|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"| ");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(ln(c(1.0) + expt(tan(c(2.0) * c(x) + c(3.0)),c(2)))/c(4.0));
> end;
exact_soln_y := proc(x)
return ln(c(1.0) + expt(tan(c(2.0)*c(x) + c(3.0)), c(2)))/c(4.0)
end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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,
> array_const_3D0,
#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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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,
> array_const_3D0,
#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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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,
> array_const_3D0,
#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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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,
> array_const_3D0,
#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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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,
> array_const_3D0,
#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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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,
> array_const_3D0,
#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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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,
> array_const_3D0,
#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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
> #emit pre tan $eq_no = 1
> array_tmp3_a1[1] := sin(array_tmp2[1]);
> array_tmp3_a2[1] := cos(array_tmp2[1]);
> array_tmp3[1] := (array_tmp3_a1[1] / array_tmp3_a2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre tan $eq_no = 1
> array_tmp3_a1[2] := array_tmp3_a2[1] * array_tmp2[2] / c(1);
> array_tmp3_a2[2] := neg(array_tmp3_a1[1]) * array_tmp2[2] / c(1);
> array_tmp3[2] := (array_tmp3_a1[2] - ats(2,array_tmp3_a2,array_tmp3,2)) / array_tmp3_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[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_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre tan $eq_no = 1
> array_tmp3_a1[3] := array_tmp3_a2[2] * array_tmp2[2] / c(2);
> array_tmp3_a2[3] := neg(array_tmp3_a1[2]) * array_tmp2[2] / c(2);
> array_tmp3[3] := (array_tmp3_a1[3] - ats(3,array_tmp3_a2,array_tmp3,2)) / array_tmp3_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[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_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre tan $eq_no = 1
> array_tmp3_a1[4] := array_tmp3_a2[3] * array_tmp2[2] / c(3);
> array_tmp3_a2[4] := neg(array_tmp3_a1[3]) * array_tmp2[2] / c(3);
> array_tmp3[4] := (array_tmp3_a1[4] - ats(4,array_tmp3_a2,array_tmp3,2)) / array_tmp3_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[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_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre tan $eq_no = 1
> array_tmp3_a1[5] := array_tmp3_a2[4] * array_tmp2[2] / c(4);
> array_tmp3_a2[5] := neg(array_tmp3_a1[4]) * array_tmp2[2] / c(4);
> array_tmp3[5] := (array_tmp3_a1[5] - ats(5,array_tmp3_a2,array_tmp3,2)) / array_tmp3_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[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_tmp4[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
> array_tmp3_a1[kkk] := array_tmp3_a2[kkk-1] * array_tmp2[2] / c(kkk - 1);
> array_tmp3_a2[kkk] := neg(array_tmp3_a1[kkk-1]) * array_tmp2[2] / c(kkk - 1);
> array_tmp3[kkk] := (array_tmp3_a1[kkk] - ats(kkk ,array_tmp3_a2,array_tmp3,2)) / array_tmp3_a2[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[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_tmp4[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_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_const_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
array_tmp3_a1[1] := sin(array_tmp2[1]);
array_tmp3_a2[1] := cos(array_tmp2[1]);
array_tmp3[1] := array_tmp3_a1[1]/array_tmp3_a2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3_a1[2] := array_tmp3_a2[1]*array_tmp2[2]/c(1);
array_tmp3_a2[2] := neg(array_tmp3_a1[1])*array_tmp2[2]/c(1);
array_tmp3[2] := (
array_tmp3_a1[2] - ats(2, array_tmp3_a2, array_tmp3, 2))/
array_tmp3_a2[1];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3_a1[3] := array_tmp3_a2[2]*array_tmp2[2]/c(2);
array_tmp3_a2[3] := neg(array_tmp3_a1[2])*array_tmp2[2]/c(2);
array_tmp3[3] := (
array_tmp3_a1[3] - ats(3, array_tmp3_a2, array_tmp3, 2))/
array_tmp3_a2[1];
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3_a1[4] := array_tmp3_a2[3]*array_tmp2[2]/c(3);
array_tmp3_a2[4] := neg(array_tmp3_a1[3])*array_tmp2[2]/c(3);
array_tmp3[4] := (
array_tmp3_a1[4] - ats(4, array_tmp3_a2, array_tmp3, 2))/
array_tmp3_a2[1];
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3_a1[5] := array_tmp3_a2[4]*array_tmp2[2]/c(4);
array_tmp3_a2[5] := neg(array_tmp3_a1[4])*array_tmp2[2]/c(4);
array_tmp3[5] := (
array_tmp3_a1[5] - ats(5, array_tmp3_a2, array_tmp3, 2))/
array_tmp3_a2[1];
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3_a1[kkk] :=
array_tmp3_a2[kkk - 1]*array_tmp2[2]/c(kkk - 1);
array_tmp3_a2[kkk] :=
neg(array_tmp3_a1[kkk - 1])*array_tmp2[2]/c(kkk - 1);
array_tmp3[kkk] := (
array_tmp3_a1[kkk] - ats(kkk, array_tmp3_a2, array_tmp3, 2))/
array_tmp3_a2[1];
array_tmp4[kkk] := array_tmp3[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_tmp4[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,
> array_const_3D0,
> #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_g,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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 := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #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..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> 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..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3_g:= Array(0..(30),[]);
> array_tmp3_a1:= Array(0..(30),[]);
> array_tmp3_a2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 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..(30) ,(0..30+ 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 <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) 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 <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <=30) do # do number 1
> term := 1;
> while (term <= 30) 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_g);
> zero_ats_ar(array_tmp3_a1);
> zero_ats_ar(array_tmp3_a2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> 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_const_3D0);
> array_const_3D0[1] := c(3.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> 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/lin_tanpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -1.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"x_start := c(-1.0);");
> omniout_str(ALWAYS,"x_end := c(-0.9) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_min_h := c(0.0001);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-0.714601837);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(ln(c(1.0) + expt(tan(c(2.0) * c(x) + c(3.0)),c(2)))/c(4.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -1.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> x_start := c(-1.0);
> x_end := c(-0.9) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_min_h := c(0.0001);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-0.714601837);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(0.0);
> 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 ) = tan ( 2.0 * x + 3.0 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T15:04:26-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"lin_tan")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"lin_tan diffeq.mxt")
> ;
> logitem_str(html_log_file,"lin_tan maple results")
> ;
> logitem_str(html_log_file,"Poor Accuracy")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, 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_g, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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 := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
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 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3_g := Array(0 .. 30, []);
array_tmp3_a1 := Array(0 .. 30, []);
array_tmp3_a2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
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 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 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 <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp3_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp3_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 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 <= 30 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 <= 30 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 <= 30 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 <= 30 do
term := 1;
while term <= 30 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_g);
zero_ats_ar(array_tmp3_a1);
zero_ats_ar(array_tmp3_a2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
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_const_3D0);
array_const_3D0[1] := c(3.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
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/lin_tanpostcpx.cpx#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -1.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "x_start := c(-1.0);");
omniout_str(ALWAYS, "x_end := c(-0.9) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_min_h := c(0.0001);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-0.714601837);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(ln(c(1.0) + expt(tan(c(2.0) * c(x) + c(3.\
0)),c(2)))/c(4.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -1.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
x_start := c(-1.0);
x_end := c(-0.9);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := c(0.0001);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-0.714601837);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(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 ) = tan ( 2.0 * \
x + 3.0 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T15:04:26-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"lin_tan");
logitem_str(html_log_file, "diff ( y , x , 1 ) = t\
an ( 2.0 * x + 3.0 ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file,
"lin_tan diffeq.mxt")
;
logitem_str(html_log_file, "lin_tan maple results");
logitem_str(html_log_file, "Poor Accuracy");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/lin_tanpostcpx.cpx#################
diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
x_start := c(-1.0);
x_end := c(-0.9) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := c(0.0001);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-0.714601837);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(0.0);
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(ln(c(1.0) + expt(tan(c(2.0) * c(x) + c(3.0)),c(2)))/c(4.0));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -1 0
h = 0.0001 0.005
y[1] (numeric) = 0.307813235193 0
y[1] (closed_form) = 0.307813235193 0
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.2854
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3567
Order of pole (three term test) = 3.158e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9999 0.005
h = 0.0001 0.003
y[1] (numeric) = 0.307900466052 0.00778955294881
y[1] (closed_form) = 0.307883330707 0.00778957527406
absolute error = 1.714e-05
relative error = 0.005564 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2853
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1713
Order of pole (three term test) = 3.138e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9998 0.008
h = 0.001 0.001
y[1] (numeric) = 0.307901993668 0.0124662625346
y[1] (closed_form) = 0.307905424767 0.0124665822947
absolute error = 3.446e-06
relative error = 0.001118 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.2853
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1344
Order of pole (three term test) = 3.124e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9988 0.009
h = 0.001 0.003
y[1] (numeric) = 0.309394049749 0.0140885602738
y[1] (closed_form) = 0.309407641019 0.0140856894053
absolute error = 1.389e-05
relative error = 0.004485 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2843
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6358
Order of pole (three term test) = 2.845e-12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=26.9MB, alloc=40.3MB, time=0.35
x[1] = -0.9978 0.012
h = 0.0001 0.004
y[1] (numeric) = 0.310764053918 0.018855749734
y[1] (closed_form) = 0.310756476622 0.0188584393061
absolute error = 8.040e-06
relative error = 0.002583 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.2835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3587
Order of pole (three term test) = 2.605e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9977 0.016
h = 0.003 0.006
y[1] (numeric) = 0.310545726211 0.0251533494125
y[1] (closed_form) = 0.310525104736 0.0251426606472
absolute error = 2.323e-05
relative error = 0.007456 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4754
Order of pole (three term test) = 2.618e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9947 0.022
h = 0.0001 0.005
y[1] (numeric) = 0.31449720396 0.034926637273
y[1] (closed_form) = 0.314455272285 0.0349953668748
absolute error = 8.051e-05
relative error = 0.02545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.281
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2095
Order of pole (three term test) = 2.020e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9946 0.027
h = 0.0001 0.003
y[1] (numeric) = 0.31376845468 0.0428979182607
y[1] (closed_form) = 0.313751352412 0.0429184880487
absolute error = 2.675e-05
relative error = 0.008447 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2813
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1688
Order of pole (three term test) = 2.066e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9945 0.03
h = 0.001 0.001
y[1] (numeric) = 0.313304785744 0.0476462559925
y[1] (closed_form) = 0.313308452993 0.0476700758451
absolute error = 2.410e-05
relative error = 0.007605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2815
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1326
Order of pole (three term test) = 2.093e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9935 0.031
h = 0.001 0.003
y[1] (numeric) = 0.314657713935 0.0494411180108
y[1] (closed_form) = 0.314672110067 0.049463171786
absolute error = 2.634e-05
relative error = 0.008268 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2806
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6275
Order of pole (three term test) = 1.916e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9925 0.034
h = 0.0001 0.004
y[1] (numeric) = 0.315572586955 0.0544158153318
y[1] (closed_form) = 0.31556479556 0.0544404287473
absolute error = 2.582e-05
relative error = 0.008062 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.28
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3542
Order of pole (three term test) = 1.785e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9924 0.038
h = 0.003 0.006
y[1] (numeric) = 0.314722482073 0.0607800887086
y[1] (closed_form) = 0.314703483891 0.0607893341341
absolute error = 2.113e-05
relative error = 0.006592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2804
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4701
Order of pole (three term test) = 1.837e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9894 0.044
h = 0.0001 0.005
y[1] (numeric) = 0.317752607483 0.0710757064064
y[1] (closed_form) = 0.317700694136 0.0711616250811
absolute error = 0.0001004
relative error = 0.03083 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2783
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2075
Order of pole (three term test) = 1.469e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9893 0.049
h = 0.0001 0.003
y[1] (numeric) = 0.316217250769 0.0790660475803
y[1] (closed_form) = 0.316197217408 0.0791074396956
absolute error = 4.599e-05
relative error = 0.01411 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.279
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1675
Order of pole (three term test) = 1.549e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9892 0.052
h = 0.001 0.001
y[1] (numeric) = 0.315275787463 0.083819178743
y[1] (closed_form) = 0.315276000523 0.0838668335547
absolute error = 4.766e-05
relative error = 0.01461 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2795
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1317
Order of pole (three term test) = 1.598e-12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=71.7MB, alloc=52.3MB, time=0.92
x[1] = -0.9882 0.053
h = 0.001 0.003
y[1] (numeric) = 0.316464180864 0.085767135968
y[1] (closed_form) = 0.316475341932 0.0858145920039
absolute error = 4.875e-05
relative error = 0.01487 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2787
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6232
Order of pole (three term test) = 1.472e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9872 0.056
h = 0.0001 0.004
y[1] (numeric) = 0.316892199246 0.0908839350765
y[1] (closed_form) = 0.316880894292 0.090930695769
absolute error = 4.811e-05
relative error = 0.01459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2783
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3521
Order of pole (three term test) = 1.398e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9871 0.06
h = 0.003 0.006
y[1] (numeric) = 0.315400088852 0.0972229480464
y[1] (closed_form) = 0.315379900465 0.0972528096237
absolute error = 3.605e-05
relative error = 0.01092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.279
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4678
Order of pole (three term test) = 1.474e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9841 0.066
h = 0.0001 0.005
y[1] (numeric) = 0.317434986794 0.107906309886
y[1] (closed_form) = 0.317371034178 0.108007263747
absolute error = 0.0001195
relative error = 0.03565 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2775
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2068
Order of pole (three term test) = 1.226e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.984 0.071
h = 0.0001 0.003
y[1] (numeric) = 0.315095839721 0.115797097333
y[1] (closed_form) = 0.31506983055 0.115858849146
absolute error = 6.701e-05
relative error = 0.01996 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2786
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1672
Order of pole (three term test) = 1.332e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9839 0.074
h = 0.001 0.001
y[1] (numeric) = 0.313680453749 0.120485506158
y[1] (closed_form) = 0.313673439433 0.120556357649
absolute error = 7.120e-05
relative error = 0.02119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2793
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1316
Order of pole (three term test) = 1.399e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9829 0.075
h = 0.001 0.003
y[1] (numeric) = 0.314683868915 0.122561020436
y[1] (closed_form) = 0.314687635039 0.122633266891
absolute error = 7.234e-05
relative error = 0.02142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2786
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6229
Order of pole (three term test) = 1.298e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9819 0.078
h = 0.0001 0.004
y[1] (numeric) = 0.314609657659 0.127747245817
y[1] (closed_form) = 0.314591481804 0.127815534044
absolute error = 7.067e-05
relative error = 0.02081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2784
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3523
Order of pole (three term test) = 1.257e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9818 0.082
h = 0.003 0.006
y[1] (numeric) = 0.312488012161 0.133967625775
y[1] (closed_form) = 0.312463599001 0.134018084272
absolute error = 5.605e-05
relative error = 0.01649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2795
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4686
Order of pole (three term test) = 1.357e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9788 0.088
h = 0.0001 0.005
y[1] (numeric) = 0.313487747412 0.144888162884
y[1] (closed_form) = 0.313410357394 0.145001645467
absolute error = 0.0001374
relative error = 0.03978 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2785
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2076
Order of pole (three term test) = 1.176e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9787 0.093
h = 0.0001 0.003
y[1] (numeric) = 0.31037660399 0.152564101616
y[1] (closed_form) = 0.310341737311 0.152645004606
absolute error = 8.810e-05
relative error = 0.02547 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.28
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1681
Order of pole (three term test) = 1.315e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9786 0.096
h = 0.001 0.001
y[1] (numeric) = 0.308507897318 0.157120950245
y[1] (closed_form) = 0.308490136985 0.15721339192
absolute error = 9.413e-05
relative error = 0.02719 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2809
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1323
Order of pole (three term test) = 1.405e-12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=116.4MB, alloc=52.3MB, time=1.45
x[1] = -0.9776 0.097
h = 0.0001 0.004
y[1] (numeric) = 0.309312597755 0.159294228312
y[1] (closed_form) = 0.30930507499 0.159389561392
absolute error = 9.563e-05
relative error = 0.02748 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2803
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7931
Order of pole (three term test) = 1.315e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9775 0.101
h = 0.003 0.006
y[1] (numeric) = 0.306701272038 0.165351211415
y[1] (closed_form) = 0.306667477548 0.165412400207
absolute error = 6.990e-05
relative error = 0.02006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2816
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4722
Order of pole (three term test) = 1.447e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9745 0.107
h = 0.0001 0.005
y[1] (numeric) = 0.306806208984 0.176339301353
y[1] (closed_form) = 0.306713466243 0.176455010018
absolute error = 0.0001483
relative error = 0.04191 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2811
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2095
Order of pole (three term test) = 1.299e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9744 0.112
h = 0.0001 0.003
y[1] (numeric) = 0.303080395913 0.183738961323
y[1] (closed_form) = 0.303032605723 0.183828435276
absolute error = 0.0001014
relative error = 0.02862 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1698
Order of pole (three term test) = 1.487e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9743 0.115
h = 0.001 0.001
y[1] (numeric) = 0.300851928627 0.188130046831
y[1] (closed_form) = 0.300819217229 0.188232680995
absolute error = 0.0001077
relative error = 0.03036 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.284
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1338
Order of pole (three term test) = 1.610e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9733 0.116
h = 0.001 0.003
y[1] (numeric) = 0.30147973811 0.190359652694
y[1] (closed_form) = 0.301456525408 0.190466293774
absolute error = 0.0001091
relative error = 0.03061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.634
Order of pole (three term test) = 1.518e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9723 0.119
h = 0.0001 0.004
y[1] (numeric) = 0.300492635248 0.19547429589
y[1] (closed_form) = 0.300450412866 0.195571756308
absolute error = 0.0001062
relative error = 0.02963 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2838
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3592
Order of pole (three term test) = 1.522e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9722 0.123
h = 0.003 0.006
y[1] (numeric) = 0.297309908779 0.201244135393
y[1] (closed_form) = 0.297266508282 0.201323831063
absolute error = 9.075e-05
relative error = 0.02528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2855
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4786
Order of pole (three term test) = 1.709e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9692 0.129
h = 0.0001 0.005
y[1] (numeric) = 0.296405643778 0.212186877045
y[1] (closed_form) = 0.296298689454 0.21231035047
absolute error = 0.0001634
relative error = 0.04481 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2854
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2128
Order of pole (three term test) = 1.597e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9691 0.134
h = 0.0001 0.003
y[1] (numeric) = 0.292033358739 0.219196320662
y[1] (closed_form) = 0.291972562848 0.219301062812
absolute error = 0.0001211
relative error = 0.03317 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2876
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1726
Order of pole (three term test) = 1.871e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.969 0.137
h = 0.001 0.001
y[1] (numeric) = 0.289427311196 0.223355642395
y[1] (closed_form) = 0.289379011367 0.223474858965
absolute error = 0.0001286
relative error = 0.03518 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2889
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1361
Order of pole (three term test) = 2.055e-12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=161.2MB, alloc=52.3MB, time=1.99
x[1] = -0.968 0.138
h = 0.001 0.003
y[1] (numeric) = 0.289851427117 0.225624432189
y[1] (closed_form) = 0.289811568108 0.225748707285
absolute error = 0.0001305
relative error = 0.03553 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2885
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6452
Order of pole (three term test) = 1.953e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.967 0.141
h = 0.0001 0.004
y[1] (numeric) = 0.288414774469 0.230610465474
y[1] (closed_form) = 0.288358197128 0.230723524438
absolute error = 0.0001264
relative error = 0.03423 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2891
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3658
Order of pole (three term test) = 1.993e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9669 0.145
h = 0.003 0.006
y[1] (numeric) = 0.284748265402 0.236048559971
y[1] (closed_form) = 0.284692936599 0.236144722782
absolute error = 0.0001109
relative error = 0.02999 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.291
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4879
Order of pole (three term test) = 2.277e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9639 0.151
h = 0.0001 0.005
y[1] (numeric) = 0.282894798356 0.246812928909
y[1] (closed_form) = 0.282773985645 0.246941912036
absolute error = 0.0001767
relative error = 0.04707 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2915
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2173
Order of pole (three term test) = 2.208e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9638 0.156
h = 0.0001 0.003
y[1] (numeric) = 0.277965576589 0.253368568698
y[1] (closed_form) = 0.27789042146 0.253485996981
absolute error = 0.0001394
relative error = 0.03707 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.294
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1765
Order of pole (three term test) = 2.640e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9637 0.159
h = 0.001 0.001
y[1] (numeric) = 0.275034699712 0.257260352408
y[1] (closed_form) = 0.274969384162 0.257392917816
absolute error = 0.0001478
relative error = 0.03924 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2955
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1392
Order of pole (three term test) = 2.932e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9627 0.16
h = 0.001 0.003
y[1] (numeric) = 0.275262243625 0.259539418265
y[1] (closed_form) = 0.275204174031 0.259677786224
absolute error = 0.0001501
relative error = 0.03966 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2952
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6601
Order of pole (three term test) = 2.810e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9617 0.163
h = 0.0001 0.004
y[1] (numeric) = 0.273420126148 0.264345783829
y[1] (closed_form) = 0.273347871992 0.264471549258
absolute error = 0.000145
relative error = 0.03813 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.296
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3746
Order of pole (three term test) = 2.911e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9616 0.167
h = 0.003 0.006
y[1] (numeric) = 0.269343091689 0.269410115558
y[1] (closed_form) = 0.269274128842 0.269520286747
absolute error = 0.00013
relative error = 0.03412 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2982
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 3.375e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9586 0.173
h = 0.0001 0.005
y[1] (numeric) = 0.266623912395 0.279886218739
y[1] (closed_form) = 0.266489952346 0.280018798277
absolute error = 0.0001885
relative error = 0.04876 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.2991
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.223
Order of pole (three term test) = 3.385e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9585 0.178
h = 0.0001 0.003
y[1] (numeric) = 0.26123305442 0.285948533846
y[1] (closed_form) = 0.26114284515 0.286075986415
absolute error = 0.0001561
relative error = 0.04031 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3019
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1812
Order of pole (three term test) = 4.111e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9584 0.181
