|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"| ");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(10.0) * ln(c(0.2) * c(x) + c(0.3)));
> end;
exact_soln_y := proc(x) return c(10.0)*ln(c(0.2)*c(x) + c(0.3)) 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_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_2D0[1] / array_tmp2[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_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := neg(array_tmp3[1])* array_tmp2[2] / array_tmp2[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 3
> #emit pre div CONST - LINEAR $eq_no = 1 i = 4
> #emit pre div CONST - LINEAR $eq_no = 1 i = 5
> #emit pre 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
> array_tmp3[3] := neg(array_tmp3[2])* array_tmp2[2] / array_tmp2[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
> array_tmp3[4] := neg(array_tmp3[3])* array_tmp2[2] / array_tmp2[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
> array_tmp3[5] := neg(array_tmp3[4])* array_tmp2[2] / array_tmp2[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
> #emit div CONST LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp3[kkk] := array_const_2D0[1] * array_tmp2[kkk];
> #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_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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_0D2[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
array_tmp3[1] := array_const_2D0[1]/array_tmp2[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_0D2[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := neg(array_tmp3[1])*array_tmp2[2]/array_tmp2[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[3] := neg(array_tmp3[2])*array_tmp2[2]/array_tmp2[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[4] := neg(array_tmp3[3])*array_tmp2[2]/array_tmp2[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[5] := neg(array_tmp3[4])*array_tmp2[2]/array_tmp2[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[kkk] := array_const_2D0[1]*array_tmp2[kkk];
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_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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:= 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[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);
> 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_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_const_0D3);
> array_const_0D3[1] := c(0.3);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := 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/div_c_linpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ");
> 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 := 2.5 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-1.5);");
> 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(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(10.0) * ln(c(0.2) * c(x) + c(0.3)));");
> 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 := 2.5 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-1.5);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(1.0);
> 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 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T14:45:49-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_c_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"div_c_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_c_lin maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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 := 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[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);
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_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_const_0D3);
array_const_0D3[1] := c(0.3);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := 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/div_c_linpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 2.0 / ( 0.2 \
* x + 0.3 ) ; ");
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 := 2.5 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-1.5);");
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(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(10.0) * ln(c(0.2) * c(x) + c(0.3)));");
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,");
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omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 2.5 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-1.5);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(1.0);
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 ) = 2.0 / ( 0.2\
* x + 0.3 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T14:45:49-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_c_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = 2\
.0 / ( 0.2 * x + 0.3 ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file, "div_c_lin diffeq.mxt");
logitem_str(html_log_file, "div_c_lin maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/div_c_linpostcpx.cpx#################
diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 2.5 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-1.5);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(1.0);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(10.0) * ln(c(0.2) * c(x) + c(0.3)));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 2.5 0.1
h = 0.0001 0.005
y[1] (numeric) = -2.2283114893 0.249947936189
y[1] (closed_form) = -2.2283114893 0.249947936189
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 4.001
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5001 0.105
h = 0.0001 0.003
y[1] (numeric) = -2.22774312012 0.262433285674
y[1] (closed_form) = -2.22774156238 0.262433174129
absolute error = 1.562e-06
relative error = 6.962e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.001
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5002 0.108
h = 0.001 0.001
y[1] (numeric) = -2.22729190813 0.269920877598
y[1] (closed_form) = -2.22729221781 0.269920929191
absolute error = 3.139e-07
relative error = 1.399e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 4.002
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5012 0.109
h = 0.001 0.003
y[1] (numeric) = -2.22472555851 0.272350471826
y[1] (closed_form) = -2.2247267534 0.272350915749
absolute error = 1.275e-06
relative error = 5.687e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.003
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5022 0.112
h = 0.0001 0.004
y[1] (numeric) = -2.22202350571 0.279773348438
y[1] (closed_form) = -2.222022866 0.27977306623
absolute error = 6.992e-07
relative error = 3.122e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5023 0.116
h = 0.003 0.006
y[1] (numeric) = -2.22149073576 0.289751495452
y[1] (closed_form) = -2.22148876037 0.289752230115
absolute error = 2.108e-06
relative error = 9.408e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5053 0.122
h = 0.0001 0.005
y[1] (numeric) = -2.21356005326 0.304508869189
y[1] (closed_form) = -2.21355748553 0.304502261688
absolute error = 7.089e-06
relative error = 0.0003173 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.007
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5054 0.127
h = 0.0001 0.003
y[1] (numeric) = -2.21292180098 0.316967742168
y[1] (closed_form) = -2.21292041139 0.316965761214
absolute error = 2.420e-06
relative error = 0.0001082 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.007
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5055 0.13
h = 0.001 0.001
y[1] (numeric) = -2.21243050267 0.324441652218
y[1] (closed_form) = -2.21243097307 0.32443985421
absolute error = 1.859e-06
relative error = 8.311e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.008
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5065 0.131
h = 0.001 0.003
y[1] (numeric) = -2.20985478289 0.326853628713
y[1] (closed_form) = -2.20985613155 0.326852231467
absolute error = 1.942e-06
relative error = 8.693e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.009
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5075 0.134
h = 0.0001 0.004
y[1] (numeric) = -2.20711639775 0.334250659528
y[1] (closed_form) = -2.20711592526 0.334248518421
absolute error = 2.193e-06
relative error = 9.822e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.01
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5076 0.138
h = 0.003 0.006
y[1] (numeric) = -2.20653016808 0.344210880173
y[1] (closed_form) = -2.20652835294 0.344209738338
absolute error = 2.144e-06
relative error = 9.602e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.01
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5106 0.144
h = 0.0001 0.005
y[1] (numeric) = -2.19853124894 0.35890281851
y[1] (closed_form) = -2.19852892295 0.358894350511
absolute error = 8.782e-06
relative error = 0.0003942 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5107 0.149
h = 0.0001 0.003
y[1] (numeric) = -2.19782634338 0.371339291379
y[1] (closed_form) = -2.19782514177 0.371335448498
absolute error = 4.026e-06
relative error = 0.0001806 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5108 0.152
h = 0.001 0.001
y[1] (numeric) = -2.19729522965 0.37879912618
y[1] (closed_form) = -2.19729588032 0.378795485841
absolute error = 3.698e-06
relative error = 0.0001659 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.014
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5118 0.153
h = 0.001 0.003
y[1] (numeric) = -2.19471035956 0.381193437123
y[1] (closed_form) = -2.19471188144 0.381190205828
absolute error = 3.572e-06
relative error = 0.0001603 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.015
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5128 0.156
h = 0.0001 0.004
y[1] (numeric) = -2.19193603356 0.38856430697
y[1] (closed_form) = -2.19193574796 0.388560314382
absolute error = 4.003e-06
relative error = 0.0001798 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.016
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5129 0.16
h = 0.003 0.006
y[1] (numeric) = -2.19129670251 0.398506076547
y[1] (closed_form) = -2.1912950676 0.398503065602
absolute error = 3.426e-06
relative error = 0.0001538 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.016
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5159 0.166
h = 0.0001 0.005
y[1] (numeric) = -2.18323046615 0.413132041264
y[1] (closed_form) = -2.18322840125 0.413121721404
absolute error = 1.052e-05
relative error = 0.0004737 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.019
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.516 0.171
h = 0.0001 0.003
y[1] (numeric) = -2.18245935594 0.425545461989
y[1] (closed_form) = -2.18245836193 0.425539764952
absolute error = 5.783e-06
relative error = 0.0002601 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5161 0.174
h = 0.001 0.001
y[1] (numeric) = -2.18188870282 0.432990834397
y[1] (closed_form) = -2.18188955308 0.432985359281
absolute error = 5.541e-06
relative error = 0.0002491 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5171 0.175
h = 0.001 0.003
y[1] (numeric) = -2.17929490203 0.435367435762
y[1] (closed_form) = -2.17929661636 0.435362377818
absolute error = 5.341e-06
relative error = 0.0002403 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.021
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5181 0.178
h = 0.0001 0.004
y[1] (numeric) = -2.17648502993 0.44271183729
y[1] (closed_form) = -2.17648495067 0.442706000926
absolute error = 5.837e-06
relative error = 0.0002628 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.022
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5182 0.182
h = 0.003 0.006
y[1] (numeric) = -2.17579296265 0.452634639367
y[1] (closed_form) = -2.17579152774 0.452629766992
absolute error = 5.079e-06
relative error = 0.0002286 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.022
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5212 0.188
h = 0.0001 0.005
y[1] (numeric) = -2.16766033293 0.467194109679
y[1] (closed_form) = -2.16765854822 0.467181946862
absolute error = 1.229e-05
relative error = 0.0005544 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.026
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5213 0.193
h = 0.0001 0.003
y[1] (numeric) = -2.16682347513 0.479583836561
y[1] (closed_form) = -2.16682270811 0.479576293422
absolute error = 7.582e-06
relative error = 0.0003416 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.026
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5214 0.196
h = 0.001 0.001
y[1] (numeric) = -2.16621356359 0.487014365734
y[1] (closed_form) = -2.16621463258 0.487007063672
absolute error = 7.380e-06
relative error = 0.0003324 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.026
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5224 0.197
h = 0.0001 0.004
y[1] (numeric) = -2.1636110514 0.489373217258
y[1] (closed_form) = -2.1636129772 0.48936634034
absolute error = 7.141e-06
relative error = 0.0003219 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.027
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5225 0.201
h = 0.003 0.006
y[1] (numeric) = -2.16287610125 0.499280211564
y[1] (closed_form) = -2.16287421857 0.499273979662
absolute error = 6.510e-06
relative error = 0.0002933 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.028
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5255 0.207
h = 0.0001 0.005
y[1] (numeric) = -2.15468626498 0.513782817804
y[1] (closed_form) = -2.15468410121 0.513769311383
absolute error = 1.368e-05
relative error = 0.0006175 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5256 0.212
h = 0.0001 0.003
y[1] (numeric) = -2.15379289364 0.526152419566
y[1] (closed_form) = -2.15379170197 0.526143530068
absolute error = 8.969e-06
relative error = 0.0004045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5257 0.215
h = 0.001 0.001
y[1] (numeric) = -2.15314923555 0.533570335071
y[1] (closed_form) = -2.15314987279 0.533561703062
absolute error = 8.655e-06
relative error = 0.0003902 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5267 0.216
h = 0.001 0.003
y[1] (numeric) = -2.15053918814 0.535913978954
y[1] (closed_form) = -2.15054067596 0.535905778915
absolute error = 8.334e-06
relative error = 0.000376 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.032
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5277 0.219
h = 0.0001 0.004
y[1] (numeric) = -2.14766391061 0.543208750147
y[1] (closed_form) = -2.14766363107 0.543199740466
absolute error = 9.014e-06
relative error = 0.0004069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.034
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5278 0.223
h = 0.003 0.006
y[1] (numeric) = -2.14687446781 0.55309552995
y[1] (closed_form) = -2.14687282143 0.553087451433
absolute error = 8.245e-06
relative error = 0.0003719 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.034
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5308 0.229
h = 0.0001 0.005
y[1] (numeric) = -2.13861996185 0.567530707948
y[1] (closed_form) = -2.1386181133 0.567515375617
absolute error = 1.544e-05
relative error = 0.000698 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.037
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5309 0.234
h = 0.0001 0.003
y[1] (numeric) = -2.13766170757 0.579875444057
y[1] (closed_form) = -2.13766077849 0.579864723942
absolute error = 1.076e-05
relative error = 0.0004858 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.531 0.237
h = 0.001 0.001
y[1] (numeric) = -2.13697932216 0.587277821184
y[1] (closed_form) = -2.13698021322 0.587267377294
absolute error = 1.048e-05
relative error = 0.000473 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.532 0.238
h = 0.001 0.003
y[1] (numeric) = -2.13436096985 0.589603647608
y[1] (closed_form) = -2.13436270408 0.589593643372
absolute error = 1.015e-05
relative error = 0.0004585 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.039
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.533 0.241
h = 0.0001 0.004
y[1] (numeric) = -2.13145128865 0.596871109771
y[1] (closed_form) = -2.13145126999 0.596860279647
absolute error = 1.083e-05
relative error = 0.0004893 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.04
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5331 0.245
h = 0.003 0.006
y[1] (numeric) = -2.13061018417 0.606737486547
y[1] (closed_form) = -2.13060879323 0.606727569896
absolute error = 1.001e-05
relative error = 0.000452 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.041
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5361 0.251
h = 0.0001 0.005
y[1] (numeric) = -2.12229194295 0.621104765227
y[1] (closed_form) = -2.12229042804 0.62108761663
absolute error = 1.722e-05
relative error = 0.0007785 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.044
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5362 0.256
h = 0.0001 0.003
y[1] (numeric) = -2.12126928551 0.633424024078
y[1] (closed_form) = -2.12126863778 0.633411482172
absolute error = 1.256e-05
relative error = 0.0005673 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.044
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5363 0.259
h = 0.001 0.001
y[1] (numeric) = -2.12054846709 0.64081050031
y[1] (closed_form) = -2.12054963048 0.64079825313
absolute error = 1.230e-05
relative error = 0.0005553 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.045
Order of pole (given) = 1 0
NO 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=48.7MB, alloc=40.3MB, time=0.67
x[1] = 2.5373 0.26
h = 0.001 0.003
y[1] (numeric) = -2.11792202784 0.643118479602
y[1] (closed_form) = -2.11792402689 0.643106679602
absolute error = 1.197e-05
relative error = 0.0005407 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.046
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5383 0.263
h = 0.0001 0.004
y[1] (numeric) = -2.11497834875 0.650358355707
y[1] (closed_form) = -2.11497860957 0.650345713886
absolute error = 1.264e-05
relative error = 0.0005714 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.047
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5384 0.267
h = 0.003 0.006
y[1] (numeric) = -2.11408597215 0.660203845696
y[1] (closed_form) = -2.11408485555 0.660192099661
absolute error = 1.180e-05
relative error = 0.0005327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.047
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5414 0.273
h = 0.0001 0.005
y[1] (numeric) = -2.10570493296 0.674502771299
y[1] (closed_form) = -2.10570376984 0.674483816324
absolute error = 1.899e-05
relative error = 0.0008589 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.051
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5415 0.278
h = 0.0001 0.003
y[1] (numeric) = -2.10461835951 0.686795952031
y[1] (closed_form) = -2.10461801164 0.686781597414
absolute error = 1.436e-05
relative error = 0.0006486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.051
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5416 0.281
h = 0.001 0.001
y[1] (numeric) = -2.1038594067 0.69416617138
y[1] (closed_form) = -2.10386086068 0.694152129752
absolute error = 1.412e-05
relative error = 0.0006372 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.051
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5426 0.282
h = 0.001 0.003
y[1] (numeric) = -2.10122509784 0.696456277498
y[1] (closed_form) = -2.10122737988 0.696442690419
absolute error = 1.378e-05
relative error = 0.0006224 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.052
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5436 0.285
h = 0.0001 0.004
y[1] (numeric) = -2.098247829 0.703668298397
y[1] (closed_form) = -2.09824838767 0.70365385388
absolute error = 1.446e-05
relative error = 0.0006532 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.054
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5437 0.289
h = 0.003 0.006
y[1] (numeric) = -2.09730457556 0.713492426507
y[1] (closed_form) = -2.09730375199 0.713478860096
absolute error = 1.359e-05
relative error = 0.0006135 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.054
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5467 0.295
h = 0.0001 0.005
y[1] (numeric) = -2.08886167819 0.727722562533
y[1] (closed_form) = -2.08886088477 0.727701811304
absolute error = 2.077e-05
relative error = 0.0009388 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.057
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5468 0.3
h = 0.0001 0.003
y[1] (numeric) = -2.08771168297 0.739989075108
y[1] (closed_form) = -2.08771165324 0.739972917111
absolute error = 1.616e-05
relative error = 0.0007295 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.058
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5469 0.303
h = 0.001 0.001
y[1] (numeric) = -2.08691489853 0.747342688165
y[1] (closed_form) = -2.08691666114 0.747326861179
absolute error = 1.592e-05
relative error = 0.0007184 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.058
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5479 0.304
h = 0.0001 0.004
y[1] (numeric) = -2.08427293667 0.749614898661
y[1] (closed_form) = -2.08427551968 0.749599533434
absolute error = 1.558e-05
relative error = 0.0007034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.059
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.548 0.308
h = 0.003 0.006
y[1] (numeric) = -2.08328833895 0.759421288856
y[1] (closed_form) = -2.08328714556 0.759406362659
absolute error = 1.497e-05
relative error = 0.0006753 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.06
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.551 0.314
h = 0.0001 0.005
y[1] (numeric) = -2.07479212409 0.773592598283
y[1] (closed_form) = -2.07479102654 0.773570508006
absolute error = 2.212e-05
relative error = 0.0009988 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.063
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5511 0.319
h = 0.0001 0.003
y[1] (numeric) = -2.07358761148 0.785836438971
y[1] (closed_form) = -2.07358723344 0.785818935776
absolute error = 1.751e-05
relative error = 0.0007895 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.064
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5512 0.322
h = 0.001 0.001
y[1] (numeric) = -2.07275830496 0.793175928811
y[1] (closed_form) = -2.07275971109 0.793158772061
absolute error = 1.721e-05
relative error = 0.0007757 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.064
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5522 0.323
h = 0.001 0.003
y[1] (numeric) = -2.07010971507 0.795432807757
y[1] (closed_form) = -2.07011193502 0.795416118936
absolute error = 1.684e-05
relative error = 0.0007592 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.065
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5532 0.326
h = 0.0001 0.004
y[1] (numeric) = -2.06707069824 0.802592695783
y[1] (closed_form) = -2.06707122272 0.802575121124
absolute error = 1.758e-05
relative error = 0.0007929 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5533 0.33
h = 0.003 0.006
y[1] (numeric) = -2.06603357833 0.812376434557
y[1] (closed_form) = -2.06603271218 0.8123597052
absolute error = 1.675e-05
relative error = 0.0007546 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5563 0.336
h = 0.0001 0.005
y[1] (numeric) = -2.05747725456 0.826478176644
y[1] (closed_form) = -2.05747655948 0.82645430935
absolute error = 2.388e-05
relative error = 0.001077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5564 0.341
h = 0.0001 0.003
y[1] (numeric) = -2.05621025102 0.838694274238
y[1] (closed_form) = -2.05621022461 0.838674985455
absolute error = 1.929e-05
relative error = 0.0008686 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5565 0.344
h = 0.001 0.001
y[1] (numeric) = -2.05534368271 0.846016521552
y[1] (closed_form) = -2.05534543051 0.84599759678
absolute error = 1.901e-05
relative error = 0.0008551 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5575 0.345
h = 0.001 0.003
y[1] (numeric) = -2.05268784064 0.848255469977
y[1] (closed_form) = -2.05269039447 0.848237020048
absolute error = 1.863e-05
relative error = 0.0008386 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5585 0.348
h = 0.0001 0.004
y[1] (numeric) = -2.0496164103 0.855386771348
y[1] (closed_form) = -2.04961728396 0.855367420871
absolute error = 1.937e-05
relative error = 0.0008722 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5586 0.352
h = 0.003 0.006
y[1] (numeric) = -2.04852956885 0.865147832589
y[1] (closed_form) = -2.04852904793 0.865129309789
absolute error = 1.853e-05
relative error = 0.0008333 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5616 0.358
h = 0.0001 0.005
y[1] (numeric) = -2.03991408113 0.879179619804
y[1] (closed_form) = -2.03991380569 0.879153986257
absolute error = 2.564e-05
relative error = 0.001154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.077
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5617 0.363
h = 0.0001 0.003
y[1] (numeric) = -2.03858509979 0.891367415543
y[1] (closed_form) = -2.03858544257 0.891346351182
absolute error = 2.107e-05
relative error = 0.0009469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5618 0.366
h = 0.001 0.001
y[1] (numeric) = -2.03768158344 0.898672089916
y[1] (closed_form) = -2.03768369026 0.89865140688
absolute error = 2.079e-05
relative error = 0.0009335 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5628 0.367
h = 0.001 0.003
y[1] (numeric) = -2.03501870347 0.900893095439
y[1] (closed_form) = -2.03502160845 0.900872894001
absolute error = 2.041e-05
relative error = 0.0009171 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.079
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5638 0.37
h = 0.0001 0.004
y[1] (numeric) = -2.03191527532 0.907995571335
y[1] (closed_form) = -2.0319165156 0.907974454958
absolute error = 2.115e-05
relative error = 0.0009504 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5639 0.374
h = 0.003 0.006
y[1] (numeric) = -2.03077912785 0.917733513882
y[1] (closed_form) = -2.03077896988 0.917713207592
absolute error = 2.031e-05
relative error = 0.0009112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5669 0.38
h = 0.0001 0.005
y[1] (numeric) = -2.02210542218 0.93169497565
y[1] (closed_form) = -2.02210558328 0.931667586824
absolute error = 2.739e-05
relative error = 0.00123 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.567 0.385
h = 0.0001 0.003
y[1] (numeric) = -2.02071498215 0.943853921852
y[1] (closed_form) = -2.02071571145 0.943831092145
absolute error = 2.284e-05
relative error = 0.001024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5671 0.388
h = 0.001 0.001
y[1] (numeric) = -2.01977483502 0.951140699582
y[1] (closed_form) = -2.01977731798 0.951118268263
absolute error = 2.257e-05
relative error = 0.001011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.086
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5681 0.389
h = 0.001 0.003
y[1] (numeric) = -2.01710513047 0.953343753258
y[1] (closed_form) = -2.01710840364 0.95332181013
absolute error = 2.219e-05
relative error = 0.0009944 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.087
