-05
relative error = 0.02166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.319
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.935
Order of pole (three term test) = 9.881e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7662 1.507
h = 0.003 0.006
y[1] (numeric) = 0.0292372823139 0.183196067036
y[1] (closed_form) = 0.0291976296513 0.183199036097
absolute error = 3.976e-05
relative error = 0.02143 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.322
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.892
Order of pole (three term test) = 1.281e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7632 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.0281710540892 0.183103408968
y[1] (closed_form) = 0.0281309885012 0.183103979313
absolute error = 4.007e-05
relative error = 0.02163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.323
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.732
Order of pole (three term test) = 1.369e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7631 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.0274881363837 0.182693179085
y[1] (closed_form) = 0.0274480501295 0.18269532436
absolute error = 4.014e-05
relative error = 0.02173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.327
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.396
Order of pole (three term test) = 1.019e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.763 1.521
h = 0.001 0.001
y[1] (numeric) = 0.0270778822685 0.182452323429
y[1] (closed_form) = 0.0270372157791 0.182454666169
absolute error = 4.073e-05
relative error = 0.02208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.328
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.097
Order of pole (three term test) = 1.044e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.762 1.522
h = 0.001 0.003
y[1] (numeric) = 0.026859453375 0.182500977823
y[1] (closed_form) = 0.0268185360252 0.182503513107
absolute error = 4.100e-05
relative error = 0.02222 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.328
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.206
Order of pole (three term test) = 8.688e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.761 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.0263734030541 0.182379092358
y[1] (closed_form) = 0.0263330141467 0.182381257456
absolute error = 4.045e-05
relative error = 0.02195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.33
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.948
Order of pole (three term test) = 1.129e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7609 1.529
h = 0.003 0.006
y[1] (numeric) = 0.0258332338091 0.182049993814
y[1] (closed_form) = 0.0257933435393 0.182052384269
absolute error = 3.996e-05
relative error = 0.02173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.332
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.91
Order of pole (three term test) = 1.492e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7579 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.0247838535556 0.181931313971
y[1] (closed_form) = 0.0247436393122 0.181931335428
absolute error = 4.021e-05
relative error = 0.0219 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.334
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.74
Order of pole (three term test) = 1.106e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7578 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.0241207346814 0.181509257275
y[1] (closed_form) = 0.0240804468176 0.181510824119
absolute error = 4.032e-05
relative error = 0.02202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.337
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.403
Order of pole (three term test) = 1.648e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7577 1.543
h = 0.001 0.001
y[1] (numeric) = 0.0237222194258 0.181261245044
y[1] (closed_form) = 0.0236813552843 0.181262986125
absolute error = 4.090e-05
relative error = 0.02237 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.339
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.102
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7567 1.544
h = 0.001 0.003
y[1] (numeric) = 0.0235055391138 0.181303676728
y[1] (closed_form) = 0.0234644222092 0.18130559835
absolute error = 4.116e-05
relative error = 0.02252 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.339
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.23
Order of pole (three term test) = 4.969e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7557 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.0230292443893 0.181171090294
y[1] (closed_form) = 0.0229886587227 0.18117266637
absolute error = 4.062e-05
relative error = 0.02224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.34
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.961
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=928.4MB, alloc=44.3MB, time=11.92
x[1] = -1.7556 1.551
h = 0.003 0.006
y[1] (numeric) = 0.0225048463528 0.180832782144
y[1] (closed_form) = 0.0224647425549 0.180834596241
absolute error = 4.014e-05
relative error = 0.02203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.343
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.927
Order of pole (three term test) = 6.698e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7526 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.0214728852436 0.180689126529
y[1] (closed_form) = 0.0214325431249 0.180688604399
absolute error = 4.035e-05
relative error = 0.02217 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.344
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.748
Order of pole (three term test) = 7.602e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7525 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.02082959939 0.180256128463
y[1] (closed_form) = 0.0207891331612 0.180257120641
absolute error = 4.048e-05
relative error = 0.02231 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.348
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.409
Order of pole (three term test) = 4.221e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7524 1.565
h = 0.001 0.001
y[1] (numeric) = 0.0204428475491 0.180001486429
y[1] (closed_form) = 0.0204018098809 0.180002630318
absolute error = 4.105e-05
relative error = 0.02266 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.349
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.107
Order of pole (three term test) = 1.223e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7514 1.566
h = 0.001 0.003
y[1] (numeric) = 0.0202280927622 0.180037868876
y[1] (closed_form) = 0.0201868009742 0.180039181502
absolute error = 4.131e-05
relative error = 0.0228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.349
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.253
Order of pole (three term test) = 5.693e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7504 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.0197617333924 0.179895106953
y[1] (closed_form) = 0.0197209745428 0.179896098219
absolute error = 4.077e-05
relative error = 0.02253 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.351
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.974
Order of pole (three term test) = 1.924e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7503 1.573
h = 0.003 0.006
y[1] (numeric) = 0.0192531240764 0.179548288863
y[1] (closed_form) = 0.0192128301878 0.179549529817
absolute error = 4.031e-05
relative error = 0.02232 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.353
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.945
Order of pole (three term test) = 8.253e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7473 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.0182390962751 0.17938070319
y[1] (closed_form) = 0.0181986463587 0.179379643496
absolute error = 4.046e-05
relative error = 0.02244 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.355
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.756
Order of pole (three term test) = 1.453e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7472 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.0176156398572 0.178937630025
y[1] (closed_form) = 0.0175750178131 0.178938052187
absolute error = 4.062e-05
relative error = 0.02259 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.358
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.416
Order of pole (three term test) = 4.842e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7471 1.587
h = 0.001 0.001
y[1] (numeric) = 0.017240653465 0.178676873725
y[1] (closed_form) = 0.0171994656406 0.178677425802
absolute error = 4.119e-05
relative error = 0.02295 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.112
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7461 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.0170279898051 0.178707383737
y[1] (closed_form) = 0.0169865470253 0.178708092965
absolute error = 4.145e-05
relative error = 0.02309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.678
Order of pole (three term test) = 4.100e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.746 1.592
h = 0.003 0.006
y[1] (numeric) = 0.016532296886 0.178354139513
y[1] (closed_form) = 0.0164920601097 0.17835494474
absolute error = 4.024e-05
relative error = 0.02247 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.363
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.961
Order of pole (three term test) = 1.084e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.743 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.0155343430294 0.178167011643
y[1] (closed_form) = 0.0154940178714 0.178165549829
absolute error = 4.035e-05
relative error = 0.02256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.365
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.763
Order of pole (three term test) = 3.284e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7429 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.0149280312589 0.177716179714
y[1] (closed_form) = 0.014887495025 0.177716170317
absolute error = 4.054e-05
relative error = 0.02273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.368
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.421
Order of pole (three term test) = 9.414e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7428 1.606
h = 0.001 0.001
y[1] (numeric) = 0.0145632221854 0.177450703906
y[1] (closed_form) = 0.0145221259022 0.177450806337
absolute error = 4.110e-05
relative error = 0.02308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.37
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.117
Order of pole (three term test) = 5.287e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7418 1.607
h = 0.001 0.003
y[1] (numeric) = 0.014352549599 0.17747633014
y[1] (closed_form) = 0.0143111981729 0.177476579941
absolute error = 4.135e-05
relative error = 0.02322 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.37
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.299
Order of pole (three term test) = 1.479e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7408 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.0139051741389 0.177316137626
y[1] (closed_form) = 0.0138643558099 0.177316109714
absolute error = 4.082e-05
relative error = 0.02295 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.371
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3
Order of pole (three term test) = 3.841e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7407 1.614
h = 0.003 0.006
y[1] (numeric) = 0.0134259731678 0.176955479701
y[1] (closed_form) = 0.0133855880367 0.176955720413
absolute error = 4.039e-05
relative error = 0.02276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.374
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.98
Order of pole (three term test) = 4.983e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7377 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.0124467509112 0.176746361889
y[1] (closed_form) = 0.0124063533079 0.176744375666
absolute error = 4.045e-05
relative error = 0.02283 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.376
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.771
Order of pole (three term test) = 1.888e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7376 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.0118601585645 0.176287010296
y[1] (closed_form) = 0.0118195064663 0.17628644194
absolute error = 4.066e-05
relative error = 0.02301 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.379
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.428
Order of pole (three term test) = 6.571e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=975.3MB, alloc=44.3MB, time=12.53
x[1] = -1.7375 1.628
h = 0.001 0.001
y[1] (numeric) = 0.0115070570804 0.176016346398
y[1] (closed_form) = 0.0114658519538 0.176015869485
absolute error = 4.121e-05
relative error = 0.02336 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.381
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.122
Order of pole (three term test) = 1.825e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7365 1.629
h = 0.001 0.003
y[1] (numeric) = 0.0112987519682 0.176036437477
y[1] (closed_form) = 0.011257291761 0.176036096815
absolute error = 4.146e-05
relative error = 0.0235 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.381
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.324
Order of pole (three term test) = 1.705e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7355 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.0108616794758 0.175867543695
y[1] (closed_form) = 0.0108207512364 0.175866947979
absolute error = 4.093e-05
relative error = 0.02323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.382
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.014
Order of pole (three term test) = 3.126e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7354 1.636
h = 0.003 0.006
y[1] (numeric) = 0.010398152292 0.175500286905
y[1] (closed_form) = 0.0103576402401 0.175499968761
absolute error = 4.051e-05
relative error = 0.02304 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.385
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.998
Order of pole (three term test) = 2.867e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7324 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.00943802208829 0.175270208451
y[1] (closed_form) = 0.00939757003111 0.175267705596
absolute error = 4.053e-05
relative error = 0.02309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.387
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.779
Order of pole (three term test) = 6.876e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7323 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.00887104895692 0.174803141419
y[1] (closed_form) = 0.00883030142589 0.174802020956
absolute error = 4.076e-05
relative error = 0.02329 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.39
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.435
Order of pole (three term test) = 5.074e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7322 1.65
h = 0.001 0.001
y[1] (numeric) = 0.00852959942741 0.174527768522
y[1] (closed_form) = 0.00848830654298 0.17452671989
absolute error = 4.131e-05
relative error = 0.02364 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.392
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.127
Order of pole (three term test) = 7.315e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7312 1.651
h = 0.001 0.003
y[1] (numeric) = 0.00832379589723 0.174542507126
y[1] (closed_form) = 0.00828224844137 0.174541583894
absolute error = 4.156e-05
relative error = 0.02378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.392
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.349
Order of pole (three term test) = 9.788e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7302 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.00789711105545 0.17436541283
y[1] (closed_form) = 0.00785609355168 0.174364256613
absolute error = 4.103e-05
relative error = 0.02351 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.394
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.029
Order of pole (three term test) = 5.695e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7301 1.658
h = 0.003 0.006
y[1] (numeric) = 0.00744917040401 0.173992191095
y[1] (closed_form) = 0.00740855212734 0.173991320498
absolute error = 4.063e-05
relative error = 0.02333 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.396
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.017
Order of pole (three term test) = 1.402e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7271 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.00650844250114 0.173742171137
y[1] (closed_form) = 0.00646795324136 0.173739159944
absolute error = 4.060e-05
relative error = 0.02335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.398
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.788
Order of pole (three term test) = 3.546e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.727 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.00596095841705 0.173268169456
y[1] (closed_form) = 0.00592013511797 0.173266504397
absolute error = 4.086e-05
relative error = 0.02357 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.402
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.442
Order of pole (three term test) = 1.182e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7269 1.672
h = 0.001 0.001
y[1] (numeric) = 0.00563108730541 0.172988552859
y[1] (closed_form) = 0.00558972692589 0.1729869408
absolute error = 4.139e-05
relative error = 0.02392 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.404
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.132
Order of pole (three term test) = 1.617e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7259 1.673
h = 0.001 0.003
y[1] (numeric) = 0.00542790889757 0.172998122639
y[1] (closed_form) = 0.00538629487684 0.172996625414
absolute error = 4.164e-05
