|\^/| 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) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));
> end;
exact_soln_y := proc(x)
return
c(10.0)*(c(0.1)*c(x) + c(0.2))*ln(c(0.1)*c(x) + c(0.2)) - c(x) - c(2.0)
end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#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_0D1,
array_const_0D2, 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_0D1,
> array_const_0D2,
#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_0D1,
array_const_0D2, 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_0D1,
> array_const_0D2,
#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_0D1,
array_const_0D2, 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_0D1,
> array_const_0D2,
#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_0D1,
array_const_0D2, 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_0D1,
> array_const_0D2,
#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_0D1,
array_const_0D2, 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_0D1,
> array_const_0D2,
#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_0D1,
array_const_0D2, 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_0D1,
> array_const_0D2,
#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_0D1,
array_const_0D2, 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_0D1,
> array_const_0D2,
#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_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre ln 1 LINEAR $eq_no = 1
> array_tmp3[1] := ln(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_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre ln 2 LINEAR $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre ln ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := neg(array_tmp2[2]) * array_tmp3[2] * c(1) / array_tmp2[1] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre ln ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := neg(array_tmp2[2]) * array_tmp3[3] * c(2) / array_tmp2[1] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre ln ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := neg(array_tmp2[2]) * array_tmp3[4] * c(3) / array_tmp2[1] / c(4);
> #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 ln LINEAR $eq_no = 1
> array_tmp3[kkk] := neg(array_tmp2[2]) * array_tmp3[kkk - 1] * c(kkk - 2)/ array_tmp2[1] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, 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_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := ln(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_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := 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_tmp2[2])*array_tmp3[2]*c(1)/(array_tmp2[1]*c(2));
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_tmp2[2])*array_tmp3[3]*c(2)/(array_tmp2[1]*c(3));
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_tmp2[2])*array_tmp3[4]*c(3)/(array_tmp2[1]*c(4));
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] := neg(array_tmp2[2])*array_tmp3[kkk - 1]*
c(kkk - 2)/(array_tmp2[1]*c(kkk - 1));
array_tmp4[kkk] := array_tmp3[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #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_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/lin_lnpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ");
> 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 := 20.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_min_h := c(0.001);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-2.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(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) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 20.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_min_h := c(0.001);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-2.0);
> 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 ) = ln ( 0.1 * x + 0.2 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T15:02:43-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"lin_ln")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"lin_ln diffeq.mxt")
> ;
> logitem_str(html_log_file,"lin_ln 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_0D1,
array_const_0D2, 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_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/lin_lnpostcpx.cpx#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ")
;
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 := 20.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_min_h := c(0.001);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-2.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(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) * (c(0.1) * c(x) + c(0.2)) * ln(\
c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 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 := 20.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-2.0);
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 ) = ln ( 0.1 * \
x + 0.2 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T15:02:43-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"lin_ln");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ln\
( 0.1 * x + 0.2 ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file,
"lin_ln diffeq.mxt");
logitem_str(html_log_file, "lin_ln 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/lin_lnpostcpx.cpx#################
diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 20.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-2.0);
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) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 20.1 0.1
h = 0.0001 0.005
y[1] (numeric) = -4.57509165037 0.0792995927942
y[1] (closed_form) = -4.57509165037 0.0792995927942
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 22.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = -4.57503542653 0.0832650814787
y[1] (closed_form) = -4.57503553964 0.0832650842682
absolute error = 1.131e-07
relative error = 2.473e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 22.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.26
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1002 0.108
h = 0.001 0.001
y[1] (numeric) = -4.57497071796 0.0856446013023
y[1] (closed_form) = -4.57497069535 0.0856445989058
absolute error = 2.274e-08
relative error = 4.969e-07 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 22.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.41
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1012 0.109
h = 0.001 0.003
y[1] (numeric) = -4.57418265651 0.0864425720596
y[1] (closed_form) = -4.57418256842 0.0864425444529
absolute error = 9.232e-08
relative error = 2.018e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 22.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = -4.57340443779 0.0888267715141