h = 0.001 0.001
y[1] (numeric) = 0.258032975327 0.289550888044
memory used=206.0MB, alloc=52.3MB, time=2.53
y[1] (closed_form) = 0.257950058633 0.289693550914
absolute error = 0.000165
relative error = 0.04254 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3036
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1431
Order of pole (three term test) = 4.609e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9574 0.182
h = 0.001 0.003
y[1] (numeric) = 0.258076364507 0.291815254936
y[1] (closed_form) = 0.257999460985 0.291964159267
absolute error = 0.0001676
relative error = 0.04301 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3034
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6785
Order of pole (three term test) = 4.451e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9564 0.185
h = 0.0001 0.004
y[1] (numeric) = 0.255879503767 0.296404350916
y[1] (closed_form) = 0.255790988552 0.296539896719
absolute error = 0.0001619
relative error = 0.04134 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3045
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3852
Order of pole (three term test) = 4.672e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9563 0.189
h = 0.003 0.006
y[1] (numeric) = 0.25146720819 0.301071465855
y[1] (closed_form) = 0.251383579431 0.301192995571
absolute error = 0.0001475
relative error = 0.0376 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3068
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5144
Order of pole (three term test) = 5.475e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9533 0.195
h = 0.0001 0.005
y[1] (numeric) = 0.247980203554 0.311175947295
y[1] (closed_form) = 0.247834019815 0.311310570958
absolute error = 0.0001987
relative error = 0.04994 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3082
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2298
Order of pole (three term test) = 5.654e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9532 0.2
h = 0.0001 0.003
y[1] (numeric) = 0.242221693415 0.31672785565
y[1] (closed_form) = 0.242116330667 0.316862777285
absolute error = 0.0001712
relative error = 0.04293 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3113
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1869
Order of pole (three term test) = 6.949e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9531 0.203
h = 0.001 0.001
y[1] (numeric) = 0.23880694677 0.320031694812
y[1] (closed_form) = 0.238706571588 0.320181418943
absolute error = 0.0001803
relative error = 0.04514 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3132
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1476
Order of pole (three term test) = 7.844e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9521 0.204
h = 0.0001 0.004
y[1] (numeric) = 0.238682184407 0.322261162823
y[1] (closed_form) = 0.238586632938 0.32241729501
absolute error = 0.0001831
relative error = 0.04564 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3131
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8858
Order of pole (three term test) = 7.628e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.952 0.208
h = 0.003 0.006
y[1] (numeric) = 0.234050273 0.326597275439
y[1] (closed_form) = 0.233954529614 0.326721067978
absolute error = 0.0001565
relative error = 0.03894 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3156
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5292
Order of pole (three term test) = 9.001e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.949 0.214
h = 0.0001 0.005
y[1] (numeric) = 0.22999063621 0.336327973093
y[1] (closed_form) = 0.229835677511 0.33645801795
absolute error = 0.0002023
relative error = 0.04965 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3174
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2366
Order of pole (three term test) = 9.494e-12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9489 0.219
h = 0.0001 0.003
y[1] (numeric) = 0.223991958249 0.341438442615
y[1] (closed_form) = 0.223874729903 0.341572531614
absolute error = 0.0001781
relative error = 0.04361 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3207
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1925
Order of pole (three term test) = 1.175e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9488 0.222
h = 0.001 0.001
y[1] (numeric) = 0.220436583487 0.344484556907
y[1] (closed_form) = 0.220322622634 0.344632787131
absolute error = 0.000187
relative error = 0.04571 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3227
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.152
Order of pole (three term test) = 1.331e-11 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=250.8MB, alloc=52.3MB, time=3.07
x[1] = -0.9478 0.223
h = 0.001 0.003
y[1] (numeric) = 0.22018205873 0.346669889939
y[1] (closed_form) = 0.220071977969 0.34682447926
absolute error = 0.0001898
relative error = 0.0462 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3227
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7215
Order of pole (three term test) = 1.301e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9468 0.226
h = 0.0001 0.004
y[1] (numeric) = 0.217468348432 0.350796665536
y[1] (closed_form) = 0.217351026498 0.35093789981
absolute error = 0.0001836
relative error = 0.04448 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.324
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.41
Order of pole (three term test) = 1.391e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9467 0.23
h = 0.003 0.006
y[1] (numeric) = 0.212624360609 0.35471458151
y[1] (closed_form) = 0.212513698652 0.354844987882
absolute error = 0.000171
relative error = 0.04135 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3268
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5478
Order of pole (three term test) = 1.650e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9437 0.236
h = 0.0001 0.005
y[1] (numeric) = 0.207989294743 0.363988470798
y[1] (closed_form) = 0.207824039111 0.364118540916
absolute error = 0.0002103
relative error = 0.05016 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3289
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2452
Order of pole (three term test) = 1.777e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9436 0.241
h = 0.0001 0.003
y[1] (numeric) = 0.201777310388 0.368604666726
y[1] (closed_form) = 0.201645960136 0.368742181131
absolute error = 0.0001902
relative error = 0.04525 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3324
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1995
Order of pole (three term test) = 2.211e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9435 0.244
h = 0.001 0.001
y[1] (numeric) = 0.19809644747 0.371362483773
y[1] (closed_form) = 0.197966678643 0.371513176803
absolute error = 0.0001989
relative error = 0.04724 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3346
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1576
Order of pole (three term test) = 2.513e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9425 0.245
h = 0.001 0.003
y[1] (numeric) = 0.197707709613 0.373488510311
y[1] (closed_form) = 0.197580846275 0.373645362202
absolute error = 0.0002017
relative error = 0.04773 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3346
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7482
Order of pole (three term test) = 2.470e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9415 0.248
h = 0.0001 0.004
y[1] (numeric) = 0.194785606646 0.377359600586
y[1] (closed_form) = 0.19465346718 0.377503616031
absolute error = 0.0001955
relative error = 0.04602 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3361
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4253
Order of pole (three term test) = 2.657e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9414 0.252
h = 0.003 0.006
y[1] (numeric) = 0.189794072818 0.38089434589
y[1] (closed_form) = 0.189669018669 0.381029172276
absolute error = 0.0001839
relative error = 0.04321 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.339
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5684
Order of pole (three term test) = 3.162e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9384 0.258
h = 0.0001 0.005
y[1] (numeric) = 0.184680574318 0.389696045042
y[1] (closed_form) = 0.184506033438 0.389825417926
absolute error = 0.0002173
relative error = 0.05038 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3415
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2546
Order of pole (three term test) = 3.463e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9383 0.263
h = 0.0001 0.003
y[1] (numeric) = 0.178322665719 0.393843225662
y[1] (closed_form) = 0.178178140171 0.393982468454
absolute error = 0.0002007
relative error = 0.04641 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3453
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2072
Order of pole (three term test) = 4.317e-11 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=295.6MB, alloc=52.3MB, time=3.61
x[1] = -0.9382 0.266
h = 0.001 0.001
y[1] (numeric) = 0.174555205108 0.396327561593
y[1] (closed_form) = 0.174410914433 0.396478882341
absolute error = 0.0002091
relative error = 0.04827 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3475
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1637
Order of pole (three term test) = 4.913e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9372 0.267
h = 0.001 0.003
y[1] (numeric) = 0.1740502737 0.39838718079
y[1] (closed_form) = 0.17390805735 0.398544339788
absolute error = 0.000212
relative error = 0.04874 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3476
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7773
Order of pole (three term test) = 4.851e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9362 0.27
h = 0.0001 0.004
y[1] (numeric) = 0.17096325426 0.402006846006
y[1] (closed_form) = 0.170817419493 0.402151914979
absolute error = 0.0002057
relative error = 0.04708 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3493
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.442
Order of pole (three term test) = 5.246e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9361 0.274
h = 0.003 0.006
y[1] (numeric) = 0.165873540812 0.405180734899
y[1] (closed_form) = 0.165734929287 0.405318121789
absolute error = 0.0001952
relative error = 0.04457 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3523
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5907
Order of pole (three term test) = 6.249e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9331 0.28
h = 0.0001 0.005
y[1] (numeric) = 0.160369639325 0.41351109186
y[1] (closed_form) = 0.160186769787 0.413639239199
absolute error = 0.0002233
relative error = 0.05034 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3552
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2648
Order of pole (three term test) = 6.932e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.933 0.285
h = 0.0001 0.003
y[1] (numeric) = 0.153921531524 0.417221291337
y[1] (closed_form) = 0.153764917863 0.417360904314
absolute error = 0.0002098
relative error = 0.04717 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3591
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2155
Order of pole (three term test) = 8.640e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9329 0.288
h = 0.001 0.001
y[1] (numeric) = 0.150099666078 0.419450759633
y[1] (closed_form) = 0.149942251718 0.419601297588
absolute error = 0.0002178
relative error = 0.04888 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3614
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1703
Order of pole (three term test) = 9.834e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9319 0.289
h = 0.001 0.003
y[1] (numeric) = 0.149495439668 0.421440257461
y[1] (closed_form) = 0.149339411321 0.421596238709
absolute error = 0.0002206
relative error = 0.04933 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3616
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8085
Order of pole (three term test) = 9.749e-11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9309 0.292
h = 0.0001 0.004
y[1] (numeric) = 0.146281214721 0.42481840194
y[1] (closed_form) = 0.146122925606 0.424963173661
absolute error = 0.0002145
relative error = 0.04773 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3634
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4598
Order of pole (three term test) = 1.058e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9308 0.296
h = 0.003 0.006
y[1] (numeric) = 0.14113369394 0.427657964533
y[1] (closed_form) = 0.140982549051 0.427796397993
absolute error = 0.000205
relative error = 0.0455 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3665
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6145
Order of pole (three term test) = 1.259e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9278 0.302
h = 0.0001 0.005
y[1] (numeric) = 0.135316831212 0.435529779906
y[1] (closed_form) = 0.135126520077 0.435656326103
absolute error = 0.0002285
relative error = 0.0501 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3697
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2756
Order of pole (three term test) = 1.410e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9277 0.307
h = 0.0001 0.003
y[1] (numeric) = 0.128823239339 0.438838575935
y[1] (closed_form) = 0.128655679496 0.438977511356
absolute error = 0.0002177
relative error = 0.04758 %
Correct digits = 3
memory used=340.5MB, alloc=52.3MB, time=4.15
Radius of convergence (given) for eq 1 = 0.3737
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2243
Order of pole (three term test) = 1.755e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9276 0.31
h = 0.001 0.001
y[1] (numeric) = 0.124972855727 0.44083376894
y[1] (closed_form) = 0.12480372942 0.440982486291
absolute error = 0.0002252
relative error = 0.04914 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3761
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1772
Order of pole (three term test) = 1.995e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9266 0.311
h = 0.0001 0.004
y[1] (numeric) = 0.124284685272 0.442752073491
y[1] (closed_form) = 0.124116389225 0.442905801404
absolute error = 0.0002279
relative error = 0.04956 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3764
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.065
Order of pole (three term test) = 1.984e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9265 0.315
h = 0.003 0.006
y[1] (numeric) = 0.119114528615 0.445339311778
y[1] (closed_form) = 0.118955544451 0.445474856015
absolute error = 0.0002089
relative error = 0.04531 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3796
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6365
Order of pole (three term test) = 2.358e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9235 0.321
h = 0.0001 0.005
y[1] (numeric) = 0.113087023572 0.452830343297
y[1] (closed_form) = 0.112893034104 0.452952530068
absolute error = 0.0002293
relative error = 0.04911 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.383
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2855
Order of pole (three term test) = 2.657e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9234 0.326
h = 0.0001 0.003
y[1] (numeric) = 0.10658674157 0.455823011493
y[1] (closed_form) = 0.106412740482 0.455957923145
absolute error = 0.0002202
relative error = 0.04703 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3871
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2324
Order of pole (three term test) = 3.296e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9233 0.329
h = 0.001 0.001
y[1] (numeric) = 0.102730676082 0.457633507827
y[1] (closed_form) = 0.102554643656 0.457777251988
absolute error = 0.0002273
relative error = 0.04844 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3896
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1836
Order of pole (three term test) = 3.741e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9223 0.33
h = 0.001 0.003
y[1] (numeric) = 0.101982048508 0.459490402783
y[1] (closed_form) = 0.10180646769 0.459638770949
absolute error = 0.0002299
relative error = 0.04883 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3899
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8719
Order of pole (three term test) = 3.729e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9213 0.333
h = 0.0001 0.004
y[1] (numeric) = 0.0986141750666 0.462456287995
y[1] (closed_form) = 0.0984381448153 0.462595215362
absolute error = 0.0002242
relative error = 0.04741 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3919
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4959
Order of pole (three term test) = 4.059e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9212 0.337
h = 0.003 0.006
y[1] (numeric) = 0.0934421008283 0.464749873752
y[1] (closed_form) = 0.0932726859159 0.464884500621
absolute error = 0.0002164
relative error = 0.04564 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3953
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6627
Order of pole (three term test) = 4.809e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9182 0.343
h = 0.0001 0.005
y[1] (numeric) = 0.0872165727485 0.471826236968
y[1] (closed_form) = 0.0870165948502 0.471946428722
absolute error = 0.0002333
relative error = 0.04862 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3989
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2974
Order of pole (three term test) = 5.447e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9181 0.348
h = 0.0001 0.003
y[1] (numeric) = 0.0807285434932 0.474485612858
y[1] (closed_form) = 0.0805456745241 0.474618593299
absolute error = 0.0002261
relative error = 0.04697 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4031
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.242
Order of pole (three term test) = 6.730e-10 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=385.1MB, alloc=52.3MB, time=4.69
x[1] = -0.918 0.351
h = 0.001 0.001
y[1] (numeric) = 0.0768775491503 0.476101197118
y[1] (closed_form) = 0.0766922650566 0.476241984963
absolute error = 0.0002327
relative error = 0.04824 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4057
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1911
Order of pole (three term test) = 7.620e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.917 0.352
h = 0.001 0.003
y[1] (numeric) = 0.076068874189 0.477889810841
y[1] (closed_form) = 0.0758836899847 0.478034786594
absolute error = 0.0002352
relative error = 0.04859 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.406
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9079
Order of pole (three term test) = 7.614e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.916 0.355
h = 0.0001 0.004
y[1] (numeric) = 0.0726505244208 0.480658105424
y[1] (closed_form) = 0.0724655588002 0.480794564672
absolute error = 0.0002299
relative error = 0.04727 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4081
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5164
Order of pole (three term test) = 8.290e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9159 0.359
h = 0.003 0.006
y[1] (numeric) = 0.0674936572639 0.482698913647
y[1] (closed_form) = 0.0673149180258 0.482831937133
absolute error = 0.0002228
relative error = 0.0457 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4116
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.69
Order of pole (three term test) = 9.786e-10 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9129 0.365
h = 0.0001 0.005
y[1] (numeric) = 0.0611177478815 0.489389083567
y[1] (closed_form) = 0.0609124561 0.489507178089
absolute error = 0.0002368
relative error = 0.04801 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4154
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3097
Order of pole (three term test) = 1.112e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9128 0.37
h = 0.0001 0.003
y[1] (numeric) = 0.0546624266533 0.491749751813
y[1] (closed_form) = 0.0544717102566 0.491880405411
absolute error = 0.0002312
relative error = 0.04671 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4197
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2519
Order of pole (three term test) = 1.367e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9127 0.373
h = 0.001 0.001
y[1] (numeric) = 0.0508284952949 0.493190418556
y[1] (closed_form) = 0.0506351269595 0.493327941521
absolute error = 0.0002373
relative error = 0.04785 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4223
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.199
Order of pole (three term test) = 1.543e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9117 0.374
h = 0.001 0.003
y[1] (numeric) = 0.0499701794786 0.494913812613
y[1] (closed_form) = 0.0497766444564 0.495055106193
absolute error = 0.0002396
relative error = 0.04816 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4228
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9453
Order of pole (three term test) = 1.545e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9107 0.377
h = 0.0001 0.004
y[1] (numeric) = 0.0465190372977 0.497501295444
y[1] (closed_form) = 0.0463262180621 0.497634948787
absolute error = 0.0002346
relative error = 0.04694 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.425
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5377
Order of pole (three term test) = 1.681e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9106 0.381
h = 0.003 0.006
y[1] (numeric) = 0.0413917000652 0.499315870019
y[1] (closed_form) = 0.0412046831944 0.499446810085
absolute error = 0.0002283
relative error = 0.04556 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4285
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7183
Order of pole (three term test) = 1.976e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9076 0.387
h = 0.0001 0.005
y[1] (numeric) = 0.0349044696768 0.505649546923
y[1] (closed_form) = 0.0346944702999 0.505765499019
absolute error = 0.0002399
relative error = 0.04732 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4325
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3224
Order of pole (three term test) = 2.249e-09 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=429.8MB, alloc=52.3MB, time=5.24
x[1] = -0.9075 0.392
h = 0.0001 0.003
y[1] (numeric) = 0.0284965166753 0.507743817956
y[1] (closed_form) = 0.0282988880268 0.507871896739
absolute error = 0.0002355
relative error = 0.0463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4369
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2622
Order of pole (three term test) = 2.748e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9074 0.395
h = 0.001 0.001
y[1] (numeric) = 0.0246883085575 0.509028265709
y[1] (closed_form) = 0.0244879040745 0.509162367863
absolute error = 0.0002411
relative error = 0.0473 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4395
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2071
Order of pole (three term test) = 3.092e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9064 0.396
h = 0.001 0.003
y[1] (numeric) = 0.0237892139603 0.510690101916
y[1] (closed_form) = 0.023588445666 0.510827583968
absolute error = 0.0002433
relative error = 0.04758 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.44
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9839
Order of pole (three term test) = 3.100e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9054 0.399
h = 0.0001 0.004
y[1] (numeric) = 0.0203192533988 0.51311316036
y[1] (closed_form) = 0.020119560078 0.51324381656
absolute error = 0.0002386
relative error = 0.04646 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4423
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5596
Order of pole (three term test) = 3.370e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9053 0.403
h = 0.003 0.006
y[1] (numeric) = 0.0152315981861 0.514726138065
y[1] (closed_form) = 0.0150372711873 0.514854679121
absolute error = 0.000233
relative error = 0.04523 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4458
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7475
Order of pole (three term test) = 3.942e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9023 0.409
h = 0.0001 0.005
y[1] (numeric) = 0.0086647128522 0.520732964043
y[1] (closed_form) = 0.00845054870084 0.520846771938
absolute error = 0.0002425
relative error = 0.04656 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.45
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3355
Order of pole (three term test) = 4.487e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9022 0.414
h = 0.0001 0.003
y[1] (numeric) = 0.00231418272265 0.522590515394
y[1] (closed_form) = 0.00211048644503 0.522715885178
absolute error = 0.0002392
relative error = 0.04576 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4545
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2728
Order of pole (three term test) = 5.448e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9021 0.417
h = 0.001 0.001
y[1] (numeric) = -0.00146229789328 0.523735941719
y[1] (closed_form) = -0.00166880914143 0.523866579938
absolute error = 0.0002444
relative error = 0.04665 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4572
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2154
Order of pole (three term test) = 6.106e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9011 0.418
h = 0.0001 0.004
y[1] (numeric) = -0.00239468703593 0.525340202031
y[1] (closed_form) = -0.00260170354304 0.525473859991
absolute error = 0.0002464
relative error = 0.04689 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4577
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.295
Order of pole (three term test) = 6.128e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.901 0.422
h = 0.003 0.006
y[1] (numeric) = -0.00744440430536 0.526805216029
y[1] (closed_form) = -0.00764258026792 0.526930316157
absolute error = 0.0002344
relative error = 0.04447 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4613
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7734
Order of pole (three term test) = 7.136e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.898 0.428
h = 0.0001 0.005
y[1] (numeric) = -0.0140558655639 0.532553201101
y[1] (closed_form) = -0.0142714952664 0.532663996322
absolute error = 0.0002424
relative error = 0.0455 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4656
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3471
Order of pole (three term test) = 8.110e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8979 0.433
h = 0.0001 0.003
y[1] (numeric) = -0.0203492954243 0.534229436768
y[1] (closed_form) = -0.0205558696133 0.534351224282
absolute error = 0.0002398
relative error = 0.04484 %
Correct digits = 3
memory used=474.3MB, alloc=52.3MB, time=5.78
Radius of convergence (given) for eq 1 = 0.4702
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2822
Order of pole (three term test) = 9.789e-09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8978 0.436
h = 0.001 0.001
y[1] (numeric) = -0.024093854099 0.535268207032
y[1] (closed_form) = -0.0243032188954 0.535394683112
absolute error = 0.0002446
relative error = 0.04564 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4729
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2228
Order of pole (three term test) = 1.093e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8968 0.437
h = 0.001 0.003
y[1] (numeric) = -0.0250492133319 0.536825892725
y[1] (closed_form) = -0.0252591657618 0.536955103102
absolute error = 0.0002465
relative error = 0.04586 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4735
Order of pole (given) = 0 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) = 1.098e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8958 0.44
h = 0.0001 0.004
y[1] (numeric) = -0.0285256150427 0.538983810829
y[1] (closed_form) = -0.0287341052487 0.539107529455
absolute error = 0.0002424
relative error = 0.04491 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4758
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6021
Order of pole (three term test) = 1.190e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8957 0.444
h = 0.003 0.006
y[1] (numeric) = -0.0335213522412 0.540280600922
y[1] (closed_form) = -0.0337252730697 0.540403041311
absolute error = 0.0002379
relative error = 0.04393 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4795
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8039
Order of pole (three term test) = 1.378e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8927 0.45
h = 0.0001 0.005
y[1] (numeric) = -0.0401696945693 0.545754251469
y[1] (closed_form) = -0.0403886311127 0.545862984255
absolute error = 0.0002445
relative error = 0.04466 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.484
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3608
Order of pole (three term test) = 1.562e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8926 0.455
h = 0.0001 0.003
y[1] (numeric) = -0.0463961998312 0.547241725136
y[1] (closed_form) = -0.0466075063732 0.547360772355
absolute error = 0.0002425
relative error = 0.04415 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4886
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2933
Order of pole (three term test) = 1.872e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8925 0.458
h = 0.001 0.001
y[1] (numeric) = -0.0501031946109 0.548169327348
y[1] (closed_form) = -0.0503172306938 0.54829246428
absolute error = 0.0002469
relative error = 0.04485 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4913
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2315
Order of pole (three term test) = 2.083e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8915 0.459
h = 0.001 0.003
y[1] (numeric) = -0.0510810461518 0.549677107259
y[1] (closed_form) = -0.0512957376519 0.549802677874
absolute error = 0.0002487
relative error = 0.04504 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4919
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.1
Order of pole (three term test) = 2.093e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8905 0.462