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5691 0.392
h = 0.0001 0.004
y[1] (numeric) = -2.01397012172 0.960417172677
y[1] (closed_form) = -2.01397174581 0.960394300539
absolute error = 2.293e-05
relative error = 0.001028 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5692 0.396
h = 0.003 0.006
y[1] (numeric) = -2.0127850884 0.970131564285
y[1] (closed_form) = -2.01278531088 0.970109484683
absolute error = 2.208e-05
relative error = 0.0009882 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5722 0.402
h = 0.0001 0.005
y[1] (numeric) = -2.00405411144 0.984022346888
y[1] (closed_form) = -2.00405472573 0.983993213958
absolute error = 2.914e-05
relative error = 0.001305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.092
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5723 0.407
h = 0.0001 0.003
y[1] (numeric) = -2.0026027376 0.996151906987
y[1] (closed_form) = -2.00260387049 0.996127322384
absolute error = 2.461e-05
relative error = 0.0011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.093
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5724 0.41
h = 0.001 0.001
y[1] (numeric) = -2.00162628027 1.00342047112
y[1] (closed_form) = -2.00162915622 1.0033963017
absolute error = 2.434e-05
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.093
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5734 0.411
h = 0.0001 0.004
y[1] (numeric) = -1.99894996342 1.00560556738
y[1] (closed_form) = -1.99895362159 1.0055818926
absolute error = 2.396e-05
relative error = 0.001071 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.094
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5735 0.415
h = 0.003 0.006
y[1] (numeric) = -1.99772522845 1.01530045966
y[1] (closed_form) = -1.99772515697 1.01527702597
absolute error = 2.343e-05
relative error = 0.001046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.095
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5765 0.421
h = 0.0001 0.005
y[1] (numeric) = -1.98894486523 1.0291308004
y[1] (closed_form) = -1.98894524786 1.02910033845
absolute error = 3.046e-05
relative error = 0.00136 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5766 0.426
h = 0.0001 0.003
y[1] (numeric) = -1.98744110753 1.04123536201
y[1] (closed_form) = -1.98744196629 1.04120943911
absolute error = 2.594e-05
relative error = 0.001156 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5767 0.429
h = 0.001 0.001
y[1] (numeric) = -1.98643343276 1.04848842709
y[1] (closed_form) = -1.98643602549 1.04846293377
absolute error = 2.562e-05
relative error = 0.001141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5777 0.43
h = 0.001 0.003
y[1] (numeric) = -1.98375137948 1.05065813967
y[1] (closed_form) = -1.98375474758 1.05063314648
absolute error = 2.522e-05
relative error = 0.001123 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5787 0.433
h = 0.0001 0.004
y[1] (numeric) = -1.98055836921 1.05767726802
y[1] (closed_form) = -1.98056011746 1.05765132031
absolute error = 2.601e-05
relative error = 0.001158 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.102
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5788 0.437
h = 0.003 0.006
y[1] (numeric) = -1.97928321185 1.06734728736
y[1] (closed_form) = -1.9792835528 1.06732209967
absolute error = 2.519e-05
relative error = 0.00112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.102
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5818 0.443
h = 0.0001 0.005
y[1] (numeric) = -1.97044733568 1.08110632394
y[1] (closed_form) = -1.97044820187 1.08107413901
absolute error = 3.220e-05
relative error = 0.001433 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.106
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5819 0.448
h = 0.0001 0.003
y[1] (numeric) = -1.96888362908 1.09318052434
y[1] (closed_form) = -1.96888492264 1.09315286634
absolute error = 2.769e-05
relative error = 0.001229 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.106
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.582 0.451
h = 0.001 0.001
y[1] (numeric) = -1.96784024536 1.10041480013
y[1] (closed_form) = -1.96784326192 1.10038758804
absolute error = 2.738e-05
relative error = 0.001214 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.583 0.452
h = 0.001 0.003
y[1] (numeric) = -1.96515197186 1.10256655132
y[1] (closed_form) = -1.96515575569 1.1025398455
absolute error = 2.697e-05
relative error = 0.001197 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.108
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.584 0.455
h = 0.0001 0.004
y[1] (numeric) = -1.96192857884 1.10955600028
y[1] (closed_form) = -1.9619307588 1.10952832678
absolute error = 2.776e-05
relative error = 0.001232 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.109
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5841 0.459
h = 0.003 0.006
y[1] (numeric) = -1.9606057567 1.11920127643
y[1] (closed_form) = -1.96060652681 1.11917434555
absolute error = 2.694e-05
relative error = 0.001193 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 1 0
NO 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=97.5MB, alloc=44.3MB, time=1.34
x[1] = 2.5871 0.465
h = 0.0001 0.005
y[1] (numeric) = -1.95171531439 1.13288870275
y[1] (closed_form) = -1.95171668 1.13285480655
absolute error = 3.392e-05
relative error = 0.001503 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5872 0.47
h = 0.0001 0.003
y[1] (numeric) = -1.95009219881 1.1449320373
y[1] (closed_form) = -1.95009394349 1.14490265524
absolute error = 2.943e-05
relative error = 0.001302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.114
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5873 0.473
h = 0.001 0.001
y[1] (numeric) = -1.94901343543 1.15214722618
y[1] (closed_form) = -1.94901689194 1.15211830609
absolute error = 2.913e-05
relative error = 0.001286 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5883 0.474
h = 0.001 0.003
y[1] (numeric) = -1.94631915073 1.15428101987
y[1] (closed_form) = -1.94632336638 1.15425261201
absolute error = 2.872e-05
relative error = 0.001269 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.116
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5893 0.477
h = 0.0001 0.004
y[1] (numeric) = -1.94306579645 1.16124058834
y[1] (closed_form) = -1.94306842432 1.16121119998
absolute error = 2.951e-05
relative error = 0.001303 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.117
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5894 0.481
h = 0.003 0.006
y[1] (numeric) = -1.94169574579 1.17086072368
y[1] (closed_form) = -1.94169696155 1.17083206059
absolute error = 2.869e-05
relative error = 0.001265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.118
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5924 0.487
h = 0.0001 0.005
y[1] (numeric) = -1.93275168348 1.18447624999
y[1] (closed_form) = -1.9327535641 1.18444065441
absolute error = 3.565e-05
relative error = 0.001572 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.121
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5925 0.492
h = 0.0001 0.003
y[1] (numeric) = -1.93106970354 1.19648822529
y[1] (closed_form) = -1.93107191541 1.19645713039
absolute error = 3.117e-05
relative error = 0.001372 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.122
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5926 0.495
h = 0.001 0.001
y[1] (numeric) = -1.92995589247 1.20368403644
y[1] (closed_form) = -1.92995980483 1.2036534193
absolute error = 3.087e-05
relative error = 0.001357 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.122
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5936 0.496
h = 0.001 0.003
y[1] (numeric) = -1.92725580435 1.20579987971
y[1] (closed_form) = -1.92726046767 1.20576978062
absolute error = 3.046e-05
relative error = 0.00134 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.124
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5946 0.499
h = 0.0001 0.004
y[1] (numeric) = -1.92397291098 1.21272937425
y[1] (closed_form) = -1.92397600269 1.21269828216
absolute error = 3.125e-05
relative error = 0.001374 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.125
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5947 0.503
h = 0.003 0.006
y[1] (numeric) = -1.92255607165 1.22232398017
y[1] (closed_form) = -1.92255774929 1.22229359606
absolute error = 3.043e-05
relative error = 0.001336 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.125
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5977 0.509
h = 0.0001 0.005
y[1] (numeric) = -1.91355933448 1.23586733298
y[1] (closed_form) = -1.91356174543 1.23583005009
absolute error = 3.736e-05
relative error = 0.00164 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.129
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5978 0.514
h = 0.0001 0.003
y[1] (numeric) = -1.91181903922 1.24784746686
y[1] (closed_form) = -1.91182173408 1.24781467052
absolute error = 3.291e-05
relative error = 0.001441 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5979 0.517
h = 0.001 0.001
y[1] (numeric) = -1.910670515 1.25502361625
y[1] (closed_form) = -1.91067489883 1.2549913132
absolute error = 3.260e-05
relative error = 0.001426 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5989 0.518
h = 0.0001 0.004
y[1] (numeric) = -1.90796482991 1.25712151935
y[1] (closed_form) = -1.90796995646 1.25708974001
absolute error = 3.219e-05
relative error = 0.001409 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.599 0.522
h = 0.003 0.006
y[1] (numeric) = -1.90651001492 1.26669503707
y[1] (closed_form) = -1.90651147187 1.26666331008
absolute error = 3.176e-05
relative error = 0.001388 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.602 0.528
h = 0.0001 0.005
y[1] (numeric) = -1.89746782894 1.28017667081
y[1] (closed_form) = -1.8974700778 1.28013807395
absolute error = 3.866e-05
relative error = 0.001689 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.136
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6021 0.533
h = 0.0001 0.003
y[1] (numeric) = -1.89567739375 1.2921297048
y[1] (closed_form) = -1.89567988599 1.29209558238
absolute error = 3.421e-05
relative error = 0.001491 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.137
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6022 0.536
h = 0.001 0.001
y[1] (numeric) = -1.8944990206 1.29928911577
y[1] (closed_form) = -1.89450319195 1.29925549993
absolute error = 3.387e-05
relative error = 0.001475 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.137
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6032 0.537
h = 0.001 0.003
y[1] (numeric) = -1.89178846863 1.30137165049
y[1] (closed_form) = -1.89179337564 1.3013385632
absolute error = 3.345e-05
relative error = 0.001457 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.138
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6042 0.54
h = 0.0001 0.004
y[1] (numeric) = -1.8884513718 1.30824503563
y[1] (closed_form) = -1.88845473745 1.30821093272
absolute error = 3.427e-05
relative error = 0.001492 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6043 0.544
h = 0.003 0.006
y[1] (numeric) = -1.88694833731 1.31779167867
y[1] (closed_form) = -1.88695028575 1.31775825178
absolute error = 3.348e-05
relative error = 0.001455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6073 0.55
h = 0.0001 0.005
y[1] (numeric) = -1.87785522854 1.33120066155
y[1] (closed_form) = -1.87785803564 1.33116040007
absolute error = 4.036e-05
relative error = 0.001753 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6074 0.555
h = 0.0001 0.003
y[1] (numeric) = -1.87600750513 1.34312098017
y[1] (closed_form) = -1.87601050919 1.34308517782
absolute error = 3.593e-05
relative error = 0.001557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.145
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6075 0.558
h = 0.001 0.001
y[1] (numeric) = -1.87479504432 1.3502602149
y[1] (closed_form) = -1.87479971565 1.35022493415
absolute error = 3.559e-05
relative error = 0.00154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.145
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6085 0.559
h = 0.001 0.003
y[1] (numeric) = -1.87207927604 1.35232483429
y[1] (closed_form) = -1.87208467474 1.35229008746
absolute error = 3.516e-05
relative error = 0.001523 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.146
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6095 0.562
h = 0.0001 0.004
y[1] (numeric) = -1.86871384811 1.35916762895
y[1] (closed_form) = -1.8687177219 1.3591318549
absolute error = 3.598e-05
relative error = 0.001557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.148
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6096 0.566
h = 0.003 0.006
y[1] (numeric) = -1.86716529713 1.36868767527
y[1] (closed_form) = -1.86716775251 1.36865256017
absolute error = 3.520e-05
relative error = 0.001521 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.148
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6126 0.572
h = 0.0001 0.005
y[1] (numeric) = -1.85802220623 1.38202377949
y[1] (closed_form) = -1.85802558608 1.38198186588
absolute error = 4.205e-05
relative error = 0.001816 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.152
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6127 0.577
h = 0.0001 0.003
y[1] (numeric) = -1.85611775499 1.39391093266
y[1] (closed_form) = -1.8561212859 1.39387346226
absolute error = 3.764e-05
relative error = 0.001621 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.153
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6128 0.58
h = 0.001 0.001
y[1] (numeric) = -1.85487154752 1.4010297265
y[1] (closed_form) = -1.85487673371 1.40099279247
absolute error = 3.730e-05
relative error = 0.001604 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.153
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6138 0.581
h = 0.001 0.003
y[1] (numeric) = -1.85215076536 1.40307644955
y[1] (closed_form) = -1.85215667059 1.40304005464
absolute error = 3.687e-05
relative error = 0.001587 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.155
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6148 0.584
h = 0.0001 0.004
y[1] (numeric) = -1.8487574297 1.40988848938
y[1] (closed_form) = -1.84876182655 1.40985105599
absolute error = 3.769e-05
relative error = 0.001621 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.156
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6149 0.588
h = 0.003 0.006
y[1] (numeric) = -1.84716381417 1.41938158514
y[1] (closed_form) = -1.84716679168 1.41934479372
absolute error = 3.691e-05
relative error = 0.001585 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.157
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6179 0.594
h = 0.0001 0.005
y[1] (numeric) = -1.83797167959 1.43264459854
y[1] (closed_form) = -1.83797564643 1.43260104546
absolute error = 4.373e-05
relative error = 0.001877 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.161
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.618 0.599
h = 0.0001 0.003
y[1] (numeric) = -1.83601106434 1.44449814739
y[1] (closed_form) = -1.83601513687 1.44445902101
absolute error = 3.934e-05
relative error = 0.001684 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.161
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6181 0.602
h = 0.001 0.001
y[1] (numeric) = -1.83473145314 1.45159624248
y[1] (closed_form) = -1.8347371688 1.45155766696
absolute error = 3.900e-05
relative error = 0.001667 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.162
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6191 0.603
h = 0.001 0.003
y[1] (numeric) = -1.83200585801 1.45362509114
y[1] (closed_form) = -1.83201228435 1.45358705977
absolute error = 3.857e-05
relative error = 0.001649 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.163
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6201 0.606
h = 0.0001 0.004
y[1] (numeric) = -1.82858503789 1.46040621922
y[1] (closed_form) = -1.82858997245 1.46036713842
absolute error = 3.939e-05
relative error = 0.001683 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.164
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6202 0.61
h = 0.003 0.006
y[1] (numeric) = -1.82694681236 1.46987201956
y[1] (closed_form) = -1.82695032691 1.46983356383
absolute error = 3.862e-05
relative error = 0.001647 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.165
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6232 0.616
h = 0.0001 0.005
y[1] (numeric) = -1.81770657002 1.48306174545
y[1] (closed_form) = -1.81771113781 1.48301656568
absolute error = 4.541e-05
relative error = 0.001936 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.169
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6233 0.621
h = 0.0001 0.003
y[1] (numeric) = -1.81569035775 1.49488126231
y[1] (closed_form) = -1.81569498637 1.49484049213
absolute error = 4.103e-05
relative error = 0.001745 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6234 0.624
h = 0.001 0.001
y[1] (numeric) = -1.81437768754 1.50195840753
y[1] (closed_form) = -1.81438394701 1.50191820244
absolute error = 4.069e-05
relative error = 0.001728 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6244 0.625
h = 0.0001 0.004
y[1] (numeric) = -1.81164747876 1.50396940661
y[1] (closed_form) = -1.81165444053 1.50392975057
absolute error = 4.026e-05
relative error = 0.00171 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.171
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6245 0.629
h = 0.003 0.006
y[1] (numeric) = -1.80997306681 1.51341270353
y[1] (closed_form) = -1.80997643089 1.5133729212
absolute error = 3.992e-05
relative error = 0.001692 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.172
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6275 0.635
h = 0.0001 0.005
y[1] (numeric) = -1.80069128633 1.52653975812
y[1] (closed_form) = -1.80069575835 1.52649328395
absolute error = 4.669e-05
relative error = 0.001978 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.176
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6276 0.64
h = 0.0001 0.003
y[1] (numeric) = -1.79862726216 1.53833030044
y[1] (closed_form) = -1.79863175661 1.53828822122
absolute error = 4.232e-05
relative error = 0.001788 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.177
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6277 0.643
h = 0.001 0.001
y[1] (numeric) = -1.79728615964 1.54538960496
y[1] (closed_form) = -1.79729227442 1.54534810299
absolute error = 4.195e-05
relative error = 0.00177 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.177
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6287 0.644
h = 0.001 0.003
y[1] (numeric) = -1.79455192583 1.54738531353
y[1] (closed_form) = -1.79455873574 1.54734436479
absolute error = 4.151e-05
relative error = 0.001752 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.179
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6297 0.647
h = 0.0001 0.004
y[1] (numeric) = -1.79108071693 1.55410884498
y[1] (closed_form) = -1.79108606598 1.55406682707
absolute error = 4.236e-05
relative error = 0.001786 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6298 0.651
h = 0.003 0.006
y[1] (numeric) = -1.78936036603 1.56352348625
y[1] (closed_form) = -1.78936429433 1.56348206222
absolute error = 4.161e-05
relative error = 0.001751 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.181
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6328 0.657
h = 0.0001 0.005
y[1] (numeric) = -1.7800322097 1.57657691687
y[1] (closed_form) = -1.78003730806 1.57652883997
absolute error = 4.835e-05
relative error = 0.002033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.185
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6329 0.662
h = 0.0001 0.003
y[1] (numeric) = -1.77791364635 1.58833265423
y[1] (closed_form) = -1.77791872328 1.58828895413
absolute error = 4.399e-05
relative error = 0.001845 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.186
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.633 0.665
h = 0.001 0.001
y[1] (numeric) = -1.77654012769 1.59537055537
y[1] (closed_form) = -1.77654681242 1.59532744624
absolute error = 4.362e-05
relative error = 0.001827 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.186
Order of pole (given) = 1 0
NO 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=146.4MB, alloc=44.3MB, time=2.00
x[1] = 2.634 0.666
h = 0.001 0.003
y[1] (numeric) = -1.77380164722 1.59734846576
y[1] (closed_form) = -1.77380901865 1.59730591445
absolute error = 4.319e-05
relative error = 0.001809 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.187
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.635 0.669
h = 0.0001 0.004
y[1] (numeric) = -1.77030416141 1.60404067181
y[1] (closed_form) = -1.77031008874 1.60399704128
absolute error = 4.403e-05
relative error = 0.001843 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.189
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6351 0.673
h = 0.003 0.006
y[1] (numeric) = -1.76854050967 1.61342707501
y[1] (closed_form) = -1.76854501632 1.61338402175
absolute error = 4.329e-05
relative error = 0.001808 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6381 0.679
h = 0.0001 0.005
y[1] (numeric) = -1.7591669048 1.6264067283
y[1] (closed_form) = -1.75917264265 1.6263570618
absolute error = 5.000e-05
relative error = 0.002087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.193
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6382 0.684
h = 0.0001 0.003
y[1] (numeric) = -1.75699437709 1.63812726482
y[1] (closed_form) = -1.7570000502 1.63808195644
absolute error = 4.566e-05
relative error = 0.001901 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.194
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6383 0.687
h = 0.001 0.001
y[1] (numeric) = -1.75558879136 1.64514353067
y[1] (closed_form) = -1.75559605962 1.64509882668
absolute error = 4.529e-05
relative error = 0.001882 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.195
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6393 0.688
h = 0.001 0.003
y[1] (numeric) = -1.75284625888 1.64710367569
y[1] (closed_form) = -1.75285420541 1.64705953398
absolute error = 4.485e-05
relative error = 0.001865 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.196
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6403 0.691
h = 0.0001 0.004
y[1] (numeric) = -1.74932291783 1.65376442739
y[1] (closed_form) = -1.74932943706 1.65371919672
absolute error = 4.570e-05
relative error = 0.001898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6404 0.695
h = 0.003 0.006
y[1] (numeric) = -1.74751642807 1.6631222821
y[1] (closed_form) = -1.74752152692 1.66307761219
absolute error = 4.496e-05
relative error = 0.001864 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6434 0.701
h = 0.0001 0.005
y[1] (numeric) = -1.73809829836 1.67602801946
y[1] (closed_form) = -1.7381046886 1.67597677659
absolute error = 5.164e-05
relative error = 0.002139 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.202
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6435 0.706
h = 0.0001 0.003
y[1] (numeric) = -1.73587238333 1.68771297032
y[1] (closed_form) = -1.73587866606 1.68766606636
absolute error = 4.732e-05
relative error = 0.001955 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.203
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6436 0.709
h = 0.001 0.001
y[1] (numeric) = -1.73443508084 1.69470737559
y[1] (closed_form) = -1.73444294594 1.6946610892
absolute error = 4.695e-05
relative error = 0.001936 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.204
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6446 0.71
h = 0.001 0.003
y[1] (numeric) = -1.73168868928 1.69664979074
y[1] (closed_form) = -1.7316972242 1.69660407091
absolute error = 4.651e-05
relative error = 0.001918 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.205
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6456 0.713
h = 0.0001 0.004
y[1] (numeric) = -1.72813991387 1.70327896622
y[1] (closed_form) = -1.72814703834 1.70323214801
absolute error = 4.736e-05
relative error = 0.001952 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.206
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6457 0.717
h = 0.003 0.006
y[1] (numeric) = -1.72629105055 1.71260797086
y[1] (closed_form) = -1.72629675519 1.71256169701
absolute error = 4.662e-05
relative error = 0.001917 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.207
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6487 0.723
h = 0.0001 0.005
y[1] (numeric) = -1.71682931585 1.72543966825
y[1] (closed_form) = -1.71683637107 1.72538686236
absolute error = 5.328e-05
relative error = 0.002189 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.211
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6488 0.728
h = 0.0001 0.003
y[1] (numeric) = -1.71455059252 1.73708865962
y[1] (closed_form) = -1.71455749803 1.73704017293
absolute error = 4.898e-05
relative error = 0.002007 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.212
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6489 0.731
h = 0.001 0.001
y[1] (numeric) = -1.71308192464 1.74406098566
y[1] (closed_form) = -1.71309039963 1.74401312942
absolute error = 4.860e-05
relative error = 0.001988 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.213
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6499 0.732
h = 0.0001 0.004
y[1] (numeric) = -1.71033186515 1.74598570907
y[1] (closed_form) = -1.7103410015 1.74593842354
absolute error = 4.816e-05
relative error = 0.00197 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.214
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.65 0.736
h = 0.003 0.006
y[1] (numeric) = -1.70844864874 1.75529096739
y[1] (closed_form) = -1.70845426974 1.75524338773
absolute error = 4.791e-05
relative error = 0.001956 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.215
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.653 0.742
h = 0.0001 0.005
y[1] (numeric) = -1.69894923008 1.76805934988
y[1] (closed_form) = -1.6989562523 1.7680052732
absolute error = 5.453e-05
relative error = 0.002224 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.219
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6531 0.747
h = 0.0001 0.003
y[1] (numeric) = -1.69662508193 1.77967771715
y[1] (closed_form) = -1.69663191833 1.77962794281
absolute error = 5.024e-05
relative error = 0.002043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6532 0.75
h = 0.001 0.001
y[1] (numeric) = -1.69512943142 1.78663123599
y[1] (closed_form) = -1.69513782627 1.78658210313
absolute error = 4.984e-05
relative error = 0.002024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6542 0.751
h = 0.001 0.003
y[1] (numeric) = -1.69237615632 1.78854080405
y[1] (closed_form) = -1.6923852053 1.78849224543
absolute error = 4.939e-05
relative error = 0.002006 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.222
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6552 0.754
h = 0.0001 0.004
y[1] (numeric) = -1.68878079129 1.79511121428
y[1] (closed_form) = -1.68878846113 1.79506154036
absolute error = 5.026e-05