y[1] (closed_form) = -4.5734044852 0.0888267898289
absolute error = 5.082e-08
relative error = 1.111e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 22.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1023 0.116
h = 0.003 0.006
y[1] (numeric) = -4.5733456653 0.0919997964824
y[1] (closed_form) = -4.57334580564 0.0919997361016
absolute error = 1.528e-07
relative error = 3.340e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.06
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = -4.5709983585 0.09677449131
y[1] (closed_form) = -4.57099857063 0.0967749606487
absolute error = 5.151e-07
relative error = 1.127e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = -4.57094729841 0.100741637483
y[1] (closed_form) = -4.57094740589 0.100741776005
absolute error = 1.753e-07
relative error = 3.835e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1055 0.13
h = 0.001 0.001
y[1] (numeric) = -4.57088554743 0.103121992064
y[1] (closed_form) = -4.57088551923 0.103122125266
absolute error = 1.362e-07
relative error = 2.978e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1065 0.131
h = 0.001 0.003
y[1] (numeric) = -4.57009823479 0.103921202035
y[1] (closed_form) = -4.57009814114 0.103921309968
absolute error = 1.429e-07
relative error = 3.126e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = -4.5693227527 0.106307131003
y[1] (closed_form) = -4.56932279449 0.10630728498
absolute error = 1.595e-07
relative error = 3.491e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1076 0.138
h = 0.003 0.006
y[1] (numeric) = -4.56926793109 0.10948123679
y[1] (closed_form) = -4.56926806585 0.109481312184
absolute error = 1.544e-07
relative error = 3.379e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.06
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = -4.56692585049 0.114260386454
y[1] (closed_form) = -4.5669260565 0.114260991509
absolute error = 6.392e-07
relative error = 1.399e-05 %
Correct digits = 7
memory used=30.3MB, alloc=40.3MB, time=0.38
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = -4.56687973351 0.11822886112
y[1] (closed_form) = -4.56687983522 0.118229135335
absolute error = 2.925e-07
relative error = 6.402e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1108 0.152
h = 0.001 0.001
y[1] (numeric) = -4.56682093857 0.120610053191
y[1] (closed_form) = -4.56682090464 0.120610321953
absolute error = 2.709e-07
relative error = 5.930e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1118 0.153
h = 0.001 0.003
y[1] (numeric) = -4.5660343733 0.121410502816
y[1] (closed_form) = -4.56603427398 0.12141074625
absolute error = 2.629e-07
relative error = 5.756e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = -4.56526162547 0.123798163589
y[1] (closed_form) = -4.56526166149 0.123798453191
absolute error = 2.918e-07
relative error = 6.390e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.98
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1129 0.16
h = 0.003 0.006
y[1] (numeric) = -4.56521075267 0.126973353854
y[1] (closed_form) = -4.56521088173 0.126973564984
absolute error = 2.475e-07
relative error = 5.418e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.07
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = -4.56287389257 0.131756962448
y[1] (closed_form) = -4.56287409233 0.131757703179
absolute error = 7.672e-07
relative error = 1.681e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.116 0.171
h = 0.0001 0.003
y[1] (numeric) = -4.56283271615 0.135726770189
y[1] (closed_form) = -4.56283281198 0.135727180058
absolute error = 4.209e-07
relative error = 9.221e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1161 0.174
h = 0.001 0.001
y[1] (numeric) = -4.56277687569 0.138108802479
y[1] (closed_form) = -4.56277683591 0.138109206761
absolute error = 4.062e-07
relative error = 8.899e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1171 0.175
h = 0.001 0.003
y[1] (numeric) = -4.5619910564 0.138910492192
y[1] (closed_form) = -4.56199095125 0.138910871088
absolute error = 3.932e-07
relative error = 8.615e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = -4.56122104041 0.141299887059
y[1] (closed_form) = -4.56122107053 0.141300312246
absolute error = 4.263e-07
relative error = 9.341e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.99
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1182 0.182
h = 0.003 0.006
y[1] (numeric) = -4.56117411439 0.144476165453
y[1] (closed_form) = -4.56117423761 0.14447651228
absolute error = 3.681e-07
relative error = 8.065e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.08
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = -4.55884246906 0.149264237058
y[1] (closed_form) = -4.55884266244 0.149265113424
absolute error = 8.974e-07
relative error = 1.968e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = -4.55880623066 0.153235382446
y[1] (closed_form) = -4.55880632046 0.153235927929
absolute error = 5.528e-07
relative error = 1.212e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1214 0.196
h = 0.001 0.001
y[1] (numeric) = -4.55875334311 0.155618257679
y[1] (closed_form) = -4.55875329733 0.155618797443
absolute error = 5.417e-07
relative error = 1.188e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = -4.55796826837 0.156421187915
y[1] (closed_form) = -4.55796815728 0.156421702234
absolute error = 5.262e-07
relative error = 1.154e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1225 0.201
h = 0.003 0.006
y[1] (numeric) = -4.55792457022 0.159598352734
y[1] (closed_form) = -4.55792473302 0.159598794929
absolute error = 4.712e-07
relative error = 1.033e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.09
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = -4.55559746225 0.16439020718
y[1] (closed_form) = -4.55559769474 0.164391178867
absolute error = 9.991e-07
relative error = 2.192e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = -4.55556548829 0.168362448848
y[1] (closed_form) = -4.5555656175 0.168363089631
absolute error = 6.537e-07
relative error = 1.434e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1257 0.215
h = 0.001 0.001
y[1] (numeric) = -4.55551515132 0.170746016687
y[1] (closed_form) = -4.555515145 0.170746651635
absolute error = 6.350e-07
relative error = 1.393e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1267 0.216
h = 0.001 0.003
y[1] (numeric) = -4.55473073112 0.171550006221
y[1] (closed_form) = -4.55473065952 0.171550615673
absolute error = 6.136e-07
relative error = 1.346e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = -4.55396581281 0.173942601423
y[1] (closed_form) = -4.55396587632 0.173943257396
absolute error = 6.590e-07
relative error = 1.446e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1278 0.223