h = 0.0001 0.004
y[1] (numeric) = -0.0545516296057 0.551712561426
y[1] (closed_form) = -0.0547647522004 0.55183325742
absolute error = 0.0002449
relative error = 0.04417 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4944
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6255
Order of pole (three term test) = 2.262e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8904 0.466
h = 0.003 0.006
y[1] (numeric) = -0.0594946433449 0.552866546784
y[1] (closed_form) = -0.0597035951334 0.5529863004
absolute error = 0.0002408
relative error = 0.0433 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4981
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.835
Order of pole (three term test) = 2.605e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8874 0.472
h = 0.0001 0.005
y[1] (numeric) = -0.066163373919 0.558091575557
y[1] (closed_form) = -0.0663852279993 0.558198315292
absolute error = 0.0002462
relative error = 0.0438 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5026
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3747
Order of pole (three term test) = 2.946e-08 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=518.8MB, alloc=52.3MB, time=6.31
x[1] = -0.8873 0.477
h = 0.0001 0.003
y[1] (numeric) = -0.0723210631347 0.559412242356
y[1] (closed_form) = -0.0725365018959 0.559528602887
absolute error = 0.0002449
relative error = 0.0434 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5073
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3045
Order of pole (three term test) = 3.507e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8872 0.48
h = 0.001 0.001
y[1] (numeric) = -0.075989232056 0.560241457783
y[1] (closed_form) = -0.0762073070302 0.560361382459
absolute error = 0.0002489
relative error = 0.04401 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5101
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2403
Order of pole (three term test) = 3.886e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8862 0.481
h = 0.001 0.003
y[1] (numeric) = -0.0769850984282 0.561703297062
y[1] (closed_form) = -0.0772038691453 0.561825385118
absolute error = 0.0002505
relative error = 0.04418 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5107
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.142
Order of pole (three term test) = 3.906e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8852 0.484
h = 0.0001 0.004
y[1] (numeric) = -0.0804449671546 0.563628772035
y[1] (closed_form) = -0.0806621146967 0.563746538125
absolute error = 0.000247
relative error = 0.04338 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5132
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6493
Order of pole (three term test) = 4.211e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8851 0.488
h = 0.003 0.006
y[1] (numeric) = -0.0853342034234 0.56465652217
y[1] (closed_form) = -0.0855475542625 0.564773617464
absolute error = 0.0002434
relative error = 0.04261 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5169
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8666
Order of pole (three term test) = 4.825e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8821 0.494
h = 0.0001 0.005
y[1] (numeric) = -0.0920104322334 0.569656756086
y[1] (closed_form) = -0.0922348585272 0.569761584642
absolute error = 0.0002477
relative error = 0.04292 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5216
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3889
Order of pole (three term test) = 5.438e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.882 0.499
h = 0.0001 0.003
y[1] (numeric) = -0.0980990382839 0.570830152163
y[1] (closed_form) = -0.0983180819297 0.570943912811
absolute error = 0.0002468
relative error = 0.0426 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5263
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3159
Order of pole (three term test) = 6.433e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8819 0.502
h = 0.001 0.001
y[1] (numeric) = -0.101728073462 0.571572373314
y[1] (closed_form) = -0.101949638672 0.571689238196
absolute error = 0.0002505
relative error = 0.04314 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5291
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2493
Order of pole (three term test) = 7.102e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8809 0.503
h = 0.001 0.003
y[1] (numeric) = -0.102738240147 0.572992063991
y[1] (closed_form) = -0.10296052048 0.573110850328
absolute error = 0.000252
relative error = 0.04328 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5298
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.185
Order of pole (three term test) = 7.140e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8799 0.506
h = 0.0001 0.004
y[1] (numeric) = -0.106183843835 0.574818916356
y[1] (closed_form) = -0.106404486162 0.574933873576
absolute error = 0.0002488
relative error = 0.04255 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5323
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6735
Order of pole (three term test) = 7.681e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8798 0.51
h = 0.003 0.006
y[1] (numeric) = -0.111019394634 0.575735165676
y[1] (closed_form) = -0.111236587918 0.575849670567
absolute error = 0.0002455
relative error = 0.04186 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5361
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8988
Order of pole (three term test) = 8.759e-08 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=563.4MB, alloc=52.3MB, time=6.85
x[1] = -0.8768 0.516
h = 0.0001 0.005
y[1] (numeric) = -0.117693157899 0.580532500241
y[1] (closed_form) = -0.117919850534 0.580635507587
absolute error = 0.000249
relative error = 0.04203 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5409
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4032
Order of pole (three term test) = 9.841e-08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8767 0.521
h = 0.0001 0.003
y[1] (numeric) = -0.123713603206 0.581575948726
y[1] (closed_form) = -0.123935789745 0.581687218481
absolute error = 0.0002485
relative error = 0.04178 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5456
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3275
Order of pole (three term test) = 1.158e-07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8766 0.524
h = 0.001 0.001
y[1] (numeric) = -0.127303900448 0.582241294855
y[1] (closed_form) = -0.127528480828 0.582355267174
absolute error = 0.0002518
relative error = 0.04224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5485
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2584
Order of pole (three term test) = 1.274e-07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8756 0.525
h = 0.0001 0.004
y[1] (numeric) = -0.128325294462 0.583622416672
y[1] (closed_form) = -0.128550593575 0.583738094634
absolute error = 0.0002533
relative error = 0.04237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5491
Order of pole (given) = 0 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) = 1.281e-07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8755 0.529
h = 0.003 0.006
y[1] (numeric) = -0.133117451963 0.5844573329
y[1] (closed_form) = -0.133336362382 0.584569205332
absolute error = 0.0002458
relative error = 0.041 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5529
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8725 0.535
h = 0.0001 0.005
y[1] (numeric) = -0.13978083423 0.589096247314
y[1] (closed_form) = -0.140008072122 0.58919729997
absolute error = 0.0002487
relative error = 0.04107 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5578
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8724 0.54
h = 0.0001 0.003
y[1] (numeric) = -0.145742700828 0.590040962502
y[1] (closed_form) = -0.145966072105 0.590149715122
absolute error = 0.0002484
relative error = 0.04087 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5626
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8723 0.543
h = 0.001 0.001
y[1] (numeric) = -0.149299589845 0.590647802832
y[1] (closed_form) = -0.149525235313 0.590758955217
absolute error = 0.0002515
relative error = 0.04128 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5654
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8713 0.544
h = 0.001 0.003
y[1] (numeric) = -0.150328194025 0.591998321202
y[1] (closed_form) = -0.150554549656 0.592111012702
absolute error = 0.0002529
relative error = 0.04139 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5661
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8703 0.547
h = 0.0001 0.004
y[1] (numeric) = -0.153740372014 0.593668456716
y[1] (closed_form) = -0.15396513805 0.593778094291
absolute error = 0.0002501
relative error = 0.04077 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5687
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8702 0.551
h = 0.003 0.006
y[1] (numeric) = -0.158477965424 0.594411443941
y[1] (closed_form) = -0.158699859434 0.594520922067
absolute error = 0.0002474
relative error = 0.04021 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5725
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8672 0.557
h = 0.0001 0.005
y[1] (numeric) = -0.165126483866 0.598883268255
y[1] (closed_form) = -0.165355510958 0.598982680298
absolute error = 0.0002497
relative error = 0.04018 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5775
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=608.0MB, alloc=52.3MB, time=7.39
x[1] = -0.8671 0.562
h = 0.0001 0.003
y[1] (numeric) = -0.171024124268 0.599725078692
y[1] (closed_form) = -0.171249929636 0.599831579299
absolute error = 0.0002497
relative error = 0.04002 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.867 0.565
h = 0.001 0.001
y[1] (numeric) = -0.174544337506 0.600270879698
y[1] (closed_form) = -0.174772280578 0.600379468769
absolute error = 0.0002525
relative error = 0.04038 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.866 0.566
h = 0.001 0.003
y[1] (numeric) = -0.175579848315 0.601588888166
y[1] (closed_form) = -0.175808486242 0.601698842924
absolute error = 0.0002537
relative error = 0.04047 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5859
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.865 0.569
h = 0.0001 0.004
y[1] (numeric) = -0.178972819607 0.603187165324
y[1] (closed_form) = -0.179199916232 0.603294416444
absolute error = 0.0002511
relative error = 0.03991 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5885
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8649 0.573
h = 0.003 0.006
y[1] (numeric) = -0.183660935192 0.603852109646
y[1] (closed_form) = -0.183885431708 0.603959315016
absolute error = 0.0002488
relative error = 0.03941 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5924
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8619 0.579
h = 0.0001 0.005
y[1] (numeric) = -0.190290196477 0.60817352693
y[1] (closed_form) = -0.190520797735 0.608271394928
absolute error = 0.0002505
relative error = 0.0393 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5974
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8618 0.584
h = 0.0001 0.003
y[1] (numeric) = -0.196126302208 0.608924579946
y[1] (closed_form) = -0.19635422801 0.609028961372
absolute error = 0.0002507
relative error = 0.03918 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6023
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8617 0.587
h = 0.001 0.001
y[1] (numeric) = -0.199611301831 0.60941647097
y[1] (closed_form) = -0.199841229177 0.609522669549
absolute error = 0.0002533
relative error = 0.03948 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6052
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8607 0.588
h = 0.001 0.003
y[1] (numeric) = -0.20065195445 0.610704866697
y[1] (closed_form) = -0.200882554997 0.610812276972
absolute error = 0.0002544
relative error = 0.03956 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6059
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8597 0.591
h = 0.0001 0.004
y[1] (numeric) = -0.204025144823 0.612238860764
y[1] (closed_form) = -0.204254263219 0.612343877617
absolute error = 0.000252
relative error = 0.03904 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6086
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8596 0.595
h = 0.003 0.006
y[1] (numeric) = -0.208665935106 0.612834930419
y[1] (closed_form) = -0.208892701163 0.612939990627
absolute error = 0.0002499
relative error = 0.03859 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6124
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=652.6MB, alloc=52.3MB, time=7.93
x[1] = -0.8566 0.601
h = 0.0001 0.005
y[1] (numeric) = -0.215272797276 0.617021024007
y[1] (closed_form) = -0.215504782792 0.617117443332
absolute error = 0.0002512
relative error = 0.03843 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6175
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8565 0.606
h = 0.0001 0.003
y[1] (numeric) = -0.221050319755 0.617692033265
y[1] (closed_form) = -0.221280092359 0.617794428556
absolute error = 0.0002516
relative error = 0.03833 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6224
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8564 0.609
h = 0.001 0.001
y[1] (numeric) = -0.224501731352 0.618136312115
y[1] (closed_form) = -0.224733372066 0.618240288111
absolute error = 0.0002539
relative error = 0.0386 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6253
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8554 0.61
h = 0.001 0.003
y[1] (numeric) = -0.225546079804 0.619397760492
y[1] (closed_form) = -0.225778367707 0.619502811544
absolute error = 0.0002549
relative error = 0.03866 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.626
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8544 0.613
h = 0.0001 0.004
y[1] (numeric) = -0.228899314507 0.620874258772
y[1] (closed_form) = -0.229130186464 0.620977190997
absolute error = 0.0002528
relative error = 0.03819 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6287
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8543 0.617
h = 0.003 0.006
y[1] (numeric) = -0.233495105512 0.62140954485
y[1] (closed_form) = -0.233723850351 0.621512589504
absolute error = 0.0002509
relative error = 0.03778 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6326
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8513 0.623
h = 0.0001 0.005
y[1] (numeric) = -0.24007742013 0.625473925873
y[1] (closed_form) = -0.240310622248 0.625568989562
absolute error = 0.0002518
relative error = 0.03758 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6378
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8512 0.628
h = 0.0001 0.003
y[1] (numeric) = -0.245799452233 0.626074338279
y[1] (closed_form) = -0.246030832945 0.626174878223
absolute error = 0.0002523
relative error = 0.0375 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6427
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8511 0.631
h = 0.001 0.001
y[1] (numeric) = -0.24921899502 0.626476566596
y[1] (closed_form) = -0.249452114783 0.626578481152
absolute error = 0.0002544
relative error = 0.03773 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6456
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8501 0.632
h = 0.0001 0.004
y[1] (numeric) = -0.250265858366 0.627713511707
y[1] (closed_form) = -0.250499596477 0.627816380109
absolute error = 0.0002554
relative error = 0.03778 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6464
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.85 0.636
h = 0.003 0.006
y[1] (numeric) = -0.254826559869 0.628204495298
y[1] (closed_form) = -0.255056026325 0.628305748212
absolute error = 0.0002508
relative error = 0.03699 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6503
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.847 0.642
h = 0.0001 0.005
y[1] (numeric) = -0.261385374365 0.632174292168
y[1] (closed_form) = -0.261618734623 0.632268108508
absolute error = 0.0002515
relative error = 0.03676 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6555
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=697.4MB, alloc=52.3MB, time=8.47
x[1] = -0.8469 0.647
h = 0.0001 0.003
y[1] (numeric) = -0.267061453038 0.63272125553
y[1] (closed_form) = -0.267293274915 0.632820143897
absolute error = 0.000252
relative error = 0.03669 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6604
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8468 0.65
h = 0.001 0.001
y[1] (numeric) = -0.270454550853 0.633091594196
y[1] (closed_form) = -0.270688002999 0.6331917025
absolute error = 0.000254
relative error = 0.03689 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6633
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8458 0.651
h = 0.001 0.003
y[1] (numeric) = -0.27150254628 0.634309230389
y[1] (closed_form) = -0.271736589355 0.634410199601
absolute error = 0.0002549
relative error = 0.03693 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6641
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8448 0.654
h = 0.0001 0.004
y[1] (numeric) = -0.274818637932 0.635694651472
y[1] (closed_form) = -0.275051400108 0.635793930701
absolute error = 0.0002531
relative error = 0.03653 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6668
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8447 0.658
h = 0.0001 0.004
y[1] (numeric) = -0.279336607498 0.636135659204
y[1] (closed_form) = -0.279567607822 0.636235136283
absolute error = 0.0002515
relative error = 0.03619 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6707
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8446 0.662
h = 0.003 0.006
y[1] (numeric) = -0.283844462321 0.636570558935
y[1] (closed_form) = -0.284075462646 0.636670036013
absolute error = 0.0002515
relative error = 0.03608 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6746
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8416 0.668
h = 0.0001 0.005
y[1] (numeric) = -0.290368749952 0.640425263342
y[1] (closed_form) = -0.290602995772 0.640518006562
absolute error = 0.0002519
relative error = 0.03582 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.68
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8415 0.673
h = 0.0001 0.003
y[1] (numeric) = -0.295985107252 0.640909081245
y[1] (closed_form) = -0.296218131648 0.641006384301
absolute error = 0.0002525
relative error = 0.03576 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8414 0.676
h = 0.001 0.001
y[1] (numeric) = -0.299343767804 0.641241673599
y[1] (closed_form) = -0.299578279193 0.641340015507
absolute error = 0.0002543
relative error = 0.03592 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6878
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8404 0.677
h = 0.001 0.003
y[1] (numeric) = -0.300392035233 0.642435454001
y[1] (closed_form) = -0.300627097738 0.64253454538
absolute error = 0.0002551
relative error = 0.03596 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6886
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8394 0.68
h = 0.0001 0.004
y[1] (numeric) = -0.303684491345 0.64377302359
y[1] (closed_form) = -0.303918364529 0.643870647134
absolute error = 0.0002534
relative error = 0.03559 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6914
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8393 0.684
h = 0.003 0.006
y[1] (numeric) = -0.30815669351 0.644166000675
y[1] (closed_form) = -0.308389003315 0.644263850927
absolute error = 0.0002521
relative error = 0.03529 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6953
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=742.1MB, alloc=52.3MB, time=9.01
x[1] = -0.8363 0.69
h = 0.0001 0.005
y[1] (numeric) = -0.314654515859 0.647932558973
y[1] (closed_form) = -0.314889584764 0.648024212758
absolute error = 0.0002523
relative error = 0.03502 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7007
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8362 0.695
h = 0.0001 0.003
y[1] (numeric) = -0.320225139655 0.648367994592
y[1] (closed_form) = -0.320459224086 0.648463817717
absolute error = 0.0002529
relative error = 0.03497 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7056
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8361 0.698
h = 0.001 0.001
y[1] (numeric) = -0.323557426526 0.648671654986
y[1] (closed_form) = -0.323792888093 0.648768380517
absolute error = 0.0002546
relative error = 0.03511 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7085
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8351 0.699
h = 0.001 0.003
y[1] (numeric) = -0.324605911598 0.649847155851
y[1] (closed_form) = -0.324841893371 0.649944546558
absolute error = 0.0002553
relative error = 0.03513 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7093
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8341 0.702
h = 0.0001 0.004
y[1] (numeric) = -0.32788027867 0.651148050965
y[1] (closed_form) = -0.328115141974 0.651244141806
absolute error = 0.0002538
relative error = 0.0348 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7121
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.834 0.706
h = 0.003 0.006
y[1] (numeric) = -0.332317437565 0.651504194802
y[1] (closed_form) = -0.332550888275 0.651600533079
absolute error = 0.0002525
relative error = 0.03452 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.716
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.831 0.712
h = 0.0001 0.005
y[1] (numeric) = -0.338788866378 0.655191496798
y[1] (closed_form) = -0.339024656924 0.655282138268
absolute error = 0.0002526
relative error = 0.03424 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7215
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8309 0.717
h = 0.0001 0.003
y[1] (numeric) = -0.344316703999 0.655584251416
y[1] (closed_form) = -0.344551710253 0.655678703116
absolute error = 0.0002533
relative error = 0.03419 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7264
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8308 0.72
h = 0.001 0.001
y[1] (numeric) = -0.347624287116 0.655862355097
y[1] (closed_form) = -0.347860567156 0.655957590054
absolute error = 0.0002548
relative error = 0.03431 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7293
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8298 0.721
h = 0.001 0.003
y[1] (numeric) = -0.34867248545 0.657021259492
y[1] (closed_form) = -0.348909255108 0.657117084787
absolute error = 0.0002554
relative error = 0.03433 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7301
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8288 0.724
h = 0.0001 0.004
y[1] (numeric) = -0.351929465656 0.658289348444
y[1] (closed_form) = -0.352165186101 0.658384022705
absolute error = 0.000254
relative error = 0.03402 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.733
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8287 0.728
h = 0.003 0.006
y[1] (numeric) = -0.356333848507 0.658612981324
y[1] (closed_form) = -0.356568292752 0.65870791678
absolute error = 0.0002529
relative error = 0.03377 %
Correct digits = 3
memory used=786.9MB, alloc=52.3MB, time=9.56
Radius of convergence (given) for eq 1 = 0.7369
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8257 0.734
h = 0.0001 0.005
y[1] (numeric) = -0.362779242501 0.662229023484
y[1] (closed_form) = -0.363015665165 0.662318725491
absolute error = 0.0002529
relative error = 0.03348 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7424
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8256 0.739
h = 0.0001 0.003
y[1] (numeric) = -0.368267131315 0.662584132556
y[1] (closed_form) = -0.368502938604 0.662677315048
absolute error = 0.0002536
relative error = 0.03344 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7473
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8255 0.742
h = 0.001 0.001
y[1] (numeric) = -0.37155162306 0.662839664476
y[1] (closed_form) = -0.371788607273 0.662933526141
absolute error = 0.0002549
relative error = 0.03354 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7502
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8245 0.743
h = 0.001 0.003
y[1] (numeric) = -0.372599134599 0.663983504128
y[1] (closed_form) = -0.372836578523 0.664077889666
absolute error = 0.0002555
relative error = 0.03355 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7511
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8235 0.746
h = 0.0001 0.004
y[1] (numeric) = -0.375839484179 0.665222247317
y[1] (closed_form) = -0.376075945941 0.665315613746
absolute error = 0.0002542
relative error = 0.03326 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7539
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8234 0.75
h = 0.003 0.006
y[1] (numeric) = -0.380213270187 0.665517189647
y[1] (closed_form) = -0.380448579087 0.665610825437
absolute error = 0.0002533
relative error = 0.03303 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7579
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8204 0.756
h = 0.0001 0.005
y[1] (numeric) = -0.386633205094 0.669069164257
y[1] (closed_form) = -0.386870180881 0.669157995385
absolute error = 0.0002531
relative error = 0.03274 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7634
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8203 0.761
h = 0.0001 0.003
y[1] (numeric) = -0.39208385771 0.669391077059
y[1] (closed_form) = -0.392320360432 0.669483086246
absolute error = 0.0002538
relative error = 0.0327 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7683
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8202 0.764
h = 0.001 0.001
y[1] (numeric) = -0.395346803507 0.66962667803
y[1] (closed_form) = -0.395584392657 0.669719275442
absolute error = 0.000255
relative error = 0.03278 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7713
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8192 0.765
h = 0.0001 0.004
y[1] (numeric) = -0.396393314702 0.670756846063
y[1] (closed_form) = -0.396631334589 0.670849908297
absolute error = 0.0002556
relative error = 0.03279 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7721
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8191 0.769
h = 0.003 0.006
y[1] (numeric) = -0.400743590452 0.671030895694
y[1] (closed_form) = -0.400979109912 0.671123477412
absolute error = 0.0002531
relative error = 0.03237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7761
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=831.6MB, alloc=52.3MB, time=10.10
x[1] = -0.8161 0.775
h = 0.0001 0.005
y[1] (numeric) = -0.407141536283 0.674533219269
y[1] (closed_form) = -0.407378493764 0.674621342206
absolute error = 0.0002528
relative error = 0.03208 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7816
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.816 0.78
h = 0.0001 0.003
y[1] (numeric) = -0.412561874715 0.674830126854
y[1] (closed_form) = -0.412798460156 0.674921186544
absolute error = 0.0002535
relative error = 0.03204 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7866
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8159 0.783
h = 0.001 0.001
y[1] (numeric) = -0.415807256312 0.675050686823
y[1] (closed_form) = -0.416044854323 0.675142266662
absolute error = 0.0002546
relative error = 0.03211 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7895
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8149 0.784
h = 0.001 0.003
y[1] (numeric) = -0.416852567804 0.676170121041
y[1] (closed_form) = -0.417090571896 0.67626212049
absolute error = 0.0002552
relative error = 0.03211 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7904
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8139 0.787
h = 0.0001 0.004
y[1] (numeric) = -0.420063811081 0.677362425251
y[1] (closed_form) = -0.420300951775 0.677453611909
absolute error = 0.0002541
relative error = 0.03187 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7932
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8138 0.791
h = 0.003 0.006
y[1] (numeric) = -0.424385868747 0.677612981223
y[1] (closed_form) = -0.424622055455 0.677704440098
absolute error = 0.0002533
relative error = 0.03167 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7972
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8108 0.797
h = 0.0001 0.005
y[1] (numeric) = -0.430759887512 0.681062740983
y[1] (closed_form) = -0.430997275743 0.681150110242
absolute error = 0.000253
relative error = 0.03138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8028
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8107 0.802
h = 0.0001 0.003
y[1] (numeric) = -0.436147717946 0.68133337564
y[1] (closed_form) = -0.436384837267 0.681423425008
absolute error = 0.0002536
relative error = 0.03135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8077
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8106 0.805
h = 0.001 0.001
y[1] (numeric) = -0.439374256599 0.681538121665
y[1] (closed_form) = -0.439612309363 0.681628620312
absolute error = 0.0002547
relative error = 0.0314 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8107
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8096 0.806
h = 0.001 0.003
y[1] (numeric) = -0.440418178764 0.682646149941
y[1] (closed_form) = -0.440656610856 0.682737020757
absolute error = 0.0002552
relative error = 0.0314 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8116
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8086 0.809
h = 0.0001 0.004
y[1] (numeric) = -0.44361510089 0.683817116715
y[1] (closed_form) = -0.443852728376 0.683907268403
absolute error = 0.0002542
relative error = 0.03117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8144
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8085 0.813
h = 0.003 0.006
y[1] (numeric) = -0.447912265738 0.684047622
y[1] (closed_form) = -0.448149031632 0.684138043725
absolute error = 0.0002534
relative error = 0.03099 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8184
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=876.3MB, alloc=52.3MB, time=10.65
x[1] = -0.8055 0.819
h = 0.0001 0.005
y[1] (numeric) = -0.454263274826 0.687450129594
y[1] (closed_form) = -0.454501038582 0.687536801957
absolute error = 0.0002531
relative error = 0.03071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.824