relative error = 0.02406 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.404
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.375
Order of pole (three term test) = 2.259e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7249 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.00501167424412 0.172813319884
y[1] (closed_form) = 0.00497058732758 0.172811611125
absolute error = 4.112e-05
relative error = 0.02379 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.405
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.043
Order of pole (three term test) = 9.294e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7248 1.68
h = 0.003 0.006
y[1] (numeric) = 0.00457920958248 0.172434748286
y[1] (closed_form) = 0.00453850502396 0.172433332325
absolute error = 4.073e-05
relative error = 0.02361 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.408
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.037
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7218 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.00365814596947 0.17216579369
y[1] (closed_form) = 0.00361763601568 0.172162282919
absolute error = 4.066e-05
relative error = 0.02361 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.41
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.797
Order of pole (three term test) = 1.158e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7217 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.00312999280119 0.171685613961
y[1] (closed_form) = 0.00308911262261 0.171683412423
absolute error = 4.094e-05
relative error = 0.02384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.413
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.448
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7216 1.694
h = 0.001 0.001
y[1] (numeric) = 0.00281160984977 0.171402204718
y[1] (closed_form) = 0.00277020140705 0.171400038137
absolute error = 4.147e-05
relative error = 0.02419 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.415
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.138
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7206 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.0026111697991 0.171406789768
y[1] (closed_form) = 0.0025695090406 0.171404727749
absolute error = 4.171e-05
relative error = 0.02433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.415
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.834
Order of pole (three term test) = 8.776e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1022.1MB, alloc=44.3MB, time=13.12
x[1] = -1.7205 1.699
h = 0.003 0.006
y[1] (numeric) = 0.00219127136232 0.171024310172
y[1] (closed_form) = 0.00215068244621 0.17102250917
absolute error = 4.063e-05
relative error = 0.02375 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.418
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.054
Order of pole (three term test) = 1.033e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7175 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.00128751802691 0.170740090368
y[1] (closed_form) = 0.00124717686927 0.17073623587
absolute error = 4.052e-05
relative error = 0.02373 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.42
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.804
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7174 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.000775919531159 0.170255406952
y[1] (closed_form) = 0.000735179324543 0.170252829114
absolute error = 4.082e-05
relative error = 0.02398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.424
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.455
Order of pole (three term test) = 1.552e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7173 1.713
h = 0.001 0.001
y[1] (numeric) = 0.000467379160694 0.169969218263
y[1] (closed_form) = 0.000426118875314 0.169966660596
absolute error = 4.134e-05
relative error = 0.02432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.426
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.143
Order of pole (three term test) = 1.061e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7163 1.714
h = 0.001 0.003
y[1] (numeric) = 0.000269435606875 0.169969694275
y[1] (closed_form) = 0.00022792456095 0.169967232595
absolute error = 4.158e-05
relative error = 0.02447 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.426
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.424
Order of pole (three term test) = 7.413e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7153 1.717
h = 0.0001 0.004
y[1] (numeric) = -0.000127180214902 0.169771949698
y[1] (closed_form) = -0.000168171724898 0.169769314637
absolute error = 4.108e-05
relative error = 0.0242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.427
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.071
Order of pole (three term test) = 8.811e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7152 1.721
h = 0.003 0.006
y[1] (numeric) = -0.000531167746652 0.16938517382
y[1] (closed_form) = -0.000571807977094 0.169382842496
absolute error = 4.071e-05
relative error = 0.02403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.43
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.074
Order of pole (three term test) = 1.033e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7122 1.727
h = 0.0001 0.005
y[1] (numeric) = -0.00141490242858 0.169083855618
y[1] (closed_form) = -0.00145523565018 0.169079519097
absolute error = 4.057e-05
relative error = 0.02399 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.432
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.813
Order of pole (three term test) = 4.257e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7121 1.732
h = 0.0001 0.003
y[1] (numeric) = -0.00190754026819 0.168594333058
y[1] (closed_form) = -0.00194830440228 0.168591235469
absolute error = 4.088e-05
relative error = 0.02425 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.435
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.462
Order of pole (three term test) = 1.420e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.712 1.735
h = 0.001 0.001
y[1] (numeric) = -0.00220480591018 0.168305150415
y[1] (closed_form) = -0.00224608044514 0.168302056428
absolute error = 4.139e-05
relative error = 0.02459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.437
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.148
Order of pole (three term test) = 1.228e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.711 1.736
h = 0.001 0.003
y[1] (numeric) = -0.00239982903343 0.168300984808
y[1] (closed_form) = -0.0024413523396 0.168297977114
absolute error = 4.163e-05
relative error = 0.02473 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.437
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.45
Order of pole (three term test) = 1.717e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.71 1.739
h = 0.0001 0.004
y[1] (numeric) = -0.00278593396838 0.168096884511
y[1] (closed_form) = -0.00282694266541 0.168093723012
absolute error = 4.113e-05
relative error = 0.02447 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.439
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.086
Order of pole (three term test) = 6.321e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7099 1.743
h = 0.003 0.006
y[1] (numeric) = -0.00317488285764 0.167706407694
y[1] (closed_form) = -0.00321555667051 0.167703554788
absolute error = 4.077e-05
relative error = 0.02431 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.442
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.094
Order of pole (three term test) = 1.298e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7069 1.749
h = 0.0001 0.005
y[1] (numeric) = -0.00403846359224 0.167388952278
y[1] (closed_form) = -0.00407877448666 0.167384143562
absolute error = 4.060e-05
relative error = 0.02425 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.444
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.822
Order of pole (three term test) = 8.834e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7068 1.754
h = 0.0001 0.003
y[1] (numeric) = -0.00451236784766 0.166895274781
y[1] (closed_form) = -0.00455313926858 0.166891666982
absolute error = 4.093e-05
relative error = 0.02452 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.447
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.469
Order of pole (three term test) = 1.472e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7067 1.757
h = 0.001 0.001
y[1] (numeric) = -0.00479849030868 0.166603506545
y[1] (closed_form) = -0.00483976205644 0.166599886564
absolute error = 4.143e-05
relative error = 0.02486 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.154
Order of pole (three term test) = 2.847e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7057 1.758
h = 0.001 0.003
y[1] (numeric) = -0.00499050761654 0.166594881915
y[1] (closed_form) = -0.00503202582312 0.166591338852
absolute error = 4.167e-05
relative error = 0.025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.477
Order of pole (three term test) = 2.320e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7047 1.761
h = 0.0001 0.004
y[1] (numeric) = -0.00536611447181 0.166384877387
y[1] (closed_form) = -0.00540712362535 0.166381199416
absolute error = 4.117e-05
relative error = 0.02473 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.451
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.101
Order of pole (three term test) = 7.328e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7046 1.765
h = 0.003 0.006
y[1] (numeric) = -0.0057402103469 0.165991237489
y[1] (closed_form) = -0.00578090078784 0.165987872215
absolute error = 4.083e-05
relative error = 0.02458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.454
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.114
Order of pole (three term test) = 6.728e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7016 1.771
h = 0.0001 0.005
y[1] (numeric) = -0.00658354220889 0.165658587286
y[1] (closed_form) = -0.0066238171122 0.165653316493
absolute error = 4.062e-05
relative error = 0.0245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.456
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.831
Order of pole (three term test) = 7.236e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1069.0MB, alloc=44.3MB, time=13.73
x[1] = -1.7015 1.776
h = 0.0001 0.003
y[1] (numeric) = -0.00703896052444 0.165161413213
y[1] (closed_form) = -0.00707972337341 0.165157305146
absolute error = 4.097e-05
relative error = 0.02478 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.46
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.476
Order of pole (three term test) = 1.991e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7014 1.779
h = 0.001 0.001
y[1] (numeric) = -0.00731408369605 0.164867452489
y[1] (closed_form) = -0.00735533644952 0.164863317237
absolute error = 4.146e-05
relative error = 0.02512 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.462
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 3.303e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7004 1.78
h = 0.001 0.003
y[1] (numeric) = -0.00750301892628 0.164854550125
y[1] (closed_form) = -0.00754451552741 0.164850482739
absolute error = 4.170e-05
relative error = 0.02527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.462
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.504
Order of pole (three term test) = 6.926e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6994 1.783
h = 0.0001 0.004
y[1] (numeric) = -0.00786815746144 0.164639081051
y[1] (closed_form) = -0.00790915114498 0.16463489697
absolute error = 4.121e-05
relative error = 0.025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.463
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.117
Order of pole (three term test) = 2.168e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6993 1.787
h = 0.003 0.006
y[1] (numeric) = -0.0082276018331 0.164242795345
y[1] (closed_form) = -0.00826829272437 0.164238927346
absolute error = 4.087e-05
relative error = 0.02486 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.466
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.134
Order of pole (three term test) = 1.562e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6963 1.793
h = 0.0001 0.005
y[1] (numeric) = -0.00905062819219 0.163895872743
y[1] (closed_form) = -0.0090908541586 0.163890150244
absolute error = 4.063e-05
relative error = 0.02475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.468
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.84
Order of pole (three term test) = 8.403e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6962 1.798
h = 0.0001 0.003
y[1] (numeric) = -0.0094878269841 0.163395834456
y[1] (closed_form) = -0.00952856617909 0.16339123642
absolute error = 4.100e-05
relative error = 0.02505 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.472
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.484
Order of pole (three term test) = 7.149e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6961 1.801
h = 0.001 0.001
y[1] (numeric) = -0.00975210603471 0.163100058991
y[1] (closed_form) = -0.00979332440944 0.163095419539
absolute error = 4.148e-05
relative error = 0.02539 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.474
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.166
Order of pole (three term test) = 1.918e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6951 1.802
h = 0.0001 0.004
y[1] (numeric) = -0.0099378917125 0.163083058503
y[1] (closed_form) = -0.00997935104866 0.163078478194
absolute error = 4.171e-05
relative error = 0.02553 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.474
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7
Order of pole (three term test) = 1.059e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.695 1.806
h = 0.003 0.006
y[1] (numeric) = -0.0102855106481 0.162685001186
y[1] (closed_form) = -0.0103260435449 0.162680802747
absolute error = 4.075e-05
relative error = 0.025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.477
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.152
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.692 1.812
h = 0.0001 0.005
y[1] (numeric) = -0.0110908856179 0.162326757995
y[1] (closed_form) = -0.0111309142335 0.162320749962
absolute error = 4.048e-05
relative error = 0.02488 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.479
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.848
Order of pole (three term test) = 6.782e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6919 1.817
h = 0.0001 0.003
y[1] (numeric) = -0.0115126036824 0.161824953167
y[1] (closed_form) = -0.0115531651707 0.161820036413
absolute error = 4.086e-05
relative error = 0.02519 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.483
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.49
Order of pole (three term test) = 6.790e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6918 1.82
h = 0.001 0.001
y[1] (numeric) = -0.0117676647959 0.161528032837
y[1] (closed_form) = -0.0118086958667 0.16152306316
absolute error = 4.133e-05
relative error = 0.02552 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.485
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.171
Order of pole (three term test) = 6.923e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6908 1.821
h = 0.001 0.003
y[1] (numeric) = -0.0119506459254 0.161507685565
y[1] (closed_form) = -0.011991915172 0.161502767823
absolute error = 4.156e-05
relative error = 0.02566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.485
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.556
Order of pole (three term test) = 8.659e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6898 1.824
h = 0.0001 0.004
y[1] (numeric) = -0.0122963849644 0.161283299523
y[1] (closed_form) = -0.0123371642839 0.16127829704
absolute error = 4.109e-05
relative error = 0.0254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.486
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.146
Order of pole (three term test) = 8.592e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6897 1.828
h = 0.003 0.006
y[1] (numeric) = -0.0126291332388 0.160883564684
y[1] (closed_form) = -0.0126696386601 0.160878882607
absolute error = 4.078e-05
relative error = 0.02527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.489
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.173
Order of pole (three term test) = 2.072e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6867 1.834
h = 0.0001 0.005
y[1] (numeric) = -0.0134142025556 0.160512708063
y[1] (closed_form) = -0.0134541601469 0.160506268285
absolute error = 4.047e-05
relative error = 0.02513 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.492
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.858
Order of pole (three term test) = 7.889e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6866 1.839
h = 0.0001 0.003
y[1] (numeric) = -0.0138182476657 0.160009142751
y[1] (closed_form) = -0.0138587596068 0.160003756138
absolute error = 4.087e-05
relative error = 0.02545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.495
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6865 1.842
h = 0.001 0.001
y[1] (numeric) = -0.0140627839536 0.159711067491
y[1] (closed_form) = -0.0141037543134 0.159705615135
absolute error = 4.133e-05
relative error = 0.02578 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.497
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.177
Order of pole (three term test) = 5.696e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6855 1.843
h = 0.001 0.003
y[1] (numeric) = -0.0142425142617 0.159686951252
y[1] (closed_form) = -0.014283719464 0.159681542723
absolute error = 4.156e-05
relative error = 0.02592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.498
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.585
Order of pole (three term test) = 7.125e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6845 1.846
h = 0.0001 0.004
y[1] (numeric) = -0.0145779591414 0.159458288959
y[1] (closed_form) = -0.0146186819376 0.159452811911
absolute error = 4.109e-05