h = 0.003 0.006
y[1] (numeric) = -4.55392623839 0.177120867319
y[1] (closed_form) = -4.55392639511 0.177121445138
absolute error = 5.987e-07
relative error = 1.314e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.1
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = -4.55160433458 0.181917192399
y[1] (closed_form) = -4.55160456045 0.181918299648
absolute error = 1.130e-06
relative error = 2.481e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = -4.55157729394 0.185890780236
y[1] (closed_form) = -4.55157741688 0.185891556561
absolute error = 7.860e-07
relative error = 1.725e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.131 0.237
h = 0.001 0.001
y[1] (numeric) = -4.55152990699 0.188275196094
y[1] (closed_form) = -4.55152989443 0.188275966452
absolute error = 7.705e-07
relative error = 1.691e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.132 0.238
h = 0.001 0.003
y[1] (numeric) = -4.55074622871 0.189080426964
y[1] (closed_form) = -4.55074615091 0.189081171768
absolute error = 7.489e-07
relative error = 1.644e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=74.7MB, alloc=52.3MB, time=0.92
x[1] = 20.133 0.241
h = 0.0001 0.004
y[1] (numeric) = -4.5499840354 0.191474762799
y[1] (closed_form) = -4.54998409264 0.191475554245
absolute error = 7.935e-07
relative error = 1.742e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.01
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1331 0.245
h = 0.003 0.006
y[1] (numeric) = -4.5499484019 0.194654127266
y[1] (closed_form) = -4.54994855239 0.194654840671
absolute error = 7.291e-07
relative error = 1.601e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.11
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = -4.54763169653 0.199454927022
y[1] (closed_form) = -4.54763191563 0.199456169792
absolute error = 1.262e-06
relative error = 2.772e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = -4.54760958663 0.203429865581
y[1] (closed_form) = -4.54760970315 0.203430777408
absolute error = 9.192e-07
relative error = 2.019e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.29
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1363 0.259
h = 0.001 0.001
y[1] (numeric) = -4.54756514811 0.20581513217
y[1] (closed_form) = -4.54756512918 0.205816037897
absolute error = 9.059e-07
relative error = 1.990e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1373 0.26
h = 0.001 0.003
y[1] (numeric) = -4.54678221034 0.206621604801
y[1] (closed_form) = -4.54678212621 0.206622484915
absolute error = 8.841e-07
relative error = 1.943e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = -4.54602273963 0.209017683532
y[1] (closed_form) = -4.54602279046 0.209018610411
absolute error = 9.283e-07
relative error = 2.040e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.01
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1384 0.267
h = 0.003 0.006
y[1] (numeric) = -4.54599104495 0.2121981502
y[1] (closed_form) = -4.54599118909 0.21219899915
absolute error = 8.611e-07
relative error = 1.892e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.12
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = -4.54367953228 0.217003428661
y[1] (closed_form) = -4.54367974448 0.217004806911
absolute error = 1.394e-06
relative error = 3.066e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = -4.54366235055 0.220979722487
y[1] (closed_form) = -4.54366246053 0.220980769776
absolute error = 1.053e-06
relative error = 2.315e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.29
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1416 0.281
h = 0.001 0.001
y[1] (numeric) = -4.54362085888 0.223365842514
y[1] (closed_form) = -4.54362083345 0.22336688357
absolute error = 1.041e-06
relative error = 2.289e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1426 0.282
h = 0.001 0.003
y[1] (numeric) = -4.5428386602 0.224173557326
y[1] (closed_form) = -4.54283856961 0.224174572712
absolute error = 1.019e-06
relative error = 2.241e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = -4.54208190968 0.226571381213
y[1] (closed_form) = -4.54208195397 0.226572443485
absolute error = 1.063e-06
relative error = 2.338e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.02
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1437 0.289
h = 0.003 0.006
y[1] (numeric) = -4.54205415175 0.229752953706
y[1] (closed_form) = -4.5420542894 0.229753938161
absolute error = 9.940e-07
relative error = 2.186e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.13
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = -4.53974782603 0.234562714886
y[1] (closed_form) = -4.53974803121 0.234564228575
absolute error = 1.528e-06
relative error = 3.360e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = -4.53973556988 0.238540368517
y[1] (closed_form) = -4.53973567319 0.238541551227
absolute error = 1.187e-06
relative error = 2.612e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.29
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1469 0.303
h = 0.001 0.001
y[1] (numeric) = -4.53969702347 0.240927344684
y[1] (closed_form) = -4.5396969914 0.240928521029
absolute error = 1.177e-06
relative error = 2.589e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = -4.53891556247 0.241736302096
y[1] (closed_form) = -4.53891546529 0.241737452712
absolute error = 1.155e-06
relative error = 2.540e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.148 0.308
h = 0.003 0.006
y[1] (numeric) = -4.53889102422 0.24491877548
y[1] (closed_form) = -4.53889120095 0.244919855378
absolute error = 1.094e-06
relative error = 2.407e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.14
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.151 0.314
h = 0.0001 0.005
y[1] (numeric) = -4.53658921212 0.249732336746
y[1] (closed_form) = -4.5365894559 0.249733945827
absolute error = 1.627e-06
relative error = 3.582e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = -4.53658120994 0.253711105849
y[1] (closed_form) = -4.53658135216 0.253712383933
absolute error = 1.286e-06
relative error = 2.830e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.3
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1512 0.322
h = 0.001 0.001
y[1] (numeric) = -4.53654520768 0.256098786056
y[1] (closed_form) = -4.53654521456 0.25610005766
absolute error = 1.272e-06
relative error = 2.799e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1522 0.323
h = 0.001 0.003
y[1] (numeric) = -4.53576439531 0.256908804625
y[1] (closed_form) = -4.53576433711 0.25691005045
absolute error = 1.247e-06
relative error = 2.745e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = -4.53501272085 0.259309849495
y[1] (closed_form) = -4.53501279738 0.259311142433
absolute error = 1.295e-06
relative error = 2.851e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.03