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8054 0.824
h = 0.0001 0.003
y[1] (numeric) = -0.459620914151 0.687697622401
y[1] (closed_form) = -0.459858495286 0.687786739998
absolute error = 0.0002537
relative error = 0.03067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8053 0.827
h = 0.001 0.001
y[1] (numeric) = -0.462829937424 0.687888419298
y[1] (closed_form) = -0.463068378515 0.687977924216
absolute error = 0.0002547
relative error = 0.03071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.832
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8043 0.828
h = 0.001 0.003
y[1] (numeric) = -0.46387232914 0.688986100895
y[1] (closed_form) = -0.464111124079 0.689075935792
absolute error = 0.0002551
relative error = 0.03071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8328
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8033 0.831
h = 0.0001 0.004
y[1] (numeric) = -0.467055722467 0.690137985432
y[1] (closed_form) = -0.467293768499 0.69022718434
absolute error = 0.0002542
relative error = 0.0305 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8357
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8032 0.835
h = 0.003 0.006
y[1] (numeric) = -0.471329768705 0.690350822043
y[1] (closed_form) = -0.471567036674 0.690440286546
absolute error = 0.0002536
relative error = 0.03033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8397
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8002 0.841
h = 0.0001 0.005
y[1] (numeric) = -0.477658741897 0.693710856725
y[1] (closed_form) = -0.477896832477 0.693796885169
absolute error = 0.0002532
relative error = 0.03005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8453
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8001 0.846
h = 0.0001 0.003
y[1] (numeric) = -0.482988369654 0.693937978264
y[1] (closed_form) = -0.483226349544 0.694026237097
absolute error = 0.0002538
relative error = 0.03001 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8503
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8 0.849
h = 0.001 0.001
y[1] (numeric) = -0.486181128474 0.694116478085
y[1] (closed_form) = -0.486419900172 0.694205070074
absolute error = 0.0002547
relative error = 0.03004 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8533
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.799 0.85
h = 0.001 0.003
y[1] (numeric) = -0.487221890176 0.695204775327
y[1] (closed_form) = -0.487460991552 0.695293659764
absolute error = 0.0002551
relative error = 0.03004 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8542
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.798 0.853
h = 0.0001 0.004
y[1] (numeric) = -0.490392531481 0.696339597366
y[1] (closed_form) = -0.490630936543 0.696427919633
absolute error = 0.0002542
relative error = 0.02984 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8571
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7979 0.857
h = 0.003 0.006
y[1] (numeric) = -0.494645127617 0.696536874393
y[1] (closed_form) = -0.494882830135 0.696625456067
absolute error = 0.0002537
relative error = 0.02969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.861
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=921.0MB, alloc=52.3MB, time=11.20
x[1] = -0.7949 0.863
h = 0.0001 0.005
y[1] (numeric) = -0.500953071816 0.699858737017
y[1] (closed_form) = -0.501191446293 0.699944170893
absolute error = 0.0002532
relative error = 0.02941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8667
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7948 0.868
h = 0.0001 0.003
y[1] (numeric) = -0.506256733058 0.700067939446
y[1] (closed_form) = -0.50649505653 0.700155407263
absolute error = 0.0002539
relative error = 0.02938 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8717
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7947 0.871
h = 0.001 0.001
y[1] (numeric) = -0.509434402929 0.700235606066
y[1] (closed_form) = -0.509673455091 0.700323359696
absolute error = 0.0002547
relative error = 0.0294 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8747
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7937 0.872
h = 0.0001 0.004
y[1] (numeric) = -0.510473469216 0.701315393105
y[1] (closed_form) = -0.510712828205 0.701403405792
absolute error = 0.000255
relative error = 0.02939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8756
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7936 0.876
h = 0.003 0.006
y[1] (numeric) = -0.51470966973 0.701501372841
y[1] (closed_form) = -0.514947418891 0.701589276167
absolute error = 0.0002535
relative error = 0.02913 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8796
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7906 0.882
h = 0.0001 0.005
y[1] (numeric) = -0.52099993794 0.704793726694
y[1] (closed_form) = -0.521238249624 0.704878713141
absolute error = 0.000253
relative error = 0.02886 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8853
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7905 0.887
h = 0.0001 0.003
y[1] (numeric) = -0.526282607144 0.704989531339
y[1] (closed_form) = -0.526520908707 0.70507639566
absolute error = 0.0002536
relative error = 0.02882 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8902
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7904 0.89
h = 0.001 0.001
y[1] (numeric) = -0.529448065764 0.705149079698
y[1] (closed_form) = -0.529687045008 0.705236194571
absolute error = 0.0002544
relative error = 0.02884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8932
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7894 0.891
h = 0.001 0.003
y[1] (numeric) = -0.530485553144 0.70622220077
y[1] (closed_form) = -0.530724820254 0.706309549168
absolute error = 0.0002547
relative error = 0.02883 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8941
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7884 0.894
h = 0.0001 0.004
y[1] (numeric) = -0.533634301131 0.707330075822
y[1] (closed_form) = -0.533872962322 0.707416977592
absolute error = 0.000254
relative error = 0.02866 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.897
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7883 0.898
h = 0.003 0.006
y[1] (numeric) = -0.537850936362 0.707503421013
y[1] (closed_form) = -0.538089016697 0.707590566724
absolute error = 0.0002535
relative error = 0.02852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.901
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=965.7MB, alloc=52.3MB, time=11.75
x[1] = -0.7853 0.904
h = 0.0001 0.005
y[1] (numeric) = -0.544122117457 0.710764482542
y[1] (closed_form) = -0.544360646786 0.710848957609
absolute error = 0.000253
relative error = 0.02826 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9068
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7852 0.909
h = 0.0001 0.003
y[1] (numeric) = -0.549382304305 0.710946185907
y[1] (closed_form) = -0.549620865191 0.711032372782
absolute error = 0.0002537
relative error = 0.02822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9117
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7851 0.912
h = 0.001 0.001
y[1] (numeric) = -0.552534681023 0.71109718435
y[1] (closed_form) = -0.552773865066 0.71118358491
absolute error = 0.0002543
relative error = 0.02823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9147
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7841 0.913
h = 0.001 0.003
y[1] (numeric) = -0.553570430083 0.712163214139
y[1] (closed_form) = -0.553809881591 0.71224982133
absolute error = 0.0002546
relative error = 0.02822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9156
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7831 0.916
h = 0.0001 0.004
y[1] (numeric) = -0.556708533409 0.713258708633
y[1] (closed_form) = -0.556947422925 0.71334492181
absolute error = 0.000254
relative error = 0.02806 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9186
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.783 0.92
h = 0.003 0.006
y[1] (numeric) = -0.560907949972 0.713421272288
y[1] (closed_form) = -0.561146315239 0.713507720387
absolute error = 0.0002536
relative error = 0.02793 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9225
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.78 0.926
h = 0.0001 0.005
y[1] (numeric) = -0.567161053466 0.71665422477
y[1] (closed_form) = -0.567399770561 0.716738228415
absolute error = 0.0002531
relative error = 0.02768 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9283
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7799 0.931
h = 0.0001 0.003
y[1] (numeric) = -0.57240044142 0.716823558596
y[1] (closed_form) = -0.572639223978 0.716909122319
absolute error = 0.0002536
relative error = 0.02764 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9333
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7798 0.934
h = 0.001 0.001
y[1] (numeric) = -0.575540707422 0.716967044296
y[1] (closed_form) = -0.575780062768 0.717052789517
absolute error = 0.0002543
relative error = 0.02765 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9363
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7788 0.935
h = 0.001 0.003
y[1] (numeric) = -0.576574718932 0.718026646369
y[1] (closed_form) = -0.576814322586 0.718112574285
absolute error = 0.0002545
relative error = 0.02764 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9372
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7778 0.938
h = 0.0001 0.004
y[1] (numeric) = -0.579702851267 0.719111082615
y[1] (closed_form) = -0.579941934048 0.719196663257
absolute error = 0.0002539
relative error = 0.02749 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9401
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7777 0.942
h = 0.003 0.006
y[1] (numeric) = -0.583886337384 0.719264185824
y[1] (closed_form) = -0.584124947108 0.719349991871
absolute error = 0.0002536
relative error = 0.02736 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9441
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1010.4MB, alloc=52.3MB, time=12.30
x[1] = -0.7747 0.948
h = 0.0001 0.005
y[1] (numeric) = -0.59012235501 0.722471895401
y[1] (closed_form) = -0.590361233589 0.722555464683
absolute error = 0.0002531
relative error = 0.02712 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9499
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7746 0.953
h = 0.0001 0.003
y[1] (numeric) = -0.595342513156 0.72263039277
y[1] (closed_form) = -0.595581484489 0.722715383525
absolute error = 0.0002536
relative error = 0.02708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9549
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7745 0.956
h = 0.001 0.001
y[1] (numeric) = -0.598471574659 0.722767284976
y[1] (closed_form) = -0.598711072277 0.722852429154
absolute error = 0.0002542
relative error = 0.02708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9579
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7735 0.957
h = 0.001 0.003
y[1] (numeric) = -0.599503864786 0.723821061987
y[1] (closed_form) = -0.599743592756 0.723906367553
absolute error = 0.0002545
relative error = 0.02707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9588
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7725 0.96
h = 0.0001 0.004
y[1] (numeric) = -0.602622668732 0.724895625235
y[1] (closed_form) = -0.602861914261 0.724980625044
absolute error = 0.0002539
relative error = 0.02693 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9617
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7724 0.964
h = 0.003 0.006
y[1] (numeric) = -0.606791425122 0.725040438089
y[1] (closed_form) = -0.60703024389 0.725125653483
absolute error = 0.0002536
relative error = 0.02681 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9657
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7694 0.97
h = 0.0001 0.005
y[1] (numeric) = -0.613011324077 0.728225485553
y[1] (closed_form) = -0.613250341041 0.728308654812
absolute error = 0.0002531
relative error = 0.02658 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9715
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7693 0.975
h = 0.0001 0.003
y[1] (numeric) = -0.618213713147 0.728374503463
y[1] (closed_form) = -0.618452844525 0.728458967602
absolute error = 0.0002536
relative error = 0.02654 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9765
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7692 0.978
h = 0.001 0.001
y[1] (numeric) = -0.621332414667 0.728505616794
y[1] (closed_form) = -0.621572029425 0.728590209887
absolute error = 0.0002541
relative error = 0.02653 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9795
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7682 0.979
h = 0.0001 0.004
y[1] (numeric) = -0.622363011867 0.729554116046
y[1] (closed_form) = -0.622602840173 0.729638851566
absolute error = 0.0002544
relative error = 0.02652 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9805
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7681 0.983
h = 0.003 0.006
y[1] (numeric) = -0.626520545079 0.729692944794
y[1] (closed_form) = -0.626759342959 0.729777726723
absolute error = 0.0002534
relative error = 0.02634 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9845
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7651 0.989
h = 0.0001 0.005
y[1] (numeric) = -0.632727088807 0.732860532168
y[1] (closed_form) = -0.632966034692 0.732943420089
absolute error = 0.0002529
relative error = 0.02612 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9903
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1055.0MB, alloc=52.3MB, time=12.85
x[1] = -0.765 0.994
h = 0.0001 0.003
y[1] (numeric) = -0.637915180485 0.733002547291
y[1] (closed_form) = -0.63815425424 0.733086629779
absolute error = 0.0002534
relative error = 0.02607 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9953
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7649 0.997
h = 0.001 0.001
y[1] (numeric) = -0.641025538734 0.733129378272
y[1] (closed_form) = -0.641265061379 0.733213571662
absolute error = 0.0002539
relative error = 0.02606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9983
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7639 0.998
h = 0.001 0.003
y[1] (numeric) = -0.642054654034 0.734173753878
y[1] (closed_form) = -0.642294376453 0.734258075239
absolute error = 0.0002541
relative error = 0.02605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9992
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7629 1.001
h = 0.0001 0.004
y[1] (numeric) = -0.645157612234 0.735232783704
y[1] (closed_form) = -0.645396917388 0.735316864207
absolute error = 0.0002536
relative error = 0.02593 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.002
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7628 1.005
h = 0.003 0.006
y[1] (numeric) = -0.649301803587 0.735364982283
y[1] (closed_form) = -0.649540756547 0.735449259364
absolute error = 0.0002534
relative error = 0.02582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.006
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7598 1.011
h = 0.0001 0.005
y[1] (numeric) = -0.655493970938 0.738514035176
y[1] (closed_form) = -0.655733019815 0.738596580533
absolute error = 0.0002529
relative error = 0.02561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.012
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7597 1.016
h = 0.0001 0.003
y[1] (numeric) = -0.660666756014 0.738648679137
y[1] (closed_form) = -0.660905946229 0.73873231221
absolute error = 0.0002534
relative error = 0.02556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.017
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7596 1.019
h = 0.001 0.001
y[1] (numeric) = -0.663768180175 0.738770999306
y[1] (closed_form) = -0.664007782425 0.738854724363
absolute error = 0.0002538
relative error = 0.02555 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.02
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7586 1.02
h = 0.001 0.003
y[1] (numeric) = -0.664795684792 0.739810984665
y[1] (closed_form) = -0.665035472036 0.739894822423
absolute error = 0.000254
relative error = 0.02553 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.021
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7576 1.023
h = 0.0001 0.004
y[1] (numeric) = -0.667890988221 0.740862890272
y[1] (closed_form) = -0.668130389618 0.740946516751
absolute error = 0.0002536
relative error = 0.02542 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.024
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7575 1.027
h = 0.003 0.006
y[1] (numeric) = -0.672023452328 0.740989445391
y[1] (closed_form) = -0.672262536256 0.741073258557
absolute error = 0.0002533
relative error = 0.02532 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.028
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7545 1.033
h = 0.0001 0.005
y[1] (numeric) = -0.678202114841 0.744121876343
y[1] (closed_form) = -0.67844125081 0.744204106613
absolute error = 0.0002529
relative error = 0.02511 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.034
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1099.9MB, alloc=52.3MB, time=13.39
x[1] = -0.7544 1.038
h = 0.0001 0.003
y[1] (numeric) = -0.683360775831 0.744250105752
y[1] (closed_form) = -0.683600063087 0.744333326189
absolute error = 0.0002533
relative error = 0.02507 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.039
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7543 1.041
h = 0.001 0.001
y[1] (numeric) = -0.686453951367 0.744368491322
y[1] (closed_form) = -0.686693616699 0.744451787317
absolute error = 0.0002537
relative error = 0.02505 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.042
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7533 1.042
h = 0.001 0.003
y[1] (numeric) = -0.687479895472 0.745404501723
y[1] (closed_form) = -0.687719732013 0.745487896838
absolute error = 0.0002539
relative error = 0.02504 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.043
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7523 1.045
h = 0.0001 0.004
y[1] (numeric) = -0.690568064609 0.746450060359
y[1] (closed_form) = -0.690807544543 0.746533270446
absolute error = 0.0002535
relative error = 0.02493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.046
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7522 1.049
h = 0.003 0.006
y[1] (numeric) = -0.694689706623 0.746571703276
y[1] (closed_form) = -0.69492890049 0.746655090297
absolute error = 0.0002533
relative error = 0.02483 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.05
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7492 1.055
h = 0.0001 0.005
y[1] (numeric) = -0.700855699022 0.749689234434
y[1] (closed_form) = -0.701094908171 0.749771175014
absolute error = 0.0002529
relative error = 0.02463 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.056
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7491 1.06
h = 0.0001 0.003
y[1] (numeric) = -0.706001333044 0.749811894812
y[1] (closed_form) = -0.706240700457 0.749894736515
absolute error = 0.0002533
relative error = 0.02459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.061
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.749 1.063
h = 0.001 0.001
y[1] (numeric) = -0.709086896446 0.749926855723
y[1] (closed_form) = -0.70932661066 0.750009758749
absolute error = 0.0002536
relative error = 0.02457 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.064
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.748 1.064
h = 0.001 0.003
y[1] (numeric) = -0.710111334626 0.750959268232
y[1] (closed_form) = -0.710351207205 0.751042258302
absolute error = 0.0002538
relative error = 0.02455 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.065
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.747 1.067
h = 0.0001 0.004
y[1] (numeric) = -0.713192860036 0.751999176474
y[1] (closed_form) = -0.713432403196 0.752082004803
absolute error = 0.0002535
relative error = 0.02445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.067
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7469 1.071
h = 0.003 0.006
y[1] (numeric) = -0.717304519824 0.752116553748
y[1] (closed_form) = -0.717543805312 0.752199549461
absolute error = 0.0002533
relative error = 0.02436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.071
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1144.4MB, alloc=52.3MB, time=13.93
x[1] = -0.7439 1.077
h = 0.0001 0.005
y[1] (numeric) = -0.723458639041 0.755220735677
y[1] (closed_form) = -0.723697909214 0.755302410027
absolute error = 0.0002528
relative error = 0.02417 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.077
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7438 1.082
h = 0.0001 0.003
y[1] (numeric) = -0.728592263282 0.755338573878
y[1] (closed_form) = -0.728831696202 0.755421068082
absolute error = 0.0002532
relative error = 0.02413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.082
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7437 1.085
h = 0.001 0.001
y[1] (numeric) = -0.73167080514 0.755450561149
y[1] (closed_form) = -0.731910556064 0.755533104366
absolute error = 0.0002536
relative error = 0.0241 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.085
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7427 1.086
h = 0.0001 0.004
y[1] (numeric) = -0.732693795103 0.756479718097
y[1] (closed_form) = -0.732933692436 0.756562337625
absolute error = 0.0002537
relative error = 0.02409 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.086
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7426 1.09
h = 0.003 0.006
y[1] (numeric) = -0.736797866817 0.756594048309
y[1] (closed_form) = -0.737037108385 0.756676768721
absolute error = 0.0002531
relative error = 0.02396 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.09
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7396 1.096
h = 0.0001 0.005
y[1] (numeric) = -0.742942238263 0.759687992031
y[1] (closed_form) = -0.743181443799 0.759769490617
absolute error = 0.0002527
relative error = 0.02378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7395 1.101
h = 0.0001 0.003
y[1] (numeric) = -0.748066235296 0.759802338286
y[1] (closed_form) = -0.748305604894 0.759884592469
absolute error = 0.0002531
relative error = 0.02373 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7394 1.104
h = 0.001 0.001
y[1] (numeric) = -0.751139144215 0.759912161812
y[1] (closed_form) = -0.751378808755 0.759994456079
absolute error = 0.0002534
relative error = 0.02371 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.104
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7384 1.105
h = 0.001 0.003
y[1] (numeric) = -0.752160901588 0.760938782703
y[1] (closed_form) = -0.752400702807 0.761021145138
absolute error = 0.0002536
relative error = 0.02369 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.105
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7374 1.108
h = 0.0001 0.004
y[1] (numeric) = -0.755231220849 0.76196985495
y[1] (closed_form) = -0.755470738412 0.762052091895
absolute error = 0.0002532
relative error = 0.0236 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.108
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7373 1.112
h = 0.003 0.006
y[1] (numeric) = -0.759326299052 0.76208086216
y[1] (closed_form) = -0.759565604627 0.762163249154
absolute error = 0.0002531
relative error = 0.02352 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.112
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7343 1.118
h = 0.0001 0.005
y[1] (numeric) = -0.765460193048 0.765163933471
y[1] (closed_form) = -0.765699441222 0.76524520489
absolute error = 0.0002527
relative error = 0.02334 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.118
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1189.0MB, alloc=52.3MB, time=14.47
x[1] = -0.7342 1.123
h = 0.0001 0.003
y[1] (numeric) = -0.770573884651 0.765274611373
y[1] (closed_form) = -0.770813297834 0.765356569879
absolute error = 0.0002531
relative error = 0.0233 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.123
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7341 1.126
h = 0.001 0.001
y[1] (numeric) = -0.773640762793 0.765382159622
y[1] (closed_form) = -0.773880446268 0.765464148855
absolute error = 0.0002533
relative error = 0.02327 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.126
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7331 1.127
h = 0.001 0.003
y[1] (numeric) = -0.774661187343 0.766406079388
y[1] (closed_form) = -0.774900997066 0.766488128175
absolute error = 0.0002535
relative error = 0.02325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.127
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7321 1.13
h = 0.0001 0.004
y[1] (numeric) = -0.777726115754 0.7674331141
y[1] (closed_form) = -0.777965663787 0.767515053891
absolute error = 0.0002532
relative error = 0.02317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.13
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.732 1.134
h = 0.003 0.006
y[1] (numeric) = -0.781813295539 0.767541309915
y[1] (closed_form) = -0.782052652865 0.767623391044
absolute error = 0.000253
relative error = 0.02309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.134
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.729 1.14
h = 0.0001 0.005
y[1] (numeric) = -0.787937398838 0.770614656685
y[1] (closed_form) = -0.788176681461 0.770695719567
absolute error = 0.0002526
relative error = 0.02292 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.14
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7289 1.145
h = 0.0001 0.003
y[1] (numeric) = -0.793041600759 0.770722188285
y[1] (closed_form) = -0.793281047851 0.770803875756
absolute error = 0.000253
relative error = 0.02287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.145
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7288 1.148
h = 0.001 0.001
y[1] (numeric) = -0.796102922725 0.77082777777
y[1] (closed_form) = -0.796342617435 0.770909487939
absolute error = 0.0002532
relative error = 0.02285 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.148
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7278 1.149
h = 0.001 0.003
y[1] (numeric) = -0.797122075474 0.77184925586
y[1] (closed_form) = -0.797361886743 0.771931017941
absolute error = 0.0002534
relative error = 0.02283 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.149
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7268 1.152
h = 0.0001 0.004
y[1] (numeric) = -0.800181997298 0.772872708603
y[1] (closed_form) = -0.80042156725 0.772954376282
absolute error = 0.0002531
relative error = 0.02275 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.152
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7267 1.156
h = 0.003 0.006
y[1] (numeric) = -0.804261903396 0.772978492677
y[1] (closed_form) = -0.804501301872 0.773060293315
absolute error = 0.000253
relative error = 0.02267 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.156
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7237 1.162
h = 0.0001 0.005
y[1] (numeric) = -0.81037686585 0.776043147701
y[1] (closed_form) = -0.810616175825 0.776124019223
absolute error = 0.0002526
relative error = 0.02251 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.162
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1233.6MB, alloc=52.3MB, time=15.02
x[1] = -0.7236 1.167
h = 0.0001 0.003
y[1] (numeric) = -0.815472332777 0.776147992515
y[1] (closed_form) = -0.815711805458 0.776229431623
absolute error = 0.0002529
relative error = 0.02246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.167
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7235 1.17
h = 0.001 0.001
y[1] (numeric) = -0.818528537935 0.776251902262
y[1] (closed_form) = -0.818768237386 0.776333357205
absolute error = 0.0002532
relative error = 0.02244 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.17
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7225 1.171
h = 0.001 0.003
y[1] (numeric) = -0.819546479838 0.777271174098
y[1] (closed_form) = -0.819786286853 0.777352674177
absolute error = 0.0002533
relative error = 0.02242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.171
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7215 1.174
h = 0.0001 0.004
y[1] (numeric) = -0.822601754876 0.778291452601
y[1] (closed_form) = -0.822841339455 0.778372871178
absolute error = 0.000253
relative error = 0.02234 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.174
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7214 1.178
h = 0.003 0.006
y[1] (numeric) = -0.826674965315 0.7783951768
y[1] (closed_form) = -0.826914395795 0.778476720302
absolute error = 0.0002529
relative error = 0.02227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.178
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7184 1.184
h = 0.0001 0.005
y[1] (numeric) = -0.832781400776 0.781452069072
y[1] (closed_form) = -0.83302073197 0.781532765065
absolute error = 0.0002526
relative error = 0.02211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.184
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7183 1.189
h = 0.0001 0.003
y[1] (numeric) = -0.837868830567 0.781554631062
y[1] (closed_form) = -0.838108321708 0.781635842661
absolute error = 0.0002529
relative error = 0.02207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.189
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7182 1.192
h = 0.001 0.001
y[1] (numeric) = -0.84092032546 0.781657106763
y[1] (closed_form) = -0.841160024207 0.781738328355
absolute error = 0.0002531
relative error = 0.02204 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.192
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7172 1.193
h = 0.0001 0.004
y[1] (numeric) = -0.841937116901 0.782674385923
y[1] (closed_form) = -0.842176914866 0.782755646649
absolute error = 0.0002532
relative error = 0.02202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.193
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7171 1.197
h = 0.003 0.006
y[1] (numeric) = -0.84600524784 0.782776666456
y[1] (closed_form) = -0.846244631299 0.78285803629
absolute error = 0.0002528
relative error = 0.02193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.197
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7141 1.203
h = 0.0001 0.005