relative error = 0.002039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.223
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6553 0.758
h = 0.0001 0.004
y[1] (numeric) = -1.68685396995 1.80438625471
y[1] (closed_form) = -1.68686022143 1.80433709492
absolute error = 4.956e-05
relative error = 0.002006 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.224
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6554 0.762
h = 0.003 0.006
y[1] (numeric) = -1.68491750339 1.81365822523
y[1] (closed_form) = -1.68492375487 1.81360906544
absolute error = 4.956e-05
relative error = 0.002002 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.225
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6584 0.768
h = 0.0001 0.005
y[1] (numeric) = -1.67536626922 1.82634105233
y[1] (closed_form) = -1.67537399067 1.82628544278
absolute error = 5.614e-05
relative error = 0.002265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.229
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6585 0.773
h = 0.0001 0.003
y[1] (numeric) = -1.67298013831 1.83791832352
y[1] (closed_form) = -1.67298762496 1.83786699358
absolute error = 5.187e-05
relative error = 0.002087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6586 0.776
h = 0.001 0.001
y[1] (numeric) = -1.67144766355 1.84484659483
y[1] (closed_form) = -1.67145669374 1.84479592137
absolute error = 5.147e-05
relative error = 0.002068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6596 0.777
h = 0.001 0.003
y[1] (numeric) = -1.66868986483 1.84673562403
y[1] (closed_form) = -1.66869953937 1.84668552964
absolute error = 5.102e-05
relative error = 0.00205 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.232
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6606 0.78
h = 0.0001 0.004
y[1] (numeric) = -1.66506492915 1.85326950848
y[1] (closed_form) = -1.66507324407 1.85321828817
absolute error = 5.189e-05
relative error = 0.002083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.233
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6607 0.784
h = 0.003 0.006
y[1] (numeric) = -1.66308891166 1.86251123336
y[1] (closed_form) = -1.66309580909 1.86246050829
absolute error = 5.119e-05
relative error = 0.00205 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.234
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6637 0.79
h = 0.0001 0.005
y[1] (numeric) = -1.65349683316 1.87511968692
y[1] (closed_form) = -1.65350525677 1.87506255481
absolute error = 5.775e-05
relative error = 0.00231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.238
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6638 0.795
h = 0.0001 0.003
y[1] (numeric) = -1.65105964385 1.88665990259
y[1] (closed_form) = -1.65106779216 1.88660702891
absolute error = 5.350e-05
relative error = 0.002134 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6639 0.798
h = 0.001 0.001
y[1] (numeric) = -1.6494968652 1.89356545416
y[1] (closed_form) = -1.64950654385 1.89351324902
absolute error = 5.309e-05
relative error = 0.002114 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6649 0.799
h = 0.001 0.003
y[1] (numeric) = -1.64673596959 1.89543691365
y[1] (closed_form) = -1.64674628411 1.89538529127
absolute error = 5.264e-05
relative error = 0.002097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.241
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6659 0.802
h = 0.0001 0.004
y[1] (numeric) = -1.64308728229 1.90193878015
y[1] (closed_form) = -1.64309625414 1.90188602365
absolute error = 5.351e-05
relative error = 0.002129 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.242
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.666 0.806
h = 0.003 0.006
y[1] (numeric) = -1.64107076475 1.91115050423
y[1] (closed_form) = -1.6410783206 1.91109822706
absolute error = 5.282e-05
relative error = 0.002097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.243
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.669 0.812
h = 0.0001 0.005
y[1] (numeric) = -1.63143874436 1.92368451713
y[1] (closed_form) = -1.63144788161 1.92362587617
absolute error = 5.935e-05
relative error = 0.002353 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6691 0.817
h = 0.0001 0.003
y[1] (numeric) = -1.62895108188 1.93518734716
y[1] (closed_form) = -1.62895990391 1.935132943
absolute error = 5.511e-05
relative error = 0.002179 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.248
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6692 0.82
h = 0.001 0.001
y[1] (numeric) = -1.62735835398 1.94206998664
y[1] (closed_form) = -1.62736869307 1.94201626282
absolute error = 5.471e-05
relative error = 0.002159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.249
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6702 0.821
h = 0.001 0.003
y[1] (numeric) = -1.62459454527 1.94392392462
y[1] (closed_form) = -1.62460551176 1.94387078709
absolute error = 5.426e-05
relative error = 0.002142 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6712 0.824
h = 0.0001 0.004
y[1] (numeric) = -1.62092252173 1.95039368578
y[1] (closed_form) = -1.62093216248 1.95033940624
absolute error = 5.513e-05
relative error = 0.002174 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.252
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6713 0.828
h = 0.003 0.006
y[1] (numeric) = -1.61886597449 1.95957515121
y[1] (closed_form) = -1.61887420096 1.95952133519
absolute error = 5.444e-05
relative error = 0.002142 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.253
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6743 0.834
h = 0.0001 0.005
y[1] (numeric) = -1.60919490959 1.97203466985
y[1] (closed_form) = -1.60920477169 1.97197453382
absolute error = 6.094e-05
relative error = 0.002394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.257
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6744 0.839
h = 0.0001 0.003
y[1] (numeric) = -1.60665736002 1.98349979478
y[1] (closed_form) = -1.60666686756 1.98344387348
absolute error = 5.672e-05
relative error = 0.002222 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.258
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6745 0.842
h = 0.001 0.001
y[1] (numeric) = -1.6050350379 1.99035933625
y[1] (closed_form) = -1.60504604912 1.99030410681
absolute error = 5.632e-05
relative error = 0.002203 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.259
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6755 0.843
h = 0.001 0.003
y[1] (numeric) = -1.60226849795 1.99219580326
y[1] (closed_form) = -1.60228012811 1.9921411635
absolute error = 5.586e-05
relative error = 0.002185 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6765 0.846
h = 0.0001 0.004
y[1] (numeric) = -1.59857355199 1.99863337828
y[1] (closed_form) = -1.59858387336 1.99857758892
absolute error = 5.674e-05
relative error = 0.002217 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.261
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6766 0.85
h = 0.003 0.006
y[1] (numeric) = -1.59647744597 2.00778433573
y[1] (closed_form) = -1.59648635499 2.00772899422
absolute error = 5.605e-05
relative error = 0.002185 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.262
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6796 0.856
h = 0.0001 0.005
y[1] (numeric) = -1.58676822865 2.02016931983
y[1] (closed_form) = -1.58677882652 2.02010770255
absolute error = 6.252e-05
relative error = 0.002434 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.266
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6797 0.861
h = 0.0001 0.003
y[1] (numeric) = -1.58418137871 2.03159643079
y[1] (closed_form) = -1.58419158327 2.03153900578
absolute error = 5.832e-05
relative error = 0.002264 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.267
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6798 0.864
h = 0.001 0.001
y[1] (numeric) = -1.58252981766 2.03843269468
y[1] (closed_form) = -1.58254151246 2.03837597279
absolute error = 5.791e-05
relative error = 0.002244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.268
Order of pole (given) = 1 0
NO 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=195.1MB, alloc=44.3MB, time=2.66
x[1] = 2.6808 0.865
h = 0.0001 0.004
y[1] (numeric) = -1.57976072638 2.04025174353
y[1] (closed_form) = -1.57977303167 2.04019561456
absolute error = 5.746e-05
relative error = 0.002227 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6809 0.869
h = 0.003 0.006
y[1] (numeric) = -1.57763257079 2.04937763296
y[1] (closed_form) = -1.57764147417 2.04932101658
absolute error = 5.731e-05
relative error = 0.002216 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6839 0.875
h = 0.0001 0.005
y[1] (numeric) = -1.56789033503 2.06169887806
y[1] (closed_form) = -1.56790097282 2.06163602375
absolute error = 6.375e-05
relative error = 0.002461 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.274
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.684 0.88
h = 0.0001 0.003
y[1] (numeric) = -1.56526106151 2.07309360634
y[1] (closed_form) = -1.56527127282 2.07303492507
absolute error = 5.956e-05
relative error = 0.002293 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.276
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6841 0.883
h = 0.001 0.001
y[1] (numeric) = -1.56358433713 2.07991003724
y[1] (closed_form) = -1.56359602718 2.07985206872
absolute error = 5.914e-05
relative error = 0.002273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.276
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6851 0.884
h = 0.001 0.003
y[1] (numeric) = -1.5608129857 2.08171416459
y[1] (closed_form) = -1.56082527901 2.08165679178
absolute error = 5.868e-05
relative error = 0.002255 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.277
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6861 0.887
h = 0.0001 0.004
y[1] (numeric) = -1.55707609681 2.08809191736
y[1] (closed_form) = -1.55708711275 2.0880333814
absolute error = 5.956e-05
relative error = 0.002287 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.279
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6862 0.891
h = 0.003 0.006
y[1] (numeric) = -1.55490726567 2.09718592985
y[1] (closed_form) = -1.55491687322 2.09712781291
absolute error = 5.891e-05
relative error = 0.002256 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6892 0.897
h = 0.0001 0.005
y[1] (numeric) = -1.54512852258 2.10943258963
y[1] (closed_form) = -1.54513991591 2.10936827986
absolute error = 6.531e-05
relative error = 0.002498 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.284
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6893 0.902
h = 0.0001 0.003
y[1] (numeric) = -1.54245103804 2.12078875015
y[1] (closed_form) = -1.54246196722 2.12072859021
absolute error = 6.114e-05
relative error = 0.002332 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.285
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6894 0.905
h = 0.001 0.001
y[1] (numeric) = -1.54074573418 2.12758158189
y[1] (closed_form) = -1.54075812855 2.12752214546
absolute error = 6.071e-05
relative error = 0.002311 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.286
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6904 0.906
h = 0.001 0.003
y[1] (numeric) = -1.53797216156 2.12936839311
y[1] (closed_form) = -1.53798515076 2.12930955536
absolute error = 6.025e-05
relative error = 0.002294 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.287
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6914 0.909
h = 0.0001 0.004
y[1] (numeric) = -1.53421352398 2.13571375932
y[1] (closed_form) = -1.53422525272 2.13565375166
absolute error = 6.114e-05
relative error = 0.002325 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.289
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6915 0.913
h = 0.003 0.006
y[1] (numeric) = -1.53200648016 2.14477659139
y[1] (closed_form) = -1.53201680303 2.14471698748
absolute error = 6.049e-05
relative error = 0.002295 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6945 0.919
h = 0.0001 0.005
y[1] (numeric) = -1.52219210574 2.15694866247
y[1] (closed_form) = -1.52220426477 2.15688291124
absolute error = 6.687e-05
relative error = 0.002533 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.294
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6946 0.924
h = 0.0001 0.003
y[1] (numeric) = -1.51946699771 2.16826597622
y[1] (closed_form) = -1.51947865552 2.16820435123
absolute error = 6.272e-05
relative error = 0.002369 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.295
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6947 0.927
h = 0.001 0.001
y[1] (numeric) = -1.51773346986 2.17503504717
y[1] (closed_form) = -1.51774657922 2.17497415618
absolute error = 6.229e-05
relative error = 0.002348 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.296
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6957 0.928
h = 0.001 0.003
y[1] (numeric) = -1.51495785023 2.17680460126
y[1] (closed_form) = -1.51497154601 2.17674431179
absolute error = 6.183e-05
relative error = 0.002331 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.297
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6967 0.931
h = 0.0001 0.004
y[1] (numeric) = -1.51117787091 2.18311752472
y[1] (closed_form) = -1.51119032312 2.18305605887
absolute error = 6.271e-05
relative error = 0.002362 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.299
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6968 0.935
h = 0.003 0.006
y[1] (numeric) = -1.50893308602 2.19214895931
y[1] (closed_form) = -1.50894413509 2.19208788208
absolute error = 6.207e-05
relative error = 0.002332 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6998 0.941
h = 0.0001 0.005
y[1] (numeric) = -1.49908395023 2.20424645075
y[1] (closed_form) = -1.49909688484 2.20417927211
absolute error = 6.841e-05
relative error = 0.002566 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.304
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6999 0.946
h = 0.0001 0.003
y[1] (numeric) = -1.4963118061 2.21552464896
y[1] (closed_form) = -1.496324203 2.21546157261
absolute error = 6.428e-05
relative error = 0.002405 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.305
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7 0.949
h = 0.001 0.001
y[1] (numeric) = -1.49455040952 2.22226980364
y[1] (closed_form) = -1.49456424429 2.22220747151
absolute error = 6.385e-05
relative error = 0.002384 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.306
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.701 0.95
h = 0.001 0.003
y[1] (numeric) = -1.49177291503 2.22402216167
y[1] (closed_form) = -1.49178732783 2.22396043376
absolute error = 6.339e-05
relative error = 0.002367 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.307
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.702 0.953
h = 0.0001 0.004
y[1] (numeric) = -1.48797199889 2.23030259233
y[1] (closed_form) = -1.48798518499 2.23023968185
absolute error = 6.428e-05
relative error = 0.002397 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.309
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7021 0.957
h = 0.003 0.006
y[1] (numeric) = -1.4856899443 2.23930242055
y[1] (closed_form) = -1.48570173016 2.23923988369
absolute error = 6.364e-05
relative error = 0.002368 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7051 0.963
h = 0.0001 0.005
y[1] (numeric) = -1.47580691089 2.25132535362
y[1] (closed_form) = -1.47582063068 2.25125676163
absolute error = 6.995e-05
relative error = 0.002599 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.314
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7052 0.968
h = 0.0001 0.003
y[1] (numeric) = -1.4729883177 2.26256417767
y[1] (closed_form) = -1.4730014639 2.26249966369
absolute error = 6.584e-05
relative error = 0.002439 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.315
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7053 0.971
h = 0.001 0.001
y[1] (numeric) = -1.47119940736 2.26928526669
y[1] (closed_form) = -1.4712139777 2.26922150688
absolute error = 6.540e-05
relative error = 0.002418 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.316
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7063 0.972
h = 0.0001 0.004
y[1] (numeric) = -1.46842020806 2.27102049171
y[1] (closed_form) = -1.46843534806 2.27095733869
absolute error = 6.494e-05
relative error = 0.002401 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.317
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7064 0.976
h = 0.003 0.006
y[1] (numeric) = -1.46610797408 2.27999437985
y[1] (closed_form) = -1.46611981265 2.27993059723
absolute error = 6.487e-05
relative error = 0.002393 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.318
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7094 0.982
h = 0.0001 0.005
y[1] (numeric) = -1.45619556194 2.29195355165
y[1] (closed_form) = -1.45620937586 2.29188375345
absolute error = 7.115e-05
relative error = 0.00262 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.322
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7095 0.987
h = 0.0001 0.003
y[1] (numeric) = -1.45333698362 2.30315882813
y[1] (closed_form) = -1.45335019323 2.30309308718
absolute error = 6.705e-05
relative error = 0.002462 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.324
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7096 0.99
h = 0.001 0.001
y[1] (numeric) = -1.45152438529 2.30985940921
y[1] (closed_form) = -1.45153900732 2.30979443096
absolute error = 6.660e-05
relative error = 0.002441 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.324
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7106 0.991
h = 0.001 0.003
y[1] (numeric) = -1.44874365011 2.31157995626
y[1] (closed_form) = -1.44875883463 2.311515587
absolute error = 6.614e-05
relative error = 0.002424 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.326
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7116 0.994
h = 0.0001 0.004
y[1] (numeric) = -1.44490445757 2.31780005096
y[1] (closed_form) = -1.4449184466 2.31773448817
absolute error = 6.704e-05
relative error = 0.002455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.327
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7117 0.998
h = 0.003 0.006
y[1] (numeric) = -1.44255392392 2.32674096951
y[1] (closed_form) = -1.44256651848 2.32667575279
absolute error = 6.642e-05
relative error = 0.002426 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.328
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7147 1.004
h = 0.0001 0.005
y[1] (numeric) = -1.43260920483 2.33862564411
y[1] (closed_form) = -1.43262382129 2.33855445874
absolute error = 7.267e-05
relative error = 0.00265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.333
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7148 1.009
h = 0.0001 0.003
y[1] (numeric) = -1.42970526549 2.34979108492
y[1] (closed_form) = -1.42971924286 2.3497239319
absolute error = 6.859e-05
relative error = 0.002494 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.334
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7149 1.012
h = 0.001 0.001
y[1] (numeric) = -1.4278658111 2.35646733414
y[1] (closed_form) = -1.42788118706 2.35640095329
absolute error = 6.814e-05
relative error = 0.002473 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.335
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7159 1.013
h = 0.001 0.003
y[1] (numeric) = -1.42508368279 2.35817086866
y[1] (closed_form) = -1.42509961293 2.35810509912
absolute error = 6.767e-05
relative error = 0.002456 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.336
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7169 1.016
h = 0.0001 0.004
y[1] (numeric) = -1.42122469931 2.36435835572
y[1] (closed_form) = -1.42123945073 2.36429138724
absolute error = 6.857e-05
relative error = 0.002486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.338
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.717 1.02
h = 0.003 0.006
y[1] (numeric) = -1.41883823966 2.37326710912
y[1] (closed_form) = -1.41885160004 2.37320047215
absolute error = 6.796e-05
relative error = 0.002458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.339
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.72 1.026
h = 0.0001 0.005
y[1] (numeric) = -1.40886205879 2.38507734151
y[1] (closed_form) = -1.40887748664 2.38500478313
absolute error = 7.418e-05
relative error = 0.002678 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.343
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7201 1.031
h = 0.0001 0.003
y[1] (numeric) = -1.40591334362 2.39620271654
y[1] (closed_form) = -1.40592809819 2.3961341653
absolute error = 7.012e-05
relative error = 0.002524 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.344
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7202 1.034
h = 0.001 0.001
y[1] (numeric) = -1.4040473867 2.40285450159
y[1] (closed_form) = -1.40406352603 2.40278673174
absolute error = 6.967e-05
relative error = 0.002503 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.345
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7212 1.035
h = 0.001 0.003
y[1] (numeric) = -1.40126402935 2.40454109204
y[1] (closed_form) = -1.40128071455 2.40447393567
absolute error = 6.920e-05
relative error = 0.002486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.346
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7222 1.038
h = 0.0001 0.004
y[1] (numeric) = -1.39738565114 2.41069594425
y[1] (closed_form) = -1.39740117433 2.41062758382
absolute error = 7.010e-05
relative error = 0.002516 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.348
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7223 1.042
h = 0.003 0.006
y[1] (numeric) = -1.39496373466 2.41957235439
y[1] (closed_form) = -1.39497787045 2.41950431106
absolute error = 6.950e-05
relative error = 0.002488 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.349
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7253 1.048
h = 0.0001 0.005
y[1] (numeric) = -1.38495693034 2.4313082109
y[1] (closed_form) = -1.38497317819 2.43123429367
absolute error = 7.568e-05
relative error = 0.002705 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.353
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7254 1.053
h = 0.0001 0.003
y[1] (numeric) = -1.38196402351 2.44239329975
y[1] (closed_form) = -1.38197956448 2.44232336419
absolute error = 7.164e-05
relative error = 0.002553 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.355
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7255 1.056
h = 0.001 0.001
y[1] (numeric) = -1.38007191688 2.44902049417
y[1] (closed_form) = -1.38008882875 2.44895134895
absolute error = 7.118e-05
relative error = 0.002532 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.355
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7265 1.057
h = 0.001 0.003
y[1] (numeric) = -1.37728749242 2.45069021078
y[1] (closed_form) = -1.37730494189 2.45062168109
absolute error = 7.072e-05
relative error = 0.002516 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.357
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7275 1.06
h = 0.0001 0.004
y[1] (numeric) = -1.37339011322 2.45681240659
y[1] (closed_form) = -1.37340641734 2.45674266799
absolute error = 7.162e-05
relative error = 0.002545 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.358
Order of pole (given) = 1 0
NO 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=243.8MB, alloc=44.3MB, time=3.31
x[1] = 2.7276 1.064
h = 0.003 0.006
y[1] (numeric) = -1.37093320817 2.46565630313
y[1] (closed_form) = -1.37094812868 2.46558686736
absolute error = 7.102e-05
relative error = 0.002517 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.359
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7306 1.07
h = 0.0001 0.005
y[1] (numeric) = -1.36089661175 2.47731786114
y[1] (closed_form) = -1.36091368794 2.47724259927
absolute error = 7.717e-05
relative error = 0.00273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.364
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7307 1.075
h = 0.0001 0.003
y[1] (numeric) = -1.35786009621 2.48836245309
y[1] (closed_form) = -1.35787643251 2.48829114711
absolute error = 7.315e-05
relative error = 0.002581 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.365
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7308 1.078
h = 0.001 0.001
y[1] (numeric) = -1.35594219188 2.49496493618
y[1] (closed_form) = -1.3559598852 2.49489442923
absolute error = 7.269e-05
relative error = 0.00256 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.366
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7318 1.079
h = 0.0001 0.004
y[1] (numeric) = -1.35315686011 2.4966178509
y[1] (closed_form) = -1.35317508279 2.49654796141
absolute error = 7.223e-05
relative error = 0.002543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.367
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7319 1.083
h = 0.003 0.006
y[1] (numeric) = -1.35067163706 2.5054350902
y[1] (closed_form) = -1.3506866646 2.50536444063
absolute error = 7.223e-05
relative error = 0.002538 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.368
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7349 1.089
h = 0.0001 0.005
y[1] (numeric) = -1.3406091733 2.51703310632
y[1] (closed_form) = -1.34062639384 2.5169566715
absolute error = 7.835e-05
relative error = 0.002747 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.373
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.735 1.094
h = 0.0001 0.003
y[1] (numeric) = -1.33753510099 2.52804318844
y[1] (closed_form) = -1.3375515534 2.52797068749
absolute error = 7.434e-05
relative error = 0.002599 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.374
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7351 1.097
h = 0.001 0.001
y[1] (numeric) = -1.33559497582 2.53462461015
y[1] (closed_form) = -1.33561277338 2.53455291569
absolute error = 7.387e-05
relative error = 0.002578 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.375
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7361 1.098
h = 0.001 0.003
y[1] (numeric) = -1.33280879045 2.5362631295
y[1] (closed_form) = -1.33282711032 2.53619205416
absolute error = 7.340e-05
relative error = 0.002562 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.376
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7371 1.101
h = 0.0001 0.004
y[1] (numeric) = -1.32887670457 2.54232473642
y[1] (closed_form) = -1.32889390992 2.54225244363
absolute error = 7.431e-05
relative error = 0.002591 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.378
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7372 1.105
h = 0.003 0.006
y[1] (numeric) = -1.32635554474 2.55110810923
y[1] (closed_form) = -1.32637137382 2.5510360931
absolute error = 7.374e-05
relative error = 0.002564 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.379
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7402 1.111
h = 0.0001 0.005
y[1] (numeric) = -1.31626481801 2.56263198984
y[1] (closed_form) = -1.3162828819 2.56255423669
absolute error = 7.982e-05
relative error = 0.002771 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.383