relative error = 0.02566 %
Correct digits = 4
memory used=1115.9MB, alloc=44.3MB, time=14.32
Radius of convergence (given) for eq 1 = 2.499
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.162
Order of pole (three term test) = 3.714e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6844 1.85
h = 0.003 0.006
y[1] (numeric) = -0.0148967129575 0.159057270966
y[1] (closed_form) = -0.0149371769222 0.159052115845
absolute error = 4.079e-05
relative error = 0.02553 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.502
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.195
Order of pole (three term test) = 1.348e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6814 1.856
h = 0.0001 0.005
y[1] (numeric) = -0.0156615179037 0.15867465989
y[1] (closed_form) = -0.0157013935156 0.158667799235
absolute error = 4.046e-05
relative error = 0.02538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.504
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.867
Order of pole (three term test) = 9.894e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6813 1.861
h = 0.0001 0.003
y[1] (numeric) = -0.0160482004408 0.158169891922
y[1] (closed_form) = -0.0160886499287 0.158164046509
absolute error = 4.087e-05
relative error = 0.02571 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.508
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.505
Order of pole (three term test) = 1.564e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6812 1.864
h = 0.001 0.001
y[1] (numeric) = -0.0162823935571 0.157870995413
y[1] (closed_form) = -0.0163232901175 0.157865072175
absolute error = 4.132e-05
relative error = 0.02604 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.51
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.183
Order of pole (three term test) = 6.633e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6802 1.865
h = 0.001 0.003
y[1] (numeric) = -0.0164588287638 0.157843283122
y[1] (closed_form) = -0.0164999566222 0.157837395934
absolute error = 4.155e-05
relative error = 0.02618 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.51
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.613
Order of pole (three term test) = 1.174e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6792 1.868
h = 0.0001 0.004
y[1] (numeric) = -0.0167840648415 0.15761073527
y[1] (closed_form) = -0.0168247182148 0.157604795091
absolute error = 4.109e-05
relative error = 0.02592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.512
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.178
Order of pole (three term test) = 1.209e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6791 1.872
h = 0.003 0.006
y[1] (numeric) = -0.0170890739216 0.157208871564
y[1] (closed_form) = -0.0171294831977 0.157203254244
absolute error = 4.080e-05
relative error = 0.0258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.515
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.216
Order of pole (three term test) = 1.412e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6761 1.878
h = 0.0001 0.005
y[1] (numeric) = -0.0178336861914 0.156815341442
y[1] (closed_form) = -0.0178734695364 0.156808070887
absolute error = 4.044e-05
relative error = 0.02562 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.517
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.877
Order of pole (three term test) = 1.207e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.676 1.883
h = 0.0001 0.003
y[1] (numeric) = -0.0182033289134 0.156309902935
y[1] (closed_form) = -0.0182437037789 0.156303609969
absolute error = 4.086e-05
relative error = 0.02597 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.521
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.513
Order of pole (three term test) = 1.430e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6759 1.886
h = 0.001 0.001
y[1] (numeric) = -0.0184273679949 0.156010503646
y[1] (closed_form) = -0.0184681784414 0.156004121496
absolute error = 4.131e-05
relative error = 0.02629 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.523
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.189
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6749 1.887
h = 0.001 0.003
y[1] (numeric) = -0.0186004712559 0.155979365375
y[1] (closed_form) = -0.0186415092659 0.155973011828
absolute error = 4.153e-05
relative error = 0.02644 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.523
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.642
Order of pole (three term test) = 6.841e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6739 1.89
h = 0.0001 0.004
y[1] (numeric) = -0.0189155959135 0.155743309476
y[1] (closed_form) = -0.0189561677169 0.155736917778
absolute error = 4.107e-05
relative error = 0.02618 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.525
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.195
Order of pole (three term test) = 1.261e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6738 1.894
h = 0.003 0.006
y[1] (numeric) = -0.0192071194332 0.155341017133
y[1] (closed_form) = -0.0192474615261 0.155334948669
absolute error = 4.080e-05
relative error = 0.02606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.528
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.238
Order of pole (three term test) = 3.276e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6708 1.9
h = 0.0001 0.005
y[1] (numeric) = -0.0199316391653 0.154937379213
y[1] (closed_form) = -0.0199713206074 0.154929709814
absolute error = 4.042e-05
relative error = 0.02587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.53
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.886
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6707 1.905
h = 0.0001 0.003
y[1] (numeric) = -0.0202845757067 0.154431776836
y[1] (closed_form) = -0.0203248645023 0.154425047716
absolute error = 4.085e-05
relative error = 0.02622 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.534
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.521
Order of pole (three term test) = 5.897e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6706 1.908
h = 0.001 0.001
y[1] (numeric) = -0.0204986564817 0.15413217817
y[1] (closed_form) = -0.0205393692574 0.154125349215
absolute error = 4.128e-05
relative error = 0.02655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.536
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.195
Order of pole (three term test) = 5.705e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6696 1.909
h = 0.0001 0.004
y[1] (numeric) = -0.0206683980351 0.154097780918
y[1] (closed_form) = -0.0207093344697 0.154090973446
absolute error = 4.150e-05
relative error = 0.02669 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.536
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.175
Order of pole (three term test) = 4.985e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6695 1.913
h = 0.003 0.006
y[1] (numeric) = -0.0209490913935 0.15369545422
y[1] (closed_form) = -0.0209892476217 0.153689110003
absolute error = 4.065e-05
relative error = 0.02621 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.539
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.257
Order of pole (three term test) = 5.931e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6665 1.919
h = 0.0001 0.005
y[1] (numeric) = -0.0216563089121 0.153283983898
y[1] (closed_form) = -0.0216957774457 0.153276084039
absolute error = 4.025e-05
relative error = 0.026 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.542
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.895
Order of pole (three term test) = 1.459e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6664 1.924
h = 0.0001 0.003
y[1] (numeric) = -0.0219951455368 0.152778820424
y[1] (closed_form) = -0.0220352332185 0.152771828894
absolute error = 4.069e-05
relative error = 0.02636 %
Correct digits = 4
memory used=1162.6MB, alloc=44.3MB, time=14.92
Radius of convergence (given) for eq 1 = 2.545
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.528
Order of pole (three term test) = 6.754e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6663 1.927
h = 0.001 0.001
y[1] (numeric) = -0.0222008179382 0.152479397079
y[1] (closed_form) = -0.022241319437 0.152472297238
absolute error = 4.112e-05
relative error = 0.02669 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.548
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.2
Order of pole (three term test) = 9.526e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6653 1.928
h = 0.001 0.003
y[1] (numeric) = -0.0223676109855 0.152442366234
y[1] (closed_form) = -0.022408332581 0.152435282055
absolute error = 4.133e-05
relative error = 0.02683 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.548
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.697
Order of pole (three term test) = 6.634e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6643 1.931
h = 0.0001 0.004
y[1] (numeric) = -0.0226641853189 0.152200859078
y[1] (closed_form) = -0.0227044570831 0.152193762446
absolute error = 4.089e-05
relative error = 0.02657 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.549
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.226
Order of pole (three term test) = 3.770e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6642 1.935
h = 0.003 0.006
y[1] (numeric) = -0.0229313383831 0.15179896342
y[1] (closed_form) = -0.0229714062293 0.151792189187
absolute error = 4.064e-05
relative error = 0.02647 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.552
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.279
Order of pole (three term test) = 6.195e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6612 1.941
h = 0.0001 0.005
y[1] (numeric) = -0.0236187278072 0.151378827098
y[1] (closed_form) = -0.0236580783156 0.151370549174
absolute error = 4.021e-05
relative error = 0.02625 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.555
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.905
Order of pole (three term test) = 1.671e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6611 1.946
h = 0.0001 0.003
y[1] (numeric) = -0.023941508498 0.150874371767
y[1] (closed_form) = -0.0239814908128 0.150866965693
absolute error = 4.066e-05
relative error = 0.02662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.559
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.536
Order of pole (three term test) = 1.697e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.661 1.949
h = 0.001 0.001
y[1] (numeric) = -0.0241376046563 0.150575271707
y[1] (closed_form) = -0.0241779890793 0.150567747939
absolute error = 4.108e-05
relative error = 0.02694 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.561
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.206
Order of pole (three term test) = 1.169e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.66 1.95
h = 0.001 0.003
y[1] (numeric) = -0.0243010001531 0.150535283922
y[1] (closed_form) = -0.0243416005062 0.150527769297
absolute error = 4.129e-05
relative error = 0.02708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.561
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.726
Order of pole (three term test) = 9.674e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.659 1.953
h = 0.0001 0.004
y[1] (numeric) = -0.0245878036963 0.150291273564
y[1] (closed_form) = -0.0246279632926 0.150283759394
absolute error = 4.086e-05
relative error = 0.02683 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.563
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.242
Order of pole (three term test) = 1.970e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6589 1.957
h = 0.003 0.006
y[1] (numeric) = -0.0248422587476 0.149890028825
y[1] (closed_form) = -0.024882227748 0.149882836019
absolute error = 4.061e-05
relative error = 0.02673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.566
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.301
Order of pole (three term test) = 5.119e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6559 1.963
h = 0.0001 0.005
y[1] (numeric) = -0.0255099908157 0.149461966138
y[1] (closed_form) = -0.0255492154301 0.149453321266
absolute error = 4.017e-05
relative error = 0.02649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.568
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.915
Order of pole (three term test) = 1.381e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6558 1.968
h = 0.0001 0.003
y[1] (numeric) = -0.0258170723623 0.148958654751
y[1] (closed_form) = -0.025856939836 0.148950845766
absolute error = 4.063e-05
relative error = 0.02687 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.572
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 1.459e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6557 1.971
h = 0.001 0.001
y[1] (numeric) = -0.0260038021314 0.148660139393
y[1] (closed_form) = -0.0260440599855 0.148652203985
absolute error = 4.103e-05
relative error = 0.02719 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.574
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.213
Order of pole (three term test) = 8.491e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6547 1.972
h = 0.001 0.003
y[1] (numeric) = -0.0261637885952 0.14861735174
y[1] (closed_form) = -0.0262042580954 0.148609419273
absolute error = 4.124e-05
relative error = 0.02733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.574
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.756
Order of pole (three term test) = 9.008e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6537 1.975
h = 0.0001 0.004
y[1] (numeric) = -0.0264409564048 0.148371164114
y[1] (closed_form) = -0.0264809944328 0.148363244355
absolute error = 4.081e-05
relative error = 0.02708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.576
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.259
Order of pole (three term test) = 1.401e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6536 1.979
h = 0.003 0.006
y[1] (numeric) = -0.0266829983656 0.147970911239
y[1] (closed_form) = -0.0267228587334 0.147963311372
absolute error = 4.058e-05
relative error = 0.02699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.579
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.324
Order of pole (three term test) = 1.821e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6506 1.985
h = 0.0001 0.005
y[1] (numeric) = -0.0273312650964 0.147535636454
y[1] (closed_form) = -0.0273703565299 0.147526635724
absolute error = 4.011e-05
relative error = 0.02673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.582
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.925
Order of pole (three term test) = 5.110e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6505 1.99
h = 0.0001 0.003
y[1] (numeric) = -0.0276230100223 0.147033880946
y[1] (closed_form) = -0.027662753835 0.147025680708
absolute error = 4.058e-05
relative error = 0.02713 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.585
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6504 1.993
h = 0.001 0.001
y[1] (numeric) = -0.0278005867899 0.146736197558
y[1] (closed_form) = -0.0278407092635 0.146727862803
absolute error = 4.098e-05
relative error = 0.02744 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.588
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.219
Order of pole (three term test) = 7.383e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6494 1.994
h = 0.001 0.003
y[1] (numeric) = -0.0279571584764 0.146690763373
y[1] (closed_form) = -0.0279974882114 0.146682425668
absolute error = 4.118e-05
relative error = 0.02758 %
Correct digits = 4
memory used=1209.4MB, alloc=44.3MB, time=15.52
Radius of convergence (given) for eq 1 = 2.588
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.786
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6484 1.997
h = 0.0001 0.004
y[1] (numeric) = -0.0282248333314 0.146442711152
y[1] (closed_form) = -0.0282647410556 0.146434397765
absolute error = 4.076e-05
relative error = 0.02733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.589
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.276
Order of pole (three term test) = 3.813e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6483 2.001
h = 0.003 0.006
y[1] (numeric) = -0.0284547513905 0.146043772254
y[1] (closed_form) = -0.0284944939979 0.146035776883
absolute error = 4.054e-05
relative error = 0.02725 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.592
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.346
Order of pole (three term test) = 4.953e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6453 2.007
h = 0.0001 0.005
y[1] (numeric) = -0.0290837643608 0.145601974193
y[1] (closed_form) = -0.0291227158887 0.145592628649
absolute error = 4.006e-05
relative error = 0.02698 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.595
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.935
Order of pole (three term test) = 3.783e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6452 2.012
h = 0.0001 0.003
y[1] (numeric) = -0.0293605397578 0.145102163158
y[1] (closed_form) = -0.0294001517235 0.145093583322
absolute error = 4.053e-05
relative error = 0.02738 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.599
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.56
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6451 2.015
h = 0.001 0.001
y[1] (numeric) = -0.0295291797508 0.144805545161
y[1] (closed_form) = -0.0295691586923 0.144796823328
absolute error = 4.092e-05
relative error = 0.02769 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.601
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.226
Order of pole (three term test) = 8.644e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6441 2.016
h = 0.0001 0.004
y[1] (numeric) = -0.0296823363185 0.144757613926
y[1] (closed_form) = -0.0297225180521 0.144748883556
absolute error = 4.112e-05
relative error = 0.02783 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.601
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.36
Order of pole (three term test) = 1.512e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.644 2.02