y[1] (numeric) = -0.852104729267 0.785827641251
y[1] (closed_form) = -0.852344007102 -0.784888098442
absolute error = 1.571
relative error = 135.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.203
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.714 1.208
h = 0.0001 0.003
y[1] (numeric) = -0.857185737772 0.785928609326
y[1] (closed_form) = -0.857425171985 -0.784786655766
absolute error = 1.571
relative error = 135.1 %
Correct digits = 0
memory used=1278.2MB, alloc=52.3MB, time=15.56
Radius of convergence (given) for eq 1 = 1.208
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7139 1.211
h = 0.001 0.001
y[1] (numeric) = -0.860233466738 0.786030074759
y[1] (closed_form) = -0.860473093254 -0.784685184445
absolute error = 1.571
relative error = 134.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.211
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7129 1.212
h = 0.001 0.003
y[1] (numeric) = -0.861249294876 0.787045807247
y[1] (closed_form) = -0.861489013854 -0.783669417344
absolute error = 1.571
relative error = 134.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.212
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7119 1.215
h = 0.0001 0.004
y[1] (numeric) = -0.86429677392 0.788061166743
y[1] (closed_form) = -0.864536302084 -0.78265411942
absolute error = 1.571
relative error = 134.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.215
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7118 1.219
h = 0.003 0.006
y[1] (numeric) = -0.86835890056 0.788161918022
y[1] (closed_form) = -0.868598302522 -0.78255325739
absolute error = 1.571
relative error = 134.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.219
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7088 1.225
h = 0.0001 0.005
y[1] (numeric) = -0.874450913795 0.791206610161
y[1] (closed_form) = -0.874690203777 -0.7795092788
absolute error = 1.571
relative error = 134.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.225
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7087 1.23
h = 0.0001 0.003
y[1] (numeric) = -0.87952504943 0.791305913121
y[1] (closed_form) = -0.879764491723 -0.779409544988
absolute error = 1.571
relative error = 133.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.23
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7086 1.233
h = 0.001 0.001
y[1] (numeric) = -0.882568747069 0.791406321315
y[1] (closed_form) = -0.882808365303 -0.779309135193
absolute error = 1.571
relative error = 133.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.233
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7076 1.234
h = 0.001 0.003
y[1] (numeric) = -0.883583536279 0.792420406381
y[1] (closed_form) = -0.883823239735 -0.778295020297
absolute error = 1.571
relative error = 133.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.234
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7066 1.237
h = 0.0001 0.004
y[1] (numeric) = -0.886627276859 0.793433531946
y[1] (closed_form) = -0.886866804637 -0.777281947278
absolute error = 1.571
relative error = 133.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.237
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7065 1.241
h = 0.003 0.006
y[1] (numeric) = -0.890684134345 0.793533005997
y[1] (closed_form) = -0.890923548907 -0.777182369483
absolute error = 1.571
relative error = 132.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.241
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7035 1.247
h = 0.0001 0.005
y[1] (numeric) = -0.896769195714 0.796572100693
y[1] (closed_form) = -0.897008493871 -0.774143925038
absolute error = 1.571
relative error = 132.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.247
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1322.9MB, alloc=52.3MB, time=16.10
x[1] = -0.7034 1.252
h = 0.0001 0.003
y[1] (numeric) = -0.901837014459 0.796670016147
y[1] (closed_form) = -0.902076460342 -0.7740456186
absolute error = 1.571
relative error = 132.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.252
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7033 1.255
h = 0.001 0.001
y[1] (numeric) = -0.904877005207 0.796769536819
y[1] (closed_form) = -0.905116612006 -0.773946099917
absolute error = 1.571
relative error = 131.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.255
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7023 1.256
h = 0.001 0.003
y[1] (numeric) = -0.905890812087 0.797782135922
y[1] (closed_form) = -0.9061304974 -0.772933475208
absolute error = 1.571
relative error = 131.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.256
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7013 1.259
h = 0.0001 0.004
y[1] (numeric) = -0.908931090439 0.798793292231
y[1] (closed_form) = -0.909170614076 -0.771922363504
absolute error = 1.571
relative error = 131.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.259
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7012 1.263
h = 0.003 0.006
y[1] (numeric) = -0.912983104767 0.798891701798
y[1] (closed_form) = -0.913222526907 -0.771823856848
absolute error = 1.571
relative error = 131.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.263
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6982 1.269
h = 0.0001 0.005
y[1] (numeric) = -0.919061699392 0.801925814516
y[1] (closed_form) = -0.919301002341 -0.768790336485
absolute error = 1.571
relative error = 131.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.269
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6981 1.274
h = 0.0001 0.003
y[1] (numeric) = -0.924123714497 0.802022584968
y[1] (closed_form) = -0.924363160195 -0.768693211372
absolute error = 1.571
relative error = 130.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.274
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.698 1.277
h = 0.001 0.001
y[1] (numeric) = -0.927160298024 0.802121366687
y[1] (closed_form) = -0.927399890844 -0.768594434622
absolute error = 1.571
relative error = 130.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.277
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.697 1.278
h = 0.001 0.003
y[1] (numeric) = -0.928173177466 0.803132626166
y[1] (closed_form) = -0.92841284259 -0.767583153263
absolute error = 1.571
relative error = 130.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.278
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.696 1.281
h = 0.0001 0.004
y[1] (numeric) = -0.931210251121 0.804142049473
y[1] (closed_form) = -0.931449767515 -0.766573767584
absolute error = 1.571
relative error = 130.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.281
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6959 1.285
h = 0.003 0.006
y[1] (numeric) = -0.935257815581 0.804239580433
y[1] (closed_form) = -0.935497241052 -0.766476145847
absolute error = 1.571
relative error = 129.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.285
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6929 1.291
h = 0.0001 0.005
y[1] (numeric) = -0.941330398745 0.807269263724
y[1] (closed_form) = -0.941569703622 -0.763447001968
absolute error = 1.571
relative error = 129.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.291
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1367.5MB, alloc=52.3MB, time=16.64
x[1] = -0.6928 1.296
h = 0.0001 0.003
y[1] (numeric) = -0.946387083818 0.807365100552
y[1] (closed_form) = -0.946626526183 -0.763350843564
absolute error = 1.571
relative error = 129.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.296
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6927 1.299
h = 0.001 0.001
y[1] (numeric) = -0.949420536799 0.807463273113
y[1] (closed_form) = -0.949660113623 -0.763252678423
absolute error = 1.571
relative error = 128.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.299
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6917 1.3
h = 0.003 0.006
y[1] (numeric) = -0.950432541836 0.808473325564
y[1] (closed_form) = -0.950672185217 -0.762242607373
absolute error = 1.571
relative error = 128.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.3
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6887 1.306
h = 0.0001 0.005
y[1] (numeric) = -0.956501800151 0.811500150408
y[1] (closed_form) = -0.956740857265 -0.759216324507
absolute error = 1.571
relative error = 128.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.306
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6886 1.311
h = 0.0001 0.003
y[1] (numeric) = -0.961555092416 0.811595331932
y[1] (closed_form) = -0.961794284024 -0.759120842571
absolute error = 1.571
relative error = 128.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.311
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6885 1.314
h = 0.001 0.001
y[1] (numeric) = -0.964586553303 0.811693080782
y[1] (closed_form) = -0.964825871321 -0.759023102845
absolute error = 1.571
relative error = 128 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.314
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6875 1.315
h = 0.001 0.003
y[1] (numeric) = -0.965598013432 0.812702352828
y[1] (closed_form) = -0.965837394377 -0.758013814356
absolute error = 1.571
relative error = 127.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.315
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6865 1.318
h = 0.0001 0.004
y[1] (numeric) = -0.968630246182 0.813709248957
y[1] (closed_form) = -0.968869497929 -0.757006945701
absolute error = 1.571
relative error = 127.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.318
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6864 1.322
h = 0.003 0.006
y[1] (numeric) = -0.972671122125 0.813805560405
y[1] (closed_form) = -0.972910298634 -0.756910553157
absolute error = 1.571
relative error = 127.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.322
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6834 1.328
h = 0.0001 0.005
y[1] (numeric) = -0.978734598444 0.816828736308
y[1] (closed_form) = -0.978973653433 -0.75388783739
absolute error = 1.571
relative error = 127.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.328
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6833 1.333
h = 0.0001 0.003
y[1] (numeric) = -0.983783274203 0.816923290083
y[1] (closed_form) = -0.984022458073 -0.753793011447
absolute error = 1.571
relative error = 126.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.333
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6832 1.336
h = 0.001 0.001
y[1] (numeric) = -0.986812021539 0.817020617915
y[1] (closed_form) = -0.987051320861 -0.753695694424
absolute error = 1.571
relative error = 126.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.336
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1412.1MB, alloc=52.3MB, time=17.18
x[1] = -0.6822 1.337
h = 0.001 0.003
y[1] (numeric) = -0.987822689581 0.818028880229
y[1] (closed_form) = -0.988062046785 -0.752687418297
absolute error = 1.571
relative error = 126.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.337
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6812 1.34
h = 0.0001 0.004
y[1] (numeric) = -0.990852321314 0.819034564205
y[1] (closed_form) = -0.9910915598 -0.751681756934
absolute error = 1.571
relative error = 126.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.34
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6811 1.344
h = 0.003 0.006
y[1] (numeric) = -0.994889657192 0.819130393626
y[1] (closed_form) = -0.995128828435 -0.751585851864
absolute error = 1.571
relative error = 126 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.344
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6781 1.35
h = 0.0001 0.005
y[1] (numeric) = -1.00094819876 0.822150368669
y[1] (closed_form) = -1.00118724987 -0.74856629537
absolute error = 1.571
relative error = 125.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.35
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.678 1.355
h = 0.0001 0.003
y[1] (numeric) = -1.00599263936 0.822244438146
y[1] (closed_form) = -1.00623181367 -0.748471979426
absolute error = 1.571
relative error = 125.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.355
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6779 1.358
h = 0.001 0.001
y[1] (numeric) = -1.00901889624 0.822341433721
y[1] (closed_form) = -1.00925817596 -0.748374995988
absolute error = 1.571
relative error = 125 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.358
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6769 1.359
h = 0.001 0.003
y[1] (numeric) = -1.01002882004 0.823348787796
y[1] (closed_form) = -1.01026815297 -0.747367630404
absolute error = 1.571
relative error = 125 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.36
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6759 1.362
h = 0.0001 0.004
y[1] (numeric) = -1.01305604883 0.824353413602
y[1] (closed_form) = -1.01329527273 -0.746363022974
absolute error = 1.571
relative error = 124.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.363
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6758 1.366
h = 0.003 0.006
y[1] (numeric) = -1.01709013695 0.824448871015
y[1] (closed_form) = -1.0173293008 -0.746267495047
absolute error = 1.571
relative error = 124.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.367
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6728 1.372
h = 0.0001 0.005
y[1] (numeric) = -1.0231441019 0.827466014037
y[1] (closed_form) = -1.02338314771 -0.743250732588
absolute error = 1.571
relative error = 124.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.373
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6727 1.377
h = 0.0001 0.003
y[1] (numeric) = -1.0281846587 0.827559722888
y[1] (closed_form) = -1.02842382201 -0.743156800654
absolute error = 1.571
relative error = 123.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.378
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6726 1.38
h = 0.001 0.001
y[1] (numeric) = -1.03120863079 0.827656462976
y[1] (closed_form) = -1.03144789029 -0.74306007372
absolute error = 1.571
relative error = 123.6 %
Correct digits = 0
memory used=1456.8MB, alloc=52.3MB, time=17.72
Radius of convergence (given) for eq 1 = 1.381
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6716 1.381
h = 0.0001 0.004
y[1] (numeric) = -1.03221785604 0.82866300065
y[1] (closed_form) = -1.03245716446 -0.742053526552
absolute error = 1.571
relative error = 123.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.382
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6715 1.385
h = 0.003 0.006
y[1] (numeric) = -1.03624948873 0.828758229437
y[1] (closed_form) = -1.03648861609 -0.741958212238
absolute error = 1.571
relative error = 123.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.386
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6685 1.391
h = 0.0001 0.005
y[1] (numeric) = -1.04229975457 0.83177324962
y[1] (closed_form) = -1.04253876654 -0.738943542608
absolute error = 1.571
relative error = 122.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.392
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6684 1.396
h = 0.0001 0.003
y[1] (numeric) = -1.04733722582 0.831866774778
y[1] (closed_form) = -1.04757635017 -0.738849812725
absolute error = 1.571
relative error = 122.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.397
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6683 1.399
h = 0.001 0.001
y[1] (numeric) = -1.05035938155 0.831963372482
y[1] (closed_form) = -1.05059859477 -0.738753228739
absolute error = 1.571
relative error = 122.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.4
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6673 1.4
h = 0.001 0.003
y[1] (numeric) = -1.0513680321 0.832969281865
y[1] (closed_form) = -1.05160729078 -0.737747311343
absolute error = 1.571
relative error = 122.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.401
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6663 1.403
h = 0.0001 0.004
y[1] (numeric) = -1.0543912604 0.833972314907
y[1] (closed_form) = -1.05463042612 -0.73674429031
absolute error = 1.571
relative error = 122.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.404
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6662 1.407
h = 0.003 0.006
y[1] (numeric) = -1.05842000374 0.834067353823
y[1] (closed_form) = -1.0586591209 -0.736649189713
absolute error = 1.571
relative error = 121.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.408
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6632 1.413
h = 0.0001 0.005
y[1] (numeric) = -1.06446630103 0.837080124686
y[1] (closed_form) = -1.06470530581 -0.733636737342
absolute error = 1.571
relative error = 121.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.414
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6631 1.418
h = 0.0001 0.003
y[1] (numeric) = -1.06950047101 0.837173470992
y[1] (closed_form) = -1.06973958258 -0.733543205905
absolute error = 1.571
relative error = 121.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.419
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.663 1.421
h = 0.001 0.001
y[1] (numeric) = -1.07252068317 0.837269926783
y[1] (closed_form) = -1.07275987579 -0.733446764391
absolute error = 1.571
relative error = 120.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.422
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1501.6MB, alloc=52.3MB, time=18.27
x[1] = -0.662 1.422
h = 0.001 0.003
y[1] (numeric) = -1.07352871543 0.838275167435
y[1] (closed_form) = -1.0737679498 -0.732441517291
absolute error = 1.571
relative error = 120.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.423
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.661 1.425
h = 0.0001 0.004
y[1] (numeric) = -1.07655003429 0.839277492449
y[1] (closed_form) = -1.07678918337 -0.731439201458
absolute error = 1.571
relative error = 120.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.426
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6609 1.429
h = 0.003 0.006
y[1] (numeric) = -1.08057624577 0.839372393679
y[1] (closed_form) = -1.08081535162 -0.731344242848
absolute error = 1.571
relative error = 120.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.43
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6579 1.435
h = 0.0001 0.005
y[1] (numeric) = -1.0866188683 0.842383183593
y[1] (closed_form) = -1.08685786513 -0.728333742171
absolute error = 1.571
relative error = 120.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.436
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6578 1.44
h = 0.0001 0.003
y[1] (numeric) = -1.09165001421 0.842476430347
y[1] (closed_form) = -1.09188911235 -0.728240328094
absolute error = 1.571
relative error = 119.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.441
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6577 1.443
h = 0.001 0.001
y[1] (numeric) = -1.09466844527 0.842572794028
y[1] (closed_form) = -1.09490761731 -0.728143979049
absolute error = 1.571
relative error = 119.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.444
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6567 1.444
h = 0.001 0.003
y[1] (numeric) = -1.09567589883 0.843577434802
y[1] (closed_form) = -1.09591510918 -0.727139333185
absolute error = 1.571
relative error = 119.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.445
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6557 1.447
h = 0.0001 0.004
y[1] (numeric) = -1.09869545681 0.844579149048
y[1] (closed_form) = -1.09893458895 -0.726137625686
absolute error = 1.571
relative error = 119.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.448
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6556 1.451
h = 0.003 0.006
y[1] (numeric) = -1.10271934896 0.844673973443
y[1] (closed_form) = -1.10295844265 -0.726042747948
absolute error = 1.571
relative error = 119 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.452
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6526 1.457
h = 0.0001 0.005
y[1] (numeric) = -1.10875857059 0.847683022102
y[1] (closed_form) = -1.10899755891 -0.723033961835
absolute error = 1.571
relative error = 118.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.458
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6525 1.462
h = 0.0001 0.003
y[1] (numeric) = -1.11378694746 0.84777623644
y[1] (closed_form) = -1.11402603174 -0.722940596353
absolute error = 1.571
relative error = 118.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.463
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6524 1.465
h = 0.001 0.001
y[1] (numeric) = -1.11680374697 0.847872550404
y[1] (closed_form) = -1.11704289858 -0.722844297217
absolute error = 1.571
relative error = 118.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.466
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1546.3MB, alloc=52.3MB, time=18.82
x[1] = -0.6514 1.466
h = 0.001 0.003
y[1] (numeric) = -1.11781065934 0.848876653496
y[1] (closed_form) = -1.11804984611 -0.721840190211
absolute error = 1.571
relative error = 118 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.467
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6504 1.469
h = 0.0001 0.004
y[1] (numeric) = -1.1208285942 0.849877843029
y[1] (closed_form) = -1.12106770927 -0.720839005333
absolute error = 1.571
relative error = 117.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.47
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6503 1.473
h = 0.003 0.006
y[1] (numeric) = -1.12485036257 0.849972642115
y[1] (closed_form) = -1.12508944349 -0.720744156689
absolute error = 1.571
relative error = 117.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.474
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6473 1.479
h = 0.0001 0.005
y[1] (numeric) = -1.13088643839 0.852980163412
y[1] (closed_form) = -1.1311254178 -0.717736873599
absolute error = 1.571
relative error = 117.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.481
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6472 1.484
h = 0.0001 0.003
y[1] (numeric) = -1.13591228077 0.853073401789
y[1] (closed_form) = -1.13615135092 -0.717643498772
absolute error = 1.571
relative error = 116.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.486
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6471 1.487
h = 0.001 0.001
y[1] (numeric) = -1.13892758632 0.853169701903
y[1] (closed_form) = -1.13916671779 -0.717547213532
absolute error = 1.571
relative error = 116.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.489
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6461 1.488
h = 0.0001 0.004
y[1] (numeric) = -1.13993399302 0.854173323468
y[1] (closed_form) = -1.14017315675 -0.716543589067
absolute error = 1.571
relative error = 116.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.49
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.646 1.492
h = 0.003 0.006
y[1] (numeric) = -1.14395415881 0.854268137329
y[1] (closed_form) = -1.14419321113 -0.716448707919
absolute error = 1.571
relative error = 116.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.494
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.643 1.498
h = 0.0001 0.005
y[1] (numeric) = -1.14998770245 0.857274531081
y[1] (closed_form) = -1.15022665694 -0.713442533204
absolute error = 1.571
relative error = 116 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.5
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6429 1.503
h = 0.0001 0.003
y[1] (numeric) = -1.15501153758 0.857367854917
y[1] (closed_form) = -1.15525057829 -0.713349084416
absolute error = 1.571
relative error = 115.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.505
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6428 1.506
h = 0.001 0.001
y[1] (numeric) = -1.15802565919 0.857464183211
y[1] (closed_form) = -1.15826475648 -0.713252770876
absolute error = 1.571
relative error = 115.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.508
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6418 1.507
h = 0.001 0.003
y[1] (numeric) = -1.15903165268 0.858467436546
y[1] (closed_form) = -1.15927077989 -0.712249515368
absolute error = 1.571
relative error = 115.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.509
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1591.1MB, alloc=52.3MB, time=19.36
x[1] = -0.6408 1.51
h = 0.0001 0.004
y[1] (numeric) = -1.16204689556 0.859467861135
y[1] (closed_form) = -1.16228596186 -0.711249092393
absolute error = 1.571
relative error = 115.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.512
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6407 1.514
h = 0.003 0.006
y[1] (numeric) = -1.16606518037 0.859562743465
y[1] (closed_form) = -1.16630421935 -0.711154166957
absolute error = 1.571
relative error = 115 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.516
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6377 1.52
h = 0.0001 0.005
y[1] (numeric) = -1.17209600869 0.862567945314
y[1] (closed_form) = -1.1723349539 -0.708149163663
absolute error = 1.571
relative error = 114.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.522
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6376 1.525
h = 0.0001 0.003
y[1] (numeric) = -1.17711769692 0.862661371934
y[1] (closed_form) = -1.17735672345 -0.708055624364
absolute error = 1.571
relative error = 114.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.527
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6375 1.528
h = 0.001 0.001
y[1] (numeric) = -1.1801305521 0.862757737077
y[1] (closed_form) = -1.18036963012 -0.70795927382
absolute error = 1.571
relative error = 114.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.53
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6365 1.529
h = 0.001 0.003
y[1] (numeric) = -1.18113610143 0.86376059881
y[1] (closed_form) = -1.18137520688 -0.706956410677
absolute error = 1.571
relative error = 114.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.531
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6355 1.532
h = 0.0001 0.004
y[1] (numeric) = -1.18415006246 0.864760691818
y[1] (closed_form) = -1.18438911213 -0.705956317966
absolute error = 1.571
relative error = 113.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.534
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6354 1.536
h = 0.003 0.006
y[1] (numeric) = -1.18816670052 0.864855652631
y[1] (closed_form) = -1.18840572603 -0.705861317174
absolute error = 1.571
relative error = 113.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.538
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6324 1.542
h = 0.0001 0.005
y[1] (numeric) = -1.19419502077 0.867859816315
y[1] (closed_form) = -1.19443395661 -0.702857333389
absolute error = 1.571
relative error = 113.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.544
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6323 1.547
h = 0.0001 0.003
y[1] (numeric) = -1.19921474618 0.867953378597
y[1] (closed_form) = -1.19945375864 -0.702763669559
absolute error = 1.571
relative error = 113 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.549
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6322 1.55
h = 0.001 0.001
y[1] (numeric) = -1.20222644306 0.868049802006
y[1] (closed_form) = -1.20246550235 -0.702667260508
absolute error = 1.571
relative error = 112.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.552
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6312 1.551
h = 0.001 0.003
y[1] (numeric) = -1.20323157831 0.869052313956
y[1] (closed_form) = -1.20347066273 -0.7016647478
absolute error = 1.571
relative error = 112.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.553
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1635.9MB, alloc=52.3MB, time=19.90
x[1] = -0.6302 1.554
h = 0.0001 0.004
y[1] (numeric) = -1.20624435977 0.870052128342
y[1] (closed_form) = -1.20648339314 -0.700664932604
absolute error = 1.571
relative error = 112.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.556
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6301 1.558
h = 0.003 0.006
y[1] (numeric) = -1.21025949227 0.870147192889
y[1] (closed_form) = -1.21049850429 -0.700569831
absolute error = 1.571
relative error = 112.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.56
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6271 1.564
h = 0.0001 0.005
y[1] (numeric) = -1.216285497 0.873150455039
y[1] (closed_form) = -1.21652442347 -0.69756673176
absolute error = 1.571
relative error = 112 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.566
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.627 1.569
h = 0.0001 0.003
y[1] (numeric) = -1.22130342864 0.873244179504
y[1] (closed_form) = -1.22154242721 -0.697472915839
absolute error = 1.571
relative error = 111.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.571
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6269 1.572
h = 0.001 0.001
y[1] (numeric) = -1.22431406655 0.87334067868
y[1] (closed_form) = -1.2245531077 -0.697376430712
absolute error = 1.571
relative error = 111.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.574
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6259 1.573
h = 0.001 0.003
y[1] (numeric) = -1.22531881605 0.874342878523
y[1] (closed_form) = -1.22555788021 -0.696374230661
absolute error = 1.571
relative error = 111.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.575
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6249 1.576
h = 0.0001 0.004
y[1] (numeric) = -1.22833051255 0.875342460759
y[1] (closed_form) = -1.22856953001 -0.695374646696
absolute error = 1.571
relative error = 111.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.579
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6248 1.58
h = 0.003 0.006
y[1] (numeric) = -1.23234426911 0.875437649412
y[1] (closed_form) = -1.23258326775 -0.695279423713
absolute error = 1.571
relative error = 111 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.583
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6218 1.586
h = 0.0001 0.005
y[1] (numeric) = -1.23836813714 0.878440131307
y[1] (closed_form) = -1.23860705432 -0.692277089265
absolute error = 1.571
relative error = 110.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.589
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6217 1.591
h = 0.0001 0.003
y[1] (numeric) = -1.2433844302 0.87853403895
y[1] (closed_form) = -1.24362341513 -0.692183099311
absolute error = 1.571