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7403 1.116
h = 0.0001 0.003
y[1] (numeric) = -1.31314821575 2.57360120124
y[1] (closed_form) = -1.3131654796 2.57352735572
absolute error = 7.584e-05
relative error = 0.002625 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.385
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7404 1.119
h = 0.001 0.001
y[1] (numeric) = -1.31118294406 2.58015769797
y[1] (closed_form) = -1.31120153915 2.58008466717
absolute error = 7.536e-05
relative error = 0.002604 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.386
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7414 1.12
h = 0.001 0.003
y[1] (numeric) = -1.3083961439 2.58177955186
y[1] (closed_form) = -1.30841525313 2.58170714186
absolute error = 7.489e-05
relative error = 0.002587 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.387
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7424 1.123
h = 0.0001 0.004
y[1] (numeric) = -1.30444616895 2.58780846656
y[1] (closed_form) = -1.30446418015 2.587734835
absolute error = 7.580e-05
relative error = 0.002616 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.389
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7425 1.127
h = 0.003 0.006
y[1] (numeric) = -1.30189135205 2.59655887495
y[1] (closed_form) = -1.30190799125 2.59648550624
absolute error = 7.523e-05
relative error = 0.00259 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7455 1.133
h = 0.0001 0.005
y[1] (numeric) = -1.29177317313 2.60800872789
y[1] (closed_form) = -1.29179208798 2.60792967063
absolute error = 8.129e-05
relative error = 0.002793 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.394
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7456 1.138
h = 0.0001 0.003
y[1] (numeric) = -1.28861461966 2.61893688478
y[1] (closed_form) = -1.28863270317 2.61886170865
absolute error = 7.732e-05
relative error = 0.002649 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.395
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7457 1.141
h = 0.001 0.001
y[1] (numeric) = -1.28662455065 2.62546835195
y[1] (closed_form) = -1.28664395147 2.62539399852
absolute error = 7.684e-05
relative error = 0.002628 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.396
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7467 1.142
h = 0.001 0.003
y[1] (numeric) = -1.28383728934 2.62707361695
y[1] (closed_form) = -1.28385719616 2.62699988589
absolute error = 7.637e-05
relative error = 0.002612 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.398
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7477 1.145
h = 0.0001 0.004
y[1] (numeric) = -1.2798698088 2.63306983886
y[1] (closed_form) = -1.27988863402 2.63299488238
absolute error = 7.728e-05
relative error = 0.00264 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.399
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7478 1.149
h = 0.003 0.006
y[1] (numeric) = -1.27728179836 2.64178714157
y[1] (closed_form) = -1.277299256 2.64171243429
absolute error = 7.672e-05
relative error = 0.002615 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7508 1.155
h = 0.0001 0.005
y[1] (numeric) = -1.26713697056 2.6531630849
y[1] (closed_form) = -1.26715674374 2.65308273771
absolute error = 8.274e-05
relative error = 0.002814 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.405
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7509 1.16
h = 0.0001 0.003
y[1] (numeric) = -1.26393704282 2.66405001263
y[1] (closed_form) = -1.26395595393 2.66397351987
absolute error = 7.880e-05
relative error = 0.002672 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.406
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.751 1.163
h = 0.001 0.001
y[1] (numeric) = -1.26192252449 2.67055635117
y[1] (closed_form) = -1.26194273899 2.67048068883
absolute error = 7.832e-05
relative error = 0.002652 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.407
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.752 1.164
h = 0.001 0.003
y[1] (numeric) = -1.25913495349 2.67214510535
y[1] (closed_form) = -1.25915566589 2.67207006683
absolute error = 7.784e-05
relative error = 0.002635 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.408
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.753 1.167
h = 0.0001 0.004
y[1] (numeric) = -1.255150348 2.67810863906
y[1] (closed_form) = -1.25516999517 2.67803237152
absolute error = 7.876e-05
relative error = 0.002663 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7531 1.171
h = 0.003 0.006
y[1] (numeric) = -1.252529606 2.68679270215
y[1] (closed_form) = -1.25254789016 2.68671667031
absolute error = 7.820e-05
relative error = 0.002638 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.411
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7561 1.177
h = 0.0001 0.005
y[1] (numeric) = -1.24235892505 2.69809486384
y[1] (closed_form) = -1.24237956369 2.69801324091
absolute error = 8.419e-05
relative error = 0.002834 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.416
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7562 1.182
h = 0.0001 0.003
y[1] (numeric) = -1.23911819803 2.70894039684
y[1] (closed_form) = -1.23913794446 2.70886260142
absolute error = 8.026e-05
relative error = 0.002694 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.417
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7563 1.185
h = 0.001 0.001
y[1] (numeric) = -1.2370795771 2.71542151306
y[1] (closed_form) = -1.237100613 2.71534455555
absolute error = 7.978e-05
relative error = 0.002674 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.418
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7573 1.186
h = 0.0001 0.004
y[1] (numeric) = -1.23429184569 2.71699383596
y[1] (closed_form) = -1.23431337143 2.7169175036
absolute error = 7.931e-05
relative error = 0.002658 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.419
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7574 1.19
h = 0.003 0.006
y[1] (numeric) = -1.23164462535 2.72565067124
y[1] (closed_form) = -1.23166306677 2.72557345996
absolute error = 7.938e-05
relative error = 0.002654 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.421
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7604 1.196
h = 0.0001 0.005
y[1] (numeric) = -1.2214514456 2.73688972924
y[1] (closed_form) = -1.22147227483 2.73680696858
absolute error = 8.534e-05
relative error = 0.002848 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.425
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7605 1.201
h = 0.0001 0.003
y[1] (numeric) = -1.21817556313 2.74769998199
y[1] (closed_form) = -1.21819547436 2.74762102584
absolute error = 8.143e-05
relative error = 0.002709 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.427
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7606 1.204
h = 0.001 0.001
y[1] (numeric) = -1.21611617025 2.75415959826
y[1] (closed_form) = -1.21613735905 2.75408148644
absolute error = 8.093e-05
relative error = 0.002688 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.427
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7616 1.205
h = 0.001 0.003
y[1] (numeric) = -1.21332822423 2.75571784195
y[1] (closed_form) = -1.21334989598 2.75564035642
absolute error = 8.046e-05
relative error = 0.002672 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.429
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7626 1.208
h = 0.0001 0.004
y[1] (numeric) = -1.20931236729 2.76162077353
y[1] (closed_form) = -1.20933300402 2.76154205271
absolute error = 8.138e-05
relative error = 0.002699 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7627 1.212
h = 0.003 0.006
y[1] (numeric) = -1.20663154391 2.77024303046
y[1] (closed_form) = -1.20665082637 2.77016452062
absolute error = 8.084e-05
relative error = 0.002676 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.432
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7657 1.218
h = 0.0001 0.005
y[1] (numeric) = -1.19641397298 2.78140856133
y[1] (closed_form) = -1.19643568044 2.7813245512
absolute error = 8.677e-05
relative error = 0.002866 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.436
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7658 1.223
h = 0.0001 0.003
y[1] (numeric) = -1.19309835371 2.79217712813
y[1] (closed_form) = -1.19311911412 2.79209689522
absolute error = 8.288e-05
relative error = 0.002729 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.438
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7659 1.226
h = 0.001 0.001
y[1] (numeric) = -1.1910154988 2.79861135782
y[1] (closed_form) = -1.19103752286 2.79853197629
absolute error = 8.238e-05
relative error = 0.002709 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.439
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7669 1.227
h = 0.001 0.003
y[1] (numeric) = -1.18822766531 2.80015332018
y[1] (closed_form) = -1.18825016436 2.80007456604
absolute error = 8.190e-05
relative error = 0.002693 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7679 1.23
h = 0.0001 0.004
y[1] (numeric) = -1.18419575636 2.80602359996
y[1] (closed_form) = -1.18421723652 2.80594360763
absolute error = 8.283e-05
relative error = 0.00272 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.442
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.768 1.234
h = 0.003 0.006
y[1] (numeric) = -1.18148351216 2.81461226802
y[1] (closed_form) = -1.18150364304 2.81453247364
absolute error = 8.229e-05
relative error = 0.002696 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.443
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.771 1.24
h = 0.0001 0.005
y[1] (numeric) = -1.1712423237 2.82570442694
y[1] (closed_form) = -1.17126491583 2.8256191815
absolute error = 8.819e-05
relative error = 0.002883 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.447
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7711 1.245
h = 0.0001 0.003
y[1] (numeric) = -1.16788753634 2.83643116744
y[1] (closed_form) = -1.16790915295 2.83634967174
absolute error = 8.431e-05
relative error = 0.002749 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.449
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7712 1.248
h = 0.001 0.001
y[1] (numeric) = -1.1657815621 2.84283993197
y[1] (closed_form) = -1.16580442846 2.84275929445
absolute error = 8.382e-05
relative error = 0.002728 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7722 1.249
h = 0.001 0.003
y[1] (numeric) = -1.1629939842 2.8443656964
y[1] (closed_form) = -1.16301731761 2.84428568727
absolute error = 8.334e-05
relative error = 0.002712 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.451
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7732 1.252
h = 0.0001 0.004
y[1] (numeric) = -1.15894639238 2.85020334805
y[1] (closed_form) = -1.15896872296 2.85012209805
absolute error = 8.426e-05
relative error = 0.002739 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.453
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7733 1.256
h = 0.003 0.006
y[1] (numeric) = -1.15620318242 2.85875832051
y[1] (closed_form) = -1.15622416883 2.8586772556
absolute error = 8.374e-05
relative error = 0.002716 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.454
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7763 1.262
h = 0.0001 0.005
y[1] (numeric) = -1.14593914212 2.86977727173
y[1] (closed_form) = -1.14596262511 2.86969080507
absolute error = 8.960e-05
relative error = 0.0029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.459
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7764 1.267
h = 0.0001 0.003
y[1] (numeric) = -1.14254575291 2.88046205414
y[1] (closed_form) = -1.1425682325 2.8803793096
absolute error = 8.574e-05
relative error = 0.002767 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.46
Order of pole (given) = 1 0
NO 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=292.6MB, alloc=44.3MB, time=3.96
x[1] = 2.7765 1.27
h = 0.001 0.001
y[1] (numeric) = -1.14041700048 2.88684528001
y[1] (closed_form) = -1.14044071593 2.88676340022
absolute error = 8.525e-05
relative error = 0.002746 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.461
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7775 1.271
h = 0.001 0.003
y[1] (numeric) = -1.13762981901 2.88835493117
y[1] (closed_form) = -1.13765399363 2.88827368066
absolute error = 8.477e-05
relative error = 0.002731 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.462
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7785 1.274
h = 0.0001 0.004
y[1] (numeric) = -1.13356691034 2.89415998303
y[1] (closed_form) = -1.13359009811 2.89407748919
absolute error = 8.569e-05
relative error = 0.002757 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.464
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7786 1.278
h = 0.003 0.006
y[1] (numeric) = -1.1307931876 2.90268115997
y[1] (closed_form) = -1.13081503643 2.90259883853
absolute error = 8.517e-05
relative error = 0.002734 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.465
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7816 1.284
h = 0.0001 0.005
y[1] (numeric) = -1.12050705315 2.91362707652
y[1] (closed_form) = -1.12053143298 2.91353940274
absolute error = 9.100e-05
relative error = 0.002915 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7817 1.289
h = 0.0001 0.003
y[1] (numeric) = -1.11707562573 2.92426977749
y[1] (closed_form) = -1.11709897483 2.92418579804
absolute error = 8.716e-05
relative error = 0.002785 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.472
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7818 1.292
h = 0.001 0.001
y[1] (numeric) = -1.11492443457 2.93062739626
y[1] (closed_form) = -1.11494900567 2.93054428789
absolute error = 8.666e-05
relative error = 0.002764 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.472
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7828 1.293
h = 0.0001 0.004
y[1] (numeric) = -1.1121377882 2.93212102
y[1] (closed_form) = -1.11216281063 2.93203854169
absolute error = 8.619e-05
relative error = 0.002749 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.474
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7829 1.297
h = 0.003 0.006
y[1] (numeric) = -1.10933939381 2.940614536
y[1] (closed_form) = -1.10936144605 2.94053107137
absolute error = 8.633e-05
relative error = 0.002747 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.475
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7859 1.303
h = 0.0001 0.005
y[1] (numeric) = -1.09903397499 2.9514979829
y[1] (closed_form) = -1.09905858771 2.95140920814
absolute error = 9.212e-05
relative error = 0.002925 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.786 1.308
h = 0.0001 0.003
y[1] (numeric) = -1.09556975169 2.96210481317
y[1] (closed_form) = -1.09559331029 2.96201970901
absolute error = 8.830e-05
relative error = 0.002796 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.481
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7861 1.311
h = 0.001 0.001
y[1] (numeric) = -1.09339921051 2.96844060098
y[1] (closed_form) = -1.09342397927 2.96835637334
absolute error = 8.779e-05
relative error = 0.002775 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.482
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7871 1.312
h = 0.001 0.003
y[1] (numeric) = -1.09061294459 2.9699204899
y[1] (closed_form) = -1.09063815799 2.96983689298
absolute error = 8.732e-05
relative error = 0.00276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.483
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7881 1.315
h = 0.0001 0.004
y[1] (numeric) = -1.0865221108 2.97566514445
y[1] (closed_form) = -1.0865463668 2.97558030008
absolute error = 8.824e-05
relative error = 0.002786 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.485
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7882 1.319
h = 0.003 0.006
y[1] (numeric) = -1.08369240394 2.98412354356
y[1] (closed_form) = -1.08371533095 2.98403884833
absolute error = 8.774e-05
relative error = 0.002764 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.486
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7912 1.325
h = 0.0001 0.005
y[1] (numeric) = -1.07336628158 2.99493429163
y[1] (closed_form) = -1.0733918018 2.99484433579
absolute error = 9.351e-05
relative error = 0.002939 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.491
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7913 1.33
h = 0.0001 0.003
y[1] (numeric) = -1.06986506027 3.00549882627
y[1] (closed_form) = -1.06988950012 3.00541251299
absolute error = 8.971e-05
relative error = 0.002812 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.493
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7914 1.333
h = 0.001 0.001
y[1] (numeric) = -1.06767270675 3.01180888873
y[1] (closed_form) = -1.06769834293 3.01172345788
absolute error = 8.919e-05
relative error = 0.002791 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.494
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7924 1.334
h = 0.001 0.003
y[1] (numeric) = -1.06488722917 3.01327291141
y[1] (closed_form) = -1.06491330226 3.01318811186
absolute error = 8.872e-05
relative error = 0.002776 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.495
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7934 1.337
h = 0.0001 0.004
y[1] (numeric) = -1.06078210846 3.0189850679
y[1] (closed_form) = -1.06080723985 3.01889901909
absolute error = 8.964e-05
relative error = 0.002801 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.497
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7935 1.341
h = 0.003 0.006
y[1] (numeric) = -1.05792317146 3.02740941694
y[1] (closed_form) = -1.05794697945 3.02732350505
absolute error = 8.915e-05
relative error = 0.00278 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.498
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7965 1.347
h = 0.0001 0.005
y[1] (numeric) = -1.04757708005 3.03814766322
y[1] (closed_form) = -1.04760351308 3.03805654029
absolute error = 9.488e-05
relative error = 0.002952 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.503
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7966 1.352
h = 0.0001 0.003
y[1] (numeric) = -1.04403941635 3.04866980232
y[1] (closed_form) = -1.04406474333 3.04858229379
absolute error = 9.110e-05
relative error = 0.002827 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.504
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7967 1.355
h = 0.001 0.001
y[1] (numeric) = -1.04182558491 3.05495408495
y[1] (closed_form) = -1.04185209444 3.05486746453
absolute error = 9.059e-05
relative error = 0.002807 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.505
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7977 1.356
h = 0.001 0.003
y[1] (numeric) = -1.03904102811 3.0564023304
y[1] (closed_form) = -1.03906796685 3.05631634175
absolute error = 9.011e-05
relative error = 0.002791 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.507
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7987 1.359
h = 0.0001 0.004
y[1] (numeric) = -1.03492197404 3.06208203431
y[1] (closed_form) = -1.03494798669 3.06199479481
absolute error = 9.104e-05
relative error = 0.002817 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.508
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7988 1.363
h = 0.003 0.006
y[1] (numeric) = -1.03203425106 3.07047225864
y[1] (closed_form) = -1.03205894602 3.070385144
absolute error = 9.055e-05
relative error = 0.002795 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8018 1.369
h = 0.0001 0.005
y[1] (numeric) = -1.02166891683 3.08113820811
y[1] (closed_form) = -1.02169626778 3.08104593203
absolute error = 9.624e-05
relative error = 0.002965 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.514
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8019 1.374
h = 0.0001 0.003
y[1] (numeric) = -1.01809536334 3.09161785967
y[1] (closed_form) = -1.0181215831 3.0915291697
absolute error = 9.248e-05
relative error = 0.002841 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.516
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.802 1.377
h = 0.001 0.001
y[1] (numeric) = -1.0158603865 3.0978763127
y[1] (closed_form) = -1.01588777505 3.09778851632
absolute error = 9.197e-05
relative error = 0.002821 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.517
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.803 1.378
h = 0.001 0.003
y[1] (numeric) = -1.01307688072 3.09930887095
y[1] (closed_form) = -1.01310469086 3.09922170671
absolute error = 9.149e-05
relative error = 0.002806 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.518
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.804 1.381
h = 0.0001 0.004
y[1] (numeric) = -1.0089442435 3.10495617194
y[1] (closed_form) = -1.00897114306 3.10486775546
absolute error = 9.242e-05
relative error = 0.002831 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8041 1.385
h = 0.003 0.006
y[1] (numeric) = -1.00602817621 3.11331220319
y[1] (closed_form) = -1.00605376389 3.1132238997
absolute error = 9.194e-05
relative error = 0.00281 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.521
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8071 1.391
h = 0.0001 0.005
y[1] (numeric) = -0.995644317086 3.12390606854
y[1] (closed_form) = -0.995672590823 3.1238126532
absolute error = 9.760e-05
relative error = 0.002977 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.526
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8072 1.396
h = 0.0001 0.003
y[1] (numeric) = -0.992035423227 3.13434314833
y[1] (closed_form) = -0.992062541214 3.13425329073
absolute error = 9.386e-05
relative error = 0.002855 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.528
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8073 1.399
h = 0.001 0.001
y[1] (numeric) = -0.989779631523 3.14057572665
y[1] (closed_form) = -0.98980790459 3.14048676789
absolute error = 9.334e-05
relative error = 0.002835 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.529
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8083 1.4
h = 0.003 0.006
y[1] (numeric) = -0.986997304844 3.14199268869
y[1] (closed_form) = -0.987025991919 3.14190436233
absolute error = 9.287e-05
relative error = 0.00282 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8113 1.406
h = 0.0001 0.005
y[1] (numeric) = -0.976606484897 3.15254032542
y[1] (closed_form) = -0.976634316228 3.15244324681
absolute error = 0.000101
relative error = 0.00306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.535
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8114 1.411
h = 0.0001 0.003
y[1] (numeric) = -0.97297467267 3.16294720185
y[1] (closed_form) = -0.973001332389 3.1628536608
absolute error = 9.727e-05
relative error = 0.002939 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.536
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8115 1.414
h = 0.001 0.001
y[1] (numeric) = -0.970705406448 3.16916144297
y[1] (closed_form) = -0.97073321171 3.1690688039
absolute error = 9.672e-05
relative error = 0.002918 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.537
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8125 1.415
h = 0.001 0.003
y[1] (numeric) = -0.967924354175 3.17056776331
y[1] (closed_form) = -0.967952568262 3.17047575658
absolute error = 9.624e-05
relative error = 0.002903 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.539
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8135 1.418
h = 0.0001 0.004
y[1] (numeric) = -0.963770388203 3.17616017263
y[1] (closed_form) = -0.96379771766 3.17606691219
absolute error = 9.718e-05
relative error = 0.002928 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.541
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8136 1.422
h = 0.003 0.006
y[1] (numeric) = -0.960808337983 3.18445766203
y[1] (closed_form) = -0.960834365903 3.18436449505
absolute error = 9.673e-05
relative error = 0.002908 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.542
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8166 1.428
h = 0.0001 0.005
y[1] (numeric) = -0.950396619441 3.19492993285
y[1] (closed_form) = -0.950425380972 3.19483173842
absolute error = 0.0001023
relative error = 0.00307 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.547
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8167 1.433
h = 0.0001 0.003
y[1] (numeric) = -0.946730388517 3.20529412629
y[1] (closed_form) = -0.946757954801 3.20519944093
absolute error = 9.862e-05
relative error = 0.002951 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.548
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8168 1.436
h = 0.001 0.001
y[1] (numeric) = -0.944440861616 3.21148243505
y[1] (closed_form) = -0.944469559807 3.21138865656
absolute error = 9.807e-05
relative error = 0.00293 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.549
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8178 1.437
h = 0.001 0.003
y[1] (numeric) = -0.941661197375 3.2128733179
y[1] (closed_form) = -0.941690296912 3.21278017185
absolute error = 9.759e-05
relative error = 0.002915 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.551
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8188 1.44
h = 0.0001 0.004
y[1] (numeric) = -0.937494571184 3.21843348627
y[1] (closed_form) = -0.937522801304 3.21833908568
absolute error = 9.853e-05
relative error = 0.002939 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.553
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8189 1.444
h = 0.003 0.006
y[1] (numeric) = -0.934505351958 3.22669664004
y[1] (closed_form) = -0.934532286627 3.22660232147
absolute error = 9.809e-05
relative error = 0.00292 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.554
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8219 1.45
h = 0.0001 0.005
y[1] (numeric) = -0.924076990773 3.23709745227
y[1] (closed_form) = -0.924106686818 3.23699815578
absolute error = 0.0001036
relative error = 0.003079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.559
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.822 1.455
h = 0.0001 0.003
y[1] (numeric) = -0.920376881458 3.24741889868
y[1] (closed_form) = -0.920405359165 3.24732308267
absolute error = 9.996e-05
relative error = 0.002962 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8221 1.458
h = 0.001 0.001
y[1] (numeric) = -0.918067418736 3.25358124197
y[1] (closed_form) = -0.91809701476 3.25348633751
absolute error = 9.941e-05
relative error = 0.002941 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.561
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8231 1.459
h = 0.001 0.003
y[1] (numeric) = -0.915289264781 3.2549567806
y[1] (closed_form) = -0.915319254731 3.25486250859
absolute error = 9.893e-05
relative error = 0.002926 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.563
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8241 1.462
h = 0.0001 0.004
y[1] (numeric) = -0.911110315867 3.26048477215
y[1] (closed_form) = -0.911139451504 3.26038924498
absolute error = 9.987e-05
relative error = 0.00295 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.565
Order of pole (given) = 1 0
NO 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=341.3MB, alloc=44.3MB, time=4.60