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1533 0.33
h = 0.003 0.006
y[1] (numeric) = -4.53499229601 0.262493442459
y[1] (closed_form) = -4.534992466 0.262494657789
absolute error = 1.227e-06
relative error = 2.701e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.14
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = -4.5326956602 0.267311493948
y[1] (closed_form) = -4.53269589671 0.267313238392
absolute error = 1.760e-06
relative error = 3.877e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=119.0MB, alloc=52.3MB, time=1.43
x[1] = 20.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = -4.53269257883 0.271291631312
y[1] (closed_form) = -4.53269271413 0.271293044742
absolute error = 1.420e-06
relative error = 3.127e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.3
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1565 0.344
h = 0.001 0.001
y[1] (numeric) = -4.53265951889 0.273680172694
y[1] (closed_form) = -4.53265951889 0.273681579513
absolute error = 1.407e-06
relative error = 3.098e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1575 0.345
h = 0.001 0.003
y[1] (numeric) = -4.53187944157 0.27449143465
y[1] (closed_form) = -4.53187937653 0.274492815632
absolute error = 1.383e-06
relative error = 3.045e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = -4.53113048041 0.276894231133
y[1] (closed_form) = -4.53113055002 0.276895659349
absolute error = 1.430e-06
relative error = 3.150e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.04
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1586 0.352
h = 0.003 0.006
y[1] (numeric) = -4.53111398636 0.280078940282
y[1] (closed_form) = -4.53111414949 0.280080291001
absolute error = 1.361e-06
relative error = 2.997e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.15
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = -4.52882252109 0.28490148597
y[1] (closed_form) = -4.52882275019 0.284903365735
absolute error = 1.894e-06
relative error = 4.173e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = -4.52882435792 0.288882996111
y[1] (closed_form) = -4.52882448617 0.288884544847
absolute error = 1.554e-06
relative error = 3.424e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.3
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1618 0.366
h = 0.001 0.001
y[1] (numeric) = -4.52879423871 0.291272401359
y[1] (closed_form) = -4.52879423169 0.291273943351
absolute error = 1.542e-06
relative error = 3.398e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1628 0.367
h = 0.001 0.003
y[1] (numeric) = -4.52801489501 0.292084907112
y[1] (closed_form) = -4.528014823 0.292086423209
absolute error = 1.518e-06
relative error = 3.345e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = -4.52726864473 0.294489457443
y[1] (closed_form) = -4.52726870728 0.294491020896
absolute error = 1.565e-06
relative error = 3.449e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.05
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1639 0.374
h = 0.003 0.006
y[1] (numeric) = -4.52725607937 0.297675286377
y[1] (closed_form) = -4.5272562355 0.297676772445
absolute error = 1.494e-06
relative error = 3.293e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.16
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = -4.52496977888 0.302502330228
y[1] (closed_form) = -4.52497000044 0.302504345271
absolute error = 2.027e-06
relative error = 4.470e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.167 0.385
h = 0.0001 0.003
y[1] (numeric) = -4.5249765313 0.306485217655
y[1] (closed_form) = -4.52497665235 0.306486901655
absolute error = 1.688e-06
relative error = 3.723e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.31
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1671 0.388
h = 0.001 0.001
y[1] (numeric) = -4.52494935119 0.308875489454
y[1] (closed_form) = -4.52494933704 0.308877166577
absolute error = 1.677e-06
relative error = 3.698e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1681 0.389
h = 0.001 0.003
y[1] (numeric) = -4.52417073971 0.309689239409
y[1] (closed_form) = -4.5241706606 0.309690890581
absolute error = 1.653e-06
relative error = 3.645e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = -4.52342719787 0.312095545819
y[1] (closed_form) = -4.52342725325 0.312097244467
absolute error = 1.700e-06
relative error = 3.748e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.06
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1692 0.396
h = 0.003 0.006
y[1] (numeric) = -4.5234185591 0.315282498133
y[1] (closed_form) = -4.52341870809 0.315284119509
absolute error = 1.628e-06
relative error = 3.591e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = -4.52113741762 0.320114044097
y[1] (closed_form) = -4.52113763151 0.320116194376
absolute error = 2.161e-06
relative error = 4.768e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = -4.521149083 0.324098313312
y[1] (closed_form) = -4.52114919673 0.324100132534
absolute error = 1.823e-06
relative error = 4.021e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.31
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1724 0.41
h = 0.001 0.001
y[1] (numeric) = -4.5211248404 0.326489454342
y[1] (closed_form) = -4.52112481896 0.326491266555
absolute error = 1.812e-06
relative error = 3.998e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = -4.52034695971 0.327304448904
y[1] (closed_form) = -4.52034687336 0.327306235108
absolute error = 1.788e-06
relative error = 3.946e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1735 0.415
h = 0.003 0.006
y[1] (numeric) = -4.52034153231 0.33049231646
y[1] (closed_form) = -4.52034171987 0.330494033349
absolute error = 1.727e-06
relative error = 3.811e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.18
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = -4.5180648806 0.335327679484
y[1] (closed_form) = -4.51806513259 0.335329925221
absolute error = 2.260e-06
relative error = 4.988e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = -4.51808078932 0.339313083216
y[1] (closed_form) = -4.51808094146 0.339314997879
absolute error = 1.921e-06
relative error = 4.239e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.31
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1767 0.429
h = 0.001 0.001
y[1] (numeric) = -4.51805908433 0.341704939628
y[1] (closed_form) = -4.51805910134 0.34170684717
absolute error = 1.908e-06
relative error = 4.210e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1777 0.43
h = 0.001 0.003
y[1] (numeric) = -4.51728184639 0.342520997145
y[1] (closed_form) = -4.51728179851 0.342522878627
absolute error = 1.882e-06
relative error = 4.154e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = -4.51654335884 0.344930544926
y[1] (closed_form) = -4.51654344531 0.34493247411
absolute error = 1.931e-06