h = 0.003 0.006
y[1] (numeric) = -0.0299025591688 0.144359994298
y[1] (closed_form) = -0.0299421002878 0.144351775184
absolute error = 4.039e-05
relative error = 0.02739 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.604
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.366
Order of pole (three term test) = 1.223e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.641 2.026
h = 0.0001 0.005
y[1] (numeric) = -0.0305151152624 0.143913338973
y[1] (closed_form) = -0.0305538486842 0.143903813074
absolute error = 3.989e-05
relative error = 0.02711 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.607
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.944
Order of pole (three term test) = 6.871e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6409 2.031
h = 0.0001 0.003
y[1] (numeric) = -0.0307793310602 0.143415667738
y[1] (closed_form) = -0.0308187303372 0.143406878054
absolute error = 4.037e-05
relative error = 0.02752 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.611
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.567
Order of pole (three term test) = 1.026e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6408 2.034
h = 0.001 0.001
y[1] (numeric) = -0.0309404696327 0.143120246289
y[1] (closed_form) = -0.0309802257932 0.143111308782
absolute error = 4.075e-05
relative error = 0.02783 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.613
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.231
Order of pole (three term test) = 9.928e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6398 2.035
h = 0.001 0.003
y[1] (numeric) = -0.0310906627938 0.143070322956
y[1] (closed_form) = -0.0311306177814 0.143061372398
absolute error = 4.095e-05
relative error = 0.02797 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.613
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.844
Order of pole (three term test) = 1.112e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6388 2.038
h = 0.0001 0.004
y[1] (numeric) = -0.0313410626443 0.142819697146
y[1] (closed_form) = -0.0313806137094 0.142810790729
absolute error = 4.054e-05
relative error = 0.02773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.615
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.309
Order of pole (three term test) = 5.129e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6387 2.042
h = 0.003 0.006
y[1] (numeric) = -0.0315492253692 0.142424134003
y[1] (closed_form) = -0.0315886335689 0.14241554099
absolute error = 4.033e-05
relative error = 0.02765 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.618
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.39
Order of pole (three term test) = 4.805e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6357 2.048
h = 0.0001 0.005
y[1] (numeric) = -0.0321429752961 0.141972166505
y[1] (closed_form) = -0.0321815578577 0.141962316209
absolute error = 3.982e-05
relative error = 0.02736 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.621
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.954
Order of pole (three term test) = 7.630e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6356 2.053
h = 0.0001 0.003
y[1] (numeric) = -0.0323929170846 0.141477098172
y[1] (closed_form) = -0.0324321710388 0.141467950563
absolute error = 4.031e-05
relative error = 0.02777 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.625
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.575
Order of pole (three term test) = 1.202e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6355 2.056
h = 0.001 0.001
y[1] (numeric) = -0.0325455289845 0.141183138107
y[1] (closed_form) = -0.032585128269 0.14117383628
absolute error = 4.068e-05
relative error = 0.02808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.627
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.238
Order of pole (three term test) = 1.565e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6345 2.057
h = 0.001 0.003
y[1] (numeric) = -0.0326923213193 0.141130985165
y[1] (closed_form) = -0.032732114847 0.141121665253
absolute error = 4.087e-05
relative error = 0.02821 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.627
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.875
Order of pole (three term test) = 1.629e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6335 2.06
h = 0.0001 0.004
y[1] (numeric) = -0.032933675599 0.140879315139
y[1] (closed_form) = -0.0329730749936 0.140870049214
absolute error = 4.047e-05
relative error = 0.02798 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.629
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.327
Order of pole (three term test) = 4.251e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6334 2.064
h = 0.003 0.006
y[1] (numeric) = -0.0331305605053 0.140485883835
y[1] (closed_form) = -0.033169828435 0.140476928438
absolute error = 4.028e-05
relative error = 0.0279 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.632
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.413
Order of pole (three term test) = 7.811e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6304 2.07
h = 0.0001 0.005
y[1] (numeric) = -0.0337057625286 0.140029220328
y[1] (closed_form) = -0.033744189003 0.140019056425
absolute error = 3.975e-05
relative error = 0.0276 %
Correct digits = 4
memory used=1256.2MB, alloc=44.3MB, time=16.11
Radius of convergence (given) for eq 1 = 2.635
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.964
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6303 2.075
h = 0.0001 0.003
y[1] (numeric) = -0.0339418043813 0.139537079872
y[1] (closed_form) = -0.033980906527 0.139527585842
absolute error = 4.024e-05
relative error = 0.02802 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.639
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.584
Order of pole (three term test) = 1.417e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6302 2.078
h = 0.001 0.001
y[1] (numeric) = -0.034086110332 0.139244776849
y[1] (closed_form) = -0.0341255463518 0.139235122758
absolute error = 4.060e-05
relative error = 0.02832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.641
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 1.371e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6292 2.079
h = 0.001 0.003
y[1] (numeric) = -0.0342295151184 0.139190532232
y[1] (closed_form) = -0.0342691407535 0.139180855307
absolute error = 4.079e-05
relative error = 0.02846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.641
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.906
Order of pole (three term test) = 1.920e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6282 2.082
h = 0.0001 0.004
y[1] (numeric) = -0.034461989167 0.138938080673
y[1] (closed_form) = -0.0345012305222 0.138928466996
absolute error = 4.040e-05
relative error = 0.02822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.643
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.344
Order of pole (three term test) = 4.985e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6281 2.086
h = 0.003 0.006
y[1] (numeric) = -0.0346478936735 0.13854703481
y[1] (closed_form) = -0.0346870145646 0.138537728486
absolute error = 4.021e-05
relative error = 0.02816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.646
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.436
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6251 2.092
h = 0.0001 0.005
y[1] (numeric) = -0.0352048195478 0.138086266466
y[1] (closed_form) = -0.0352430851935 0.13807579963
absolute error = 3.967e-05
relative error = 0.02784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.649
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.975
Order of pole (three term test) = 7.005e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.625 2.097
h = 0.0001 0.003
y[1] (numeric) = -0.0354273362427 0.137597357834
y[1] (closed_form) = -0.035466280648 0.137587528795
absolute error = 4.017e-05
relative error = 0.02827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.653
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.592
Order of pole (three term test) = 1.158e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6249 2.1
h = 0.001 0.001
y[1] (numeric) = -0.0355635575033 0.137306895018
y[1] (closed_form) = -0.035602824442 0.137296900606
absolute error = 4.052e-05
relative error = 0.02857 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.655
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.251
Order of pole (three term test) = 3.201e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6239 2.101
h = 0.001 0.003
y[1] (numeric) = -0.0357035921977 0.137250692536
y[1] (closed_form) = -0.0357430440926 0.13724067082
absolute error = 4.070e-05
relative error = 0.0287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.655
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.938
Order of pole (three term test) = 5.116e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6229 2.104
h = 0.0001 0.004
y[1] (numeric) = -0.0359273555641 0.136997709664
y[1] (closed_form) = -0.0359664330706 0.136987759884
absolute error = 4.032e-05
relative error = 0.02847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.657
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.362
Order of pole (three term test) = 8.273e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6228 2.108
h = 0.003 0.006
y[1] (numeric) = -0.0361025774457 0.136609286297
y[1] (closed_form) = -0.0361415450906 0.136599640424
absolute error = 4.014e-05
relative error = 0.02841 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.66
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.46
Order of pole (three term test) = 1.075e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6198 2.114
h = 0.0001 0.005
y[1] (numeric) = -0.0366415110019 0.136144979573
y[1] (closed_form) = -0.0366796115426 0.136134220342
absolute error = 3.959e-05
relative error = 0.02808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.663
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.985
Order of pole (three term test) = 5.813e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6197 2.119
h = 0.0001 0.003
y[1] (numeric) = -0.0368508771759 0.135659586334
y[1] (closed_form) = -0.036889658441 0.135649433584
absolute error = 4.009e-05
relative error = 0.02852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.667
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.601
Order of pole (three term test) = 1.980e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6196 2.122
h = 0.001 0.001
y[1] (numeric) = -0.0369792350361 0.135371134778
y[1] (closed_form) = -0.0370183276266 0.135360811855
absolute error = 4.043e-05
relative error = 0.02881 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.669
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.258
Order of pole (three term test) = 3.945e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6186 2.123
h = 0.0001 0.004
y[1] (numeric) = -0.0371159209781 0.135313104085
y[1] (closed_form) = -0.037155193846 0.135302749658
absolute error = 4.061e-05
relative error = 0.02895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.67
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.553
Order of pole (three term test) = 1.039e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6185 2.127
h = 0.003 0.006
y[1] (numeric) = -0.0372826320291 0.134927006338
y[1] (closed_form) = -0.0373213924038 0.134917184275
absolute error = 3.999e-05
relative error = 0.02856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.673
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.481
Order of pole (three term test) = 8.746e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6155 2.133
h = 0.0001 0.005
y[1] (numeric) = -0.0378062804856 0.134460298388
y[1] (closed_form) = -0.0378441655697 0.134449402961
absolute error = 3.942e-05
relative error = 0.02822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.676
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.995
Order of pole (three term test) = 1.338e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6154 2.138
h = 0.0001 0.003
y[1] (numeric) = -0.0380046725463 0.133978293676
y[1] (closed_form) = -0.0380432388366 0.133967978394
absolute error = 3.992e-05
relative error = 0.02867 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.68
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 1.303e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6153 2.141
h = 0.001 0.001
y[1] (numeric) = -0.0381264652463 0.133691791451
y[1] (closed_form) = -0.0381653332828 0.133681302385
absolute error = 4.026e-05
relative error = 0.02896 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.682
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.264
Order of pole (three term test) = 4.324e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6143 2.142
h = 0.001 0.003
y[1] (numeric) = -0.0382602687825 0.133632327212
y[1] (closed_form) = -0.0382993130161 0.133621803293
absolute error = 4.044e-05
relative error = 0.02909 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.682
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.998
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1303.1MB, alloc=44.3MB, time=16.72
x[1] = -1.6133 2.145
h = 0.0001 0.004
y[1] (numeric) = -0.0384682868563 0.133379078807
y[1] (closed_form) = -0.0385069752196 0.133368641418
absolute error = 4.007e-05
relative error = 0.02887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.684
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.396
Order of pole (three term test) = 1.118e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6132 2.149
h = 0.003 0.006
y[1] (numeric) = -0.0386244590965 0.132996230633
y[1] (closed_form) = -0.0386630562273 0.132986089972
absolute error = 3.991e-05
relative error = 0.02882 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.687
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.505
Order of pole (three term test) = 1.072e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6102 2.155
h = 0.0001 0.005
y[1] (numeric) = -0.0391306770156 0.132526970055
y[1] (closed_form) = -0.0391683903283 0.132515801482
absolute error = 3.933e-05
relative error = 0.02846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.69
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.006
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6101 2.16
h = 0.0001 0.003
y[1] (numeric) = -0.0393166154834 0.132048952002
y[1] (closed_form) = -0.03935501006 0.132038333734
absolute error = 3.984e-05
relative error = 0.02891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.694
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.617
Order of pole (three term test) = 1.114e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.61 2.163
h = 0.001 0.001
y[1] (numeric) = -0.039430956768 0.131764745816
y[1] (closed_form) = -0.0394696421741 0.131753949851
absolute error = 4.016e-05
relative error = 0.0292 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.696
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.27
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.609 2.164
h = 0.001 0.003
y[1] (numeric) = -0.0395614620509 0.131703683169
y[1] (closed_form) = -0.039600318971 0.131692848635
absolute error = 4.034e-05
relative error = 0.02933 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.697
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.03
Order of pole (three term test) = 7.955e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.608 2.167
h = 0.0001 0.004
y[1] (numeric) = -0.0397612748072 0.131450550506
y[1] (closed_form) = -0.0397997857292 0.131439809656
absolute error = 3.998e-05
relative error = 0.02911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.698
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.414
Order of pole (three term test) = 1.000e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6079 2.171
h = 0.003 0.006
y[1] (numeric) = -0.0399076147914 0.1310709128
y[1] (closed_form) = -0.039946043957 0.131060464582
absolute error = 3.982e-05
relative error = 0.02907 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.702
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.529
Order of pole (three term test) = 4.826e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6049 2.177
h = 0.0001 0.005
y[1] (numeric) = -0.0403967130452 0.130599597209
y[1] (closed_form) = -0.0404342515293 0.130588165575
absolute error = 3.924e-05
relative error = 0.0287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.705
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.016
Order of pole (three term test) = 9.642e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6048 2.182
h = 0.0001 0.003
y[1] (numeric) = -0.0405705678056 0.130125794807
y[1] (closed_form) = -0.0406087866714 0.130114884442
absolute error = 3.975e-05
relative error = 0.02916 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.709
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.626
Order of pole (three term test) = 1.272e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6047 2.185
h = 0.001 0.001
y[1] (numeric) = -0.0406776764531 0.129844023252
y[1] (closed_form) = -0.0407161754037 0.129832931726
absolute error = 4.006e-05
relative error = 0.02944 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.711
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 4.220e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6037 2.186
h = 0.001 0.003
y[1] (numeric) = -0.0408049143389 0.129781479889
y[1] (closed_form) = -0.0408435801302 0.129770346324
absolute error = 4.024e-05
relative error = 0.02958 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.711
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.062
Order of pole (three term test) = 9.348e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6027 2.189
h = 0.0001 0.004
y[1] (numeric) = -0.0409967019102 0.129528667433
y[1] (closed_form) = -0.0410350315332 0.129517634203
absolute error = 3.989e-05
relative error = 0.02936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.713
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.433