x[1] = 2.8242 1.466
h = 0.003 0.006
y[1] (numeric) = -0.908094359211 3.26871354407
y[1] (closed_form) = -0.908122205578 3.26861808765
absolute error = 9.944e-05
relative error = 0.002931 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.566
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8272 1.472
h = 0.0001 0.005
y[1] (numeric) = -0.897650042158 3.27904313668
y[1] (closed_form) = -0.897680676823 3.27894275182
absolute error = 0.000105
relative error = 0.003087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.571
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8273 1.477
h = 0.0001 0.003
y[1] (numeric) = -0.893916591266 3.28932177929
y[1] (closed_form) = -0.893945985046 3.28922484627
absolute error = 0.0001013
relative error = 0.002972 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.572
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8274 1.48
h = 0.001 0.001
y[1] (numeric) = -0.891587515408 3.29545812833
y[1] (closed_form) = -0.891618013965 3.29536211133
absolute error = 0.0001007
relative error = 0.002951 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.573
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8284 1.481
h = 0.0001 0.004
y[1] (numeric) = -0.888810991854 3.2968184168
y[1] (closed_form) = -0.888841876973 3.29672303217
absolute error = 0.0001003
relative error = 0.002936 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.575
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8285 1.485
h = 0.003 0.006
y[1] (numeric) = -0.885773433877 3.30501908165
y[1] (closed_form) = -0.885801554837 3.3049225494
absolute error = 0.0001005
relative error = 0.002939 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.576
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8315 1.491
h = 0.0001 0.005
y[1] (numeric) = -0.875315081663 3.31528774635
y[1] (closed_form) = -0.875346014017 3.31518632789
absolute error = 0.000106
relative error = 0.003092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.581
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8316 1.496
h = 0.0001 0.003
y[1] (numeric) = -0.871552847929 3.3255298934
y[1] (closed_form) = -0.871582520077 3.32543190235
absolute error = 0.0001024
relative error = 0.002978 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.583
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8317 1.499
h = 0.001 0.001
y[1] (numeric) = -0.869206836412 3.33164407611
y[1] (closed_form) = -0.869237601775 3.33154700493
absolute error = 0.0001018
relative error = 0.002958 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.584
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8327 1.5
h = 0.001 0.003
y[1] (numeric) = -0.866431630686 3.33299129231
y[1] (closed_form) = -0.86646277632 3.33289485344
absolute error = 0.0001013
relative error = 0.002943 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.585
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8337 1.503
h = 0.0001 0.004
y[1] (numeric) = -0.862230257037 3.33845973112
y[1] (closed_form) = -0.86226057616 3.33836203625
absolute error = 0.0001023
relative error = 0.002967 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.587
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8338 1.507
h = 0.003 0.006
y[1] (numeric) = -0.859165276494 3.3466247296
y[1] (closed_form) = -0.859194317958 3.34652708489
absolute error = 0.0001019
relative error = 0.002948 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.588
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8368 1.513
h = 0.0001 0.005
y[1] (numeric) = -0.848692226825 3.35682262903
y[1] (closed_form) = -0.848724105066 3.35672014746
absolute error = 0.0001073
relative error = 0.0031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.593
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8369 1.518
h = 0.0001 0.003
y[1] (numeric) = -0.844897640351 3.36702187928
y[1] (closed_form) = -0.844928236831 3.36692279639
absolute error = 0.0001037
relative error = 0.002987 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.595
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.837 1.521
h = 0.001 0.001
y[1] (numeric) = -0.842532609974 3.37311002167
y[1] (closed_form) = -0.842564286228 3.37301186274
absolute error = 0.0001031
relative error = 0.002967 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.596
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.838 1.522
h = 0.001 0.003
y[1] (numeric) = -0.839759253624 3.37444216332
y[1] (closed_form) = -0.839791302899 3.37434463645
absolute error = 0.0001027
relative error = 0.002952 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.597
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.839 1.525
h = 0.0001 0.004
y[1] (numeric) = -0.835546504309 3.37987862508
y[1] (closed_form) = -0.835577741851 3.37977984213
absolute error = 0.0001036
relative error = 0.002976 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.599
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8391 1.529
h = 0.003 0.006
y[1] (numeric) = -0.832456004643 3.38800913595
y[1] (closed_form) = -0.832485970959 3.38791039236
absolute error = 0.0001032
relative error = 0.002958 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.601
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8421 1.535
h = 0.0001 0.005
y[1] (numeric) = -0.821968920104 3.39813652772
y[1] (closed_form) = -0.822001747766 3.39803299655
absolute error = 0.0001086
relative error = 0.003107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.605
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8422 1.54
h = 0.0001 0.003
y[1] (numeric) = -0.818142507351 3.40829284453
y[1] (closed_form) = -0.818174032226 3.40819268328
absolute error = 0.000105
relative error = 0.002996 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.607
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8423 1.543
h = 0.001 0.001
y[1] (numeric) = -0.815758774378 3.4143549298
y[1] (closed_form) = -0.815791365642 3.4142556964
absolute error = 0.0001044
relative error = 0.002975 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.608
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8433 1.544
h = 0.001 0.003
y[1] (numeric) = -0.812987381455 3.415672093
y[1] (closed_form) = -0.813020338551 3.41557349132
absolute error = 0.000104
relative error = 0.002961 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8443 1.547
h = 0.0001 0.004
y[1] (numeric) = -0.808763580412 3.42107665571
y[1] (closed_form) = -0.808795740436 3.42097679804
absolute error = 0.0001049
relative error = 0.002984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.612
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8444 1.551
h = 0.003 0.006
y[1] (numeric) = -0.805647981876 3.42917265445
y[1] (closed_form) = -0.805678877189 3.42907282553
absolute error = 0.0001045
relative error = 0.002967 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.613
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8474 1.557
h = 0.0001 0.005
y[1] (numeric) = -0.795147516539 3.43922980226
y[1] (closed_form) = -0.795181296963 3.43912523494
absolute error = 0.0001099
relative error = 0.003113 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.618
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8475 1.562
h = 0.0001 0.003
y[1] (numeric) = -0.791289800175 3.44934315576
y[1] (closed_form) = -0.791322257307 3.44924192957
absolute error = 0.0001063
relative error = 0.003004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8476 1.565
h = 0.001 0.001
y[1] (numeric) = -0.788887678521 3.45537917111
y[1] (closed_form) = -0.78892118872 3.45527887647
absolute error = 0.0001057
relative error = 0.002984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.621
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8486 1.566
h = 0.001 0.003
y[1] (numeric) = -0.786118360974 3.45668145259
y[1] (closed_form) = -0.786152229878 3.45658178925
absolute error = 0.0001053
relative error = 0.002969 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.622
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8496 1.569
h = 0.0001 0.004
y[1] (numeric) = -0.781883828569 3.46205419757
y[1] (closed_form) = -0.781916914942 3.46195327851
absolute error = 0.0001062
relative error = 0.002992 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.624
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8497 1.573
h = 0.003 0.006
y[1] (numeric) = -0.778743548322 3.47011566502
y[1] (closed_form) = -0.778775376575 3.47001476425
absolute error = 0.0001058
relative error = 0.002975 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.625
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8527 1.579
h = 0.0001 0.005
y[1] (numeric) = -0.76823034774 3.48010283844
y[1] (closed_form) = -0.768265084077 3.47999724835
absolute error = 0.0001112
relative error = 0.003119 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8528 1.584
h = 0.0001 0.003
y[1] (numeric) = -0.764341846568 3.49017320539
y[1] (closed_form) = -0.764375239625 3.49007092762
absolute error = 0.0001076
relative error = 0.003011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.632
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8529 1.587
h = 0.001 0.001
y[1] (numeric) = -0.761921647761 3.49618314199
y[1] (closed_form) = -0.761956080625 3.49608179927
absolute error = 0.000107
relative error = 0.002991 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.633
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8539 1.588
h = 0.0001 0.004
y[1] (numeric) = -0.759154515453 3.49747063905
y[1] (closed_form) = -0.759189299958 3.49736992713
absolute error = 0.0001065
relative error = 0.002977 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.634
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.854 1.592
h = 0.003 0.006
y[1] (numeric) = -0.755994303975 3.50550389375
y[1] (closed_form) = -0.756026442105 3.50540195649
absolute error = 0.0001069
relative error = 0.002981 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.636
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.857 1.598
h = 0.0001 0.005
y[1] (numeric) = -0.745469822693 3.51543119715
y[1] (closed_form) = -0.745504888637 3.51532461245
absolute error = 0.0001122
relative error = 0.003122 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.641
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8571 1.603
h = 0.0001 0.003
y[1] (numeric) = -0.741554723118 3.52546490744
y[1] (closed_form) = -0.741588428645 3.52536161049
absolute error = 0.0001087
relative error = 0.003016 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.643
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8572 1.606
h = 0.001 0.001
y[1] (numeric) = -0.739118900993 3.5314526025
y[1] (closed_form) = -0.739153635004 3.53135024363
absolute error = 0.0001081
relative error = 0.002996 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.644
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8582 1.607
h = 0.001 0.003
y[1] (numeric) = -0.73635356153 3.53272742419
y[1] (closed_form) = -0.736388641145 3.5326256957
absolute error = 0.0001076
relative error = 0.002982 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.645
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8592 1.61
h = 0.0001 0.004
y[1] (numeric) = -0.732099524358 3.53804131031
y[1] (closed_form) = -0.732133848183 3.5379383269
absolute error = 0.0001086
relative error = 0.003005 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.647
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8593 1.614
h = 0.003 0.006
y[1] (numeric) = -0.728914005037 3.54603877236
y[1] (closed_form) = -0.728947083081 3.54593578814
absolute error = 0.0001082
relative error = 0.002988 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.648
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8623 1.62
h = 0.0001 0.005
y[1] (numeric) = -0.718377970417 3.55589661049
y[1] (closed_form) = -0.718413997798 3.55578902768
absolute error = 0.0001135
relative error = 0.003128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.653
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8624 1.625
h = 0.0001 0.003
y[1] (numeric) = -0.714433040803 3.56588730209
y[1] (closed_form) = -0.714467688727 3.56578297821
absolute error = 0.0001099
relative error = 0.003023 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.655
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8625 1.628
h = 0.001 0.001
y[1] (numeric) = -0.711979714725 3.57184890848
y[1] (closed_form) = -0.712015377995 3.57174552583
absolute error = 0.0001094
relative error = 0.003003 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.656
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8635 1.629
h = 0.001 0.003
y[1] (numeric) = -0.70921676059 3.57310912698
y[1] (closed_form) = -0.709252762518 3.57300637406
absolute error = 0.0001089
relative error = 0.002989 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.658
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8645 1.632
h = 0.0001 0.004
y[1] (numeric) = -0.704952889785 3.578391442
y[1] (closed_form) = -0.704988150114 3.57828743492
absolute error = 0.0001098
relative error = 0.003011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8646 1.636
h = 0.003 0.006
y[1] (numeric) = -0.701743864564 3.58635434166
y[1] (closed_form) = -0.701777885907 3.58625032378
absolute error = 0.0001094
relative error = 0.002995 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.661
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8676 1.642
h = 0.0001 0.005
y[1] (numeric) = -0.691196897844 3.59614299989
y[1] (closed_form) = -0.691233889284 3.59603443213
absolute error = 0.0001147
relative error = 0.003132 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.666
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8677 1.647
h = 0.0001 0.003
y[1] (numeric) = -0.687222645665 3.60609066783
y[1] (closed_form) = -0.68725823911 3.60598533018
absolute error = 0.0001112
relative error = 0.003029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.668
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8678 1.65
h = 0.001 0.001
y[1] (numeric) = -0.684752120175 3.61202618753
y[1] (closed_form) = -0.684788715897 3.6119217941
absolute error = 0.0001106
relative error = 0.003009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.669
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8688 1.651
h = 0.001 0.003
y[1] (numeric) = -0.681991655337 3.61327190163
y[1] (closed_form) = -0.682028582836 3.61316813718
absolute error = 0.0001101
relative error = 0.002995 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8698 1.654
h = 0.0001 0.004
y[1] (numeric) = -0.677718257377 3.61852273895
y[1] (closed_form) = -0.677754457344 3.61841772127
absolute error = 0.0001111
relative error = 0.003017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.672
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8699 1.658
h = 0.003 0.006
y[1] (numeric) = -0.67448613105 3.62645107672
y[1] (closed_form) = -0.674521098889 3.62634603842
absolute error = 0.0001107
relative error = 0.003001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.674
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8729 1.664
h = 0.0001 0.005
y[1] (numeric) = -0.663928844955 3.63617084554
y[1] (closed_form) = -0.6639668029 3.63606130592
absolute error = 0.0001159
relative error = 0.003136 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.679
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.873 1.669
h = 0.0001 0.003
y[1] (numeric) = -0.659925773585 3.64607549096
y[1] (closed_form) = -0.659962315493 3.64596915265
absolute error = 0.0001124
relative error = 0.003035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.681
Order of pole (given) = 1 0
NO 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=390.2MB, alloc=44.3MB, time=5.27
x[1] = 2.8731 1.672
h = 0.001 0.001
y[1] (numeric) = -0.657438350702 3.65198492961
y[1] (closed_form) = -0.657475881889 3.65187953831
absolute error = 0.0001119
relative error = 0.003015 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.682
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8741 1.673
h = 0.001 0.003
y[1] (numeric) = -0.654680477095 3.65321623851
y[1] (closed_form) = -0.654718333244 3.65311147538
absolute error = 0.0001114
relative error = 0.003001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.683
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8751 1.676
h = 0.0001 0.004
y[1] (numeric) = -0.650397854831 3.65843569443
y[1] (closed_form) = -0.650434997387 3.65832967916
absolute error = 0.0001123
relative error = 0.003023 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.685
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8752 1.68
h = 0.003 0.006
y[1] (numeric) = -0.647143028858 3.66632947566
y[1] (closed_form) = -0.647178946206 3.6662234301
absolute error = 0.000112
relative error = 0.003007 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.687
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8782 1.686
h = 0.0001 0.005
y[1] (numeric) = -0.636576027617 3.67598065048
y[1] (closed_form) = -0.636614954336 3.675870152
absolute error = 0.0001172
relative error = 0.00314 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.692
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8783 1.691
h = 0.0001 0.003
y[1] (numeric) = -0.632544636279 3.6858422805
y[1] (closed_form) = -0.632582129409 3.68573495456
absolute error = 0.0001137
relative error = 0.00304 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.694
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8784 1.694
h = 0.001 0.001
y[1] (numeric) = -0.630040615466 3.69172564724
y[1] (closed_form) = -0.630079084953 3.69161927092
absolute error = 0.0001131
relative error = 0.003021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.695
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8794 1.695
h = 0.0001 0.004
y[1] (numeric) = -0.627285433008 3.69294265056
y[1] (closed_form) = -0.627324220706 3.69283690153
absolute error = 0.0001126
relative error = 0.003007 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.696
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8795 1.699
h = 0.003 0.006
y[1] (numeric) = -0.624012284948 3.70080821317
y[1] (closed_form) = -0.624048543763 3.70070117091
absolute error = 0.000113
relative error = 0.003011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.698
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8825 1.705
h = 0.0001 0.005
y[1] (numeric) = -0.613436586388 3.71040069081
y[1] (closed_form) = -0.613475871145 3.71028923694
absolute error = 0.0001182
relative error = 0.003142 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.702
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8826 1.71
h = 0.0001 0.003
y[1] (numeric) = -0.609380702551 3.72022563411
y[1] (closed_form) = -0.609418538657 3.72011732823
absolute error = 0.0001147
relative error = 0.003043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.704
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8827 1.713
h = 0.001 0.001
y[1] (numeric) = -0.606862322272 3.72608676193
y[1] (closed_form) = -0.606901123701 3.72597940794
absolute error = 0.0001142
relative error = 0.003024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.706
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8837 1.714
h = 0.001 0.003
y[1] (numeric) = -0.60410936596 3.72729149787
y[1] (closed_form) = -0.604148479831 3.72718477042
absolute error = 0.0001137
relative error = 0.00301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.707
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8847 1.717
h = 0.0001 0.004
y[1] (numeric) = -0.599810002025 3.73245292772
y[1] (closed_form) = -0.599848427919 3.73234495041
absolute error = 0.0001146
relative error = 0.003032 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.709
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8848 1.721
h = 0.003 0.006
y[1] (numeric) = -0.596513582983 3.74028269686
y[1] (closed_form) = -0.596550796582 3.74017467163
absolute error = 0.0001143
relative error = 0.003017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8878 1.727
h = 0.0001 0.005
y[1] (numeric) = -0.585929274682 3.74980713568
y[1] (closed_form) = -0.585969532135 3.74969474691
absolute error = 0.0001194
relative error = 0.003146 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.715
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8879 1.732
h = 0.0001 0.003
y[1] (numeric) = -0.581845988851 3.75958908647
y[1] (closed_form) = -0.581884780998 3.75947981697
absolute error = 0.000116
relative error = 0.003048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.717
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.888 1.735
h = 0.001 0.001
y[1] (numeric) = -0.579311561194 3.76542416511
y[1] (closed_form) = -0.579351305882 3.76531584979
absolute error = 0.0001154
relative error = 0.003029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.719
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.889 1.736
h = 0.001 0.003
y[1] (numeric) = -0.57656147783 3.76661478059
y[1] (closed_form) = -0.576601528334 3.7665070908
absolute error = 0.0001149
relative error = 0.003015 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.89 1.739
h = 0.0001 0.004
y[1] (numeric) = -0.57225373713 3.77174511627
y[1] (closed_form) = -0.572293113229 3.77163617815
absolute error = 0.0001158
relative error = 0.003036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.722
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8901 1.743
h = 0.003 0.006
y[1] (numeric) = -0.568935748449 3.77954036521
y[1] (closed_form) = -0.56897391933 3.77943136996
absolute error = 0.0001155
relative error = 0.003022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.723
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8931 1.749
h = 0.0001 0.005
y[1] (numeric) = -0.558343410468 3.78899707376
y[1] (closed_form) = -0.558384642404 3.78888376286
absolute error = 0.0001206
relative error = 0.003148 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.728
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8932 1.754
h = 0.0001 0.003
y[1] (numeric) = -0.554233209798 3.79873605559
y[1] (closed_form) = -0.554272960247 3.79862583529
absolute error = 0.0001172
relative error = 0.003052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8933 1.757
h = 0.001 0.001
y[1] (numeric) = -0.551683026817 3.80454510396
y[1] (closed_form) = -0.551723717105 3.80443583996
absolute error = 0.0001166
relative error = 0.003033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.732
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8943 1.758
h = 0.001 0.003
y[1] (numeric) = -0.548935910638 3.80572169954
y[1] (closed_form) = -0.548976900182 3.80561305999
absolute error = 0.0001161
relative error = 0.00302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.733
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8953 1.761
h = 0.0001 0.004
y[1] (numeric) = -0.544620081994 3.81082104776
y[1] (closed_form) = -0.544660410574 3.81071116155
absolute error = 0.0001171
relative error = 0.003041 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.735
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8954 1.765
h = 0.003 0.006
y[1] (numeric) = -0.541280911984 3.81858179953
y[1] (closed_form) = -0.541320042472 3.81847184714
absolute error = 0.0001167
relative error = 0.003026 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.737
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8984 1.771
h = 0.0001 0.005
y[1] (numeric) = -0.530681115959 3.82797109057
y[1] (closed_form) = -0.530723324001 3.82785687021
absolute error = 0.0001218
relative error = 0.003151 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8985 1.776
h = 0.0001 0.003
y[1] (numeric) = -0.526544483283 3.83766713248
y[1] (closed_form) = -0.526585194126 3.83755597411
absolute error = 0.0001184
relative error = 0.003056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8986 1.779
h = 0.001 0.001
y[1] (numeric) = -0.523978834384 3.8434501727
y[1] (closed_form) = -0.524020472444 3.8433399726
absolute error = 0.0001178
relative error = 0.003037 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.745
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.8996 1.78
h = 0.001 0.003
y[1] (numeric) = -0.521234777671 3.84461284922
y[1] (closed_form) = -0.521276708494 3.8445032724
absolute error = 0.0001173
relative error = 0.003024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9006 1.783
h = 0.0001 0.004
y[1] (numeric) = -0.516911146258 3.84968131913
y[1] (closed_form) = -0.516952429429 3.84957049747
absolute error = 0.0001183
relative error = 0.003045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9007 1.787
h = 0.003 0.006
y[1] (numeric) = -0.513551179729 3.85740760109
y[1] (closed_form) = -0.513591271978 3.85729670437
absolute error = 0.0001179
relative error = 0.00303 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9037 1.793
h = 0.0001 0.005
y[1] (numeric) = -0.502944488902 3.8667297914
y[1] (closed_form) = -0.502987674516 3.86661467419
absolute error = 0.000123
relative error = 0.003153 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.755
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9038 1.798
h = 0.0001 0.003
y[1] (numeric) = -0.498781902695 3.87638292779
y[1] (closed_form) = -0.498823575858 3.87627084399
absolute error = 0.0001196
relative error = 0.00306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.757
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9039 1.801
h = 0.001 0.001
y[1] (numeric) = -0.49620107461 3.88213998518
y[1] (closed_form) = -0.496243662452 3.88202886145
absolute error = 0.000119
relative error = 0.003041 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.758
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9049 1.802
h = 0.0001 0.004
y[1] (numeric) = -0.493460167707 3.88328884367
y[1] (closed_form) = -0.493503041886 3.88317834201
absolute error = 0.0001185
relative error = 0.003028 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.759
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.905 1.806
h = 0.003 0.006
y[1] (numeric) = -0.49008342318 3.89098699099
y[1] (closed_form) = -0.490123884958 3.89087513751
absolute error = 0.0001189
relative error = 0.003033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.761
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.908 1.812
h = 0.0001 0.005
y[1] (numeric) = -0.479470448085 3.90025175301
y[1] (closed_form) = -0.479514016855 3.90013571957
absolute error = 0.0001239
relative error = 0.003154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.766
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9081 1.817
h = 0.0001 0.003
y[1] (numeric) = -0.475285391303 3.90986829077
y[1] (closed_form) = -0.47532743452 3.90975526638
absolute error = 0.0001206
relative error = 0.003062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.768
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9082 1.82
h = 0.001 0.001
y[1] (numeric) = -0.472691415997 3.91560318185
y[1] (closed_form) = -0.472734363187 3.91549111909
absolute error = 0.00012
relative error = 0.003043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.769