relative error = 4.263e-05 %
Correct digits = 6
memory used=163.3MB, alloc=52.3MB, time=1.94
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.07
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1788 0.437
h = 0.003 0.006
y[1] (numeric) = -4.51654203436 0.348119550422
y[1] (closed_form) = -4.51654221454 0.348121402543
absolute error = 1.861e-06
relative error = 4.108e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.19
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = -4.51427053096 0.352959422941
y[1] (closed_form) = -4.51427077504 0.352961803836
absolute error = 2.393e-06
relative error = 5.286e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = -4.5142913478 0.35694621685
y[1] (closed_form) = -4.51429149238 0.356948266659
absolute error = 2.055e-06
relative error = 4.538e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.32
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.182 0.451
h = 0.001 0.001
y[1] (numeric) = -4.51427257734 0.359338947488
y[1] (closed_form) = -4.51427258682 0.359340990044
absolute error = 2.043e-06
relative error = 4.510e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.183 0.452
h = 0.001 0.003
y[1] (numeric) = -4.51349606755 0.360156250371
y[1] (closed_form) = -4.5134960122 0.36015826681
absolute error = 2.017e-06
relative error = 4.455e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.184 0.455
h = 0.0001 0.004
y[1] (numeric) = -4.51276028153 0.362567560606
y[1] (closed_form) = -4.51276036043 0.362569624867
absolute error = 2.066e-06
relative error = 4.563e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.08
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1841 0.459
h = 0.003 0.006
y[1] (numeric) = -4.51276287759 0.365757699758
y[1] (closed_form) = -4.51276305026 0.365759687068
absolute error = 1.995e-06
relative error = 4.406e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.2
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = -4.51049651671 0.370602085684
y[1] (closed_form) = -4.51049675274 0.370604601694
absolute error = 2.527e-06
relative error = 5.584e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = -4.51052223903 0.37459027425
y[1] (closed_form) = -4.51052237592 0.374592459161
absolute error = 2.189e-06
relative error = 4.837e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.32
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1873 0.473
h = 0.001 0.001
y[1] (numeric) = -4.51050640148 0.376983881782
y[1] (closed_form) = -4.51050640331 0.376986059309
absolute error = 2.178e-06
relative error = 4.811e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1883 0.474
h = 0.001 0.003
y[1] (numeric) = -4.50973061843 0.377802430426
y[1] (closed_form) = -4.50973055547 0.377804581779
absolute error = 2.152e-06
relative error = 4.756e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = -4.50899753148 0.380215505321
y[1] (closed_form) = -4.50899760269 0.380217704616
absolute error = 2.200e-06
relative error = 4.863e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.08
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1894 0.481
h = 0.003 0.006
y[1] (numeric) = -4.50900404595 0.383406781701
y[1] (closed_form) = -4.50900421098 0.383408904157
absolute error = 2.129e-06
relative error = 4.704e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.21
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = -4.50674282182 0.388255684931
y[1] (closed_form) = -4.50674304967 0.388258336013
absolute error = 2.661e-06
relative error = 5.882e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = -4.50677344696 0.392245272627
y[1] (closed_form) = -4.50677357602 0.392247592598
absolute error = 2.324e-06
relative error = 5.136e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.32
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1926 0.495
h = 0.001 0.001
y[1] (numeric) = -4.50676054068 0.394639759715
y[1] (closed_form) = -4.50676053473 0.394642072171
absolute error = 2.312e-06
relative error = 5.112e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1936 0.496
h = 0.001 0.003
y[1] (numeric) = -4.50598548296 0.395459554513
y[1] (closed_form) = -4.50598541226 0.395461840738
absolute error = 2.287e-06
relative error = 5.057e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = -4.50525509264 0.397874396269
y[1] (closed_form) = -4.50525515603 0.397876730555
absolute error = 2.335e-06
relative error = 5.163e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.09
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1947 0.503
h = 0.003 0.006
y[1] (numeric) = -4.50526552338 0.401066813443
y[1] (closed_form) = -4.50526568064 0.401069071003
absolute error = 2.263e-06
relative error = 5.003e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.22
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = -4.50300943019 0.405920237862
y[1] (closed_form) = -4.50300964974 0.405923023971
absolute error = 2.795e-06
relative error = 6.181e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = -4.5030449555 0.409911229154
y[1] (closed_form) = -4.50304507661 0.409913684142
absolute error = 2.458e-06
relative error = 5.436e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.33
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1979 0.517
h = 0.001 0.001
y[1] (numeric) = -4.50303497887 0.412306598456
y[1] (closed_form) = -4.503034965 0.412309045798
absolute error = 2.447e-06
relative error = 5.412e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = -4.50226064506 0.413127639796
y[1] (closed_form) = -4.50226056649 0.413130060851
absolute error = 2.422e-06
relative error = 5.358e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.82
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.199 0.522
h = 0.003 0.006
y[1] (numeric) = -4.50227427874 0.416320986448
y[1] (closed_form) = -4.50227447406 0.416323339587
absolute error = 2.361e-06
relative error = 5.222e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.23
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.202 0.528
h = 0.0001 0.005
y[1] (numeric) = -4.50002265138 0.42117824463
y[1] (closed_form) = -4.50002290852 0.421181126258
absolute error = 2.893e-06
relative error = 6.401e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = -4.50006240925 0.425170389332
y[1] (closed_form) = -4.50006256825 0.425172939827
absolute error = 2.555e-06
relative error = 5.654e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.33
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=207.6MB, alloc=52.3MB, time=2.44
x[1] = 20.2022 0.536
h = 0.001 0.001
y[1] (numeric) = -4.50005496359 0.42756648527
y[1] (closed_form) = -4.50005498766 0.427569028005
absolute error = 2.543e-06
relative error = 5.625e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2032 0.537
h = 0.001 0.003
y[1] (numeric) = -4.49928126662 0.428388591301