Order of pole (three term test) = 1.211e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6026 2.193
h = 0.003 0.006
y[1] (numeric) = -0.0411335028882 0.129152418346
y[1] (closed_form) = -0.0411717598466 0.129141673466
absolute error = 3.974e-05
relative error = 0.02932 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.716
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.554
Order of pole (three term test) = 1.375e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5996 2.199
h = 0.0001 0.005
y[1] (numeric) = -0.0416057995814 0.128679522165
y[1] (closed_form) = -0.041643160569 0.128667837375
absolute error = 3.915e-05
relative error = 0.02895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.719
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.027
Order of pole (three term test) = 1.091e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5995 2.204
h = 0.0001 0.003
y[1] (numeric) = -0.0417679376779 0.128210146636
y[1] (closed_form) = -0.0418059772856 0.128198954894
absolute error = 3.965e-05
relative error = 0.02941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.723
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.635
Order of pole (three term test) = 5.127e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5994 2.207
h = 0.001 0.001
y[1] (numeric) = -0.0418680308805 0.127930937728
y[1] (closed_form) = -0.0419063400114 0.127919561788
absolute error = 3.996e-05
relative error = 0.02969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.726
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.284
Order of pole (three term test) = 7.016e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5984 2.208
h = 0.001 0.003
y[1] (numeric) = -0.0419920350625 0.127867027197
y[1] (closed_form) = -0.0420305063795 0.127855605986
absolute error = 4.013e-05
relative error = 0.02982 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.726
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.095
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5974 2.211
h = 0.0001 0.004
y[1] (numeric) = -0.0421759790866 0.127614728264
y[1] (closed_form) = -0.0422141240051 0.127603413554
absolute error = 3.979e-05
relative error = 0.0296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.728
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.451
Order of pole (three term test) = 1.382e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5973 2.215
h = 0.003 0.006
y[1] (numeric) = -0.0423035319193 0.127242031998
y[1] (closed_form) = -0.0423416128864 0.127231001192
absolute error = 3.965e-05
relative error = 0.02957 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.731
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.578
Order of pole (three term test) = 1.667e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1349.7MB, alloc=44.3MB, time=17.31
x[1] = -1.5943 2.221
h = 0.0001 0.005
y[1] (numeric) = -0.0427593512899 0.126768006938
y[1] (closed_form) = -0.0427965324834 0.126756078713
absolute error = 3.905e-05
relative error = 0.02919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.734
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.038
Order of pole (three term test) = 6.681e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5942 2.226
h = 0.0001 0.003
y[1] (numeric) = -0.0429101363561 0.126303252421
y[1] (closed_form) = -0.0429479935874 0.126291789842
absolute error = 3.955e-05
relative error = 0.02965 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.738
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.643
Order of pole (three term test) = 1.279e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5941 2.229
h = 0.001 0.001
y[1] (numeric) = -0.0430034293799 0.126026724001
y[1] (closed_form) = -0.0430415457658 0.126015074594
absolute error = 3.986e-05
relative error = 0.02993 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.291
Order of pole (three term test) = 5.833e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5931 2.23
h = 0.0001 0.004
y[1] (numeric) = -0.0431242361428 0.125961555735
y[1] (closed_form) = -0.0431625100871 0.125949858056
absolute error = 4.002e-05
relative error = 0.03006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.741
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.754
Order of pole (three term test) = 1.944e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.593 2.234
h = 0.003 0.006
y[1] (numeric) = -0.0432444456782 0.125591891417
y[1] (closed_form) = -0.0432823211191 0.12558072654
absolute error = 3.949e-05
relative error = 0.02973 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.744
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.6
Order of pole (three term test) = 3.842e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.59 2.24
h = 0.0001 0.005
y[1] (numeric) = -0.0436863389391 0.125117430335
y[1] (closed_form) = -0.0437233129471 0.12510540381
absolute error = 3.888e-05
relative error = 0.02934 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.747
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.048
Order of pole (three term test) = 1.471e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5899 2.245
h = 0.0001 0.003
y[1] (numeric) = -0.0438276977857 0.124656925766
y[1] (closed_form) = -0.0438653446817 0.124645342001
absolute error = 3.939e-05
relative error = 0.02981 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.751
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.651
Order of pole (three term test) = 1.121e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5898 2.248
h = 0.001 0.001
y[1] (numeric) = -0.0439153417798 0.124382869069
y[1] (closed_form) = -0.0439532390412 0.124371096642
absolute error = 3.968e-05
relative error = 0.03008 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.753
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.297
Order of pole (three term test) = 6.723e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5888 2.249
h = 0.001 0.003
y[1] (numeric) = -0.0440334138879 0.124316740162
y[1] (closed_form) = -0.0440714647198 0.124304917113
absolute error = 3.985e-05
relative error = 0.03021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.754
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.157
Order of pole (three term test) = 6.694e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5878 2.252
h = 0.0001 0.004
y[1] (numeric) = -0.0442032606446 0.124065962679
y[1] (closed_form) = -0.0442410031053 0.124054256262
absolute error = 3.952e-05
relative error = 0.03 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.755
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.487
Order of pole (three term test) = 5.218e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5877 2.256
h = 0.003 0.006
y[1] (numeric) = -0.044314415322 0.123700371019
y[1] (closed_form) = -0.0443521090014 0.123688939762
absolute error = 3.939e-05
relative error = 0.02998 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.759
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.625
Order of pole (three term test) = 6.779e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5847 2.262
h = 0.0001 0.005
y[1] (numeric) = -0.0447404521757 0.123225558923
y[1] (closed_form) = -0.0447772431466 0.123213306551
absolute error = 3.878e-05
relative error = 0.02958 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.762
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.059
Order of pole (three term test) = 5.193e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5846 2.267
h = 0.0001 0.003
y[1] (numeric) = -0.044871125685 0.12276998926
y[1] (closed_form) = -0.0449085855937 0.122758153785
absolute error = 3.929e-05
relative error = 0.03005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.766
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 1.029e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5845 2.27
h = 0.001 0.001
y[1] (numeric) = -0.0449523650279 0.122498804127
y[1] (closed_form) = -0.0449900653184 0.12248677806
absolute error = 3.957e-05
relative error = 0.03033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.768
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.304
Order of pole (three term test) = 1.276e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5835 2.271
h = 0.001 0.003
y[1] (numeric) = -0.0450673145245 0.122431609813
y[1] (closed_form) = -0.04510516383 0.122419530529
absolute error = 3.973e-05
relative error = 0.03045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.769
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.191
Order of pole (three term test) = 3.918e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5825 2.274
h = 0.0001 0.004
y[1] (numeric) = -0.0452298435479 0.122181837911
y[1] (closed_form) = -0.0452673939926 0.12216988014
absolute error = 3.941e-05
relative error = 0.03025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.77
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.505
Order of pole (three term test) = 1.650e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5824 2.278
h = 0.003 0.006
y[1] (numeric) = -0.0453325666652 0.121820193296
y[1] (closed_form) = -0.0453700759936 0.121808505871
absolute error = 3.929e-05
relative error = 0.03023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.774
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.65
Order of pole (three term test) = 5.945e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5794 2.284
h = 0.0001 0.005
y[1] (numeric) = -0.0457430831293 0.121345419797
y[1] (closed_form) = -0.0457796897213 0.121332950727
absolute error = 3.867e-05
relative error = 0.02982 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.777
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.07
Order of pole (three term test) = 6.111e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5793 2.289
h = 0.0001 0.003
y[1] (numeric) = -0.0458634223162 0.120894934113
y[1] (closed_form) = -0.0459006932316 0.1208828569
absolute error = 3.918e-05
relative error = 0.0303 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.781
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.669
Order of pole (three term test) = 2.059e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5792 2.292
h = 0.001 0.001
y[1] (numeric) = -0.0459384650418 0.120626711522
y[1] (closed_form) = -0.0459759665694 0.120614442138
absolute error = 3.946e-05
relative error = 0.03057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.783
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.311
Order of pole (three term test) = 1.316e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1396.5MB, alloc=44.3MB, time=17.92
x[1] = -1.5782 2.293
h = 0.001 0.003
y[1] (numeric) = -0.0460503343167 0.120558549688
y[1] (closed_form) = -0.0460879803507 0.120546224698
absolute error = 3.961e-05
relative error = 0.03069 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.784
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.224
Order of pole (three term test) = 1.847e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5772 2.296
h = 0.0001 0.004
y[1] (numeric) = -0.046205728877 0.12030993659
y[1] (closed_form) = -0.0462430854467 0.120297737575
absolute error = 3.930e-05
relative error = 0.03049 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.786
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.525
Order of pole (three term test) = 9.930e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5771 2.3
h = 0.003 0.006
y[1] (numeric) = -0.0463002981748 0.119952354476
y[1] (closed_form) = -0.0463376209417 0.119940420899
absolute error = 3.918e-05
relative error = 0.03047 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.789
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.675
Order of pole (three term test) = 6.996e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5741 2.306
h = 0.0001 0.005
y[1] (numeric) = -0.0466956327368 0.119477988587
y[1] (closed_form) = -0.0467320539087 0.119465311762
absolute error = 3.856e-05
relative error = 0.03006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.792
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.081
Order of pole (three term test) = 8.645e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.574 2.311
h = 0.0001 0.003
y[1] (numeric) = -0.04680598348 0.119032721475
y[1] (closed_form) = -0.0468430637478 0.119020412284
absolute error = 3.907e-05
relative error = 0.03055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.796
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.678
Order of pole (three term test) = 8.358e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5739 2.314
h = 0.001 0.001
y[1] (numeric) = -0.0468750346568 0.118767543771
y[1] (closed_form) = -0.0469123359866 0.118755041159
absolute error = 3.934e-05
relative error = 0.03081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.799
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.319
Order of pole (three term test) = 7.784e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5729 2.315
h = 0.001 0.003
y[1] (numeric) = -0.0469838678431 0.118698508387
y[1] (closed_form) = -0.047021309223 0.118685947979
absolute error = 3.949e-05
relative error = 0.03094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.799
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.258
Order of pole (three term test) = 2.171e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5719 2.318
h = 0.0001 0.004
y[1] (numeric) = -0.047132310754 0.118451197718
y[1] (closed_form) = -0.0471694719416 0.118438767352
absolute error = 3.919e-05
relative error = 0.03074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.801
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.544
Order of pole (three term test) = 6.339e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5718 2.322
h = 0.003 0.006
y[1] (numeric) = -0.0472189998191 0.11809778222
y[1] (closed_form) = -0.0472561341742 0.1180856123
absolute error = 3.908e-05
relative error = 0.03072 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.804
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.701
Order of pole (three term test) = 1.518e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5688 2.328
h = 0.0001 0.005
y[1] (numeric) = -0.0475994926273 0.117624172934
y[1] (closed_form) = -0.0476357276219 0.117611297084
absolute error = 3.845e-05
relative error = 0.03031 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.807
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.093
Order of pole (three term test) = 8.927e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5687 2.333
h = 0.0001 0.003
y[1] (numeric) = -0.0477001953276 0.117184245166
y[1] (closed_form) = -0.047737083626 0.117171713541
absolute error = 3.896e-05
relative error = 0.03079 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.811
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.687
Order of pole (three term test) = 1.333e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5686 2.336
h = 0.001 0.001
y[1] (numeric) = -0.0477634568519 0.116922186441
y[1] (closed_form) = -0.047800556886 0.116909460458
absolute error = 3.922e-05
relative error = 0.03105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.814
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.326
Order of pole (three term test) = 9.163e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5676 2.337
h = 0.0001 0.004
y[1] (numeric) = -0.0478692996313 0.116852367626
y[1] (closed_form) = -0.0479065353168 0.116839581845
absolute error = 3.937e-05
relative error = 0.03118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.814
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.962
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5675 2.341
h = 0.003 0.006
y[1] (numeric) = -0.0479497509869 0.116502441118
y[1] (closed_form) = -0.0479866870133 0.116490173456
absolute error = 3.892e-05
relative error = 0.03089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.817
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.723
Order of pole (three term test) = 9.497e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5645 2.347
h = 0.0001 0.005
y[1] (numeric) = -0.0483177559093 0.116029918978
y[1] (closed_form) = -0.0483537957451 0.116016976598
absolute error = 3.829e-05
relative error = 0.03047 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.821
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.103
Order of pole (three term test) = 7.281e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5644 2.352
h = 0.0001 0.003
y[1] (numeric) = -0.048410487388 0.115594783286
y[1] (closed_form) = -0.04844717486 0.115582165705
absolute error = 3.880e-05
relative error = 0.03096 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.825
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.695
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5643 2.355
h = 0.001 0.001
y[1] (numeric) = -0.0484689626959 0.115335528343
y[1] (closed_form) = -0.0485058540513 0.115322715941
absolute error = 3.905e-05
relative error = 0.03122 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.827
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.332
Order of pole (three term test) = 3.155e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5633 2.356
h = 0.001 0.003
y[1] (numeric) = -0.0485722611181 0.115265139312
y[1] (closed_form) = -0.0486092843674 0.115252265585
absolute error = 3.920e-05
relative error = 0.03134 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.827
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.322
Order of pole (three term test) = 1.539e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5623 2.359
h = 0.0001 0.004
y[1] (numeric) = -0.04870827144 0.115020680654
y[1] (closed_form) = -0.0487450314234 0.115007943428
absolute error = 3.890e-05
relative error = 0.03115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.829
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.58
Order of pole (three term test) = 5.445e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5622 2.363
h = 0.003 0.006
y[1] (numeric) = -0.0487810621627 0.114675345028
y[1] (closed_form) = -0.0488178073376 0.114662858723
absolute error = 3.881e-05