relative error = 110.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.594
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6216 1.594
h = 0.001 0.001
y[1] (numeric) = -1.24639410034 0.878630627985
y[1] (closed_form) = -1.24663312398 -0.692086523959
absolute error = 1.571
relative error = 110.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.597
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6206 1.595
h = 0.0001 0.004
y[1] (numeric) = -1.24739849074 0.879632549645
y[1] (closed_form) = -1.24763753545 -0.691084602555
absolute error = 1.571
relative error = 110.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.598
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1680.7MB, alloc=52.3MB, time=20.45
x[1] = -0.6205 1.599
h = 0.003 0.006
y[1] (numeric) = -1.25141121111 0.879727853855
y[1] (closed_form) = -1.25165018816 -0.690989247426
absolute error = 1.571
relative error = 109.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.602
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6175 1.605
h = 0.0001 0.005
y[1] (numeric) = -1.25743336569 0.882729773486
y[1] (closed_form) = -1.25767226494 -0.6879874631
absolute error = 1.571
relative error = 109.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.608
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6174 1.61
h = 0.0001 0.003
y[1] (numeric) = -1.26244836521 0.882823869187
y[1] (closed_form) = -1.26268732853 -0.687893292221
absolute error = 1.571
relative error = 109.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.613
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6173 1.613
h = 0.001 0.001
y[1] (numeric) = -1.2654572709 0.882920554769
y[1] (closed_form) = -1.26569626986 -0.68779661993
absolute error = 1.571
relative error = 109 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.616
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6163 1.614
h = 0.001 0.003
y[1] (numeric) = -1.26646136947 0.883922265414
y[1] (closed_form) = -1.26670038795 -0.686794909857
absolute error = 1.571
relative error = 109 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.617
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6153 1.617
h = 0.0001 0.004
y[1] (numeric) = -1.26947127307 0.88492153061
y[1] (closed_form) = -1.26971025201 -0.685795641678
absolute error = 1.571
relative error = 108.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.62
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6152 1.621
h = 0.003 0.006
y[1] (numeric) = -1.27348278043 0.885017003542
y[1] (closed_form) = -1.27372174454 -0.685700139035
absolute error = 1.571
relative error = 108.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.624
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6122 1.627
h = 0.0001 0.005
y[1] (numeric) = -1.27950309853 0.88801833124
y[1] (closed_form) = -1.2797419888 -0.682698933673
absolute error = 1.571
relative error = 108.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.63
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6121 1.632
h = 0.0001 0.003
y[1] (numeric) = -1.28451671505 0.888112635453
y[1] (closed_form) = -1.28475566543 -0.682604561891
absolute error = 1.571
relative error = 108 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.635
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.612 1.635
h = 0.001 0.001
y[1] (numeric) = -1.28752480334 0.888209428653
y[1] (closed_form) = -1.28776378608 -0.682507781547
absolute error = 1.571
relative error = 107.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.638
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.611 1.636
h = 0.001 0.003
y[1] (numeric) = -1.28852858847 0.889210915162
y[1] (closed_form) = -1.28876758907 -0.681506295939
absolute error = 1.571
relative error = 107.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.639
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.61 1.639
h = 0.0001 0.004
y[1] (numeric) = -1.2915376403 0.890210050478
y[1] (closed_form) = -1.29177660477 -0.680507157127
absolute error = 1.571
relative error = 107.6 %
Correct digits = 0
memory used=1725.6MB, alloc=52.3MB, time=21.00
Radius of convergence (given) for eq 1 = 1.642
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6099 1.643
h = 0.003 0.006
y[1] (numeric) = -1.29554808677 0.890305683126
y[1] (closed_form) = -1.29578703823 -0.680411496996
absolute error = 1.571
relative error = 107.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.646
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6069 1.649
h = 0.0001 0.005
y[1] (numeric) = -1.30156671245 0.893306504593
y[1] (closed_form) = -1.30180559396 -0.677410786078
absolute error = 1.571
relative error = 107 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.653
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6068 1.654
h = 0.0001 0.003
y[1] (numeric) = -1.30657906714 0.893401026439
y[1] (closed_form) = -1.30681800497 -0.677316203547
absolute error = 1.571
relative error = 106.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.658
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6067 1.657
h = 0.001 0.001
y[1] (numeric) = -1.30958640932 0.893497933972
y[1] (closed_form) = -1.30982537653 -0.677219308407
absolute error = 1.571
relative error = 106.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.661
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6057 1.658
h = 0.001 0.003
y[1] (numeric) = -1.31058990322 0.894499221397
y[1] (closed_form) = -1.31082888675 -0.676218022154
absolute error = 1.571
relative error = 106.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.662
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6047 1.661
h = 0.0001 0.004
y[1] (numeric) = -1.31359817289 0.895498254324
y[1] (closed_form) = -1.31383712342 -0.675218985327
absolute error = 1.571
relative error = 106.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.665
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6046 1.665
h = 0.003 0.006
y[1] (numeric) = -1.31760765139 0.89559405371
y[1] (closed_form) = -1.31784659054 -0.675123160533
absolute error = 1.571
relative error = 106.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.669
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6016 1.671
h = 0.0001 0.005
y[1] (numeric) = -1.32362471814 0.898594444582
y[1] (closed_form) = -1.32386359113 -0.672122869495
absolute error = 1.571
relative error = 105.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.675
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6015 1.676
h = 0.0001 0.003
y[1] (numeric) = -1.32863592204 0.89868919007
y[1] (closed_form) = -1.32887484776 -0.672028069551
absolute error = 1.571
relative error = 105.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.68
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6014 1.679
h = 0.001 0.001
y[1] (numeric) = -1.3316425835 0.898786216706
y[1] (closed_form) = -1.33188153587 -0.671931054828
absolute error = 1.571
relative error = 105.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.683
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6004 1.68
h = 0.001 0.003
y[1] (numeric) = -1.33264580697 0.89978732754
y[1] (closed_form) = -1.33288477425 -0.670929945383
absolute error = 1.571
relative error = 105.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.684
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1770.4MB, alloc=52.3MB, time=21.54
x[1] = -0.5994 1.683
h = 0.0001 0.004
y[1] (numeric) = -1.33565335872 0.900786281893
y[1] (closed_form) = -1.33589229587 -0.66993098682
absolute error = 1.571
relative error = 105.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.687
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5993 1.687
h = 0.003 0.006
y[1] (numeric) = -1.33966195441 0.900882252645
y[1] (closed_form) = -1.33990088164 -0.669834992591
absolute error = 1.571
relative error = 104.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.691
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5963 1.693
h = 0.0001 0.005
y[1] (numeric) = -1.34567758587 0.903882279563
y[1] (closed_form) = -1.3459164506 -0.666835055776
absolute error = 1.571
relative error = 104.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.697
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5962 1.698
h = 0.0001 0.003
y[1] (numeric) = -1.35068774072 0.903977252045
y[1] (closed_form) = -1.35092665477 -0.666740034467
absolute error = 1.571
relative error = 104.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.702
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5961 1.701
h = 0.001 0.001
y[1] (numeric) = -1.35369378138 0.904074400886
y[1] (closed_form) = -1.35393271959 -0.666642897048
absolute error = 1.571
relative error = 104.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.705
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5951 1.702
h = 0.0001 0.004
y[1] (numeric) = -1.35469675388 0.905075355312
y[1] (closed_form) = -1.35493570572 -0.665641944181
absolute error = 1.571
relative error = 104 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.706
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.595 1.706
h = 0.003 0.006
y[1] (numeric) = -1.35870468614 0.905171469436
y[1] (closed_form) = -1.35894359753 -0.665545792603
absolute error = 1.571
relative error = 103.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.71
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.592 1.712
h = 0.0001 0.005
y[1] (numeric) = -1.36471917069 0.908171245538
y[1] (closed_form) = -1.36495802274 -0.66254609899
absolute error = 1.571
relative error = 103.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.716
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5919 1.717
h = 0.0001 0.003
y[1] (numeric) = -1.36972850018 0.908266425373
y[1] (closed_form) = -1.3699673987 -0.6624508747
absolute error = 1.571
relative error = 103.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.721
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5918 1.72
h = 0.001 0.001
y[1] (numeric) = -1.37273405209 0.908363687313
y[1] (closed_form) = -1.37297297282 -0.662353623727
absolute error = 1.571
relative error = 103 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.724
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5908 1.721
h = 0.001 0.003
y[1] (numeric) = -1.37373682162 0.909364524369
y[1] (closed_form) = -1.37397575495 -0.661352788333
absolute error = 1.571
relative error = 103 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.725
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5898 1.724
h = 0.0001 0.004
y[1] (numeric) = -1.37674319121 0.910363391973
y[1] (closed_form) = -1.37698209913 -0.660353916181
absolute error = 1.571
relative error = 102.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.729
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1815.2MB, alloc=52.3MB, time=22.08
x[1] = -0.5897 1.728
h = 0.003 0.006
y[1] (numeric) = -1.38075034896 0.910459695611
y[1] (closed_form) = -1.38098924924 -0.660257592316
absolute error = 1.571
relative error = 102.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.733
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5867 1.734
h = 0.0001 0.005
y[1] (numeric) = -1.38676360483 0.913459209791
y[1] (closed_form) = -1.38700244919 -0.657258152497
absolute error = 1.571
relative error = 102.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5866 1.739
h = 0.0001 0.003
y[1] (numeric) = -1.39177205229 0.913554616161
y[1] (closed_form) = -1.39201094005 -0.657162706331
absolute error = 1.571
relative error = 102 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5865 1.742
h = 0.001 0.001
y[1] (numeric) = -1.39477708185 0.913652001883
y[1] (closed_form) = -1.39501598972 -0.65706533108
absolute error = 1.571
relative error = 101.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.747
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5855 1.743
h = 0.001 0.003
y[1] (numeric) = -1.39577963352 0.914652714488
y[1] (closed_form) = -1.3960185529 -0.656064620239
absolute error = 1.571
relative error = 101.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5845 1.746
h = 0.0001 0.004
y[1] (numeric) = -1.39878544278 0.915651554303
y[1] (closed_form) = -1.39902433898 -0.655065775769
absolute error = 1.571
relative error = 101.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5844 1.75
h = 0.003 0.006
y[1] (numeric) = -1.40279192388 0.915748031579
y[1] (closed_form) = -1.40303081348 -0.65496927983
absolute error = 1.571
relative error = 101.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5814 1.756
h = 0.0001 0.005
y[1] (numeric) = -1.40880404994 0.918747329791
y[1] (closed_form) = -1.40904288691 -0.651970048605
absolute error = 1.571
relative error = 101.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.761
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5813 1.761
h = 0.0001 0.003
y[1] (numeric) = -1.41381169438 0.918842960615
y[1] (closed_form) = -1.41405057185 -0.651874382193
absolute error = 1.571
relative error = 100.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.766
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5812 1.764
h = 0.001 0.001
y[1] (numeric) = -1.41681624816 0.918940469762
y[1] (closed_form) = -1.41705514385 -0.651776883019
absolute error = 1.571
relative error = 100.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.769
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5802 1.765
h = 0.001 0.003
y[1] (numeric) = -1.417818598 0.919941072664
y[1] (closed_form) = -1.41805750417 -0.650776281956
absolute error = 1.571
relative error = 100.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.77
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5792 1.768
h = 0.0001 0.004
y[1] (numeric) = -1.42082389379 0.920939897893
y[1] (closed_form) = -1.42106277884 -0.649777452016
absolute error = 1.571
relative error = 100.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.773
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1859.9MB, alloc=52.3MB, time=22.62
x[1] = -0.5791 1.772
h = 0.003 0.006
y[1] (numeric) = -1.42482975883 0.921036547222
y[1] (closed_form) = -1.42506863821 -0.649680785474
absolute error = 1.571
relative error = 100.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.777
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5761 1.778
h = 0.0001 0.005
y[1] (numeric) = -1.43084084648 0.924035669616
y[1] (closed_form) = -1.43107967638 -0.646681723382
absolute error = 1.571
relative error = 100 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.783
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.576 1.783
h = 0.0001 0.003
y[1] (numeric) = -1.43584776016 0.924131521459
y[1] (closed_form) = -1.43608662782 -0.646585839746
absolute error = 1.571
relative error = 99.73 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5759 1.786
h = 0.001 0.001
y[1] (numeric) = -1.43885188081 0.924229152808
y[1] (closed_form) = -1.43909076495 -0.64648821788
absolute error = 1.571
relative error = 99.56 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.791
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5749 1.787
h = 0.001 0.003
y[1] (numeric) = -1.43985404375 0.925229659194
y[1] (closed_form) = -1.44009293746 -0.64548771338
absolute error = 1.571
relative error = 99.53 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.792
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5739 1.79
h = 0.0001 0.004
y[1] (numeric) = -1.44285886922 0.926228481015
y[1] (closed_form) = -1.44309774368 -0.644488886837
absolute error = 1.571
relative error = 99.38 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.796
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5738 1.794
h = 0.003 0.006
y[1] (numeric) = -1.44686417365 0.926325299778
y[1] (closed_form) = -1.44710304324 -0.644392052208
absolute error = 1.571
relative error = 99.16 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.8
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5708 1.8
h = 0.0001 0.005
y[1] (numeric) = -1.45287430729 0.929324281336
y[1] (closed_form) = -1.45311313043 -0.641393124893
absolute error = 1.571
relative error = 98.89 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.806
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5707 1.805
h = 0.0001 0.003
y[1] (numeric) = -1.4578805563 0.92942034966
y[1] (closed_form) = -1.45811941462 -0.641297028196
absolute error = 1.571
relative error = 98.61 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.811
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5706 1.808
h = 0.001 0.001
y[1] (numeric) = -1.46088428281 0.929518101265
y[1] (closed_form) = -1.46112315603 -0.641199285591
absolute error = 1.571
relative error = 98.44 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.814
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5696 1.809
h = 0.0001 0.004
y[1] (numeric) = -1.46188627279 0.930518522917
y[1] (closed_form) = -1.46212515474 -0.640198865851
absolute error = 1.571
relative error = 98.41 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.815
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5695 1.813
h = 0.003 0.006
y[1] (numeric) = -1.46589115685 0.930615478473
y[1] (closed_form) = -1.46613001507 -0.640101883351
absolute error = 1.571
relative error = 98.18 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1904.6MB, alloc=52.3MB, time=23.16
x[1] = -0.5665 1.819
h = 0.0001 0.005
y[1] (numeric) = -1.47190053077 0.933614373412
y[1] (closed_form) = -1.47213934508 -0.637103037934
absolute error = 1.571
relative error = 97.92 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5664 1.824
h = 0.0001 0.003
y[1] (numeric) = -1.4769062587 0.933710630704
y[1] (closed_form) = -1.47714510607 -0.63700675491
absolute error = 1.571
relative error = 97.64 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5663 1.827
h = 0.001 0.001
y[1] (numeric) = -1.47990967601 0.933808487936
y[1] (closed_form) = -1.48014853704 -0.636908906255
absolute error = 1.571
relative error = 97.48 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.833
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5653 1.828
h = 0.001 0.003
y[1] (numeric) = -1.4809115267 0.934808846969
y[1] (closed_form) = -1.48115039579 -0.635908549133
absolute error = 1.571
relative error = 97.45 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.834
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5643 1.831
h = 0.0001 0.004
y[1] (numeric) = -1.48391558045 0.935807690807
y[1] (closed_form) = -1.48415443338 -0.634909700666
absolute error = 1.571
relative error = 97.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.837
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5642 1.835
h = 0.003 0.006
y[1] (numeric) = -1.4879199752 0.935904820415
y[1] (closed_form) = -1.48815882451 -0.634812557445
absolute error = 1.571
relative error = 97.08 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.841
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5612 1.841
h = 0.0001 0.005
y[1] (numeric) = -1.49392853563 0.938903626948
y[1] (closed_form) = -1.49416734377 -0.631813795397
absolute error = 1.571
relative error = 96.82 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.847
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5611 1.846
h = 0.0001 0.003
y[1] (numeric) = -1.49893370699 0.939000089406
y[1] (closed_form) = -1.4991725459 -0.631717310024
absolute error = 1.571
relative error = 96.55 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.561 1.849
h = 0.001 0.001
y[1] (numeric) = -1.501936794 0.939098061419
y[1] (closed_form) = -1.50217564525 -0.631619346127
absolute error = 1.571
relative error = 96.39 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.855
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.56 1.85
h = 0.001 0.003
y[1] (numeric) = -1.50293849529 0.940098354226
y[1] (closed_form) = -1.50317735388 -0.630619055225
absolute error = 1.571
relative error = 96.36 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.856
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.559 1.853
h = 0.0001 0.004
y[1] (numeric) = -1.5059421841 0.941097217141
y[1] (closed_form) = -1.50618102798 -0.62962018776
absolute error = 1.571
relative error = 96.22 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.86
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5589 1.857
h = 0.003 0.006
y[1] (numeric) = -1.50994615186 0.941194504052
y[1] (closed_form) = -1.51018499269 -0.629522888317
absolute error = 1.571
relative error = 96 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1949.5MB, alloc=52.3MB, time=23.71
x[1] = -0.5559 1.863
h = 0.0001 0.005
y[1] (numeric) = -1.51595396585 0.944193245412
y[1] (closed_form) = -1.51619276815 -0.626524186884
absolute error = 1.571
relative error = 95.74 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.87
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5558 1.868
h = 0.0001 0.003
y[1] (numeric) = -1.52095863169 0.944289906471
y[1] (closed_form) = -1.52119746259 -0.626427505443
absolute error = 1.571
relative error = 95.48 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.875
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5557 1.871
h = 0.001 0.001
y[1] (numeric) = -1.52396141855 0.944387989962
y[1] (closed_form) = -1.52420026059 -0.626329429621
absolute error = 1.571
relative error = 95.32 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.878
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5547 1.872
h = 0.001 0.003
y[1] (numeric) = -1.52496298177 0.945388225036
y[1] (closed_form) = -1.52520183049 -0.625329196433
absolute error = 1.571
relative error = 95.29 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.879
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5537 1.875
h = 0.0001 0.004
y[1] (numeric) = -1.52796633687 0.946387112484
y[1] (closed_form) = -1.52820517221 -0.624330304534
absolute error = 1.571
relative error = 95.15 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.882
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5536 1.879
h = 0.003 0.006
y[1] (numeric) = -1.53196991678 0.946484551672
y[1] (closed_form) = -1.53220874958 -0.624232853814
absolute error = 1.571
relative error = 94.94 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.886
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5506 1.885
h = 0.0001 0.005
y[1] (numeric) = -1.53797704618 0.94948324783
y[1] (closed_form) = -1.53821584292 -0.621234193462
absolute error = 1.571
relative error = 94.68 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.892
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5505 1.89
h = 0.0001 0.003
y[1] (numeric) = -1.54298125306 0.949580100497
y[1] (closed_form) = -1.54322007638 -0.62113732269
absolute error = 1.571
relative error = 94.42 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5504 1.893
h = 0.001 0.001
y[1] (numeric) = -1.5459837673 0.949678291856
y[1] (closed_form) = -1.54622260068 -0.621039138567
absolute error = 1.571
relative error = 94.26 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5494 1.894
h = 0.001 0.003
y[1] (numeric) = -1.54698520302 0.950678476753
y[1] (closed_form) = -1.54722404247 -0.620038955527
absolute error = 1.571
relative error = 94.23 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.901
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5484 1.897
h = 0.0001 0.004
y[1] (numeric) = -1.54998825308 0.951677393127
y[1] (closed_form) = -1.55022708038 -0.619040034819
absolute error = 1.571
relative error = 94.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.904
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5483 1.901
h = 0.003 0.006
y[1] (numeric) = -1.55399148088 0.951774979234
y[1] (closed_form) = -1.55423030607 -0.618942438105
absolute error = 1.571
relative error = 93.89 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.908
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1994.4MB, alloc=52.3MB, time=24.25
x[1] = -0.5453 1.907
h = 0.0001 0.005
y[1] (numeric) = -1.55999798268 0.954773647275
y[1] (closed_form) = -1.56023677416 -0.615943802145
absolute error = 1.571
relative error = 93.64 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.915
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5452 1.912
h = 0.0001 0.003
y[1] (numeric) = -1.56500177311 0.954870684246
y[1] (closed_form) = -1.56524058928 -0.615846749114
absolute error = 1.571
relative error = 93.38 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.919
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5451 1.915
h = 0.001 0.001
y[1] (numeric) = -1.56800403987 0.95496897964
y[1] (closed_form) = -1.5682428651 -0.61574846054
absolute error = 1.571
relative error = 93.23 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.922
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5441 1.916
h = 0.0001 0.004
y[1] (numeric) = -1.56900535788 0.95596912107
y[1] (closed_form) = -1.56924418864 -0.614748320927
absolute error = 1.571
relative error = 93.2 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.924
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.544 1.92
h = 0.003 0.006
y[1] (numeric) = -1.57300832228 0.956066823667
y[1] (closed_form) = -1.57324713945 -0.614650599295
absolute error = 1.571
relative error = 92.99 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.928
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.541 1.926
h = 0.0001 0.005
y[1] (numeric) = -1.57901432595 0.959065485868
y[1] (closed_form) = -1.57925311137 -0.611651966284
absolute error = 1.571
relative error = 92.75 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.934
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5409 1.931
h = 0.0001 0.003
y[1] (numeric) = -1.58401779117 0.959162679817
y[1] (closed_form) = -1.58425659972 -0.611554757846
absolute error = 1.571
relative error = 92.49 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.939
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5408 1.934
h = 0.001 0.001
y[1] (numeric) = -1.58701986451 0.959261064145
y[1] (closed_form) = -1.58725868135 -0.611456379982
absolute error = 1.571
relative error = 92.34 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.942
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5398 1.935
h = 0.001 0.003
y[1] (numeric) = -1.5880210881 0.960261174212
y[1] (closed_form) = -1.58825991003 -0.610456271687
absolute error = 1.571
relative error = 92.31 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.943
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5388 1.938
h = 0.0001 0.004
y[1] (numeric) = -1.59102363945 0.96126015595
y[1] (closed_form) = -1.59126245122 -0.609457285878
absolute error = 1.571
relative error = 92.18 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.946
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5387 1.942
h = 0.003 0.006
y[1] (numeric) = -1.59502629824 0.961358003757
y[1] (closed_form) = -1.59526510856 -0.609359429008
absolute error = 1.571
relative error = 91.98 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5357 1.948
h = 0.0001 0.005
y[1] (numeric) = -1.60103176878 0.964356662525
y[1] (closed_form) = -1.60127054948 -0.606360796348
absolute error = 1.571
relative error = 91.74 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.956
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2039.3MB, alloc=52.3MB, time=24.80
x[1] = -0.5356 1.953
h = 0.0001 0.003
y[1] (numeric) = -1.60603488685 0.964454026308
y[1] (closed_form) = -1.606273689 -0.60626341975
absolute error = 1.571
relative error = 91.49 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.961
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5355 1.956
h = 0.001 0.001
y[1] (numeric) = -1.6090367537 0.964552506905
y[1] (closed_form) = -1.60927556332 -0.606164945231
absolute error = 1.571
relative error = 91.34 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.964
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5345 1.957
h = 0.001 0.003
y[1] (numeric) = -1.61003787606 0.965552583941
y[1] (closed_form) = -1.61027669031 -0.605164869916
absolute error = 1.571
relative error = 91.31 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.965
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5335 1.96
h = 0.0001 0.004
y[1] (numeric) = -1.61304019214 0.96655160221
y[1] (closed_form) = -1.61327899715 -0.604165847723
absolute error = 1.571
relative error = 91.18 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.968
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5334 1.964
h = 0.003 0.006
y[1] (numeric) = -1.61704258458 0.966649580253
y[1] (closed_form) = -1.61728138845 -0.604067861356
absolute error = 1.571
relative error = 90.98 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.972
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5304 1.97
h = 0.0001 0.005
y[1] (numeric) = -1.62304756699 0.969648246209
y[1] (closed_form) = -1.62328634323 -0.601069218727
absolute error = 1.571
relative error = 90.74 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.979
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5303 1.975
h = 0.0001 0.003
y[1] (numeric) = -1.62805037053 0.969745772201
y[1] (closed_form) = -1.62828916666 -0.600971681418
absolute error = 1.571
relative error = 90.5 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.984
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5302 1.978
h = 0.001 0.001
y[1] (numeric) = -1.63105205021 0.969844344935
y[1] (closed_form) = -1.63129085306 -0.600873114393
absolute error = 1.571
relative error = 90.35 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.987
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5292 1.979
h = 0.001 0.003
y[1] (numeric) = -1.63205307926 0.970844393692
y[1] (closed_form) = -1.63229188631 -0.5998730673
absolute error = 1.571
relative error = 90.32 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.988
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5282 1.982
h = 0.0001 0.004
y[1] (numeric) = -1.63505518065 0.971843449966
y[1] (closed_form) = -1.63529397933 -0.598874007256
absolute error = 1.571
relative error = 90.19 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.991
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5281 1.986
h = 0.003 0.006
y[1] (numeric) = -1.63905733178 0.9719415524
y[1] (closed_form) = -1.63929612957 -0.598775897179
absolute error = 1.571
relative error = 90 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 1.995