y[1] (closed_form) = -4.49928122602 0.428391107699
absolute error = 2.517e-06
relative error = 5.568e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = -4.4985559087 0.430806694557
y[1] (closed_form) = -4.49855600204 0.430809259239
absolute error = 2.566e-06
relative error = 5.679e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.1
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2043 0.544
h = 0.003 0.006
y[1] (numeric) = -4.49857363467 0.434001197361
y[1] (closed_form) = -4.49857382198 0.434003685526
absolute error = 2.495e-06
relative error = 5.521e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.24
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = -4.49632712752 0.438862983994
y[1] (closed_form) = -4.49632737611 0.43886600057
absolute error = 3.027e-06
relative error = 6.700e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = -4.49637178064 0.442856540612
y[1] (closed_form) = -4.49637193144 0.442859226045
absolute error = 2.690e-06
relative error = 5.953e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.33
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2075 0.558
h = 0.001 0.001
y[1] (numeric) = -4.49636726161 0.445253523718
y[1] (closed_form) = -4.49636727752 0.44525620126
absolute error = 2.678e-06
relative error = 5.926e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2085 0.559
h = 0.001 0.003
y[1] (numeric) = -4.49559428592 0.446076877024
y[1] (closed_form) = -4.4955942372 0.446079528173
absolute error = 2.652e-06
relative error = 5.869e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = -4.49487161766 0.448496753434
y[1] (closed_form) = -4.4948717028 0.448499452986
absolute error = 2.701e-06
relative error = 5.979e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.11
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2096 0.566
h = 0.003 0.006
y[1] (numeric) = -4.49489325377 0.451692407225
y[1] (closed_form) = -4.49489343293 0.451695030372
absolute error = 2.629e-06
relative error = 5.820e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.25
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = -4.49265186102 0.456558726154
y[1] (closed_form) = -4.49265210093 0.456561877633
absolute error = 3.161e-06
relative error = 6.999e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = -4.49270140671 0.460553699132
y[1] (closed_form) = -4.49270154919 0.460556519459
absolute error = 2.824e-06
relative error = 6.253e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.34
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2128 0.58
h = 0.001 0.001
y[1] (numeric) = -4.49269981267 0.462951572051
y[1] (closed_form) = -4.49269982029 0.462954384357
absolute error = 2.812e-06
relative error = 6.227e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2138 0.581
h = 0.001 0.003
y[1] (numeric) = -4.49192755684 0.463776173013
y[1] (closed_form) = -4.49192749987 0.463778958869
absolute error = 2.786e-06
relative error = 6.170e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = -4.49120757577 0.466197824754
y[1] (closed_form) = -4.49120765259 0.466200659132
absolute error = 2.835e-06
relative error = 6.280e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.12
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2149 0.588
h = 0.003 0.006
y[1] (numeric) = -4.49123311988 0.469394633073
y[1] (closed_form) = -4.49123329076 0.469397391159
absolute error = 2.763e-06
relative error = 6.119e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.26
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = -4.48899683572 0.474265488131
y[1] (closed_form) = -4.48899706681 0.474268774469
absolute error = 3.294e-06
relative error = 7.298e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.218 0.599
h = 0.0001 0.003
y[1] (numeric) = -4.4890512713 0.478261881905
y[1] (closed_form) = -4.48905140531 0.478264837083
absolute error = 2.958e-06
relative error = 6.553e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.34
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2181 0.602
h = 0.001 0.001
y[1] (numeric) = -4.48905260059 0.480660647279
y[1] (closed_form) = -4.48905259979 0.480663594305
absolute error = 2.947e-06
relative error = 6.528e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2191 0.603
h = 0.001 0.003
y[1] (numeric) = -4.48828106319 0.481486496273
y[1] (closed_form) = -4.48828099786 0.481489416793
absolute error = 2.921e-06
relative error = 6.471e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = -4.48756376687 0.483909925518
y[1] (closed_form) = -4.48756383523 0.483912894678
absolute error = 2.970e-06
relative error = 6.580e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.13
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2202 0.61
h = 0.003 0.006
y[1] (numeric) = -4.48759321679 0.487107891901
y[1] (closed_form) = -4.48759337927 0.487110784882
absolute error = 2.898e-06
relative error = 6.419e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = -4.48536203541 0.491983286907
y[1] (closed_form) = -4.48536225756 0.491986708059
absolute error = 3.428e-06
relative error = 7.598e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = -4.48542135819 0.495981105905
y[1] (closed_form) = -4.4854214836 0.49598419589
absolute error = 3.093e-06
relative error = 6.853e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.34
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2234 0.624
h = 0.001 0.001
y[1] (numeric) = -4.48542560915 0.498380766369
y[1] (closed_form) = -4.48542559981 0.498383848072
absolute error = 3.082e-06
relative error = 6.828e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = -4.48465478878 0.499207863771
y[1] (closed_form) = -4.48465471494 0.49921091891
absolute error = 3.056e-06
relative error = 6.773e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.9
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=251.8MB, alloc=52.3MB, time=2.95
x[1] = 20.2245 0.629
h = 0.003 0.006
y[1] (numeric) = -4.4846874331 0.502406773749
y[1] (closed_form) = -4.48468763313 0.502409762369
absolute error = 2.995e-06
relative error = 6.637e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = -4.4824606935 0.50728601895
y[1] (closed_form) = -4.48246095274 0.507289535677
absolute error = 3.526e-06
relative error = 7.817e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = -4.4825242379 0.511285010102
y[1] (closed_form) = -4.48252440071 0.511288195651
absolute error = 3.190e-06
relative error = 7.070e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.35
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2277 0.643
h = 0.001 0.001
y[1] (numeric) = -4.48253101312 0.51368540836
y[1] (closed_form) = -4.48253104121 0.513688585515
absolute error = 3.177e-06
relative error = 7.042e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2287 0.644
h = 0.001 0.003