relative error = 0.03114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.833
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.749
Order of pole (three term test) = 1.500e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1443.2MB, alloc=44.3MB, time=18.52
x[1] = -1.5592 2.369
h = 0.0001 0.005
y[1] (numeric) = -0.0491348637658 0.1142041736
y[1] (closed_form) = -0.0491707168133 0.11419104787
absolute error = 3.818e-05
relative error = 0.03071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.836
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.114
Order of pole (three term test) = 3.834e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5591 2.374
h = 0.0001 0.003
y[1] (numeric) = -0.0492185660998 0.113774563495
y[1] (closed_form) = -0.0492550600731 0.113761740653
absolute error = 3.868e-05
relative error = 0.0312 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.84
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.705
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.559 2.377
h = 0.001 0.001
y[1] (numeric) = -0.0492716190516 0.11351854243
y[1] (closed_form) = -0.0493083080102 0.113505524362
absolute error = 3.893e-05
relative error = 0.03146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.843
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.339
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.558 2.378
h = 0.001 0.003
y[1] (numeric) = -0.049372016536 0.113447527083
y[1] (closed_form) = -0.0494088331112 0.113434446018
absolute error = 3.907e-05
relative error = 0.03158 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.843
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.357
Order of pole (three term test) = 1.322e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.557 2.381
h = 0.0001 0.004
y[1] (numeric) = -0.0495015942567 0.113204729578
y[1] (closed_form) = -0.0495381564267 0.113191788038
absolute error = 3.878e-05
relative error = 0.03139 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.845
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.6
Order of pole (three term test) = 6.875e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5569 2.385
h = 0.003 0.006
y[1] (numeric) = -0.0495672630917 0.112863797273
y[1] (closed_form) = -0.0496038164881 0.112851101513
absolute error = 3.870e-05
relative error = 0.03139 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.848
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.775
Order of pole (three term test) = 6.301e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5539 2.391
h = 0.0001 0.005
y[1] (numeric) = -0.0499072020746 0.112394271613
y[1] (closed_form) = -0.0499428682977 0.112380970644
absolute error = 3.807e-05
relative error = 0.03095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.852
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.126
Order of pole (three term test) = 9.077e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5538 2.396
h = 0.0001 0.003
y[1] (numeric) = -0.0499821983107 0.111970271908
y[1] (closed_form) = -0.0500184983127 0.111957252703
absolute error = 3.856e-05
relative error = 0.03145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.856
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.714
Order of pole (three term test) = 1.537e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5537 2.399
h = 0.001 0.001
y[1] (numeric) = -0.0500300207082 0.11171753733
y[1] (closed_form) = -0.0500665070287 0.111704322756
absolute error = 3.881e-05
relative error = 0.0317 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.858
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.347
Order of pole (three term test) = 1.571e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5527 2.4
h = 0.001 0.003
y[1] (numeric) = -0.0501275663397 0.111645975173
y[1] (closed_form) = -0.050164176069 0.111632696096
absolute error = 3.894e-05
relative error = 0.03182 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.858
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.392
Order of pole (three term test) = 7.371e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5517 2.403
h = 0.0001 0.004
y[1] (numeric) = -0.0502508896177 0.111404948523
y[1] (closed_form) = -0.0502872536459 0.111391811663
absolute error = 3.866e-05
relative error = 0.03164 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.619
Order of pole (three term test) = 1.634e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5516 2.407
h = 0.003 0.006
y[1] (numeric) = -0.0503096918189 0.111068484673
y[1] (closed_form) = -0.0503460527989 0.111055588424
absolute error = 3.858e-05
relative error = 0.03164 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.864
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.801
Order of pole (three term test) = 1.430e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5486 2.413
h = 0.0001 0.005
y[1] (numeric) = -0.0506361079216 0.110600882166
y[1] (closed_form) = -0.0506715875076 0.110587413849
absolute error = 3.795e-05
relative error = 0.0312 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.867
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.137
Order of pole (three term test) = 6.403e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5485 2.418
h = 0.0001 0.003
y[1] (numeric) = -0.0507027146678 0.110182566262
y[1] (closed_form) = -0.0507388204899 0.110169359363
absolute error = 3.845e-05
relative error = 0.0317 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.871
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.723
Order of pole (three term test) = 1.784e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5484 2.421
h = 0.001 0.001
y[1] (numeric) = -0.0507454945562 0.109933163958
y[1] (closed_form) = -0.0507817782626 0.109919761793
absolute error = 3.868e-05
relative error = 0.03194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.874
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.354
Order of pole (three term test) = 2.003e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5474 2.422
h = 0.001 0.003
y[1] (numeric) = -0.0508402383113 0.109861130951
y[1] (closed_form) = -0.0508766412915 0.109847662936
absolute error = 3.881e-05
relative error = 0.03206 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.874
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.427
Order of pole (three term test) = 9.928e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5464 2.425
h = 0.0001 0.004
y[1] (numeric) = -0.0509574835185 0.109621976862
y[1] (closed_form) = -0.0509936493391 0.10960865344
absolute error = 3.854e-05
relative error = 0.03188 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.876
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.639
Order of pole (three term test) = 6.290e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5463 2.429
h = 0.003 0.006
y[1] (numeric) = -0.0510096691932 0.109290037677
y[1] (closed_form) = -0.0510458373907 0.109276949676
absolute error = 3.846e-05
relative error = 0.03189 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.879
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.827
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5433 2.435
h = 0.0001 0.005
y[1] (numeric) = -0.0513229006353 0.108824618642
y[1] (closed_form) = -0.0513581939809 0.108810990651
absolute error = 3.783e-05
relative error = 0.03144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.883
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.149
Order of pole (three term test) = 9.316e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5432 2.44
h = 0.0001 0.003
y[1] (numeric) = -0.0513814278906 0.108412049123
y[1] (closed_form) = -0.0514173395724 0.108398662969
absolute error = 3.833e-05
relative error = 0.03194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.887
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.733
Order of pole (three term test) = 4.676e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1490.0MB, alloc=44.3MB, time=19.12
x[1] = -1.5431 2.443
h = 0.001 0.001
y[1] (numeric) = -0.0514193494541 0.108166018404
y[1] (closed_form) = -0.0514554308191 0.108152437315
absolute error = 3.855e-05
relative error = 0.03219 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.89
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.361
Order of pole (three term test) = 6.397e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5421 2.444
h = 0.0001 0.004
y[1] (numeric) = -0.0515113420537 0.108093587045
y[1] (closed_form) = -0.0515475386332 0.108079938911
absolute error = 3.868e-05
relative error = 0.03231 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.89
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.176
Order of pole (three term test) = 3.543e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.542 2.448
h = 0.003 0.006
y[1] (numeric) = -0.0515583059134 0.107765393819
y[1] (closed_form) = -0.0515942866805 0.107752238693
absolute error = 3.831e-05
relative error = 0.03207 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.893
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.85
Order of pole (three term test) = 1.922e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.539 2.454
h = 0.0001 0.005
y[1] (numeric) = -0.0518604876572 0.107302201733
y[1] (closed_form) = -0.0518956001332 0.107288533292
absolute error = 3.768e-05
relative error = 0.03162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.897
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.159
Order of pole (three term test) = 7.230e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5389 2.459
h = 0.0001 0.003
y[1] (numeric) = -0.0519123727195 0.10689471213
y[1] (closed_form) = -0.0519480962529 0.106881269373
absolute error = 3.817e-05
relative error = 0.03212 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.901
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.741
Order of pole (three term test) = 5.038e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5388 2.462
h = 0.001 0.001
y[1] (numeric) = -0.0519462975615 0.106651665305
y[1] (closed_form) = -0.0519821839128 0.106638028167
absolute error = 3.839e-05
relative error = 0.03236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.903
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.368
Order of pole (three term test) = 7.001e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5378 2.463
h = 0.001 0.003
y[1] (numeric) = -0.0520359595075 0.106578978475
y[1] (closed_form) = -0.0520719576299 0.106565273424
absolute error = 3.852e-05
relative error = 0.03248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.904
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.493
Order of pole (three term test) = 7.806e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5368 2.466
h = 0.0001 0.004
y[1] (numeric) = -0.0521423821081 0.106343620978
y[1] (closed_form) = -0.0521781585348 0.106330064055
absolute error = 3.826e-05
relative error = 0.0323 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.906
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.677
Order of pole (three term test) = 1.209e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5367 2.47
h = 0.003 0.006
y[1] (numeric) = -0.0521829585899 0.10602029412
y[1] (closed_form) = -0.0522187466592 0.106006962894
absolute error = 3.819e-05
relative error = 0.03232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.909
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.877
Order of pole (three term test) = 1.110e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5337 2.476
h = 0.0001 0.005
y[1] (numeric) = -0.0524725818877 0.105559722608
y[1] (closed_form) = -0.0525075094565 0.105545908182
absolute error = 3.756e-05
relative error = 0.03186 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.913
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.171
Order of pole (three term test) = 1.205e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5336 2.481
h = 0.0001 0.003
y[1] (numeric) = -0.0525169467109 0.105158065495
y[1] (closed_form) = -0.0525524768782 0.105144458561
absolute error = 3.805e-05
relative error = 0.03237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.917
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.751
Order of pole (three term test) = 8.451e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5335 2.484
h = 0.001 0.001
y[1] (numeric) = -0.0525463456912 0.104918445246
y[1] (closed_form) = -0.0525820309107 0.104904644649
absolute error = 3.826e-05
relative error = 0.03261 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.919
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.375
Order of pole (three term test) = 5.187e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5325 2.485
h = 0.001 0.003
y[1] (numeric) = -0.0526333531457 0.104845485445
y[1] (closed_form) = -0.0526691462257 0.104831615999
absolute error = 3.839e-05
relative error = 0.03272 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.92
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.528
Order of pole (three term test) = 1.207e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5315 2.488
h = 0.0001 0.004
y[1] (numeric) = -0.0527341915121 0.10461224817
y[1] (closed_form) = -0.0527697709438 0.104598528411
absolute error = 3.813e-05
relative error = 0.03255 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.922
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.697
Order of pole (three term test) = 1.007e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5314 2.492
h = 0.003 0.006
y[1] (numeric) = -0.0527688378461 0.104293558814
y[1] (closed_form) = -0.0528044335378 0.104280059571
absolute error = 3.807e-05
relative error = 0.03257 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.925
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.904
Order of pole (three term test) = 1.308e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5284 2.498
h = 0.0001 0.005
y[1] (numeric) = -0.0530462336846 0.103835822771
y[1] (closed_form) = -0.0530809772643 0.10382186941
absolute error = 3.744e-05
relative error = 0.03211 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.928
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.183
Order of pole (three term test) = 1.003e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5283 2.503
h = 0.0001 0.003
y[1] (numeric) = -0.0530833685692 0.103440032968
y[1] (closed_form) = -0.0531187060316 0.103426269632
absolute error = 3.792e-05
relative error = 0.03262 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.933
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.76
Order of pole (three term test) = 4.735e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5282 2.506
h = 0.001 0.001
y[1] (numeric) = -0.0531084143365 0.103203861974
y[1] (closed_form) = -0.0531438993165 0.103189905882
absolute error = 3.813e-05
relative error = 0.03285 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.935
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.383
Order of pole (three term test) = 6.605e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5272 2.507
h = 0.001 0.003
y[1] (numeric) = -0.0531928193776 0.103130692295
y[1] (closed_form) = -0.0532284083893 0.103116666548
absolute error = 3.825e-05
relative error = 0.03296 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.936
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.564
Order of pole (three term test) = 6.422e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5262 2.51
h = 0.0001 0.004
y[1] (numeric) = -0.0532882411333 0.102899649091
y[1] (closed_form) = -0.0533236243659 0.102885774332
absolute error = 3.801e-05
relative error = 0.0328 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.938
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.717
Order of pole (three term test) = 2.373e-14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1536.8MB, alloc=44.3MB, time=19.71
x[1] = -1.5261 2.514
h = 0.003 0.006
y[1] (numeric) = -0.0533171864699 0.102585623285
y[1] (closed_form) = -0.0533525903157 0.102571963878
absolute error = 3.795e-05
relative error = 0.03282 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.941
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.931
Order of pole (three term test) = 1.540e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5231 2.52
h = 0.0001 0.005
y[1] (numeric) = -0.0535826825604 0.102130922873
y[1] (closed_form) = -0.053617243228 0.102116837413
absolute error = 3.732e-05
relative error = 0.03236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.945
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.195
Order of pole (three term test) = 1.182e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.523 2.525
h = 0.0001 0.003
y[1] (numeric) = -0.0536128708047 0.101741026503
y[1] (closed_form) = -0.0536480164136 0.101727114309
absolute error = 3.780e-05
relative error = 0.03287 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.949
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.77
Order of pole (three term test) = 3.944e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5229 2.528
h = 0.001 0.001
y[1] (numeric) = -0.0536337319004 0.101508322226
y[1] (closed_form) = -0.053669017722 0.101494218357
absolute error = 3.800e-05
relative error = 0.0331 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.951
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.39
Order of pole (three term test) = 1.206e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5219 2.529
h = 0.001 0.003
y[1] (numeric) = -0.0537155868643 0.101435002654
y[1] (closed_form) = -0.0537509729719 0.101420828449
absolute error = 3.812e-05
relative error = 0.03321 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.952
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.6
Order of pole (three term test) = 5.349e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5209 2.532
h = 0.0001 0.004
y[1] (numeric) = -0.053805757021 0.101206220894
y[1] (closed_form) = -0.0538409450384 0.101192198733
absolute error = 3.788e-05
relative error = 0.03305 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.954
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.737