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9092 1.821
h = 0.001 0.003
y[1] (numeric) = -0.469953128267 3.91674018836
y[1] (closed_form) = -0.469996356303 3.91662874664
absolute error = 0.0001195
relative error = 0.00303 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9102 1.824
h = 0.0001 0.004
y[1] (numeric) = -0.46561535962 3.92175158474
y[1] (closed_form) = -0.465657964445 3.92163890177
absolute error = 0.0001205
relative error = 0.00305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.773
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9103 1.828
h = 0.003 0.006
y[1] (numeric) = -0.462217298066 3.92941405066
y[1] (closed_form) = -0.462258725321 3.92930127642
absolute error = 0.0001201
relative error = 0.003037 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.774
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9133 1.834
h = 0.0001 0.005
y[1] (numeric) = -0.451598457879 3.93861230509
y[1] (closed_form) = -0.45164300668 3.93849539797
absolute error = 0.0001251
relative error = 0.003156 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.779
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9134 1.839
h = 0.0001 0.003
y[1] (numeric) = -0.447388326731 3.94818600955
y[1] (closed_form) = -0.447431335572 3.94807208303
absolute error = 0.0001218
relative error = 0.003065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.781
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9135 1.842
h = 0.001 0.001
y[1] (numeric) = -0.444779698998 3.95389496971
y[1] (closed_form) = -0.44482359943 3.95378200633
absolute error = 0.0001212
relative error = 0.003046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.782
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9145 1.843
h = 0.001 0.003
y[1] (numeric) = -0.442044725304 3.95501834569
y[1] (closed_form) = -0.442088900282 3.95490600201
absolute error = 0.0001207
relative error = 0.003033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.784
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9155 1.846
h = 0.0001 0.004
y[1] (numeric) = -0.437699951008 3.95999918573
y[1] (closed_form) = -0.437743515708 3.959885603
absolute error = 0.0001217
relative error = 0.003053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.786
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9156 1.85
h = 0.003 0.006
y[1] (numeric) = -0.434282174709 3.9676272786
y[1] (closed_form) = -0.434324569125 3.96751359616
absolute error = 0.0001213
relative error = 0.00304 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.787
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9186 1.856
h = 0.0001 0.005
y[1] (numeric) = -0.423658008883 3.9767593529
y[1] (closed_form) = -0.423703538739 3.97664158444
absolute error = 0.0001263
relative error = 0.003157 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.793
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9187 1.861
h = 0.0001 0.003
y[1] (numeric) = -0.419423269253 3.98629027311
y[1] (closed_form) = -0.419467245186 3.98617545688
absolute error = 0.0001229
relative error = 0.003067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.795
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9188 1.864
h = 0.001 0.001
y[1] (numeric) = -0.416800268122 3.99197333634
y[1] (closed_form) = -0.416845123352 3.9918594846
absolute error = 0.0001224
relative error = 0.003049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.796
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9198 1.865
h = 0.001 0.003
y[1] (numeric) = -0.414068693372 3.99308318333
y[1] (closed_form) = -0.414113816916 3.99296994989
absolute error = 0.0001219
relative error = 0.003036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.797
Order of pole (given) = 1 0
NO 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=438.8MB, alloc=44.3MB, time=5.91
x[1] = 2.9208 1.868
h = 0.0001 0.004
y[1] (numeric) = -0.409717184594 3.99803358501
y[1] (closed_form) = -0.40976171066 3.99791911485
absolute error = 0.0001228
relative error = 0.003056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.799
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9209 1.872
h = 0.003 0.006
y[1] (numeric) = -0.406280064654 4.00562734796
y[1] (closed_form) = -0.406323427756 4.0055127698
absolute error = 0.0001225
relative error = 0.003043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.801
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9239 1.878
h = 0.0001 0.005
y[1] (numeric) = -0.395651104381 4.01469357298
y[1] (closed_form) = -0.39569761617 4.01457495541
absolute error = 0.0001274
relative error = 0.003158 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.806
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.924 1.883
h = 0.0001 0.003
y[1] (numeric) = -0.391392217678 4.02418176287
y[1] (closed_form) = -0.391437162021 4.02406606924
absolute error = 0.0001241
relative error = 0.00307 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.808
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9241 1.886
h = 0.001 0.001
y[1] (numeric) = -0.388755119445 4.02983896601
y[1] (closed_form) = -0.388800930877 4.02972423807
absolute error = 0.0001235
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.809
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9251 1.887
h = 0.001 0.003
y[1] (numeric) = -0.386027026679 4.03093538565
y[1] (closed_form) = -0.386073100263 4.03082127456
absolute error = 0.0001231
relative error = 0.003039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.811
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9261 1.89
h = 0.0001 0.004
y[1] (numeric) = -0.381669050969 4.03585546904
y[1] (closed_form) = -0.381714539739 4.03574012368
absolute error = 0.000124
relative error = 0.003059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.813
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9262 1.894
h = 0.003 0.006
y[1] (numeric) = -0.378212954877 4.04341494903
y[1] (closed_form) = -0.378257288035 4.04329948753
absolute error = 0.0001237
relative error = 0.003046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.814
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9292 1.9
h = 0.0001 0.005
y[1] (numeric) = -0.367579723134 4.05241565881
y[1] (closed_form) = -0.36762721759 4.05229620428
absolute error = 0.0001286
relative error = 0.003159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9293 1.905
h = 0.0001 0.003
y[1] (numeric) = -0.363297146269 4.06186117706
y[1] (closed_form) = -0.363343060187 4.06174461827
absolute error = 0.0001253
relative error = 0.003072 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.822
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9294 1.908
h = 0.001 0.001
y[1] (numeric) = -0.360646224479 4.06749255977
y[1] (closed_form) = -0.36069299337 4.06737696772
absolute error = 0.0001247
relative error = 0.003054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.823
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9304 1.909
h = 0.0001 0.004
y[1] (numeric) = -0.357921694894 4.06857565379
y[1] (closed_form) = -0.357968719841 4.06846067707
absolute error = 0.0001242
relative error = 0.003042 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.824
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9305 1.913
h = 0.003 0.006
y[1] (numeric) = -0.354450296908 4.07610716336
y[1] (closed_form) = -0.354495024313 4.07599078494
absolute error = 0.0001247
relative error = 0.003047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.826
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9335 1.919
h = 0.0001 0.005
y[1] (numeric) = -0.343813026025 4.08505179221
y[1] (closed_form) = -0.343860925628 4.08493146033
absolute error = 0.0001295
relative error = 0.003159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.831
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9336 1.924
h = 0.0001 0.003
y[1] (numeric) = -0.339509912623 4.09446090553
y[1] (closed_form) = -0.339556220427 4.09434344533
absolute error = 0.0001263
relative error = 0.003073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.833
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9337 1.927
h = 0.001 0.001
y[1] (numeric) = -0.336847002043 4.10007025699
y[1] (closed_form) = -0.336894154472 4.09995376446
absolute error = 0.0001257
relative error = 0.003055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.834
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9347 1.928
h = 0.001 0.003
y[1] (numeric) = -0.334125446064 4.10114191852
y[1] (closed_form) = -0.334172849339 4.10102604006
absolute error = 0.0001252
relative error = 0.003043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.836
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9357 1.931
h = 0.0001 0.004
y[1] (numeric) = -0.329755778955 4.10600598264
y[1] (closed_form) = -0.329802620657 4.10588887466
absolute error = 0.0001261
relative error = 0.003062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9358 1.935
h = 0.003 0.006
y[1] (numeric) = -0.326264931429 4.11350202364
y[1] (closed_form) = -0.326310631183 4.11338478469
absolute error = 0.0001258
relative error = 0.003049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.839
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9388 1.941
h = 0.0001 0.005
y[1] (numeric) = -0.315624344556 4.12238176085
y[1] (closed_form) = -0.315673227961 4.12226061436
absolute error = 0.0001306
relative error = 0.00316 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.845
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9389 1.946
h = 0.0001 0.003
y[1] (numeric) = -0.311298379985 4.13174831863
y[1] (closed_form) = -0.311345659286 4.13163001577
absolute error = 0.0001274
relative error = 0.003075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.847
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.939 1.949
h = 0.001 0.001
y[1] (numeric) = -0.308622148055 4.13733192746
y[1] (closed_form) = -0.308670260033 4.13721459307
absolute error = 0.0001268
relative error = 0.003057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.848
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.94 1.95
h = 0.001 0.003
y[1] (numeric) = -0.30590430271 4.13839045185
y[1] (closed_form) = -0.305952659567 4.13827372991
absolute error = 0.0001263
relative error = 0.003045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.849
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.941 1.953
h = 0.0001 0.004
y[1] (numeric) = -0.301528915674 4.14322454887
y[1] (closed_form) = -0.301576723238 4.14310660019
absolute error = 0.0001273
relative error = 0.003064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.851
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9411 1.957
h = 0.003 0.006
y[1] (numeric) = -0.298020123902 4.15068645732
y[1] (closed_form) = -0.298066796948 4.15056836998
absolute error = 0.000127
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.853
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9441 1.963
h = 0.0001 0.005
y[1] (numeric) = -0.287376720795 4.15950164538
y[1] (closed_form) = -0.287426588336 4.15937969613
absolute error = 0.0001318
relative error = 0.00316 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.858
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9442 1.968
h = 0.0001 0.003
y[1] (numeric) = -0.283028349043 4.16882571924
y[1] (closed_form) = -0.283076600593 4.16870658571
absolute error = 0.0001285
relative error = 0.003076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9443 1.971
h = 0.001 0.001
y[1] (numeric) = -0.280339061427 4.17438363276
y[1] (closed_form) = -0.280388133798 4.17426546833
absolute error = 0.0001279
relative error = 0.003058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.862
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9453 1.972
h = 0.001 0.003
y[1] (numeric) = -0.277625002741 4.17542912181
y[1] (closed_form) = -0.277674314092 4.17531156817
absolute error = 0.0001275
relative error = 0.003046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.863
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9463 1.975
h = 0.0001 0.004
y[1] (numeric) = -0.273244149475 4.18023337912
y[1] (closed_form) = -0.273292923678 4.18011460165
absolute error = 0.0001284
relative error = 0.003065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.865
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9464 1.979
h = 0.003 0.006
y[1] (numeric) = -0.269717766895 4.18766121593
y[1] (closed_form) = -0.269765414033 4.18754229224
absolute error = 0.0001281
relative error = 0.003053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.867
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9494 1.985
h = 0.0001 0.005
y[1] (numeric) = -0.259072039271 4.19641219992
y[1] (closed_form) = -0.259122891153 4.1962894597
absolute error = 0.0001329
relative error = 0.00316 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.872
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9495 1.99
h = 0.0001 0.003
y[1] (numeric) = -0.254701699766 4.20569386582
y[1] (closed_form) = -0.254750924177 4.20557391349
absolute error = 0.0001297
relative error = 0.003077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.874
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9496 1.993
h = 0.001 0.001
y[1] (numeric) = -0.251999619345 4.21122613384
y[1] (closed_form) = -0.252049652815 4.21110715113
absolute error = 0.0001291
relative error = 0.00306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.876
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9506 1.994
h = 0.001 0.003
y[1] (numeric) = -0.249289421574 4.21225868935
y[1] (closed_form) = -0.249339688193 4.21214031569
absolute error = 0.0001286
relative error = 0.003048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.877
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9516 1.997
h = 0.0001 0.004
y[1] (numeric) = -0.244903352214 4.21703323606
y[1] (closed_form) = -0.244953093696 4.2169136416
absolute error = 0.0001295
relative error = 0.003066 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.879
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9517 2.001
h = 0.003 0.006
y[1] (numeric) = -0.241359728585 4.22442706551
y[1] (closed_form) = -0.241408350472 4.22430731741
absolute error = 0.0001292
relative error = 0.003055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.881
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9547 2.007
h = 0.0001 0.005
y[1] (numeric) = -0.230712160181 4.23311419297
y[1] (closed_form) = -0.230763996478 4.23299067345
absolute error = 0.000134
relative error = 0.00316 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.886
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9548 2.012
h = 0.0001 0.003
y[1] (numeric) = -0.226320287774 4.24235353102
y[1] (closed_form) = -0.226370485522 4.24223277167
absolute error = 0.0001308
relative error = 0.003078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.888
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9549 2.015
h = 0.001 0.001
y[1] (numeric) = -0.223605674641 4.24786020583
y[1] (closed_form) = -0.223656669782 4.24774041647
absolute error = 0.0001302
relative error = 0.003061 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.889
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9559 2.016
h = 0.0001 0.004
y[1] (numeric) = -0.220899410293 4.24887992951
y[1] (closed_form) = -0.220950632821 4.24876074744
absolute error = 0.0001297
relative error = 0.003049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.891
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.956 2.02
h = 0.003 0.006
y[1] (numeric) = -0.217341891007 4.25624602379
y[1] (closed_form) = -0.217390928708 4.25612539825
absolute error = 0.0001302
relative error = 0.003055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.892
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.959 2.026
h = 0.0001 0.005
y[1] (numeric) = -0.206692364449 4.26487848001
y[1] (closed_form) = -0.206744624952 4.26475412153
absolute error = 0.0001349
relative error = 0.003159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.898
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9591 2.031
h = 0.0001 0.003
y[1] (numeric) = -0.20228179912 4.27408170044
y[1] (closed_form) = -0.202332411528 4.2739600785
absolute error = 0.0001317
relative error = 0.003079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9592 2.034
h = 0.001 0.001
y[1] (numeric) = -0.199556300419 4.27956653428
y[1] (closed_form) = -0.199607700255 4.2794458827
absolute error = 0.0001311
relative error = 0.003061 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.901
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9602 2.035
h = 0.001 0.003
y[1] (numeric) = -0.196853327368 4.28057524616
y[1] (closed_form) = -0.196904949665 4.28045520037
absolute error = 0.0001307
relative error = 0.00305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.903
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9612 2.038
h = 0.0001 0.004
y[1] (numeric) = -0.19245785548 4.28529491284
y[1] (closed_form) = -0.192508974665 4.285173652
absolute error = 0.0001316
relative error = 0.003068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.905
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9613 2.042
h = 0.003 0.006
y[1] (numeric) = -0.188882665415 4.29262584047
y[1] (closed_form) = -0.188932678867 4.2925044125
absolute error = 0.0001313
relative error = 0.003056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.906
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9643 2.048
h = 0.0001 0.005
y[1] (numeric) = -0.178232181346 4.30119508741
y[1] (closed_form) = -0.178285426203 4.30106997108
absolute error = 0.000136
relative error = 0.003159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.912
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9644 2.053
h = 0.0001 0.003
y[1] (numeric) = -0.173800881133 4.31035613472
y[1] (closed_form) = -0.173852467551 4.31023372744
absolute error = 0.0001328
relative error = 0.003079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.914
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9645 2.056
h = 0.001 0.001
y[1] (numeric) = -0.171063326952 4.31581547593
y[1] (closed_form) = -0.171115689309 4.31569403914
absolute error = 0.0001322
relative error = 0.003062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.915
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9655 2.057
h = 0.001 0.003
y[1] (numeric) = -0.168364418871 4.31681154422
y[1] (closed_form) = -0.168416998053 4.31669071137
absolute error = 0.0001318
relative error = 0.00305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.916
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9665 2.06
h = 0.0001 0.004
y[1] (numeric) = -0.163964428543 4.32150187563
y[1] (closed_form) = -0.164016516236 4.32137983104
absolute error = 0.0001327
relative error = 0.003068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.919
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9666 2.064
h = 0.003 0.006
y[1] (numeric) = -0.160372978529 4.32879899355
y[1] (closed_form) = -0.160423968006 4.32867677482
absolute error = 0.0001324
relative error = 0.003057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.92
Order of pole (given) = 1 0
NO 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=487.4MB, alloc=44.3MB, time=6.56
x[1] = 2.9696 2.07
h = 0.0001 0.005
y[1] (numeric) = -0.149721998184 4.33730538512
y[1] (closed_form) = -0.149776227114 4.33717952234
absolute error = 0.000137
relative error = 0.003158 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.926
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9697 2.075
h = 0.0001 0.003
y[1] (numeric) = -0.145270384855 4.3464243508
y[1] (closed_form) = -0.145322945385 4.34630116968
absolute error = 0.0001339
relative error = 0.00308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.928
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9698 2.078
h = 0.001 0.001
y[1] (numeric) = -0.142521027324 4.35185825834
y[1] (closed_form) = -0.1425743524 4.35173604772
absolute error = 0.0001333
relative error = 0.003062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.929
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9708 2.079
h = 0.001 0.003
y[1] (numeric) = -0.139826251832 4.3528417845
y[1] (closed_form) = -0.139879788166 4.35272017593
absolute error = 0.0001329
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.931
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9718 2.082
h = 0.0001 0.004
y[1] (numeric) = -0.13542197962 4.35750291575
y[1] (closed_form) = -0.135475035954 4.35738009884
absolute error = 0.0001338
relative error = 0.003069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.933
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9719 2.086
h = 0.003 0.006
y[1] (numeric) = -0.131814605197 4.36476630044
y[1] (closed_form) = -0.131866570842 4.36464330253
absolute error = 0.0001335
relative error = 0.003058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.934
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9749 2.092
h = 0.0001 0.005
y[1] (numeric) = -0.12116358205 4.37321019248
y[1] (closed_form) = -0.121218794651 4.37308359451
absolute error = 0.0001381
relative error = 0.003157 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.94
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.975 2.097
h = 0.0001 0.003
y[1] (numeric) = -0.116692072773 4.38228717174
y[1] (closed_form) = -0.116745607394 4.3821632282
absolute error = 0.000135
relative error = 0.00308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.942
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9751 2.1
h = 0.001 0.001
y[1] (numeric) = -0.113931161225 4.38769570678
y[1] (closed_form) = -0.113985449097 4.38757273363
absolute error = 0.0001344
relative error = 0.003063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.943
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9761 2.101
h = 0.001 0.003
y[1] (numeric) = -0.111240584275 4.38866679213
y[1] (closed_form) = -0.111295077906 4.38854441909
absolute error = 0.000134
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.945
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9771 2.104
h = 0.0001 0.004
y[1] (numeric) = -0.106832263256 4.39329885967
y[1] (closed_form) = -0.106886288241 4.3931752818
absolute error = 0.0001349
relative error = 0.003069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.947
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9772 2.108
h = 0.003 0.006
y[1] (numeric) = -0.103209296266 4.40052859055
y[1] (closed_form) = -0.103262238096 4.40040482495
absolute error = 0.0001346
relative error = 0.003058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.949
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9802 2.114
h = 0.0001 0.005
y[1] (numeric) = -0.0925586760892 4.40891034068
y[1] (closed_form) = -0.0926148718467 4.40878301873
absolute error = 0.0001392
relative error = 0.003156 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.954
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9803 2.119
h = 0.0001 0.003
y[1] (numeric) = -0.0880676834372 4.41794543239
y[1] (closed_form) = -0.0881221920048 4.41782073774
absolute error = 0.0001361
relative error = 0.00308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.956
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9804 2.122
h = 0.001 0.001
y[1] (numeric) = -0.0852954644085 4.42332865823
y[1] (closed_form) = -0.0853507150302 4.42320493375
absolute error = 0.0001355
relative error = 0.003063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.958
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9814 2.123
h = 0.0001 0.004
y[1] (numeric) = -0.0826091503057 4.42428740391
y[1] (closed_form) = -0.0826646012554 4.42416427754
absolute error = 0.000135
relative error = 0.003052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.959
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9815 2.127
h = 0.003 0.006
y[1] (numeric) = -0.0789736230631 4.43148969715
y[1] (closed_form) = -0.0790269993245 4.43136509305
absolute error = 0.0001356
relative error = 0.003059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.961
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9845 2.133
h = 0.0001 0.005
y[1] (numeric) = -0.0683229664746 4.43981823338
y[1] (closed_form) = -0.0683796027597 4.43969011022
absolute error = 0.0001401
relative error = 0.003155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.966
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9846 2.138
h = 0.0001 0.003
y[1] (numeric) = -0.063815032752 4.44881757701
y[1] (closed_form) = -0.0638699738929 4.44869205803
absolute error = 0.000137
relative error = 0.00308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.968
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9847 2.141
h = 0.001 0.001
y[1] (numeric) = -0.0610329754908 4.45417920055
y[1] (closed_form) = -0.0610886491225 4.45405465158
absolute error = 0.0001364
relative error = 0.003063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.97
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9857 2.142
h = 0.001 0.003
y[1] (numeric) = -0.0583502356029 4.45512735371
y[1] (closed_form) = -0.0584061049179 4.45500340118
absolute error = 0.000136
relative error = 0.003052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.971
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9867 2.145
h = 0.0001 0.004
y[1] (numeric) = -0.0539346469141 4.45970575
y[1] (closed_form) = -0.0539900683938 4.45958059925
absolute error = 0.0001369
relative error = 0.003069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.973
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9868 2.149
h = 0.003 0.006
y[1] (numeric) = -0.0502831378182 4.46687325662
y[1] (closed_form) = -0.0503374901049 4.46674790592
absolute error = 0.0001366
relative error = 0.003059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.975
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9898 2.155
h = 0.0001 0.005
y[1] (numeric) = -0.0396336977055 4.47514031563
y[1] (closed_form) = -0.0396913160179 4.47501148902
absolute error = 0.0001411
relative error = 0.003153 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.98
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9899 2.16
h = 0.0001 0.003
y[1] (numeric) = -0.0351070373469 4.48409796018
y[1] (closed_form) = -0.0351629519838 4.48397171089
absolute error = 0.0001381
relative error = 0.003079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.982
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.99 2.163
h = 0.001 0.001
y[1] (numeric) = -0.0323141247326 4.4894343949
y[1] (closed_form) = -0.0323707608465 4.48930911517
absolute error = 0.0001375
relative error = 0.003062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.984
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.991 2.164
h = 0.001 0.003
y[1] (numeric) = -0.0296357642383 4.49037039534
y[1] (closed_form) = -0.0296925907301 4.49024571
absolute error = 0.000137
relative error = 0.003052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.985
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.992 2.167
h = 0.0001 0.004
y[1] (numeric) = -0.0252167761824 4.49492012272
y[1] (closed_form) = -0.0252731658082 4.49479424292