y[1] (numeric) = -4.48176082369 0.514513572129
y[1] (closed_form) = -4.48176078731 0.514516722672
absolute error = 3.151e-06
relative error = 6.984e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = -4.48104853774 0.516940282741
y[1] (closed_form) = -4.4810486349 0.516943482146
absolute error = 3.201e-06
relative error = 7.096e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.14
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2298 0.651
h = 0.003 0.006
y[1] (numeric) = -4.48108526356 0.520140366937
y[1] (closed_form) = -4.48108545494 0.520143490372
absolute error = 3.129e-06
relative error = 6.937e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = -4.47886361596 0.525024159227
y[1] (closed_form) = -4.47886386602 0.525027810685
absolute error = 3.660e-06
relative error = 8.116e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = -4.47893204257 0.529024583855
y[1] (closed_form) = -4.47893219654 0.52902790413
absolute error = 3.324e-06
relative error = 7.370e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.35
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.233 0.665
h = 0.001 0.001
y[1] (numeric) = -4.47894173642 0.531425882115
y[1] (closed_form) = -4.47894175572 0.531429193866
absolute error = 3.312e-06
relative error = 7.343e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.234 0.666
h = 0.001 0.003
y[1] (numeric) = -4.47817226137 0.532255294997
y[1] (closed_form) = -4.47817221625 0.532258580079
absolute error = 3.285e-06
relative error = 7.285e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.235 0.669
h = 0.0001 0.004
y[1] (numeric) = -4.47746265315 0.534683789322
y[1] (closed_form) = -4.47746274148 0.534687123385
absolute error = 3.335e-06
relative error = 7.396e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.15
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2351 0.673
h = 0.003 0.006
y[1] (numeric) = -4.47750327859 0.53788504169
y[1] (closed_form) = -4.47750346118 0.537888299895
absolute error = 3.263e-06
relative error = 7.236e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.29
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = -4.47528671715 0.542773384849
y[1] (closed_form) = -4.47528695789 0.542777170993
absolute error = 3.794e-06
relative error = 8.416e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = -4.47536002326 0.546775247361
y[1] (closed_form) = -4.47536016827 0.546778702316
absolute error = 3.458e-06
relative error = 7.670e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.35
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2383 0.687
h = 0.001 0.001
y[1] (numeric) = -4.47537263407 0.549177448245
y[1] (closed_form) = -4.47537264444 0.549180894547
absolute error = 3.446e-06
relative error = 7.643e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2393 0.688
h = 0.001 0.003
y[1] (numeric) = -4.474603872 0.550008110606
y[1] (closed_form) = -4.474603818 0.550011530183
absolute error = 3.420e-06
relative error = 7.586e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = -4.47389693903 0.552438390793
y[1] (closed_form) = -4.4738970184 0.552441859468
absolute error = 3.470e-06
relative error = 7.697e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.15
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2404 0.695
h = 0.003 0.006
y[1] (numeric) = -4.47394146189 0.555640814845
y[1] (closed_form) = -4.47394163558 0.555644207776
absolute error = 3.397e-06
relative error = 7.536e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.3
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = -4.47172998079 0.560533712641
y[1] (closed_form) = -4.47173021209 0.560537633426
absolute error = 3.928e-06
relative error = 8.715e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = -4.47180816368 0.564537017434
y[1] (closed_form) = -4.47180829959 0.564540607026
absolute error = 3.592e-06
relative error = 7.970e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2436 0.709
h = 0.001 0.001
y[1] (numeric) = -4.47182368977 0.566940123562
y[1] (closed_form) = -4.4718236911 0.566943704369
absolute error = 3.581e-06
relative error = 7.944e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2446 0.71
h = 0.001 0.003
y[1] (numeric) = -4.47105563926 0.567772035764
y[1] (closed_form) = -4.47105557625 0.567775589791
absolute error = 3.555e-06
relative error = 7.887e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = -4.47035137907 0.570204103956
y[1] (closed_form) = -4.47035144935 0.570207707199
absolute error = 3.604e-06
relative error = 7.997e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.16
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2457 0.717
h = 0.003 0.006
y[1] (numeric) = -4.47039979716 0.573407703198
y[1] (closed_form) = -4.4703999618 0.57341123081
absolute error = 3.531e-06
relative error = 7.835e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.31
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = -4.46819339057 0.578305159385
y[1] (closed_form) = -4.46819361229 0.578309214764
absolute error = 4.061e-06
relative error = 9.014e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=296.0MB, alloc=52.3MB, time=3.46
x[1] = 20.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = -4.4682764475 0.582309910851
y[1] (closed_form) = -4.46827657419 0.582313635033
absolute error = 3.726e-06
relative error = 8.270e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2489 0.731
h = 0.001 0.001
y[1] (numeric) = -4.4682948872 0.584713924834
y[1] (closed_form) = -4.46829487935 0.584717640103
absolute error = 3.715e-06
relative error = 8.244e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = -4.46752754683 0.585547087238
y[1] (closed_form) = -4.46752747469 0.585550775671
absolute error = 3.689e-06
relative error = 8.188e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.99
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.25 0.736
h = 0.003 0.006
y[1] (numeric) = -4.46757915066 0.588751644076
y[1] (closed_form) = -4.46757935235 0.588755267381
absolute error = 3.629e-06
relative error = 8.053e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.32
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.253 0.742
h = 0.0001 0.005
y[1] (numeric) = -4.46537716171 0.593652966616
y[1] (closed_form) = -4.46537742002 0.593657117621
absolute error = 4.159e-06
relative error = 9.233e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = -4.46546442917 0.597658908826
y[1] (closed_form) = -4.46546459276 0.597662728626
absolute error = 3.823e-06
relative error = 8.486e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2532 0.75
h = 0.001 0.001
y[1] (numeric) = -4.46548538633 0.60006367167
y[1] (closed_form) = -4.46548541541 0.600067482446
absolute error = 3.811e-06
relative error = 8.458e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2542 0.751