Order of pole (three term test) = 1.425e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5208 2.536
h = 0.003 0.006
y[1] (numeric) = -0.0538292249461 0.100896877888
y[1] (closed_form) = -0.0538644376747 0.100883065943
absolute error = 3.782e-05
relative error = 0.03307 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.957
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.958
Order of pole (three term test) = 9.072e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5178 2.542
h = 0.0001 0.005
y[1] (numeric) = -0.0540831453635 0.100445399124
y[1] (closed_form) = -0.0541175243431 0.10043118819
absolute error = 3.720e-05
relative error = 0.03261 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.961
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.207
Order of pole (three term test) = 1.420e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5177 2.547
h = 0.0001 0.003
y[1] (numeric) = -0.0541066632175 0.100061414118
y[1] (closed_form) = -0.0541416180012 0.100047360382
absolute error = 3.767e-05
relative error = 0.03312 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.965
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.78
Order of pole (three term test) = 4.646e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5176 2.55
h = 0.001 0.001
y[1] (numeric) = -0.0541235040449 0.0998321891018
y[1] (closed_form) = -0.054158591964 0.0998179449355
absolute error = 3.787e-05
relative error = 0.03335 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.967
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.398
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5166 2.551
h = 0.0001 0.004
y[1] (numeric) = -0.0542028614192 0.0997587766084
y[1] (closed_form) = -0.0542380459629 0.0997444615399
absolute error = 3.799e-05
relative error = 0.03346 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.968
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.397
Order of pole (three term test) = 3.936e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5165 2.555
h = 0.003 0.006
y[1] (numeric) = -0.0542220193581 0.0994532811579
y[1] (closed_form) = -0.054257057839 0.0994394273539
absolute error = 3.768e-05
relative error = 0.03326 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.971
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.981
Order of pole (three term test) = 6.279e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5135 2.561
h = 0.0001 0.005
y[1] (numeric) = -0.054466273454 0.0990048467747
y[1] (closed_form) = -0.0545004869689 0.0989906163703
absolute error = 3.705e-05
relative error = 0.03279 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.975
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.218
Order of pole (three term test) = 1.607e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5134 2.566
h = 0.0001 0.003
y[1] (numeric) = -0.0544843360345 0.0986260336475
y[1] (closed_form) = -0.0545191171728 0.0986119472657
absolute error = 3.753e-05
relative error = 0.0333 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.979
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.788
Order of pole (three term test) = 5.360e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5133 2.569
h = 0.001 0.001
y[1] (numeric) = -0.0544978863876 0.0983998552711
y[1] (closed_form) = -0.054532794767 0.0983855797293
absolute error = 3.771e-05
relative error = 0.03353 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.982
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.405
Order of pole (three term test) = 5.183e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5123 2.57
h = 0.001 0.003
y[1] (numeric) = -0.0545751357556 0.0983264350827
y[1] (closed_form) = -0.0546101376711 0.0983120882825
absolute error = 3.783e-05
relative error = 0.03364 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.982
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.668
Order of pole (three term test) = 7.269e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5113 2.573
h = 0.0001 0.004
y[1] (numeric) = -0.0546559922171 0.098102077745
y[1] (closed_form) = -0.0546908098703 0.0980878842676
absolute error = 3.760e-05
relative error = 0.03348 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.984
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.776
Order of pole (three term test) = 7.596e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5112 2.577
h = 0.003 0.006
y[1] (numeric) = -0.0546698998906 0.0978015371653
y[1] (closed_form) = -0.0547047491727 0.0977875443944
absolute error = 3.755e-05
relative error = 0.03352 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.987
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.008
Order of pole (three term test) = 1.395e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5082 2.583
h = 0.0001 0.005
y[1] (numeric) = -0.0549031724154 0.0973566311444
y[1] (closed_form) = -0.0549372069464 0.0973422870168
absolute error = 3.693e-05
relative error = 0.03304 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.991
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.23
Order of pole (three term test) = 3.785e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5081 2.588
h = 0.0001 0.003
y[1] (numeric) = -0.0549150598145 0.0969837395117
y[1] (closed_form) = -0.0549496525484 0.0969695245852
absolute error = 3.740e-05
relative error = 0.03356 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.995
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.798
Order of pole (three term test) = 1.263e-13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1583.5MB, alloc=44.3MB, time=20.31
x[1] = -1.508 2.591
h = 0.001 0.001
y[1] (numeric) = -0.0549248847719 0.0967610497977
y[1] (closed_form) = -0.0549595980879 0.0967466472209
absolute error = 3.758e-05
relative error = 0.03378 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.998
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.412
Order of pole (three term test) = 1.365e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.507 2.592
h = 0.001 0.003
y[1] (numeric) = -0.0549997348849 0.0966876343735
y[1] (closed_form) = -0.0550345382358 0.0966731601718
absolute error = 3.769e-05
relative error = 0.03388 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.998
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.704
Order of pole (three term test) = 1.211e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.506 2.595
h = 0.0001 0.004
y[1] (numeric) = -0.0550757969515 0.0964656962105
y[1] (closed_form) = -0.0551104232028 0.0964513757674
absolute error = 3.747e-05
relative error = 0.03373 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.796
Order of pole (three term test) = 3.325e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5059 2.599
h = 0.003 0.006
y[1] (numeric) = -0.0550848358808 0.0961698570368
y[1] (closed_form) = -0.05511949718 0.0961557322772
absolute error = 3.743e-05
relative error = 0.03377 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.004
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.036
Order of pole (three term test) = 1.350e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5029 2.605
h = 0.0001 0.005
y[1] (numeric) = -0.0553074386734 0.0957286281372
y[1] (closed_form) = -0.0553412958025 0.0957141763162
absolute error = 3.681e-05
relative error = 0.0333 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.007
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.242
Order of pole (three term test) = 3.153e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5028 2.61
h = 0.0001 0.003
y[1] (numeric) = -0.0553134068194 0.0953616552188
y[1] (closed_form) = -0.0553478126106 0.0953473184209
absolute error = 3.727e-05
relative error = 0.03381 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.012
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.808
Order of pole (three term test) = 1.051e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5027 2.613
h = 0.001 0.001
y[1] (numeric) = -0.0553196588354 0.0951424542624
y[1] (closed_form) = -0.0553541787694 0.0951279314518
absolute error = 3.745e-05
relative error = 0.03403 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.014
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.42
Order of pole (three term test) = 1.017e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5017 2.614
h = 0.001 0.003
y[1] (numeric) = -0.0553921620591 0.0950690924721
y[1] (closed_form) = -0.0554267686128 0.0950544977689
absolute error = 3.756e-05
relative error = 0.03413 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.015
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.741
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5007 2.617
h = 0.0001 0.004
y[1] (numeric) = -0.0554635836133 0.0948496185907
y[1] (closed_form) = -0.055498020046 0.0948351778887
absolute error = 3.734e-05
relative error = 0.03398 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.017
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.817
Order of pole (three term test) = 5.269e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5006 2.621
h = 0.003 0.006
y[1] (numeric) = -0.0554679556747 0.094558477511
y[1] (closed_form) = -0.0555024303541 0.0945442275197
absolute error = 3.730e-05
relative error = 0.03403 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.02
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.063
Order of pole (three term test) = 8.548e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4976 2.627
h = 0.0001 0.005
y[1] (numeric) = -0.0556801958638 0.0941210625188
y[1] (closed_form) = -0.0557138772794 0.094106508833
absolute error = 3.669e-05
relative error = 0.03355 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.024
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.254
Order of pole (three term test) = 4.121e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4975 2.632
h = 0.0001 0.003
y[1] (numeric) = -0.0556804936402 0.0937599991328
y[1] (closed_form) = -0.0557147140803 0.0937455469182
absolute error = 3.715e-05
relative error = 0.03406 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.028
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.818
Order of pole (three term test) = 8.756e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4974 2.635
h = 0.001 0.001
y[1] (numeric) = -0.0556833210218 0.0935442831753
y[1] (closed_form) = -0.0557176493817 0.0935296467028
absolute error = 3.732e-05
relative error = 0.03428 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.031
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.428
Order of pole (three term test) = 8.465e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4964 2.636
h = 0.001 0.003
y[1] (numeric) = -0.0557535295303 0.093471021237
y[1] (closed_form) = -0.055787941181 0.0934563126972
absolute error = 3.742e-05
relative error = 0.03438 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.031
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.778
Order of pole (three term test) = 3.562e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4954 2.639
h = 0.0001 0.004
y[1] (numeric) = -0.0558204614026 0.0932540516333
y[1] (closed_form) = -0.055854709727 0.0932394971555
absolute error = 3.721e-05
relative error = 0.03424 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.033
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.838
Order of pole (three term test) = 6.937e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4953 2.643
h = 0.003 0.006
y[1] (numeric) = -0.0558203628929 0.092967600342
y[1] (closed_form) = -0.0558546524512 0.0929532316575
absolute error = 3.718e-05
relative error = 0.03428 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.037
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.091
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4923 2.649
h = 0.0001 0.005
y[1] (numeric) = -0.0560225426893 0.0925341246033
y[1] (closed_form) = -0.0560560501772 0.0925194746829
absolute error = 3.657e-05
relative error = 0.03381 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.04
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.267
Order of pole (three term test) = 5.320e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4922 2.654
h = 0.0001 0.003
y[1] (numeric) = -0.0560174119731 0.0921789555869
y[1] (closed_form) = -0.0560514487725 0.0921643941948
absolute error = 3.702e-05
relative error = 0.03432 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.045
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.827
Order of pole (three term test) = 1.051e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4921 2.657
h = 0.001 0.001
y[1] (numeric) = -0.0560169588998 0.0919667172658
y[1] (closed_form) = -0.056051097609 0.0919519734775
absolute error = 3.719e-05
relative error = 0.03453 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.047
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.436
Order of pole (three term test) = 1.041e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4911 2.658
h = 0.0001 0.004
y[1] (numeric) = -0.0560849246025 0.0918935988385
y[1] (closed_form) = -0.0561191433596 0.0918787828957
absolute error = 3.729e-05
relative error = 0.03463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.048
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.623
Order of pole (three term test) = 1.019e-13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1630.3MB, alloc=44.3MB, time=20.90
x[1] = -1.491 2.662
h = 0.003 0.006
y[1] (numeric) = -0.0560813192328 0.0916109800482
y[1] (closed_form) = -0.0561154489121 0.0915965899482
absolute error = 3.704e-05
relative error = 0.03448 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.051
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.115
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.488 2.668
h = 0.0001 0.005
y[1] (numeric) = -0.0562751262454 0.0911811021451
y[1] (closed_form) = -0.0563084839444 0.0911664492927
absolute error = 3.643e-05
relative error = 0.034 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.055
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.277
Order of pole (three term test) = 7.131e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4879 2.673
h = 0.0001 0.003
y[1] (numeric) = -0.0562655811036 0.0908310512678
y[1] (closed_form) = -0.0562994595646 0.0908164763931
absolute error = 3.688e-05
relative error = 0.03452 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.059
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.836
Order of pole (three term test) = 3.566e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4878 2.676
h = 0.001 0.001
y[1] (numeric) = -0.0562624578919 0.0906218347259
y[1] (closed_form) = -0.0562964332804 0.090607079204
absolute error = 3.704e-05
relative error = 0.03472 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.062
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.443
Order of pole (three term test) = 1.172e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4868 2.677
h = 0.001 0.003
y[1] (numeric) = -0.0563285367492 0.0905488987833
y[1] (closed_form) = -0.0563625894634 0.0905340711347
absolute error = 3.714e-05
relative error = 0.03483 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.062
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.847
Order of pole (three term test) = 1.620e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4858 2.68
h = 0.0001 0.004
y[1] (numeric) = -0.0563875358786 0.0903367284551
y[1] (closed_form) = -0.0564214374191 0.0903220544611
absolute error = 3.694e-05
relative error = 0.03469 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.064
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.877
Order of pole (three term test) = 5.956e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4857 2.684
h = 0.003 0.006
y[1] (numeric) = -0.0563796775829 0.0900590139112
y[1] (closed_form) = -0.0564136253251 0.0900445166922
absolute error = 3.691e-05
relative error = 0.03474 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.068
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.143
Order of pole (three term test) = 7.729e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4827 2.69
h = 0.0001 0.005
y[1] (numeric) = -0.0565639740528 0.0896332763699
y[1] (closed_form) = -0.0565971614368 0.0896185372217
absolute error = 3.631e-05
relative error = 0.03426 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.072
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.29
Order of pole (three term test) = 4.198e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4826 2.695
h = 0.0001 0.003
y[1] (numeric) = -0.0565494316987 0.0892890744125
y[1] (closed_form) = -0.0565831300523 0.089274401385
absolute error = 3.675e-05
relative error = 0.03477 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.076
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.846
Order of pole (three term test) = 2.802e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4825 2.698
h = 0.001 0.001
y[1] (numeric) = -0.0565432852537 0.0890833114273
y[1] (closed_form) = -0.0565770749113 0.0890684597852
absolute error = 3.691e-05
relative error = 0.03498 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.078
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.45
Order of pole (three term test) = 1.353e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4815 2.699
h = 0.001 0.003
y[1] (numeric) = -0.0566072174179 0.0890105931272
y[1] (closed_form) = -0.0566410813189 0.0889956694186
absolute error = 3.701e-05
relative error = 0.03508 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.079
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.885
Order of pole (three term test) = 9.110e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4805 2.702
h = 0.0001 0.004
y[1] (numeric) = -0.0566621413635 0.0888010138775
y[1] (closed_form) = -0.0566958603623 0.0887862434281
absolute error = 3.681e-05
relative error = 0.03494 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.081
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.898
Order of pole (three term test) = 4.958e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4804 2.706