absolute error = 0.0001379
relative error = 0.003069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.987
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9921 2.171
h = 0.003 0.006
y[1] (numeric) = -0.0215506044814 4.50205421436
y[1] (closed_form) = -0.0216059324643 4.50192812827
absolute error = 0.0001377
relative error = 0.003058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.989
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9951 2.177
h = 0.0001 0.005
y[1] (numeric) = -0.010902804957 4.5102601583
y[1] (closed_form) = -0.0109614044633 4.51013063913
absolute error = 0.0001422
relative error = 0.003152 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.995
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9952 2.182
h = 0.0001 0.003
y[1] (numeric) = -0.00635781743056 4.51917621249
y[1] (closed_form) = -0.006414705085 4.51904924392
absolute error = 0.0001391
relative error = 0.003079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.997
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9953 2.185
h = 0.001 0.001
y[1] (numeric) = -0.00355428804079 4.52448752746
y[1] (closed_form) = -0.00361188625816 4.52436152791
absolute error = 0.0001385
relative error = 0.003062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.998
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9963 2.186
h = 0.001 0.003
y[1] (numeric) = -0.000880366649907 4.52541147576
y[1] (closed_form) = -0.000938150007039 4.52528606848
absolute error = 0.0001381
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9973 2.189
h = 0.0001 0.004
y[1] (numeric) = 0.00354180090968 4.52993267546
y[1] (closed_form) = 0.0034844435832 4.52980607756
absolute error = 0.000139
relative error = 0.003068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.002
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.9974 2.193
h = 0.003 0.006
y[1] (numeric) = 0.0072223176043 4.5370334421
y[1] (closed_form) = 0.00716601436968 4.53690663172
absolute error = 0.0001387
relative error = 0.003058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.004
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0004 2.199
h = 0.0001 0.005
y[1] (numeric) = 0.0178680598797 4.54517863441
y[1] (closed_form) = 0.0178084801179 4.54504843347
absolute error = 0.0001432
relative error = 0.00315 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.009
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0005 2.204
h = 0.0001 0.003
y[1] (numeric) = 0.0224309796904 4.55405321019
y[1] (closed_form) = 0.0223731196082 4.55392553327
absolute error = 0.0001402
relative error = 0.003078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.011
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0006 2.207
h = 0.001 0.001
y[1] (numeric) = 0.0252448900607 4.5593394764
y[1] (closed_form) = 0.0251863302295 4.55921276783
absolute error = 0.0001396
relative error = 0.003062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.013
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0016 2.208
h = 0.001 0.003
y[1] (numeric) = 0.0279143142028 4.56025147286
y[1] (closed_form) = 0.0278555744028 4.56012535444
absolute error = 0.0001391
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.014
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0026 2.211
h = 0.0001 0.004
y[1] (numeric) = 0.0323394447745 4.56474428717
y[1] (closed_form) = 0.0322811203034 4.56461698205
absolute error = 0.00014
relative error = 0.003068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.016
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0027 2.215
h = 0.003 0.006
y[1] (numeric) = 0.0360339925338 4.57181182134
y[1] (closed_form) = 0.0359767146046 4.57168429766
absolute error = 0.0001398
relative error = 0.003058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.018
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0057 2.221
h = 0.0001 0.005
y[1] (numeric) = 0.0466772682831 4.57989662666
y[1] (closed_form) = 0.046616709307 4.57976575462
absolute error = 0.0001442
relative error = 0.003149 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.023
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0058 2.226
h = 0.0001 0.003
y[1] (numeric) = 0.0512577300709 4.5887298391
y[1] (closed_form) = 0.0511988982595 4.58860146467
absolute error = 0.0001412
relative error = 0.003077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.026
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0059 2.229
h = 0.001 0.001
y[1] (numeric) = 0.0540817884037 4.59399112935
y[1] (closed_form) = 0.0540222675565 4.59386372249
absolute error = 0.0001406
relative error = 0.003061 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.027
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0069 2.23
h = 0.0001 0.004
y[1] (numeric) = 0.0567466586945 4.59489127403
y[1] (closed_form) = 0.0566869629826 4.59476445515
absolute error = 0.0001402
relative error = 0.00305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.028
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.007 2.234
h = 0.003 0.006
y[1] (numeric) = 0.0604525023011 4.60193172219
y[1] (closed_form) = 0.0603947740698 4.60180339823
absolute error = 0.0001407
relative error = 0.003057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.03
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.01 2.24
h = 0.0001 0.005
y[1] (numeric) = 0.071094046194 4.60996480533
y[1] (closed_form) = 0.0710330329078 4.60983316904
absolute error = 0.0001451
relative error = 0.003147 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.036
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0101 2.245
h = 0.0001 0.003
y[1] (numeric) = 0.0756897892679 4.61876271079
y[1] (closed_form) = 0.0756305096319 4.61863354956
absolute error = 0.0001421
relative error = 0.003077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.038
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0102 2.248
h = 0.001 0.001
y[1] (numeric) = 0.078522694449 4.62400267936
y[1] (closed_form) = 0.078462734929 4.62387448509
absolute error = 0.0001415
relative error = 0.00306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.039
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0112 2.249
h = 0.001 0.003
y[1] (numeric) = 0.0811837403345 4.62489264718
y[1] (closed_form) = 0.0811236103163 4.62476503906
absolute error = 0.0001411
relative error = 0.00305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.041
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0122 2.252
h = 0.0001 0.004
y[1] (numeric) = 0.0856141537058 4.62933305442
y[1] (closed_form) = 0.0855544194081 4.62920426695
absolute error = 0.000142
relative error = 0.003066 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.043
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0123 2.256
h = 0.003 0.006
y[1] (numeric) = 0.0893343801984 4.63633916376
y[1] (closed_form) = 0.0892756784714 4.63621014671
absolute error = 0.0001417
relative error = 0.003057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.045
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0153 2.262
h = 0.0001 0.005
y[1] (numeric) = 0.0999727110399 4.6443125365
y[1] (closed_form) = 0.0999107206162 4.64418024873
absolute error = 0.0001461
relative error = 0.003145 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.05
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0154 2.267
h = 0.0001 0.003
y[1] (numeric) = 0.104585280512 4.65306929624
y[1] (closed_form) = 0.1045250306 4.65293945739
absolute error = 0.0001431
relative error = 0.003075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.053
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0155 2.27
h = 0.001 0.001
y[1] (numeric) = 0.107427906513 4.65828442629
y[1] (closed_form) = 0.107366987244 4.65815555343
absolute error = 0.0001425
relative error = 0.003059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.054
Order of pole (given) = 1 0
NO 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=536.2MB, alloc=44.3MB, time=7.21
x[1] = 3.0165 2.271
h = 0.001 0.003
y[1] (numeric) = 0.110084296072 4.65916272709
y[1] (closed_form) = 0.110023211286 4.65903443815
absolute error = 0.0001421
relative error = 0.003049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.055
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0175 2.274
h = 0.0001 0.004
y[1] (numeric) = 0.114517069793 4.66357515895
y[1] (closed_form) = 0.114456370404 4.66344569479
absolute error = 0.000143
relative error = 0.003065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.058
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0176 2.278
h = 0.003 0.006
y[1] (numeric) = 0.118250448339 4.67054831015
y[1] (closed_form) = 0.118190773982 4.67041861072
absolute error = 0.0001428
relative error = 0.003056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.059
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0206 2.284
h = 0.0001 0.005
y[1] (numeric) = 0.128885177581 4.67846233999
y[1] (closed_form) = 0.128822211342 4.67832941112
absolute error = 0.0001471
relative error = 0.003143 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.065
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0207 2.289
h = 0.0001 0.003
y[1] (numeric) = 0.133514196144 4.68717807755
y[1] (closed_form) = 0.133452976952 4.68704757162
absolute error = 0.0001442
relative error = 0.003074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0208 2.292
h = 0.001 0.001
y[1] (numeric) = 0.136366317829 4.69236844682
y[1] (closed_form) = 0.136304439706 4.69223890582
absolute error = 0.0001436
relative error = 0.003058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0218 2.293
h = 0.001 0.003
y[1] (numeric) = 0.139017998759 4.69323517981
y[1] (closed_form) = 0.138955960033 4.69310622048
absolute error = 0.0001431
relative error = 0.003048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0228 2.296
h = 0.0001 0.004
y[1] (numeric) = 0.143452929113 4.69761978221
y[1] (closed_form) = 0.143391265593 4.69748965186
absolute error = 0.000144
relative error = 0.003064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0229 2.3
h = 0.003 0.006
y[1] (numeric) = 0.147199159892 4.70456007687
y[1] (closed_form) = 0.147138513873 4.70442970566
absolute error = 0.0001438
relative error = 0.003055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0259 2.306
h = 0.0001 0.005
y[1] (numeric) = 0.157829906103 4.71241513205
y[1] (closed_form) = 0.157765965461 4.71228157237
absolute error = 0.0001481
relative error = 0.003141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.08
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.026 2.311
h = 0.0001 0.003
y[1] (numeric) = 0.162475000979 4.72108997373
y[1] (closed_form) = 0.162412813601 4.72095881116
absolute error = 0.0001452
relative error = 0.003073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.082
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0261 2.314
h = 0.001 0.001
y[1] (numeric) = 0.165336395959 4.72625566157
y[1] (closed_form) = 0.165273559974 4.72612546278
absolute error = 0.0001446
relative error = 0.003057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.083
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0271 2.315
h = 0.001 0.003
y[1] (numeric) = 0.167983317416 4.72711092564
y[1] (closed_form) = 0.167920325677 4.72698130621
absolute error = 0.0001441
relative error = 0.003047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0281 2.318
h = 0.0001 0.004
y[1] (numeric) = 0.172420203937 4.7314678453
y[1] (closed_form) = 0.172357577344 4.73133705912
absolute error = 0.000145
relative error = 0.003063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.087
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0282 2.322
h = 0.003 0.006
y[1] (numeric) = 0.176178990765 4.73837538714
y[1] (closed_form) = 0.176117374151 4.73824435466
absolute error = 0.0001448
relative error = 0.003054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.089
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0312 2.328
h = 0.0001 0.005
y[1] (numeric) = 0.18680537955 4.74617183656
y[1] (closed_form) = 0.186740466011 4.74603765624
absolute error = 0.0001491
relative error = 0.003138 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.094
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0313 2.333
h = 0.0001 0.003
y[1] (numeric) = 0.19146618248 4.75480591133
y[1] (closed_form) = 0.191403028107 4.75467410246
absolute error = 0.0001462
relative error = 0.003071 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.097
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0314 2.336
h = 0.001 0.001
y[1] (numeric) = 0.194336631101 4.75994699864
y[1] (closed_form) = 0.194272838343 4.7598161523
absolute error = 0.0001456
relative error = 0.003056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0324 2.337
h = 0.0001 0.004
y[1] (numeric) = 0.196978743679 4.76079089231
y[1] (closed_form) = 0.196914799953 4.76066062301
absolute error = 0.0001451
relative error = 0.003046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.099
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0325 2.341
h = 0.003 0.006
y[1] (numeric) = 0.200747632446 4.76767174622
y[1] (closed_form) = 0.200685552203 4.76753995084
absolute error = 0.0001457
relative error = 0.003053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.101
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0355 2.347
h = 0.0001 0.005
y[1] (numeric) = 0.211370668146 4.77541798774
y[1] (closed_form) = 0.211305288859 4.77528307921
absolute error = 0.0001499
relative error = 0.003136 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.107
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0356 2.352
h = 0.0001 0.003
y[1] (numeric) = 0.216045184063 4.78401725817
y[1] (closed_form) = 0.21598156908 4.78388469919
absolute error = 0.000147
relative error = 0.00307 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.109
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0357 2.355
h = 0.001 0.001
y[1] (numeric) = 0.218923543646 4.78913734044
y[1] (closed_form) = 0.218859299012 4.78900574296
absolute error = 0.0001464
relative error = 0.003055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.111
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0367 2.356
h = 0.001 0.003
y[1] (numeric) = 0.221561612276 4.7899714674
y[1] (closed_form) = 0.221497220768 4.789840445
absolute error = 0.000146
relative error = 0.003045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.112
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0377 2.359
h = 0.0001 0.004
y[1] (numeric) = 0.226001941832 4.79427728676
y[1] (closed_form) = 0.225937897043 4.79414510559
absolute error = 0.0001469
relative error = 0.00306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.114
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0378 2.363
h = 0.003 0.006
y[1] (numeric) = 0.229783703759 4.80112430784
y[1] (closed_form) = 0.229720655044 4.80099187047
absolute error = 0.0001467
relative error = 0.003052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.116
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0408 2.369
h = 0.0001 0.005
y[1] (numeric) = 0.240401699461 4.80881262716
y[1] (closed_form) = 0.24033535019 4.80867711666
absolute error = 0.0001509
relative error = 0.003134 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.122
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0409 2.374
h = 0.0001 0.003
y[1] (numeric) = 0.245091248539 4.81737137316
y[1] (closed_form) = 0.245026668903 4.81723818686
absolute error = 0.000148
relative error = 0.003069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.124
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.041 2.377
h = 0.001 0.001
y[1] (numeric) = 0.247978259275 4.82246700684
y[1] (closed_form) = 0.247913060022 4.82233478063
absolute error = 0.0001474
relative error = 0.003053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.126
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.042 2.378
h = 0.001 0.003
y[1] (numeric) = 0.25061142969 4.82328994521
y[1] (closed_form) = 0.250546088226 4.8231582917
absolute error = 0.000147
relative error = 0.003043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.127
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.043 2.381
h = 0.0001 0.004
y[1] (numeric) = 0.25505315785 4.82756850322
y[1] (closed_form) = 0.254988153417 4.82743569539
absolute error = 0.0001479
relative error = 0.003059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.129
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0431 2.385
h = 0.003 0.006
y[1] (numeric) = 0.258846647143 4.83438307609
y[1] (closed_form) = 0.258782631295 4.83425000696
absolute error = 0.0001477
relative error = 0.00305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.131
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0461 2.391
h = 0.0001 0.005
y[1] (numeric) = 0.26945924819 4.84201384351
y[1] (closed_form) = 0.269391930684 4.84187774093
absolute error = 0.0001518
relative error = 0.003131 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.137
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0462 2.396
h = 0.0001 0.003
y[1] (numeric) = 0.274163474962 4.85053220122
y[1] (closed_form) = 0.274097932126 4.85039839765
absolute error = 0.000149
relative error = 0.003067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.139
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0463 2.399
h = 0.001 0.001
y[1] (numeric) = 0.277058924942 4.85560347139
y[1] (closed_form) = 0.276992772422 4.8554706264
absolute error = 0.0001484
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0473 2.4
h = 0.001 0.003
y[1] (numeric) = 0.279687151738 4.85641531863
y[1] (closed_form) = 0.279620861608 4.85628304395
absolute error = 0.000148
relative error = 0.003042 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.142
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0483 2.403
h = 0.0001 0.004
y[1] (numeric) = 0.284130090319 4.86066676463
y[1] (closed_form) = 0.284064127656 4.86053334012
absolute error = 0.0001488
relative error = 0.003057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.144
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0484 2.407
h = 0.003 0.006
y[1] (numeric) = 0.28793502467 4.8674490007
y[1] (closed_form) = 0.28787004312 4.86731530991
absolute error = 0.0001486
relative error = 0.003049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.146
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0514 2.413
h = 0.0001 0.005
y[1] (numeric) = 0.298541883161 4.87502258678
y[1] (closed_form) = 0.298473599252 4.8748859019
absolute error = 0.0001528
relative error = 0.003128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.151
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0515 2.418
h = 0.0001 0.003
y[1] (numeric) = 0.303260436607 4.88350069465
y[1] (closed_form) = 0.30319393211 4.88336628375
absolute error = 0.00015
relative error = 0.003065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.154
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0516 2.421
h = 0.001 0.001
y[1] (numeric) = 0.306164116611 4.88854768774
y[1] (closed_form) = 0.306097012261 4.88841423383
absolute error = 0.0001494
relative error = 0.00305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.155
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0526 2.422
h = 0.001 0.003
y[1] (numeric) = 0.308787355744 4.8893485409
y[1] (closed_form) = 0.308720118321 4.88921565488
absolute error = 0.0001489
relative error = 0.00304 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.157
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0536 2.425
h = 0.0001 0.004
y[1] (numeric) = 0.313231319672 4.89357302478
y[1] (closed_form) = 0.313164400282 4.89343899349
absolute error = 0.0001498
relative error = 0.003055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.159
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0537 2.429
h = 0.003 0.006
y[1] (numeric) = 0.317047420336 4.90032303726
y[1] (closed_form) = 0.316981474603 4.90018873483
absolute error = 0.0001496
relative error = 0.003047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.161
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0567 2.435
h = 0.0001 0.005
y[1] (numeric) = 0.327648195054 4.90783981276
y[1] (closed_form) = 0.327578946652 4.90770255524
absolute error = 0.0001537
relative error = 0.003126 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.167
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0568 2.44
h = 0.0001 0.003
y[1] (numeric) = 0.332380728575 4.91627781147
y[1] (closed_form) = 0.332313264042 4.91614280309
absolute error = 0.0001509
relative error = 0.003063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.169
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0569 2.443
h = 0.001 0.001
y[1] (numeric) = 0.33529243206 4.92130061518
y[1] (closed_form) = 0.335224377404 4.92116656212
absolute error = 0.0001503
relative error = 0.003048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0579 2.444
h = 0.0001 0.004
y[1] (numeric) = 0.337910640821 4.92209057092
y[1] (closed_form) = 0.337842457563 4.9219570833
absolute error = 0.0001499
relative error = 0.003038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.172
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.058 2.448
h = 0.003 0.006
y[1] (numeric) = 0.34173571894 4.92881433293
y[1] (closed_form) = 0.341669298599 4.928679304
absolute error = 0.0001505
relative error = 0.003046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.174
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.061 2.454
h = 0.0001 0.005
y[1] (numeric) = 0.352331659474 4.93628242684
y[1] (closed_form) = 0.352261936044 4.93614447615
absolute error = 0.0001546
relative error = 0.003123 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.179
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0611 2.459
h = 0.0001 0.003
y[1] (numeric) = 0.357076427852 4.94468617623
y[1] (closed_form) = 0.357008492195 4.94455045347
absolute error = 0.0001518
relative error = 0.003062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.182
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0612 2.462
h = 0.001 0.001
y[1] (numeric) = 0.359995161018 4.949688322
y[1] (closed_form) = 0.359926643553 4.94955355317
absolute error = 0.0001512
relative error = 0.003046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.183
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0622 2.463
h = 0.001 0.003
y[1] (numeric) = 0.362609134856 4.95046891406
y[1] (closed_form) = 0.362540492619 4.95033470861
absolute error = 0.0001507
relative error = 0.003037 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.185
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0632 2.466
h = 0.0001 0.004
y[1] (numeric) = 0.36705484162 4.95464363552
y[1] (closed_form) = 0.366986500145 4.95450829329
absolute error = 0.0001516
relative error = 0.003052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.187
Order of pole (given) = 1 0
NO 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=584.9MB, alloc=44.3MB, time=7.85
x[1] = 3.0633 2.47
h = 0.003 0.006
y[1] (numeric) = 0.370891371001 4.96133411996
y[1] (closed_form) = 0.37082398941 4.96119849776
absolute error = 0.0001514
relative error = 0.003044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.189
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0663 2.476
h = 0.0001 0.005
y[1] (numeric) = 0.381480605945 4.96874608946
y[1] (closed_form) = 0.381409921665 4.96860758387
absolute error = 0.0001555
relative error = 0.00312 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.194
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0664 2.481
h = 0.0001 0.003
y[1] (numeric) = 0.386238719421 4.97710999314
y[1] (closed_form) = 0.386169826852 4.97697369096
absolute error = 0.0001527
relative error = 0.003059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.197
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0665 2.484
h = 0.001 0.001
y[1] (numeric) = 0.389165097731 4.98208811364
y[1] (closed_form) = 0.389095632896 4.98195276357
absolute error = 0.0001521
relative error = 0.003044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.198
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0675 2.485
h = 0.001 0.003
y[1] (numeric) = 0.391773964068 4.98285798648
y[1] (closed_form) = 0.391704378817 4.9827231973
absolute error = 0.0001517
relative error = 0.003035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0685 2.488
h = 0.0001 0.004
y[1] (numeric) = 0.396220181865 4.98700617515
y[1] (closed_form) = 0.396150888302 4.9868702539
absolute error = 0.0001526
relative error = 0.00305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.202
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0686 2.492
h = 0.003 0.006
y[1] (numeric) = 0.400067098221 4.99366476605
y[1] (closed_form) = 0.399998757139 4.99352856028
absolute error = 0.0001524
relative error = 0.003042 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.204
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0716 2.498
h = 0.0001 0.005
y[1] (numeric) = 0.410649305057 5.001020982
y[1] (closed_form) = 0.410577662051 5.0008819309
absolute error = 0.0001564
relative error = 0.003117 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0717 2.503
h = 0.0001 0.003
y[1] (numeric) = 0.41542042954 5.00934518663
y[1] (closed_form) = 0.415350581911 5.00920831459
absolute error = 0.0001537
relative error = 0.003057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.212
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0718 2.506
h = 0.001 0.001
y[1] (numeric) = 0.418354254009 5.01429937304
y[1] (closed_form) = 0.418283843556 5.01416345121
absolute error = 0.0001531
relative error = 0.003042 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.214
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0728 2.507
h = 0.001 0.003
y[1] (numeric) = 0.420957973845 5.01505862205
y[1] (closed_form) = 0.420887447271 5.01492325861
absolute error = 0.0001526
relative error = 0.003033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.215
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0738 2.51
h = 0.0001 0.004
y[1] (numeric) = 0.425404529347 5.01918042956
y[1] (closed_form) = 0.425334285512 5.01904393878
absolute error = 0.0001535
relative error = 0.003048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.217
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0739 2.514
h = 0.003 0.006
y[1] (numeric) = 0.42926156749 5.02580724652
y[1] (closed_form) = 0.429192268753 5.0256704668
absolute error = 0.0001533
relative error = 0.00304 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.219
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0769 2.52
h = 0.0001 0.005
y[1] (numeric) = 0.43983643009 5.03310807962
y[1] (closed_form) = 0.439763830552 5.03296849227
absolute error = 0.0001573
relative error = 0.003114 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.225
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.077 2.525
h = 0.0001 0.003
y[1] (numeric) = 0.444620235817 5.0413927338
y[1] (closed_form) = 0.444549435059 5.04125530134
absolute error = 0.0001546
relative error = 0.003055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.227