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5251 1.992
h = 0.0001 0.005
y[1] (numeric) = -1.64506186744 0.974940234399
y[1] (closed_form) = -1.64530063949 -0.595777236001
absolute error = 1.571
relative error = 89.76 %
Correct digits = 0
memory used=2084.1MB, alloc=52.3MB, time=25.34
Radius of convergence (given) for eq 1 = 2.001
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.525 1.997
h = 0.0001 0.003
y[1] (numeric) = -1.65006438617 0.975037914989
y[1] (closed_form) = -1.65030317665 -0.595679545435
absolute error = 1.571
relative error = 89.52 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.006
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5249 2
h = 0.001 0.001
y[1] (numeric) = -1.65306589629 0.975136575702
y[1] (closed_form) = -1.6533046928 -0.595580890079
absolute error = 1.571
relative error = 89.38 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.009
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5239 2.001
h = 0.001 0.003
y[1] (numeric) = -1.65406683935 0.976136600379
y[1] (closed_form) = -1.65430563969 -0.594580867007
absolute error = 1.571
relative error = 89.35 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.01
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5229 2.004
h = 0.0001 0.004
y[1] (numeric) = -1.65706874494 0.977135695607
y[1] (closed_form) = -1.65730753767 -0.593581768165
absolute error = 1.571
relative error = 89.23 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.013
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5228 2.008
h = 0.003 0.006
y[1] (numeric) = -1.66107067755 0.977233916599
y[1] (closed_form) = -1.66130946962 -0.593483540158
absolute error = 1.571
relative error = 89.04 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.017
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5198 2.014
h = 0.0001 0.005
y[1] (numeric) = -1.66707480452 0.980232621944
y[1] (closed_form) = -1.66731357262 -0.590484853376
absolute error = 1.571
relative error = 88.8 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.023
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5197 2.019
h = 0.0001 0.003
y[1] (numeric) = -1.67207706551 0.980330449591
y[1] (closed_form) = -1.67231585068 -0.590387016953
absolute error = 1.571
relative error = 88.57 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.028
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5196 2.022
h = 0.001 0.001
y[1] (numeric) = -1.67507842209 0.980429194136
y[1] (closed_form) = -1.67531721268 -0.59028827743
absolute error = 1.571
relative error = 88.43 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.031
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5186 2.023
h = 0.0001 0.004
y[1] (numeric) = -1.67607928598 0.981429198435
y[1] (closed_form) = -1.67631808003 -0.589288274675
absolute error = 1.571
relative error = 88.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.032
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5185 2.027
h = 0.003 0.006
y[1] (numeric) = -1.68008105557 0.981527512388
y[1] (closed_form) = -1.68031984207 -0.589189947482
absolute error = 1.571
relative error = 88.21 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.036
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5155 2.033
h = 0.0001 0.005
y[1] (numeric) = -1.68608485925 0.984526246947
y[1] (closed_form) = -1.68632362324 -0.586191229743
absolute error = 1.571
relative error = 87.98 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.043
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2128.9MB, alloc=52.3MB, time=25.89
x[1] = -0.5154 2.038
h = 0.0001 0.003
y[1] (numeric) = -1.69108691981 0.984624197899
y[1] (closed_form) = -1.69132569976 -0.586093270931
absolute error = 1.571
relative error = 87.75 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.048
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5153 2.041
h = 0.001 0.001
y[1] (numeric) = -1.69408815691 0.984723012908
y[1] (closed_form) = -1.6943269418 -0.585994460661
absolute error = 1.571
relative error = 87.61 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.051
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5143 2.042
h = 0.001 0.003
y[1] (numeric) = -1.69508895751 0.985723003131
y[1] (closed_form) = -1.69532774558 -0.584994471924
absolute error = 1.571
relative error = 87.58 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.052
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5133 2.045
h = 0.0001 0.004
y[1] (numeric) = -1.69809054413 0.986722173767
y[1] (closed_form) = -1.69832932589 -0.583995297975
absolute error = 1.571
relative error = 87.46 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.055
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5132 2.049
h = 0.003 0.006
y[1] (numeric) = -1.70209212522 0.986820602101
y[1] (closed_form) = -1.70233090664 -0.583896863671
absolute error = 1.571
relative error = 87.28 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.059
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5102 2.055
h = 0.0001 0.005
y[1] (numeric) = -1.70809558307 0.989819369755
y[1] (closed_form) = -1.70833434356 -0.580898110979
absolute error = 1.571
relative error = 87.05 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.065
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5101 2.06
h = 0.0001 0.003
y[1] (numeric) = -1.71309742985 0.989917453803
y[1] (closed_form) = -1.71333620509 -0.580800020045
absolute error = 1.571
relative error = 86.82 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.51 2.063
h = 0.001 0.001
y[1] (numeric) = -1.71609853946 0.990016344902
y[1] (closed_form) = -1.71633731914 -0.58070113338
absolute error = 1.571
relative error = 86.69 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.509 2.064
h = 0.001 0.003
y[1] (numeric) = -1.71709927225 0.991016320419
y[1] (closed_form) = -1.71733805482 -0.579701159286
absolute error = 1.571
relative error = 86.66 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.508 2.067
h = 0.0001 0.004
y[1] (numeric) = -1.72010070878 0.992015530325
y[1] (closed_form) = -1.72033948562 -0.578701946224
absolute error = 1.571
relative error = 86.54 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5079 2.071
h = 0.003 0.006
y[1] (numeric) = -1.72410212583 0.992114060734
y[1] (closed_form) = -1.72434090248 -0.578603410343
absolute error = 1.571
relative error = 86.36 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5049 2.077
h = 0.0001 0.005
y[1] (numeric) = -1.73010526772 0.995112865391
y[1] (closed_form) = -1.73034402491 -0.575604618978
absolute error = 1.571
relative error = 86.13 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2173.7MB, alloc=52.3MB, time=26.43
x[1] = -0.5048 2.082
h = 0.0001 0.003
y[1] (numeric) = -1.73510692134 0.995211075436
y[1] (closed_form) = -1.73534569218 -0.575506402914
absolute error = 1.571
relative error = 85.91 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5047 2.085
h = 0.001 0.001
y[1] (numeric) = -1.73810791572 0.995310038668
y[1] (closed_form) = -1.73834669053 -0.575407443829
absolute error = 1.571
relative error = 85.78 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.096
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5037 2.086
h = 0.001 0.003
y[1] (numeric) = -1.73910858614 0.996310002036
y[1] (closed_form) = -1.73934736357 -0.574407481819
absolute error = 1.571
relative error = 85.75 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5027 2.089
h = 0.0001 0.004
y[1] (numeric) = -1.742109886 0.997309250805
y[1] (closed_form) = -1.74234865825 -0.573408230049
absolute error = 1.571
relative error = 85.63 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5026 2.093
h = 0.003 0.006
y[1] (numeric) = -1.74611115486 0.997407877845
y[1] (closed_form) = -1.74634992704 -0.573309597995
absolute error = 1.571
relative error = 85.46 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.104
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4996 2.099
h = 0.0001 0.005
y[1] (numeric) = -1.75211400819 1.00040672251
y[1] (closed_form) = -1.7523527623 -0.570310765126
absolute error = 1.571
relative error = 85.23 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4995 2.104
h = 0.0001 0.003
y[1] (numeric) = -1.75711548742 1.00050505165
y[1] (closed_form) = -1.75735425414 -0.570212430737
absolute error = 1.571
relative error = 85.02 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.115
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4994 2.107
h = 0.001 0.001
y[1] (numeric) = -1.7601163777 1.00060408315
y[1] (closed_form) = -1.76035514798 -0.570113403106
absolute error = 1.571
relative error = 84.89 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.118
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4984 2.108
h = 0.001 0.003
y[1] (numeric) = -1.76111699078 1.00160403661
y[1] (closed_form) = -1.76135576343 -0.569113450945
absolute error = 1.571
relative error = 84.86 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.119
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4974 2.111
h = 0.0001 0.004
y[1] (numeric) = -1.76411816629 1.00260332361
y[1] (closed_form) = -1.76435693425 -0.568114161099
absolute error = 1.571
relative error = 84.74 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.122
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4973 2.115
h = 0.003 0.006
y[1] (numeric) = -1.76811930134 1.00270204199
y[1] (closed_form) = -1.76835806934 -0.568015438125
absolute error = 1.571
relative error = 84.57 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4943 2.121
h = 0.0001 0.005
y[1] (numeric) = -1.77412189126 1.00570092887
y[1] (closed_form) = -1.77436064249 -0.56501656169
absolute error = 1.571
relative error = 84.35 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.132
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2218.6MB, alloc=52.3MB, time=26.98
x[1] = -0.4942 2.126
h = 0.0001 0.003
y[1] (numeric) = -1.77912321314 1.00579937043
y[1] (closed_form) = -1.77936197601 -0.564918115569
absolute error = 1.571
relative error = 84.14 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.137
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4941 2.129
h = 0.001 0.001
y[1] (numeric) = -1.78212400943 1.00589846646
y[1] (closed_form) = -1.78236277549 -0.564819023155
absolute error = 1.571
relative error = 84.01 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4931 2.13
h = 0.0001 0.004
y[1] (numeric) = -1.78312456984 1.00689841195
y[1] (closed_form) = -1.78336333804 -0.563819078895
absolute error = 1.571
relative error = 83.98 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.141
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.493 2.134
h = 0.003 0.006
y[1] (numeric) = -1.78712560536 1.00699720141
y[1] (closed_form) = -1.78736436954 -0.563720280357
absolute error = 1.571
relative error = 83.81 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.145
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.49 2.14
h = 0.0001 0.005
y[1] (numeric) = -1.79312798762 1.00999612866
y[1] (closed_form) = -1.79336673609 -0.560721362521
absolute error = 1.571
relative error = 83.59 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.152
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4899 2.145
h = 0.0001 0.003
y[1] (numeric) = -1.79812918774 1.01009466344
y[1] (closed_form) = -1.79836794707 -0.560622823697
absolute error = 1.571
relative error = 83.38 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.157
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4898 2.148
h = 0.001 0.001
y[1] (numeric) = -1.80112991124 1.01019381307
y[1] (closed_form) = -1.80136867346 -0.560523677465
absolute error = 1.571
relative error = 83.26 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.16
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4888 2.149
h = 0.001 0.003
y[1] (numeric) = -1.80213042968 1.01119375363
y[1] (closed_form) = -1.80236919387 -0.559523738079
absolute error = 1.571
relative error = 83.23 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.161
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4878 2.152
h = 0.0001 0.004
y[1] (numeric) = -1.8051314034 1.01219311066
y[1] (closed_form) = -1.80537016371 -0.558524378485
absolute error = 1.571
relative error = 83.12 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.164
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4877 2.156
h = 0.003 0.006
y[1] (numeric) = -1.80913232429 1.01229198676
y[1] (closed_form) = -1.80937108478 -0.558425498489
absolute error = 1.571
relative error = 82.95 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.168
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4847 2.162
h = 0.0001 0.005
y[1] (numeric) = -1.81513448454 1.01529095839
y[1] (closed_form) = -1.81537323047 -0.555426535176
absolute error = 1.571
relative error = 82.74 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.174
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4846 2.167
h = 0.0001 0.003
y[1] (numeric) = -1.82013555487 1.01538959364
y[1] (closed_form) = -1.82037431082 -0.555327896442
absolute error = 1.571
relative error = 82.53 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.179
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2263.5MB, alloc=52.3MB, time=27.52
x[1] = -0.4845 2.17
h = 0.001 0.001
y[1] (numeric) = -1.82313620076 1.01548880105
y[1] (closed_form) = -1.8233749593 -0.555228692198
absolute error = 1.571
relative error = 82.41 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.182
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4835 2.171
h = 0.001 0.003
y[1] (numeric) = -1.82413667426 1.01648873657
y[1] (closed_form) = -1.82437543458 -0.554228757791
absolute error = 1.571
relative error = 82.38 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.183
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4825 2.174
h = 0.0001 0.004
y[1] (numeric) = -1.82713755327 1.01748812901
y[1] (closed_form) = -1.82737631008 -0.553229362929
absolute error = 1.571
relative error = 82.27 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.186
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4824 2.178
h = 0.003 0.006
y[1] (numeric) = -1.83113837458 1.01758708216
y[1] (closed_form) = -1.83137713163 -0.553130406214
absolute error = 1.571
relative error = 82.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4794 2.184
h = 0.0001 0.005
y[1] (numeric) = -1.83714033243 1.02058609872
y[1] (closed_form) = -1.83737907599 -0.550131396981
absolute error = 1.571
relative error = 81.89 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.197
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4793 2.189
h = 0.0001 0.003
y[1] (numeric) = -1.84214128588 1.02068482846
y[1] (closed_form) = -1.84238003868 -0.550032664244
absolute error = 1.571
relative error = 81.69 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.202
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4792 2.192
h = 0.001 0.001
y[1] (numeric) = -1.84514186185 1.02078409028
y[1] (closed_form) = -1.84538061696 -0.549933405377
absolute error = 1.571
relative error = 81.57 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.205
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4782 2.193
h = 0.001 0.003
y[1] (numeric) = -1.84614229411 1.02178402206
y[1] (closed_form) = -1.84638105082 -0.548933474652
absolute error = 1.571
relative error = 81.54 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4772 2.196
h = 0.0001 0.004
y[1] (numeric) = -1.84914308709 1.02278344875
y[1] (closed_form) = -1.84938184064 -0.547934045671
absolute error = 1.571
relative error = 81.43 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.209
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4771 2.2
h = 0.003 0.006
y[1] (numeric) = -1.85314381873 1.02288247438
y[1] (closed_form) = -1.85338257257 -0.547835016787
absolute error = 1.571
relative error = 81.27 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.213
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4741 2.206
h = 0.0001 0.005
y[1] (numeric) = -1.85914559215 1.02588153601
y[1] (closed_form) = -1.85938433349 -0.544835961608
absolute error = 1.571
relative error = 81.07 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.219
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.474 2.211
h = 0.0001 0.003
y[1] (numeric) = -1.86414644043 1.02598035453
y[1] (closed_form) = -1.86438519029 -0.544737140525
absolute error = 1.571
relative error = 80.87 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.224
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2308.3MB, alloc=52.3MB, time=28.06
x[1] = -0.4739 2.214
h = 0.001 0.001
y[1] (numeric) = -1.86714695343 1.02607966751
y[1] (closed_form) = -1.86738570534 -0.544637830288
absolute error = 1.571
relative error = 80.75 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.227
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4729 2.215
h = 0.001 0.003
y[1] (numeric) = -1.86814734786 1.02707959666
y[1] (closed_form) = -1.86838610122 -0.543637902132
absolute error = 1.571
relative error = 80.72 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.228
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4719 2.218
h = 0.0001 0.004
y[1] (numeric) = -1.87114806275 1.02807905639
y[1] (closed_form) = -1.87138681326 -0.542638440252
absolute error = 1.571
relative error = 80.61 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.231
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4718 2.222
h = 0.003 0.006
y[1] (numeric) = -1.87514871369 1.02817815011
y[1] (closed_form) = -1.87538746453 -0.542539343556
absolute error = 1.571
relative error = 80.46 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.235
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4688 2.228
h = 0.0001 0.005
y[1] (numeric) = -1.88115031912 1.03117725657
y[1] (closed_form) = -1.8813890584 -0.539540242753
absolute error = 1.571
relative error = 80.25 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.242
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4687 2.233
h = 0.0001 0.003
y[1] (numeric) = -1.88615107284 1.03127615841
y[1] (closed_form) = -1.88638981996 -0.539441338733
absolute error = 1.571
relative error = 80.06 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.246
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4686 2.236
h = 0.001 0.001
y[1] (numeric) = -1.88915152918 1.03137551946
y[1] (closed_form) = -1.88939027813 -0.539341980237
absolute error = 1.571
relative error = 79.94 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.249
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4676 2.237
h = 0.0001 0.004
y[1] (numeric) = -1.89015188893 1.03237544694
y[1] (closed_form) = -1.89039063919 -0.538342053696
absolute error = 1.571
relative error = 79.91 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.251
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4675 2.241
h = 0.003 0.006
y[1] (numeric) = -1.89415248005 1.03247459334
y[1] (closed_form) = -1.8943912283 -0.53824290114
absolute error = 1.571
relative error = 79.76 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.255
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4645 2.247
h = 0.0001 0.005
y[1] (numeric) = -1.90015395352 1.03547373974
y[1] (closed_form) = -1.90039269097 -0.535243759797
absolute error = 1.571
relative error = 79.56 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.261
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4644 2.252
h = 0.0001 0.003
y[1] (numeric) = -1.90515463447 1.0355727101
y[1] (closed_form) = -1.90539337923 -0.535144787546
absolute error = 1.571
relative error = 79.36 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.266
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4643 2.255
h = 0.001 0.001
y[1] (numeric) = -1.90815504718 1.03567211073
y[1] (closed_form) = -1.90839379358 -0.535045389312
absolute error = 1.571
relative error = 79.25 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.269
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2353.0MB, alloc=52.3MB, time=28.61
x[1] = -0.4633 2.256
h = 0.001 0.003
y[1] (numeric) = -1.90915537938 1.03667203779
y[1] (closed_form) = -1.90939412699 -0.534045463136
absolute error = 1.571
relative error = 79.22 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4623 2.259
h = 0.0001 0.004
y[1] (numeric) = -1.91215596809 1.0376715563
y[1] (closed_form) = -1.91239471334 -0.533045942709
absolute error = 1.571
relative error = 79.12 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.273
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4622 2.263
h = 0.003 0.006
y[1] (numeric) = -1.91615649063 1.03777076648
y[1] (closed_form) = -1.91639523626 -0.532946730017
absolute error = 1.571
relative error = 78.97 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.277
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4592 2.269
h = 0.0001 0.005
y[1] (numeric) = -1.92215782311 1.04076995638
y[1] (closed_form) = -1.92239655875 -0.529947544543
absolute error = 1.571
relative error = 78.77 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.283
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4591 2.274
h = 0.0001 0.003
y[1] (numeric) = -1.92715842656 1.04086900047
y[1] (closed_form) = -1.92739716894 -0.529848498853
absolute error = 1.571
relative error = 78.58 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.288
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.459 2.277
h = 0.001 0.001
y[1] (numeric) = -1.93015879278 1.04096844371
y[1] (closed_form) = -1.93039753662 -0.529749057839
absolute error = 1.571
relative error = 78.47 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.291
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.458 2.278
h = 0.001 0.003
y[1] (numeric) = -1.93115909552 1.04196837049
y[1] (closed_form) = -1.93139784044 -0.528749131899
absolute error = 1.571
relative error = 78.44 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.292
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.457 2.281
h = 0.0001 0.004
y[1] (numeric) = -1.93415962516 1.04296791824
y[1] (closed_form) = -1.93439836796 -0.52774958235
absolute error = 1.571
relative error = 78.34 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.295
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4569 2.285
h = 0.003 0.006
y[1] (numeric) = -1.93816008825 1.04306718498
y[1] (closed_form) = -1.93839883144 -0.527650313316
absolute error = 1.571
relative error = 78.19 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.299
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4539 2.291
h = 0.0001 0.005
y[1] (numeric) = -1.94416129247 1.04606641743
y[1] (closed_form) = -1.94440002643 -0.524651084718
absolute error = 1.571
relative error = 77.99 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.306
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4538 2.296
h = 0.0001 0.003
y[1] (numeric) = -1.94916182642 1.04616553054
y[1] (closed_form) = -1.94940056657 -0.524551970277
absolute error = 1.571
relative error = 77.81 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.311
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4537 2.299
h = 0.001 0.001
y[1] (numeric) = -1.95216215091 1.04626501369
y[1] (closed_form) = -1.95240089236 -0.524452489192
absolute error = 1.571
relative error = 77.7 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.314
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2397.9MB, alloc=52.3MB, time=29.16
x[1] = -0.4527 2.3
h = 0.001 0.003
y[1] (numeric) = -1.95316242666 1.04726494078
y[1] (closed_form) = -1.95340116908 -0.523452562894
absolute error = 1.571
relative error = 77.67 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.315
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4517 2.303
h = 0.0001 0.004
y[1] (numeric) = -1.95616290279 1.04826451644
y[1] (closed_form) = -1.95640164332 -0.522452985541
absolute error = 1.571
relative error = 77.57 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.318
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4516 2.307
h = 0.003 0.006
y[1] (numeric) = -1.96016331254 1.04836383612
y[1] (closed_form) = -1.96040205347 -0.522353663771
absolute error = 1.571
relative error = 77.42 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.322
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4486 2.313
h = 0.0001 0.005
y[1] (numeric) = -1.96616440017 1.05136311003
y[1] (closed_form) = -1.96640313257 -0.519354393218
absolute error = 1.571
relative error = 77.23 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.328
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4485 2.318
h = 0.0001 0.003
y[1] (numeric) = -1.97116487182 1.05146228767
y[1] (closed_form) = -1.97140360991 -0.519255214474
absolute error = 1.571
relative error = 77.05 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.333
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4484 2.321
h = 0.001 0.001
y[1] (numeric) = -1.97416515887 1.05156180817
y[1] (closed_form) = -1.97440389811 -0.519155695888
absolute error = 1.571
relative error = 76.94 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.336
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4474 2.322
h = 0.001 0.003
y[1] (numeric) = -1.97516540992 1.05256173607
y[1] (closed_form) = -1.97540415003 -0.518155768736
absolute error = 1.571
relative error = 76.91 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.337
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4464 2.325
h = 0.0001 0.004
y[1] (numeric) = -1.97816583761 1.05356133832
y[1] (closed_form) = -1.97840457602 -0.517156164894
absolute error = 1.571
relative error = 76.81 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.34
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4463 2.329
h = 0.003 0.006
y[1] (numeric) = -1.98216619955 1.0536607075
y[1] (closed_form) = -1.98240493837 -0.517056793807
absolute error = 1.571
relative error = 76.67 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.344
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4433 2.335
h = 0.0001 0.005
y[1] (numeric) = -1.98816718124 1.05666002162
y[1] (closed_form) = -1.98840591219 -0.514057482595
absolute error = 1.571
relative error = 76.48 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.351
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4432 2.34
h = 0.0001 0.003
y[1] (numeric) = -1.9931675971 1.05675925956
y[1] (closed_form) = -1.99340633328 -0.513958243759
absolute error = 1.571
relative error = 76.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.356
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4431 2.343
h = 0.001 0.001
y[1] (numeric) = -1.9961678506 1.05685881498
y[1] (closed_form) = -1.9964065878 -0.513858690111
absolute error = 1.571
relative error = 76.19 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.359
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2442.9MB, alloc=52.3MB, time=29.70
x[1] = -0.4421 2.344
h = 0.0001 0.004
y[1] (numeric) = -1.99716807905 1.0578587441
y[1] (closed_form) = -1.99740681703 -0.512858761696
absolute error = 1.571
relative error = 76.17 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.442 2.348
h = 0.003 0.006
y[1] (numeric) = -2.0011684057 1.0579581514
y[1] (closed_form) = -2.00140714279 -0.512759350269
absolute error = 1.571
relative error = 76.03 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.364
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.439 2.354
h = 0.0001 0.005
y[1] (numeric) = -2.00716930448 1.06095750016
y[1] (closed_form) = -2.00740803423 -0.509760004069
absolute error = 1.571
relative error = 75.84 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.37
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4389 2.359
h = 0.0001 0.003
y[1] (numeric) = -2.0121696777 1.06105678735
y[1] (closed_form) = -2.01240841231 -0.509660716132
absolute error = 1.571
relative error = 75.66 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.375
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4388 2.362
h = 0.001 0.001
y[1] (numeric) = -2.01516990553 1.06115637134
y[1] (closed_form) = -2.01540864105 -0.509561133811
absolute error = 1.571
relative error = 75.56 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.378
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4378 2.363
h = 0.001 0.003
y[1] (numeric) = -2.0161701161 1.06215630201
y[1] (closed_form) = -2.01640885234 -0.5085612038
absolute error = 1.571
relative error = 75.53 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.379
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4368 2.366
h = 0.0001 0.004
y[1] (numeric) = -2.01917046587 1.06315595074
y[1] (closed_form) = -2.01940920072 -0.507561553662
absolute error = 1.571
relative error = 75.43 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.382
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4367 2.37
h = 0.003 0.006
y[1] (numeric) = -2.02317075229 1.06325540395
y[1] (closed_form) = -2.02340948755 -0.507462098852
absolute error = 1.571
relative error = 75.3 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.386
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4337 2.376
h = 0.0001 0.005
y[1] (numeric) = -2.02917156253 1.06625479027
y[1] (closed_form) = -2.02941029101 -0.50446271474
absolute error = 1.571
relative error = 75.11 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.393
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4336 2.381
h = 0.0001 0.003
y[1] (numeric) = -2.03417189039 1.06635413041
y[1] (closed_form) = -2.03441062335 -0.504363374008
absolute error = 1.571
relative error = 74.94 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.398
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4335 2.384
h = 0.001 0.001
y[1] (numeric) = -2.03717209091 1.06645374511
y[1] (closed_form) = -2.03741082467 -0.504263760854
absolute error = 1.571
relative error = 74.84 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.401
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4325 2.385
h = 0.001 0.003
y[1] (numeric) = -2.03817228235 1.06745367754
y[1] (closed_form) = -2.03841101675 -0.503263829033
absolute error = 1.571
relative error = 74.81 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.402
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2487.7MB, alloc=52.3MB, time=30.25
x[1] = -0.4315 2.388
h = 0.0001 0.004