h = 0.003 0.006
y[1] (numeric) = -0.0566503433074 0.088527938561
y[1] (closed_form) = -0.0566841109374 0.0885133401524
absolute error = 3.679e-05
relative error = 0.035 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.084
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.171
Order of pole (three term test) = 6.433e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4774 2.712
h = 0.0001 0.005
y[1] (numeric) = -0.0568254163459 0.0881064368888
y[1] (closed_form) = -0.0568584354288 0.0880916165284
absolute error = 3.619e-05
relative error = 0.03452 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.088
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.302
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4773 2.717
h = 0.0001 0.003
y[1] (numeric) = -0.0568060988773 0.0877680538298
y[1] (closed_form) = -0.0568396191168 0.0877532882908
absolute error = 3.663e-05
relative error = 0.03503 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.093
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.856
Order of pole (three term test) = 1.655e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4772 2.72
h = 0.001 0.001
y[1] (numeric) = -0.0567970617141 0.0875657280677
y[1] (closed_form) = -0.0568306678357 0.0875507860272
absolute error = 3.678e-05
relative error = 0.03524 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.095
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.458
Order of pole (three term test) = 3.184e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4762 2.721
h = 0.001 0.003
y[1] (numeric) = -0.0568588979583 0.0874932642532
y[1] (closed_form) = -0.0568925753258 0.0874782502789
absolute error = 3.687e-05
relative error = 0.03533 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.096
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.922
Order of pole (three term test) = 2.234e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4752 2.724
h = 0.0001 0.004
y[1] (numeric) = -0.056909885313 0.0872862987349
y[1] (closed_form) = -0.0569434238703 0.0872714374844
absolute error = 3.668e-05
relative error = 0.0352 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.098
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.92
Order of pole (three term test) = 1.305e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4751 2.728
h = 0.003 0.006
y[1] (numeric) = -0.056894322603 0.0870178380978
y[1] (closed_form) = -0.0569279120416 0.0870031442239
absolute error = 3.666e-05
relative error = 0.03526 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.101
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.199
Order of pole (three term test) = 1.071e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4721 2.734
h = 0.0001 0.005
y[1] (numeric) = -0.0570604538427 0.0866006582945
y[1] (closed_form) = -0.0570933067036 0.0865857616219
absolute error = 3.607e-05
relative error = 0.03478 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.105
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.315
Order of pole (three term test) = 1.300e-13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1677.0MB, alloc=44.3MB, time=21.50
x[1] = -1.472 2.739
h = 0.0001 0.003
y[1] (numeric) = -0.0570365766132 0.0862680595947
y[1] (closed_form) = -0.057069920814 0.0862532069848
absolute error = 3.650e-05
relative error = 0.03529 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.109
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.866
Order of pole (three term test) = 1.948e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4719 2.742
h = 0.001 0.001
y[1] (numeric) = -0.0570247772661 0.0860691519891
y[1] (closed_form) = -0.0570582021241 0.0860541250627
absolute error = 3.665e-05
relative error = 0.03549 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.112
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.466
Order of pole (three term test) = 1.874e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4709 2.743
h = 0.001 0.003
y[1] (numeric) = -0.0570845678705 0.08599697729
y[1] (closed_form) = -0.0571180610613 0.0859818786304
absolute error = 3.674e-05
relative error = 0.03559 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.112
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.96
Order of pole (three term test) = 3.718e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4699 2.746
h = 0.0001 0.004
y[1] (numeric) = -0.0571317540141 0.0857926442251
y[1] (closed_form) = -0.057165114309 0.0857776976234
absolute error = 3.656e-05
relative error = 0.03546 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.115
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.941
Order of pole (three term test) = 9.713e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4698 2.75
h = 0.003 0.006
y[1] (numeric) = -0.0571125964267 0.0855287702015
y[1] (closed_form) = -0.0571460096811 0.0855139863851
absolute error = 3.654e-05
relative error = 0.03552 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.118
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.228
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4668 2.756
h = 0.0001 0.005
y[1] (numeric) = -0.057270061927 0.0851159892247
y[1] (closed_form) = -0.0573027507034 0.0851010209608
absolute error = 3.595e-05
relative error = 0.03504 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.122
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.327
Order of pole (three term test) = 6.844e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4667 2.761
h = 0.0001 0.003
y[1] (numeric) = -0.0572418336367 0.0847891361664
y[1] (closed_form) = -0.0572750039478 0.0847742017294
absolute error = 3.638e-05
relative error = 0.03556 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.126
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.877
Order of pole (three term test) = 6.843e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4666 2.764
h = 0.001 0.001
y[1] (numeric) = -0.0572273967107 0.0845936251197
y[1] (closed_form) = -0.0572606426468 0.0845785186154
absolute error = 3.652e-05
relative error = 0.03575 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.129
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.474
Order of pole (three term test) = 6.235e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4656 2.765
h = 0.0001 0.004
y[1] (numeric) = -0.0572851914155 0.0845217720384
y[1] (closed_form) = -0.0573185028549 0.0845065940646
absolute error = 3.661e-05
relative error = 0.03585 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.129
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.854
Order of pole (three term test) = 9.660e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4655 2.769
h = 0.003 0.006
y[1] (numeric) = -0.0572632234243 0.0842616311364
y[1] (closed_form) = -0.0572964915369 0.0842468421197
absolute error = 3.641e-05
relative error = 0.03573 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.133
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.252
Order of pole (three term test) = 1.027e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4625 2.775
h = 0.0001 0.005
y[1] (numeric) = -0.0574134999816 0.0838527904334
y[1] (closed_form) = -0.0574460543206 0.0838378319946
absolute error = 3.583e-05
relative error = 0.03525 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.137
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.339
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4624 2.78
h = 0.0001 0.003
y[1] (numeric) = -0.0573817562993 0.0835308976445
y[1] (closed_form) = -0.0574147836396 0.0835159647439
absolute error = 3.625e-05
relative error = 0.03576 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.141
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.885
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4623 2.783
h = 0.001 0.001
y[1] (numeric) = -0.0573651859209 0.0833383206282
y[1] (closed_form) = -0.0573982847334 0.0833232176989
absolute error = 3.638e-05
relative error = 0.03596 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.144
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.481
Order of pole (three term test) = 1.295e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4613 2.784
h = 0.001 0.003
y[1] (numeric) = -0.0574213063292 0.0832667918293
y[1] (closed_form) = -0.0574544682795 0.083251617737
absolute error = 3.647e-05
relative error = 0.03605 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.144
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.031
Order of pole (three term test) = 1.285e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4603 2.787
h = 0.0001 0.004
y[1] (numeric) = -0.0574618003094 0.08306743604
y[1] (closed_form) = -0.0574948398921 0.0830524123851
absolute error = 3.629e-05
relative error = 0.03593 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.146
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.981
Order of pole (three term test) = 4.655e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4602 2.791
h = 0.003 0.006
y[1] (numeric) = -0.057436441113 0.082812049274
y[1] (closed_form) = -0.057469537039 0.0827971800427
absolute error = 3.628e-05
relative error = 0.036 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.15
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.281
Order of pole (three term test) = 1.207e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4572 2.797
h = 0.0001 0.005
y[1] (numeric) = -0.0575785512196 0.082407724937
y[1] (closed_form) = -0.0576109456344 0.0823927032016
absolute error = 3.571e-05
relative error = 0.03552 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.154
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.351
Order of pole (three term test) = 5.566e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4571 2.802
h = 0.0001 0.003
y[1] (numeric) = -0.0575428268874 0.0820914934157
y[1] (closed_form) = -0.0575756845629 0.0820764879094
absolute error = 3.612e-05
relative error = 0.03603 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.158
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.896
Order of pole (three term test) = 1.979e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.457 2.805
h = 0.001 0.001
y[1] (numeric) = -0.0575238402085 0.0819022653101
y[1] (closed_form) = -0.0575567646714 0.0818870921218
absolute error = 3.625e-05
relative error = 0.03622 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.161
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.489
Order of pole (three term test) = 9.445e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.456 2.806
h = 0.001 0.003
y[1] (numeric) = -0.0575780560253 0.0818311126575
y[1] (closed_form) = -0.0576110409498 0.0818158686751
absolute error = 3.634e-05
relative error = 0.03631 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.161
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.069
Order of pole (three term test) = 1.511e-13 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1723.8MB, alloc=44.3MB, time=22.10
x[1] = -1.455 2.809
h = 0.0001 0.004
y[1] (numeric) = -0.0576151183901 0.0816344216143
y[1] (closed_form) = -0.057647986364 0.0816193270818
absolute error = 3.617e-05
relative error = 0.0362 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.163
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.003
Order of pole (three term test) = 1.095e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4549 2.813
h = 0.003 0.006
y[1] (numeric) = -0.0575866207995 0.0813835222521
y[1] (closed_form) = -0.0576195467461 0.0813685777746
absolute error = 3.616e-05
relative error = 0.03627 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.167
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.31
Order of pole (three term test) = 1.483e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4519 2.819
h = 0.0001 0.005
y[1] (numeric) = -0.0577208241259 0.0809837678806
y[1] (closed_form) = -0.057753060882 0.0809686870792
absolute error = 3.559e-05
relative error = 0.03578 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.171
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.364
Order of pole (three term test) = 1.091e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4518 2.824
h = 0.0001 0.003
y[1] (numeric) = -0.0576813093372 0.0806731487628
y[1] (closed_form) = -0.0577139996628 0.0806580753554
absolute error = 3.600e-05
relative error = 0.0363 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.175
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.906
Order of pole (three term test) = 8.127e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4517 2.827
h = 0.001 0.001
y[1] (numeric) = -0.0576600200228 0.0804872418067
y[1] (closed_form) = -0.0576927726309 0.0804720031078
absolute error = 3.612e-05
relative error = 0.03648 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.178
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.497
Order of pole (three term test) = 9.934e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4507 2.828
h = 0.001 0.003
y[1] (numeric) = -0.0577123792033 0.0804164921831
y[1] (closed_form) = -0.0577451896772 0.0804011831102
absolute error = 3.621e-05
relative error = 0.03658 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.178
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.107
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4497 2.831
h = 0.0001 0.004
y[1] (numeric) = -0.0577461328866 0.0802224714519
y[1] (closed_form) = -0.0577788316584 0.0802073107445
absolute error = 3.604e-05
relative error = 0.03646 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.181
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.024
Order of pole (three term test) = 1.293e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4496 2.835
h = 0.003 0.006
y[1] (numeric) = -0.0577146468085 0.0799760202852
y[1] (closed_form) = -0.0577474050392 0.0799610053444
absolute error = 3.604e-05
relative error = 0.03653 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.184
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.338
Order of pole (three term test) = 1.704e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4466 2.841
h = 0.0001 0.005
y[1] (numeric) = -0.0578411972599 0.0795808820973
y[1] (closed_form) = -0.0578732786569 0.0795657462977
absolute error = 3.547e-05
relative error = 0.03605 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.188
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.377
Order of pole (three term test) = 1.289e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4465 2.846
h = 0.0001 0.003
y[1] (numeric) = -0.0577980759715 0.0792758235031
y[1] (closed_form) = -0.0578306013075 0.0792606867196
absolute error = 3.588e-05
relative error = 0.03656 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.193
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.916
Order of pole (three term test) = 4.273e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4464 2.849
h = 0.001 0.001
y[1] (numeric) = -0.0577745939974 0.0790932080977
y[1] (closed_form) = -0.057807177286 0.0790779084509
absolute error = 3.600e-05
relative error = 0.03675 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.195
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.505
Order of pole (three term test) = 9.232e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4454 2.85
h = 0.001 0.003
y[1] (numeric) = -0.0578251438173 0.0790228865732
y[1] (closed_form) = -0.0578577824553 0.0790075170197
absolute error = 3.608e-05
relative error = 0.03684 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.196
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.146
Order of pole (three term test) = 5.794e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4444 2.853
h = 0.0001 0.004
y[1] (numeric) = -0.0578557085711 0.0788315387785
y[1] (closed_form) = -0.05788824059 0.0788163164166
absolute error = 3.592e-05
relative error = 0.03673 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.198
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.046
Order of pole (three term test) = 1.521e-13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4443 2.857
h = 0.003 0.006
y[1] (numeric) = -0.0578213789903 0.0785894942557
y[1] (closed_form) = -0.0578539718175 0.0785744134541
absolute error = 3.591e-05
relative error = 0.0368 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.201
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.367
Order of pole (three term test) = 5.888e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4413 2.863
h = 0.0001 0.005
y[1] (numeric) = -0.0579405246919 0.0781990114834
y[1] (closed_form) = -0.0579724530581 0.0781838245946
absolute error = 3.536e-05
relative error = 0.03633 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.205
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.39
Order of pole (three term test) = 6.032e-15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4412 2.868
h = 0.0001 0.003
y[1] (numeric) = -0.0578939747438 0.0778994587831
y[1] (closed_form) = -0.0579263374895 0.0778842629733
absolute error = 3.575e-05
relative error = 0.03683 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.21
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.927
Order of pole (three term test) = 7.103e-14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4411 2.871
h = 0.001 0.001
y[1] (numeric) = -0.0578684064655 0.0777201036507
y[1] (closed_form) = -0.0579008230045 0.0777047474376
absolute error = 3.587e-05
relative error = 0.03702 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.212
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.513
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4401 2.872
h = 0.001 0.003
y[1] (numeric) = -0.0579171934945 0.0776502335598
y[1] (closed_form) = -0.0579496629444 0.0776348079511
absolute error = 3.595e-05
relative error = 0.03711 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.213
Order of pole (given) = 2 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.184
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ;
Iterations = 754
Total Elapsed Time = 22 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 22 Seconds
> quit
memory used=1767.6MB, alloc=44.3MB, time=22.65