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0771 2.528
h = 0.001 0.001
y[1] (numeric) = 0.447561310078 5.0463230784
y[1] (closed_form) = 0.447489955836 5.04618659418
absolute error = 0.000154
relative error = 0.00304 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.229
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0781 2.529
h = 0.001 0.003
y[1] (numeric) = 0.450159845671 5.04707179852
y[1] (closed_form) = 0.450088379539 5.04693587017
absolute error = 0.0001536
relative error = 0.003031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0791 2.532
h = 0.0001 0.004
y[1] (numeric) = 0.454606568519 5.05116737681
y[1] (closed_form) = 0.454535376302 5.05103032591
absolute error = 0.0001544
relative error = 0.003045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.233
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0792 2.536
h = 0.003 0.006
y[1] (numeric) = 0.458473466728 5.05776254091
y[1] (closed_form) = 0.45840321225 5.05762519675
absolute error = 0.0001543
relative error = 0.003038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.235
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0822 2.542
h = 0.0001 0.005
y[1] (numeric) = 0.469040675276 5.06500836164
y[1] (closed_form) = 0.468967121469 5.06486824722
absolute error = 0.0001582
relative error = 0.003111 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0823 2.547
h = 0.0001 0.003
y[1] (numeric) = 0.473836836793 5.07325361581
y[1] (closed_form) = 0.473765084908 5.07311563229
absolute error = 0.0001555
relative error = 0.003052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.243
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0824 2.55
h = 0.001 0.001
y[1] (numeric) = 0.47678496708 5.07816021194
y[1] (closed_form) = 0.47671267095 5.07802317462
absolute error = 0.0001549
relative error = 0.003038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.244
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0834 2.551
h = 0.0001 0.004
y[1] (numeric) = 0.479378281921 5.07889849763
y[1] (closed_form) = 0.479305878073 5.07876201363
absolute error = 0.0001545
relative error = 0.003029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.245
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0835 2.555
h = 0.003 0.006
y[1] (numeric) = 0.483253100997 5.08546788164
y[1] (closed_form) = 0.483182363082 5.08532984635
absolute error = 0.0001551
relative error = 0.003036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.248
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0865 2.561
h = 0.0001 0.005
y[1] (numeric) = 0.49381412717 5.09266654991
y[1] (closed_form) = 0.493740091029 5.09252577627
absolute error = 0.0001591
relative error = 0.003109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.253
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0866 2.566
h = 0.0001 0.003
y[1] (numeric) = 0.498621133654 5.10087815366
y[1] (closed_form) = 0.498548902216 5.10073949045
absolute error = 0.0001563
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.256
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0867 2.569
h = 0.001 0.001
y[1] (numeric) = 0.501575465702 5.10576446438
y[1] (closed_form) = 0.501502697918 5.10562674567
absolute error = 0.0001558
relative error = 0.003036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.257
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0877 2.57
h = 0.001 0.003
y[1] (numeric) = 0.504164381158 5.10649378099
y[1] (closed_form) = 0.504091509229 5.10635661344
absolute error = 0.0001553
relative error = 0.003027 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.259
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0887 2.573
h = 0.0001 0.004
y[1] (numeric) = 0.508611280185 5.11054095553
y[1] (closed_form) = 0.508538666018 5.11040267436
absolute error = 0.0001562
relative error = 0.003041 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.261
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0888 2.577
h = 0.003 0.006
y[1] (numeric) = 0.512496214459 5.11707765841
y[1] (closed_form) = 0.512424524447 5.11693907614
absolute error = 0.000156
relative error = 0.003034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.263
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0918 2.583
h = 0.0001 0.005
y[1] (numeric) = 0.523049022224 5.12422199929
y[1] (closed_form) = 0.52297403609 5.12408071541
absolute error = 0.00016
relative error = 0.003105 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.268
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0919 2.588
h = 0.0001 0.003
y[1] (numeric) = 0.527867788429 5.13239448383
y[1] (closed_form) = 0.52779460967 5.13225528671
absolute error = 0.0001573
relative error = 0.003048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.271
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.092 2.591
h = 0.001 0.001
y[1] (numeric) = 0.530828821673 5.13725722022
y[1] (closed_form) = 0.530755115622 5.13711896543
absolute error = 0.0001567
relative error = 0.003034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.273
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.093 2.592
h = 0.001 0.003
y[1] (numeric) = 0.533412450547 5.13797627647
y[1] (closed_form) = 0.533338644411 5.13783857027
absolute error = 0.0001562
relative error = 0.003025 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.274
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.094 2.595
h = 0.0001 0.004
y[1] (numeric) = 0.537859043875 5.14199765603
y[1] (closed_form) = 0.537785487024 5.14185884111
absolute error = 0.0001571
relative error = 0.003039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.276
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0941 2.599
h = 0.003 0.006
y[1] (numeric) = 0.541753106947 5.14850305713
y[1] (closed_form) = 0.541680466961 5.1483639371
absolute error = 0.0001569
relative error = 0.003032 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.278
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0971 2.605
h = 0.0001 0.005
y[1] (numeric) = 0.552297404131 5.15559344011
y[1] (closed_form) = 0.552221470451 5.15545165485
absolute error = 0.0001608
relative error = 0.003102 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.284
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0972 2.61
h = 0.0001 0.003
y[1] (numeric) = 0.55712761675 5.16372696078
y[1] (closed_form) = 0.557053492872 5.16358723881
absolute error = 0.0001582
relative error = 0.003045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.286
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0973 2.613
h = 0.001 0.001
y[1] (numeric) = 0.560095164759 5.16856621899
y[1] (closed_form) = 0.560020522542 5.16842743712
absolute error = 0.0001576
relative error = 0.003031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.288
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0983 2.614
h = 0.001 0.003
y[1] (numeric) = 0.562673473968 5.16927510796
y[1] (closed_form) = 0.562598735666 5.16913687209
absolute error = 0.0001571
relative error = 0.003022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.289
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0993 2.617
h = 0.0001 0.004
y[1] (numeric) = 0.567119602416 5.1732708454
y[1] (closed_form) = 0.567045105043 5.17313150575
absolute error = 0.000158
relative error = 0.003036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.292
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.0994 2.621
h = 0.003 0.006
y[1] (numeric) = 0.571022545729 5.17974507104
y[1] (closed_form) = 0.570948957957 5.17960542236
absolute error = 0.0001579
relative error = 0.003029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.294
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1024 2.627
h = 0.0001 0.005
y[1] (numeric) = 0.581558046175 5.18678186506
y[1] (closed_form) = 0.581481167457 5.18663958721
absolute error = 0.0001617
relative error = 0.003099 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.299
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1025 2.632
h = 0.0001 0.003
y[1] (numeric) = 0.5863993961 5.19487657876
y[1] (closed_form) = 0.58632432937 5.19473634091
absolute error = 0.0001591
relative error = 0.003043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.302
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1026 2.635
h = 0.001 0.001
y[1] (numeric) = 0.589373274973 5.19969245585
y[1] (closed_form) = 0.58929769876 5.1995531558
absolute error = 0.0001585
relative error = 0.003029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.304
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1036 2.636
h = 0.001 0.003
y[1] (numeric) = 0.591946232592 5.20039127009
y[1] (closed_form) = 0.591870564235 5.20025251343
absolute error = 0.000158
relative error = 0.00302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.305
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1046 2.639
h = 0.0001 0.004
y[1] (numeric) = 0.5963917398 5.20436151844
y[1] (closed_form) = 0.596316304134 5.20422166297
absolute error = 0.0001589
relative error = 0.003033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.307
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1047 2.643
h = 0.003 0.006
y[1] (numeric) = 0.600303318155 5.21080469612
y[1] (closed_form) = 0.600228784853 5.21066452782
absolute error = 0.0001588
relative error = 0.003027 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.309
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1077 2.649
h = 0.0001 0.005
y[1] (numeric) = 0.610829741649 5.21778826956
y[1] (closed_form) = 0.610751920457 5.21764550779
absolute error = 0.0001626
relative error = 0.003095 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.315
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1078 2.654
h = 0.0001 0.003
y[1] (numeric) = 0.615681923938 5.22584433467
y[1] (closed_form) = 0.615605916687 5.22570358979
absolute error = 0.00016
relative error = 0.00304 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.317
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1079 2.657
h = 0.001 0.001
y[1] (numeric) = 0.618661952292 5.23063692855
y[1] (closed_form) = 0.618585444314 5.23049711911
absolute error = 0.0001594
relative error = 0.003026 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.319
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1089 2.658
h = 0.0001 0.004
y[1] (numeric) = 0.621229527531 5.2313257601
y[1] (closed_form) = 0.621152931291 5.23118649144
absolute error = 0.0001589
relative error = 0.003017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.109 2.662
h = 0.003 0.006
y[1] (numeric) = 0.625148036153 5.23774365506
y[1] (closed_form) = 0.625073012553 5.23760282987
absolute error = 0.0001596
relative error = 0.003025 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.323
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.112 2.668
h = 0.0001 0.005
y[1] (numeric) = 0.635667054603 5.24468159993
y[1] (closed_form) = 0.635588745566 5.24453821178
absolute error = 0.0001634
relative error = 0.003093 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.328
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1121 2.673
h = 0.0001 0.003
y[1] (numeric) = 0.640528777789 5.2527046497
memory used=633.7MB, alloc=44.3MB, time=8.50
y[1] (closed_form) = 0.640452284463 5.25256325872
absolute error = 0.0001608
relative error = 0.003038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.331
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1122 2.676
h = 0.001 0.001
y[1] (numeric) = 0.643514231816 5.25747735154
y[1] (closed_form) = 0.643437245249 5.25733689402
absolute error = 0.0001602
relative error = 0.003024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.332
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1132 2.677
h = 0.001 0.003
y[1] (numeric) = 0.646077267713 5.25815759904
y[1] (closed_form) = 0.64600019621 5.25801768008
absolute error = 0.0001597
relative error = 0.003015 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.334
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1142 2.68
h = 0.0001 0.004
y[1] (numeric) = 0.650521511629 5.26208081405
y[1] (closed_form) = 0.650444657744 5.26193980552
absolute error = 0.0001606
relative error = 0.003029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.336
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1143 2.684
h = 0.003 0.006
y[1] (numeric) = 0.654448882773 5.26846665808
y[1] (closed_form) = 0.654372917904 5.26832532981
absolute error = 0.0001605
relative error = 0.003022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.338
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1173 2.69
h = 0.0001 0.005
y[1] (numeric) = 0.664958314034 5.27535206288
y[1] (closed_form) = 0.664879067345 5.27520820672
absolute error = 0.0001642
relative error = 0.003089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.344
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1174 2.695
h = 0.0001 0.003
y[1] (numeric) = 0.669830311225 5.28333675897
y[1] (closed_form) = 0.669752881774 5.28319487722
absolute error = 0.0001616
relative error = 0.003035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.346
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1175 2.698
h = 0.001 0.001
y[1] (numeric) = 0.672821582657 5.28808635981
y[1] (closed_form) = 0.672743668538 5.28794540904
absolute error = 0.0001611
relative error = 0.003021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.348
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1185 2.699
h = 0.001 0.003
y[1] (numeric) = 0.675379180761 5.28875679414
y[1] (closed_form) = 0.67530118548 5.28861637929
absolute error = 0.0001606
relative error = 0.003013 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.349
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1195 2.702
h = 0.0001 0.004
y[1] (numeric) = 0.679822369598 5.29265495649
y[1] (closed_form) = 0.679744584033 5.29251345715
absolute error = 0.0001615
relative error = 0.003026 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.352
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1196 2.706
h = 0.003 0.006
y[1] (numeric) = 0.683757691079 5.29901012068
y[1] (closed_form) = 0.683680787377 5.29886829807
absolute error = 0.0001613
relative error = 0.00302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.354
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1226 2.712
h = 0.0001 0.005
y[1] (numeric) = 0.694257271517 5.30584335181
y[1] (closed_form) = 0.694177089898 5.30569903604
absolute error = 0.0001651
relative error = 0.003085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.359
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1227 2.717
h = 0.0001 0.003
y[1] (numeric) = 0.69913924951 5.31378985654
y[1] (closed_form) = 0.699060886436 5.3136474926
absolute error = 0.0001625
relative error = 0.003032 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.362
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1228 2.72
h = 0.001 0.001
y[1] (numeric) = 0.702136164041 5.31851645651
y[1] (closed_form) = 0.702057324775 5.31837502103
absolute error = 0.0001619
relative error = 0.003018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.364
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1238 2.721
h = 0.001 0.003
y[1] (numeric) = 0.704688296714 5.3191771682
y[1] (closed_form) = 0.704609380003 5.31903626599
absolute error = 0.0001615
relative error = 0.00301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.365
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1248 2.724
h = 0.0001 0.004
y[1] (numeric) = 0.709130284708 5.32305043115
y[1] (closed_form) = 0.709051569927 5.32290844953
absolute error = 0.0001623
relative error = 0.003023 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.367
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1249 2.728
h = 0.003 0.006
y[1] (numeric) = 0.713073324041 5.32937504718
y[1] (closed_form) = 0.712995484001 5.32923273885
absolute error = 0.0001622
relative error = 0.003017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1279 2.734
h = 0.0001 0.005
y[1] (numeric) = 0.723562795667 5.33615647022
y[1] (closed_form) = 0.723481681891 5.33601170313
absolute error = 0.0001659
relative error = 0.003082 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.375
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.128 2.739
h = 0.0001 0.003
y[1] (numeric) = 0.728454465308 5.34406494712
y[1] (closed_form) = 0.72837517117 5.34392210947
absolute error = 0.0001634
relative error = 0.003029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.378
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1281 2.742
h = 0.001 0.001
y[1] (numeric) = 0.731456851071 5.34876864707
y[1] (closed_form) = 0.731377089118 5.3486267353
absolute error = 0.0001628
relative error = 0.003016 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.379
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1291 2.743
h = 0.001 0.003
y[1] (numeric) = 0.734003491738 5.3494197261
y[1] (closed_form) = 0.733923656001 5.34927834494
absolute error = 0.0001624
relative error = 0.003007 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.381
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1301 2.746
h = 0.0001 0.004
y[1] (numeric) = 0.738444135792 5.35326824287
y[1] (closed_form) = 0.738364494313 5.35312578741
absolute error = 0.0001632
relative error = 0.00302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.383
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1302 2.75
h = 0.003 0.006
y[1] (numeric) = 0.742394663727 5.35956244334
y[1] (closed_form) = 0.742315889897 5.35941965784
absolute error = 0.0001631
relative error = 0.003014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.385
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1332 2.756
h = 0.0001 0.005
y[1] (numeric) = 0.752873774119 5.36629242298
y[1] (closed_form) = 0.75279173101 5.36614721277
absolute error = 0.0001668
relative error = 0.003078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.391
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1333 2.761
h = 0.0001 0.003
y[1] (numeric) = 0.757774850269 5.37416303677
y[1] (closed_form) = 0.757694627679 5.37401973379
absolute error = 0.0001642
relative error = 0.003026 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.394
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1334 2.764
h = 0.001 0.001
y[1] (numeric) = 0.760782537818 5.37884393818
y[1] (closed_form) = 0.760701855693 5.37870155846
absolute error = 0.0001637
relative error = 0.003013 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.395
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1344 2.765
h = 0.0001 0.004
y[1] (numeric) = 0.763323660945 5.379485474
y[1] (closed_form) = 0.763242908641 5.37934362221
absolute error = 0.0001632
relative error = 0.003004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.397
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1345 2.769
h = 0.003 0.006
y[1] (numeric) = 0.767280192341 5.3857549108
y[1] (closed_form) = 0.767200923141 5.38561150149
absolute error = 0.0001639
relative error = 0.003012 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.399
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1375 2.775
h = 0.0001 0.005
y[1] (numeric) = 0.777750793093 5.39244077359
y[1] (closed_form) = 0.777668258261 5.39229496866
absolute error = 0.0001675
relative error = 0.003075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.404
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1376 2.78
h = 0.0001 0.003
y[1] (numeric) = 0.782660189096 5.4002790363
y[1] (closed_form) = 0.782579475638 5.40013511965
absolute error = 0.000165
relative error = 0.003024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.407
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1377 2.783
h = 0.001 0.001
y[1] (numeric) = 0.785672576306 5.40494045571
y[1] (closed_form) = 0.785591410398 5.4047974601
absolute error = 0.0001644
relative error = 0.003011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.409
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1387 2.784
h = 0.001 0.003
y[1] (numeric) = 0.788209042695 5.4055737821
y[1] (closed_form) = 0.788127809698 5.40543131216
absolute error = 0.000164
relative error = 0.003002 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1397 2.787
h = 0.0001 0.004
y[1] (numeric) = 0.79264710461 5.40937663966
y[1] (closed_form) = 0.792566051833 5.40923310491
absolute error = 0.0001648
relative error = 0.003015 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.412
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1398 2.791
h = 0.003 0.006
y[1] (numeric) = 0.796611326433 5.41561468277
y[1] (closed_form) = 0.796531128235 5.41547081194
absolute error = 0.0001647
relative error = 0.003009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.415
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1428 2.797
h = 0.0001 0.005
y[1] (numeric) = 0.807071106501 5.42224977536
y[1] (closed_form) = 0.806987647619 5.42210354233
absolute error = 0.0001684
relative error = 0.003071 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1429 2.802
h = 0.0001 0.003
y[1] (numeric) = 0.811989387017 5.43005048104
y[1] (closed_form) = 0.811907750008 5.42990611444
absolute error = 0.0001659
relative error = 0.003021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.423
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.143 2.805
h = 0.001 0.001
y[1] (numeric) = 0.815006765854 5.43468929046
y[1] (closed_form) = 0.814924684497 5.43454584217
absolute error = 0.0001653
relative error = 0.003008 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.425
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.144 2.806
h = 0.001 0.003
y[1] (numeric) = 0.817537668855 5.43531323827
y[1] (closed_form) = 0.817455523911 5.43517031296
absolute error = 0.0001648
relative error = 0.002999 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.426
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.145 2.809
h = 0.0001 0.004
y[1] (numeric) = 0.821973990093 5.43909178593
y[1] (closed_form) = 0.821892018019 5.438947801
absolute error = 0.0001657
relative error = 0.003012 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.428
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1451 2.813
h = 0.003 0.006
y[1] (numeric) = 0.825945060693 5.44529979503
y[1] (closed_form) = 0.8258639362 5.44515547094
absolute error = 0.0001656
relative error = 0.003006 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1481 2.819
h = 0.0001 0.005
y[1] (numeric) = 0.836393783184 5.45188447933
y[1] (closed_form) = 0.836309403207 5.45173782613
absolute error = 0.0001692
relative error = 0.003068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.436
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1482 2.824
h = 0.0001 0.003
y[1] (numeric) = 0.841320674364 5.45964779574
y[1] (closed_form) = 0.841238116562 5.45950298729
absolute error = 0.0001667
relative error = 0.003018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.439
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1483 2.827
h = 0.001 0.001
y[1] (numeric) = 0.844342882181 5.46426409838
y[1] (closed_form) = 0.844259888038 5.46412020547
absolute error = 0.0001661
relative error = 0.003004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1493 2.828
h = 0.001 0.003
y[1] (numeric) = 0.846868199148 5.46487875543
y[1] (closed_form) = 0.846785144866 5.46473538281
absolute error = 0.0001657
relative error = 0.002996 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.442
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1503 2.831
h = 0.0001 0.004
y[1] (numeric) = 0.851302646618 5.46863314605
y[1] (closed_form) = 0.851219757965 5.46848871901
absolute error = 0.0001665
relative error = 0.003009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.444
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1504 2.835
h = 0.003 0.006
y[1] (numeric) = 0.85528034897 5.47481125698
y[1] (closed_form) = 0.855198300936 5.47466648779
absolute error = 0.0001664
relative error = 0.003003 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.446
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1534 2.841
h = 0.0001 0.005
y[1] (numeric) = 0.865717782267 5.48134589381
y[1] (closed_form) = 0.865632484193 5.48119882826
absolute error = 0.00017
relative error = 0.003064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.452
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1535 2.846
h = 0.0001 0.003
y[1] (numeric) = 0.870653014148 5.48907198962
y[1] (closed_form) = 0.870569538359 5.48892674735
absolute error = 0.0001675
relative error = 0.003014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.455
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1536 2.849
h = 0.001 0.001
y[1] (numeric) = 0.873679890637 5.49366588923
y[1] (closed_form) = 0.87359598642 5.49352155967
absolute error = 0.0001669
relative error = 0.003001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.456
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1546 2.85
h = 0.001 0.003
y[1] (numeric) = 0.876199599897 5.49427134277
y[1] (closed_form) = 0.876115638934 5.4941275308
absolute error = 0.0001665
relative error = 0.002993 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.458
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1556 2.853
h = 0.0001 0.004
y[1] (numeric) = 0.880632043022 5.49800172903
y[1] (closed_form) = 0.880548240556 5.49785686784
absolute error = 0.0001674
relative error = 0.003006 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1557 2.857
h = 0.003 0.006
y[1] (numeric) = 0.884616163203 5.50415007832
y[1] (closed_form) = 0.884533194428 5.5040048721
absolute error = 0.0001672
relative error = 0.003 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.462
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1587 2.863
h = 0.0001 0.005
y[1] (numeric) = 0.895042080893 5.51063502736
y[1] (closed_form) = 0.894955867762 5.51048755718
absolute error = 0.0001708
relative error = 0.00306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.468
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1588 2.868
h = 0.0001 0.003
y[1] (numeric) = 0.899985387364 5.51832407215
y[1] (closed_form) = 0.899900996439 5.51817840395
absolute error = 0.0001683
relative error = 0.003011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.471
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 3.1589 2.871
h = 0.001 0.001
y[1] (numeric) = 0.903016774536 5.52289567293
y[1] (closed_form) = 0.902931963001 5.52275091459
absolute error = 0.0001678
relative error = 0.002998 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.472
Order of pole (given) = 1 0
NO 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=682.5MB, alloc=44.3MB, time=9.15
x[1] = 3.1599 2.872
h = 0.001 0.003
y[1] (numeric) = 0.905530855368 5.52349200965
y[1] (closed_form) = 0.905445990426 5.52334776619
absolute error = 0.0001674
relative error = 0.00299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 5.474
Order of pole (given) = 1 0
NO 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 ) = 2.0 / ( 0.2 * x + 0.3 ) ;
Iterations = 754
Total Elapsed Time = 9 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 9 Seconds
> quit
memory used=684.4MB, alloc=44.3MB, time=9.17