y[1] (numeric) = -2.04117259577 1.06845334916
y[1] (closed_form) = -2.04141132892 -0.502264156111
absolute error = 1.571
relative error = 74.71 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.405
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4314 2.392
h = 0.003 0.006
y[1] (numeric) = -2.04517284739 1.06855284298
y[1] (closed_form) = -2.04541158094 -0.502164660827
absolute error = 1.571
relative error = 74.58 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.409
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4284 2.398
h = 0.0001 0.005
y[1] (numeric) = -2.05117357729 1.0715522654
y[1] (closed_form) = -2.0514123046 -0.499165240298
absolute error = 1.571
relative error = 74.4 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.415
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4283 2.403
h = 0.0001 0.003
y[1] (numeric) = -2.05617386466 1.0716516549
y[1] (closed_form) = -2.05641259608 -0.499065850341
absolute error = 1.571
relative error = 74.23 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.42
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4282 2.406
h = 0.001 0.001
y[1] (numeric) = -2.05917404077 1.07175129824
y[1] (closed_form) = -2.05941277289 -0.498966208426
absolute error = 1.571
relative error = 74.13 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.423
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4272 2.407
h = 0.001 0.003
y[1] (numeric) = -2.06017421473 1.07275123267
y[1] (closed_form) = -2.06041294743 -0.497966274576
absolute error = 1.571
relative error = 74.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.424
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4262 2.41
h = 0.0001 0.004
y[1] (numeric) = -2.06317449531 1.07375092593
y[1] (closed_form) = -2.06341322689 -0.496966580091
absolute error = 1.571
relative error = 74.01 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.427
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4261 2.414
h = 0.003 0.006
y[1] (numeric) = -2.06717471586 1.07385045761
y[1] (closed_form) = -2.06741344783 -0.496867047076
absolute error = 1.571
relative error = 73.87 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.431
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4231 2.42
h = 0.0001 0.005
y[1] (numeric) = -2.07317537291 1.07684991464
y[1] (closed_form) = -2.07341409913 -0.493867591657
absolute error = 1.571
relative error = 73.69 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.437
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.423 2.425
h = 0.0001 0.003
y[1] (numeric) = -2.07817562416 1.07694935012
y[1] (closed_form) = -2.07841435416 -0.49376815584
absolute error = 1.571
relative error = 73.53 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.442
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4229 2.428
h = 0.001 0.001
y[1] (numeric) = -2.08117577848 1.07704902017
y[1] (closed_form) = -2.08141450909 -0.493668487117
absolute error = 1.571
relative error = 73.43 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.445
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4219 2.429
h = 0.001 0.003
y[1] (numeric) = -2.08217593648 1.07804895675
y[1] (closed_form) = -2.0824146676 -0.492668551068
absolute error = 1.571
relative error = 73.4 %
Correct digits = 0
memory used=2532.5MB, alloc=52.3MB, time=30.80
Radius of convergence (given) for eq 1 = 2.447
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4209 2.432
h = 0.0001 0.004
y[1] (numeric) = -2.0851761874 1.07904867047
y[1] (closed_form) = -2.08541491753 -0.491668836207
absolute error = 1.571
relative error = 73.31 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.45
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4208 2.436
h = 0.003 0.006
y[1] (numeric) = -2.08917638024 1.07914823743
y[1] (closed_form) = -2.08941511075 -0.491569268044
absolute error = 1.571
relative error = 73.18 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.454
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4178 2.442
h = 0.0001 0.005
y[1] (numeric) = -2.09517697127 1.08214772755
y[1] (closed_form) = -2.09541569649 -0.488569779277
absolute error = 1.571
relative error = 73 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.46
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4177 2.447
h = 0.0001 0.003
y[1] (numeric) = -2.10017719035 1.08224720583
y[1] (closed_form) = -2.10041591902 -0.488470300766
absolute error = 1.571
relative error = 72.84 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.465
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4176 2.45
h = 0.001 0.001
y[1] (numeric) = -2.10317732523 1.08234690074
y[1] (closed_form) = -2.10341605444 -0.488370607075
absolute error = 1.571
relative error = 72.74 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.468
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4166 2.451
h = 0.0001 0.004
y[1] (numeric) = -2.10417746865 1.08334683962
y[1] (closed_form) = -2.10441619833 -0.487370668702
absolute error = 1.571
relative error = 72.71 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.469
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4165 2.455
h = 0.003 0.006
y[1] (numeric) = -2.10817764113 1.08344643363
y[1] (closed_form) = -2.1084163705 -0.487271071955
absolute error = 1.571
relative error = 72.58 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.473
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4135 2.461
h = 0.0001 0.005
y[1] (numeric) = -2.1141781807 1.08644595173
y[1] (closed_form) = -2.11441690514 -0.484271555038
absolute error = 1.571
relative error = 72.41 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.479
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4134 2.466
h = 0.0001 0.003
y[1] (numeric) = -2.1191783754 1.08654546477
y[1] (closed_form) = -2.11941710304 -0.484172041836
absolute error = 1.571
relative error = 72.25 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.484
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4133 2.469
h = 0.001 0.001
y[1] (numeric) = -2.12217849552 1.0866451799
y[1] (closed_form) = -2.12241722365 -0.484072327843
absolute error = 1.571
relative error = 72.15 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.487
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4123 2.47
h = 0.001 0.003
y[1] (numeric) = -2.12317862746 1.08764512097
y[1] (closed_form) = -2.12341735601 -0.483072387245
absolute error = 1.571
relative error = 72.13 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.488
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4113 2.473
h = 0.0001 0.004
y[1] (numeric) = -2.12617883095 1.08864487
y[1] (closed_form) = -2.12641755868 -0.482072637216
absolute error = 1.571
relative error = 72.04 %
Correct digits = 0
memory used=2577.5MB, alloc=52.3MB, time=31.34
Radius of convergence (given) for eq 1 = 2.492
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4112 2.477
h = 0.003 0.006
y[1] (numeric) = -2.13017898039 1.08874449644
y[1] (closed_form) = -2.13041770849 -0.481973009758
absolute error = 1.571
relative error = 71.91 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.496
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4082 2.483
h = 0.0001 0.005
y[1] (numeric) = -2.13617946503 1.09174404476
y[1] (closed_form) = -2.1364181886 -0.478973462422
absolute error = 1.571
relative error = 71.74 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.502
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4081 2.488
h = 0.0001 0.003
y[1] (numeric) = -2.14117963384 1.09184359514
y[1] (closed_form) = -2.14141836035 -0.478873911953
absolute error = 1.571
relative error = 71.58 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.507
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.408 2.491
h = 0.001 0.001
y[1] (numeric) = -2.14417973829 1.091943332
y[1] (closed_form) = -2.14441846522 -0.478774176148
absolute error = 1.571
relative error = 71.49 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.51
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.407 2.492
h = 0.001 0.003
y[1] (numeric) = -2.14517985794 1.09294327549
y[1] (closed_form) = -2.14541858524 -0.477774233103
absolute error = 1.571
relative error = 71.46 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.511
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.406 2.495
h = 0.0001 0.004
y[1] (numeric) = -2.14818003938 1.09394304176
y[1] (closed_form) = -2.14841876596 -0.476774465898
absolute error = 1.571
relative error = 71.37 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.514
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4059 2.499
h = 0.003 0.006
y[1] (numeric) = -2.15218016895 1.09404269685
y[1] (closed_form) = -2.15241889588 -0.476674809888
absolute error = 1.571
relative error = 71.25 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.518
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4029 2.505
h = 0.0001 0.005
y[1] (numeric) = -2.1581806039 1.0970422739
y[1] (closed_form) = -2.15841932666 -0.473675233645
absolute error = 1.571
relative error = 71.08 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.524
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4028 2.51
h = 0.0001 0.003
y[1] (numeric) = -2.16318074973 1.09714185898
y[1] (closed_form) = -2.16341947518 -0.473575648547
absolute error = 1.571
relative error = 70.92 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.529
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4027 2.513
h = 0.001 0.001
y[1] (numeric) = -2.16618084025 1.09724161603
y[1] (closed_form) = -2.16641956607 -0.473475892468
absolute error = 1.571
relative error = 70.83 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.532
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4017 2.514
h = 0.001 0.003
y[1] (numeric) = -2.1671809487 1.09824156197
y[1] (closed_form) = -2.16741967485 -0.472475946942
absolute error = 1.571
relative error = 70.81 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.533
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2622.3MB, alloc=52.3MB, time=31.89
x[1] = -0.4007 2.517
h = 0.0001 0.004
y[1] (numeric) = -2.17018111028 1.09924134446
y[1] (closed_form) = -2.17041983578 -0.471476163587
absolute error = 1.571
relative error = 70.72 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.536
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4006 2.521
h = 0.003 0.006
y[1] (numeric) = -2.17418122221 1.09934102616
y[1] (closed_form) = -2.17441994806 -0.471376481049
absolute error = 1.571
relative error = 70.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.54
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3976 2.527
h = 0.0001 0.005
y[1] (numeric) = -2.18018161222 1.10234063049
y[1] (closed_form) = -2.18042033424 -0.468376877382
absolute error = 1.571
relative error = 70.43 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.547
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3975 2.532
h = 0.0001 0.003
y[1] (numeric) = -2.18518173768 1.10244024777
y[1] (closed_form) = -2.18542046216 -0.468277260131
absolute error = 1.571
relative error = 70.28 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.552
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3974 2.535
h = 0.001 0.001
y[1] (numeric) = -2.18818181584 1.10254002358
y[1] (closed_form) = -2.18842054064 -0.468177485217
absolute error = 1.571
relative error = 70.19 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.555
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3964 2.536
h = 0.001 0.003
y[1] (numeric) = -2.18918191408 1.10353997198
y[1] (closed_form) = -2.18942063918 -0.467177537202
absolute error = 1.571
relative error = 70.16 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.556
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3954 2.539
h = 0.0001 0.004
y[1] (numeric) = -2.19218205779 1.1045397697
y[1] (closed_form) = -2.19242078232 -0.466177738676
absolute error = 1.571
relative error = 70.08 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.559
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3953 2.543
h = 0.003 0.006
y[1] (numeric) = -2.19618215409 1.10463947611
y[1] (closed_form) = -2.19642087895 -0.466078031508
absolute error = 1.571
relative error = 69.95 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.563
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3923 2.549
h = 0.0001 0.005
y[1] (numeric) = -2.20218250349 1.10763910628
y[1] (closed_form) = -2.20242122483 -0.463078401869
absolute error = 1.571
relative error = 69.79 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.569
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3922 2.554
h = 0.0001 0.003
y[1] (numeric) = -2.20718261093 1.10773875345
y[1] (closed_form) = -2.20742133452 -0.462978754778
absolute error = 1.571
relative error = 69.64 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.574
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3921 2.557
h = 0.001 0.001
y[1] (numeric) = -2.21018267814 1.10783854667
y[1] (closed_form) = -2.210421402 -0.46287896238
absolute error = 1.571
relative error = 69.55 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.577
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3911 2.558
h = 0.0001 0.004
y[1] (numeric) = -2.21118276709 1.10883849752
y[1] (closed_form) = -2.21142149121 -0.461879011888
absolute error = 1.571
relative error = 69.53 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.578
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2667.1MB, alloc=52.3MB, time=32.43
x[1] = -0.391 2.562
h = 0.003 0.006
y[1] (numeric) = -2.21518285198 1.10893822283
y[1] (closed_form) = -2.21542157609 -0.46177928479
absolute error = 1.571
relative error = 69.41 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.582
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.388 2.568
h = 0.0001 0.005
y[1] (numeric) = -2.22118316987 1.11193787455
y[1] (closed_form) = -2.2214218907 -0.458779633507
absolute error = 1.571
relative error = 69.25 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.589
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3879 2.573
h = 0.0001 0.003
y[1] (numeric) = -2.2261832638 1.11203754587
y[1] (closed_form) = -2.22642198672 -0.458679962289
absolute error = 1.571
relative error = 69.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.594
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3878 2.576
h = 0.001 0.001
y[1] (numeric) = -2.22918332279 1.11213735319
y[1] (closed_form) = -2.22942204595 -0.458580155744
absolute error = 1.571
relative error = 69.01 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.597
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3868 2.577
h = 0.001 0.003
y[1] (numeric) = -2.23018340443 1.11313730622
y[1] (closed_form) = -2.23042212783 -0.457580203044
absolute error = 1.571
relative error = 68.99 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.598
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3858 2.58
h = 0.0001 0.004
y[1] (numeric) = -2.23318351972 1.11413712998
y[1] (closed_form) = -2.23342224266 -0.45658037858
absolute error = 1.571
relative error = 68.9 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.601
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3857 2.584
h = 0.003 0.006
y[1] (numeric) = -2.23718359183 1.11423687785
y[1] (closed_form) = -2.23742231508 -0.456480630084
absolute error = 1.571
relative error = 68.79 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.605
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3827 2.59
h = 0.0001 0.005
y[1] (numeric) = -2.24318387611 1.11723655281
y[1] (closed_form) = -2.24342259635 -0.45348095546
absolute error = 1.571
relative error = 68.63 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.611
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3826 2.595
h = 0.0001 0.003
y[1] (numeric) = -2.24818395574 1.11733625007
y[1] (closed_form) = -2.24842267789 -0.453381258341
absolute error = 1.571
relative error = 68.48 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.616
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3825 2.598
h = 0.001 0.001
y[1] (numeric) = -2.251184006 1.11743607251
y[1] (closed_form) = -2.25142272835 -0.45328143661
absolute error = 1.571
relative error = 68.39 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.619
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3815 2.599
h = 0.001 0.003
y[1] (numeric) = -2.25218407984 1.11843602792
y[1] (closed_form) = -2.2524228024 -0.452281481505
absolute error = 1.571
relative error = 68.37 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.62
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3805 2.602
h = 0.0001 0.004
y[1] (numeric) = -2.25518418197 1.11943586433
y[1] (closed_form) = -2.25542290413 -0.451281644446
absolute error = 1.571
relative error = 68.29 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.623
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2712.1MB, alloc=52.3MB, time=32.98
x[1] = -0.3804 2.606
h = 0.003 0.006
y[1] (numeric) = -2.2591842431 1.11953563209
y[1] (closed_form) = -2.25942296555 -0.451181876117
absolute error = 1.571
relative error = 68.17 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.627
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3774 2.612
h = 0.0001 0.005
y[1] (numeric) = -2.26518449706 1.12253532898
y[1] (closed_form) = -2.26542321676 -0.448182179476
absolute error = 1.571
relative error = 68.02 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.634
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3773 2.617
h = 0.0001 0.003
y[1] (numeric) = -2.27018456409 1.12263505025
y[1] (closed_form) = -2.27042328552 -0.448082458363
absolute error = 1.571
relative error = 67.87 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.639
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3772 2.62
h = 0.001 0.001
y[1] (numeric) = -2.27318460666 1.12273488671
y[1] (closed_form) = -2.27342332827 -0.447982622557
absolute error = 1.571
relative error = 67.79 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.642
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3762 2.621
h = 0.001 0.003
y[1] (numeric) = -2.27418467339 1.12373484446
y[1] (closed_form) = -2.27442339519 -0.446982665098
absolute error = 1.571
relative error = 67.76 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.643
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3752 2.624
h = 0.0001 0.004
y[1] (numeric) = -2.27718476373 1.1247346927
y[1] (closed_form) = -2.27742348517 -0.445982816254
absolute error = 1.571
relative error = 67.68 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.646
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3751 2.628
h = 0.003 0.006
y[1] (numeric) = -2.28118481518 1.12483447888
y[1] (closed_form) = -2.2814235369 -0.445883029553
absolute error = 1.571
relative error = 67.57 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.65
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3721 2.634
h = 0.0001 0.005
y[1] (numeric) = -2.28718504182 1.12783419644
y[1] (closed_form) = -2.28742376101 -0.442883312171
absolute error = 1.571
relative error = 67.42 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.656
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.372 2.639
h = 0.0001 0.003
y[1] (numeric) = -2.29218509777 1.12793393995
y[1] (closed_form) = -2.29242381856 -0.442783568842
absolute error = 1.571
relative error = 67.27 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.661
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3719 2.642
h = 0.001 0.001
y[1] (numeric) = -2.29518513358 1.1280337894
y[1] (closed_form) = -2.29542385451 -0.44268372
absolute error = 1.571
relative error = 67.19 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.664
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3709 2.643
h = 0.001 0.003
y[1] (numeric) = -2.29618519386 1.12903374942
y[1] (closed_form) = -2.29642391495 -0.441683760248
absolute error = 1.571
relative error = 67.17 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.665
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3699 2.646
h = 0.0001 0.004
y[1] (numeric) = -2.29918527362 1.13003360872
y[1] (closed_form) = -2.2994239944 -0.440683900386
absolute error = 1.571
relative error = 67.09 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.668
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2756.9MB, alloc=52.3MB, time=33.52
x[1] = -0.3698 2.65
h = 0.003 0.006
y[1] (numeric) = -2.30318531658 1.13013341196
y[1] (closed_form) = -2.30342403762 -0.440584096677
absolute error = 1.571
relative error = 66.98 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.672
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3668 2.656
h = 0.0001 0.005
y[1] (numeric) = -2.30918551859 1.13313314897
y[1] (closed_form) = -2.30942423732 -0.437584359779
absolute error = 1.571
relative error = 66.82 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.679
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3667 2.661
h = 0.0001 0.003
y[1] (numeric) = -2.31418556484 1.13323291305
y[1] (closed_form) = -2.31442428502 -0.437484595892
absolute error = 1.571
relative error = 66.69 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.684
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3666 2.664
h = 0.001 0.001
y[1] (numeric) = -2.3171855947 1.13333277451
y[1] (closed_form) = -2.317424315 -0.437384734983
absolute error = 1.571
relative error = 66.6 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.687
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3656 2.665
h = 0.0001 0.004
y[1] (numeric) = -2.31818564911 1.13433273674
y[1] (closed_form) = -2.31842436956 -0.436384773006
absolute error = 1.571
relative error = 66.58 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.688
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3655 2.669
h = 0.003 0.006
y[1] (numeric) = -2.32218568593 1.13443255299
y[1] (closed_form) = -2.32242440649 -0.436284955594
absolute error = 1.571
relative error = 66.47 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.692
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3625 2.675
h = 0.0001 0.005
y[1] (numeric) = -2.32818586894 1.13743230606
y[1] (closed_form) = -2.32842458735 -0.433285202588
absolute error = 1.571
relative error = 66.32 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.698
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3624 2.68
h = 0.0001 0.003
y[1] (numeric) = -2.33318590804 1.13753208671
y[1] (closed_form) = -2.3334246278 -0.433185422149
absolute error = 1.571
relative error = 66.18 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.703
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3623 2.683
h = 0.001 0.001
y[1] (numeric) = -2.3361859335 1.13763195785
y[1] (closed_form) = -2.33642465336 -0.43308555152
absolute error = 1.571
relative error = 66.1 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.706
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3613 2.684
h = 0.001 0.003
y[1] (numeric) = -2.33718598332 1.13863192198
y[1] (closed_form) = -2.33742470331 -0.432085587624
absolute error = 1.571
relative error = 66.08 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.707
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3603 2.687
h = 0.0001 0.004
y[1] (numeric) = -2.34018604639 1.13963180006
y[1] (closed_form) = -2.34042476612 -0.431085709065
absolute error = 1.571
relative error = 66 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.71
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3602 2.691
h = 0.003 0.006
y[1] (numeric) = -2.34418607641 1.13973163178
y[1] (closed_form) = -2.34442479639 -0.430985876952
absolute error = 1.571
relative error = 65.89 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.714
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2801.7MB, alloc=52.3MB, time=34.08
x[1] = -0.3572 2.697
h = 0.0001 0.005
y[1] (numeric) = -2.35018623917 1.14273140215
y[1] (closed_form) = -2.35042495718 -0.427986106598
absolute error = 1.571
relative error = 65.75 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.721
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3571 2.702
h = 0.0001 0.003
y[1] (numeric) = -2.35518627071 1.14283120056
y[1] (closed_form) = -2.35542498995 -0.427886308404
absolute error = 1.571
relative error = 65.61 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.726
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.357 2.705
h = 0.001 0.001
y[1] (numeric) = -2.35818629152 1.14293108209
y[1] (closed_form) = -2.35842501084 -0.427786427346
absolute error = 1.571
relative error = 65.53 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.729
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.356 2.706
h = 0.001 0.003
y[1] (numeric) = -2.35918633644 1.14393104829
y[1] (closed_form) = -2.35942505588 -0.426786461371
absolute error = 1.571
relative error = 65.51 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.73
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.355 2.709
h = 0.0001 0.004
y[1] (numeric) = -2.36218639181 1.14493093543
y[1] (closed_form) = -2.36242511103 -0.425786573776
absolute error = 1.571
relative error = 65.43 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.733
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3549 2.713
h = 0.003 0.006
y[1] (numeric) = -2.36618641603 1.14503078078
y[1] (closed_form) = -2.36642513548 -0.425686728073
absolute error = 1.571
relative error = 65.33 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.737
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3519 2.719
h = 0.0001 0.005
y[1] (numeric) = -2.37218656059 1.14803056738
y[1] (closed_form) = -2.37242527824 -0.422686941448
absolute error = 1.571
relative error = 65.18 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.743
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3518 2.724
h = 0.0001 0.003
y[1] (numeric) = -2.37718658556 1.14813038221
y[1] (closed_form) = -2.37742530432 -0.422587126848
absolute error = 1.571
relative error = 65.05 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.748
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3517 2.727
h = 0.001 0.001
y[1] (numeric) = -2.38018660231 1.14823027334
y[1] (closed_form) = -2.38042532114 -0.422487236152
absolute error = 1.571
relative error = 64.97 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.751
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3507 2.728
h = 0.001 0.003
y[1] (numeric) = -2.38118664278 1.14923024151
y[1] (closed_form) = -2.38142536171 -0.421487268178
absolute error = 1.571
relative error = 64.95 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.752
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3497 2.731
h = 0.0001 0.004
y[1] (numeric) = -2.38418669128 1.15023013711
y[1] (closed_form) = -2.38442541002 -0.420487372161
absolute error = 1.571
relative error = 64.87 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.755
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3496 2.735
h = 0.003 0.006
y[1] (numeric) = -2.38818671046 1.15032999505
y[1] (closed_form) = -2.38842542941 -0.420387513903
absolute error = 1.571
relative error = 64.77 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.759
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2846.5MB, alloc=52.3MB, time=34.63
x[1] = -0.3466 2.741
h = 0.0001 0.005
y[1] (numeric) = -2.39418683867 1.15332979687
y[1] (closed_form) = -2.39442555597 -0.417387712031
absolute error = 1.571
relative error = 64.62 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.766
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3465 2.746
h = 0.0001 0.003
y[1] (numeric) = -2.39918685793 1.15342962685
y[1] (closed_form) = -2.39942557625 -0.417287882281
absolute error = 1.571
relative error = 64.49 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.771
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3464 2.749
h = 0.001 0.001
y[1] (numeric) = -2.40218687115 1.15352952685
y[1] (closed_form) = -2.40242558953 -0.417187982681
absolute error = 1.571
relative error = 64.42 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.774
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3454 2.75
h = 0.001 0.003
y[1] (numeric) = -2.40318690758 1.15452949692
y[1] (closed_form) = -2.40342562606 -0.41618801279
absolute error = 1.571
relative error = 64.39 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.775
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3444 2.753
h = 0.0001 0.004
y[1] (numeric) = -2.40618694997 1.1555294004
y[1] (closed_form) = -2.40642566827 -0.41518810893
absolute error = 1.571
relative error = 64.32 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.778
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3443 2.757
h = 0.003 0.006
y[1] (numeric) = -2.41018696476 1.15562926996
y[1] (closed_form) = -2.41042568327 -0.415088239079
absolute error = 1.571
relative error = 64.22 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.782
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3413 2.763
h = 0.0001 0.005
y[1] (numeric) = -2.4161870783 1.15862908603
y[1] (closed_form) = -2.4164257953 -0.412088422932
absolute error = 1.571
relative error = 64.08 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.788
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3412 2.768
h = 0.0001 0.003
y[1] (numeric) = -2.42118709263 1.15872892998
y[1] (closed_form) = -2.42142581056 -0.411988579199
absolute error = 1.571
relative error = 63.95 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.793
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3411 2.771
h = 0.001 0.001
y[1] (numeric) = -2.4241871028 1.15882883817
y[1] (closed_form) = -2.42442582077 -0.411888671379
absolute error = 1.571
relative error = 63.87 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.796
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.3401 2.772
h = 0.001 0.003
y[1] (numeric) = -2.42518713558 1.15982881007
y[1] (closed_form) = -2.42542585362 -0.410888699654
absolute error = 1.571
relative error = 63.85 %
Correct digits = 0
Radius of convergence (given) for eq 1 = 2.797
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ;
Iterations = 754
Total Elapsed Time = 34 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 34 Seconds
> quit
memory used=2886.7MB, alloc=52.3MB, time=35.10