h = 0.001 0.003
y[1] (numeric) = -4.46471867098 0.600897902056
y[1] (closed_form) = -4.46471863581 0.600901685947
absolute error = 3.784e-06
relative error = 8.400e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = -4.464019399 0.603333271222
y[1] (closed_form) = -4.46401949696 0.603337104548
absolute error = 3.835e-06
relative error = 8.513e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.18
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = -4.46407507342 0.606539020192
y[1] (closed_form) = -4.46407526583 0.606542778095
absolute error = 3.763e-06
relative error = 8.352e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2554 0.762
h = 0.003 0.006
y[1] (numeric) = -4.46413155872 0.609744754086
y[1] (closed_form) = -4.46413175113 0.60974851199
absolute error = 3.763e-06
relative error = 8.351e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.33
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = -4.46193567775 0.614651243946
y[1] (closed_form) = -4.46193592615 0.614655529465
absolute error = 4.293e-06
relative error = 9.531e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = -4.46202870978 0.618658712383
y[1] (closed_form) = -4.46202886386 0.618662666682
absolute error = 3.957e-06
relative error = 8.785e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.37
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2586 0.776
h = 0.001 0.001
y[1] (numeric) = -4.46205311439 0.62106443806
y[1] (closed_form) = -4.46205313401 0.621068383181
absolute error = 3.945e-06
relative error = 8.757e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2596 0.777
h = 0.001 0.003
y[1] (numeric) = -4.46128727514 0.621900109398
y[1] (closed_form) = -4.46128723056 0.621904027568
absolute error = 3.918e-06
relative error = 8.699e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.8
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = -4.4605911961 0.624337484235
y[1] (closed_form) = -4.46059128456 0.624341451979
absolute error = 3.969e-06
relative error = 8.811e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.18
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2607 0.784
h = 0.003 0.006
y[1] (numeric) = -4.46065147563 0.627544479431
y[1] (closed_form) = -4.4606516586 0.627548371884
absolute error = 3.897e-06
relative error = 8.651e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.34
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = -4.45846065161 0.632455539273
y[1] (closed_form) = -4.45846089004 0.632459959253
absolute error = 4.426e-06
relative error = 9.830e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = -4.45855854958 0.636464467792
y[1] (closed_form) = -4.45855869404 0.63646855655
absolute error = 4.091e-06
relative error = 9.084e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.37
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2639 0.798
h = 0.001 0.001
y[1] (numeric) = -4.45858586282 0.638871109307
y[1] (closed_form) = -4.45858587287 0.638875188757
absolute error = 4.079e-06
relative error = 9.057e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2649 0.799
h = 0.001 0.003
y[1] (numeric) = -4.45782072943 0.63970803199
y[1] (closed_form) = -4.45782067532 0.639712084434
absolute error = 4.053e-06
relative error = 8.999e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.82
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = -4.45712731328 0.642147203536
y[1] (closed_form) = -4.45712739212 0.642151305671
absolute error = 4.103e-06
relative error = 9.111e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.19
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.266 0.806
h = 0.003 0.006
y[1] (numeric) = -4.45719147928 0.64535538811
y[1] (closed_form) = -4.45719165268 0.645359415067
absolute error = 4.031e-06
relative error = 8.950e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.35
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.269 0.812
h = 0.0001 0.005
y[1] (numeric) = -4.45500570637 0.650271021635
y[1] (closed_form) = -4.4550059347 0.650275576028
absolute error = 4.560e-06
relative error = 0.0001013 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = -4.45510846752 0.654281414596
y[1] (closed_form) = -4.45510860223 0.654285637766
absolute error = 4.225e-06
relative error = 9.384e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2692 0.82
h = 0.001 0.001
y[1] (numeric) = -4.4551386877 0.656688974543
y[1] (closed_form) = -4.45513868805 0.656693188276
absolute error = 4.214e-06
relative error = 9.357e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2702 0.821
h = 0.001 0.003
y[1] (numeric) = -4.45437425875 0.657527148919
y[1] (closed_form) = -4.45437419498 0.657531335591
absolute error = 4.187e-06
relative error = 9.299e-05 %
Correct digits = 6
memory used=340.3MB, alloc=52.3MB, time=3.97
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.83
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = -4.453683503 0.659968119286
y[1] (closed_form) = -4.45368357211 0.659972355766
absolute error = 4.237e-06
relative error = 9.411e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.2
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2713 0.828
h = 0.003 0.006
y[1] (numeric) = -4.45375155325 0.663177496714
y[1] (closed_form) = -4.45375171696 0.663181658128
absolute error = 4.165e-06
relative error = 9.249e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = -4.45157082559 0.668097707607
y[1] (closed_form) = -4.4515710437 0.668102396367
absolute error = 4.694e-06
relative error = 0.0001043 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = -4.45167844715 0.672109569364
y[1] (closed_form) = -4.45167857199 0.6721139269
absolute error = 4.359e-06
relative error = 9.683e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2745 0.842
h = 0.001 0.001
y[1] (numeric) = -4.45171157258 0.674518050332
y[1] (closed_form) = -4.4517115631 0.674522398303
absolute error = 4.348e-06
relative error = 9.657e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2755 0.843
h = 0.001 0.003
y[1] (numeric) = -4.45094784665 0.675357476746
y[1] (closed_form) = -4.4509477731 0.6753617976
absolute error = 4.321e-06
relative error = 9.599e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.85
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = -4.45025974883 0.677800248042
y[1] (closed_form) = -4.45025980806 0.677804618819
absolute error = 4.371e-06
relative error = 9.710e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.21
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2766 0.85
h = 0.003 0.006
y[1] (numeric) = -4.45033168108 0.681010821792
y[1] (closed_form) = -4.45033183497 0.681015117617
absolute error = 4.299e-06
relative error = 9.548e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.37
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = -4.44815599281 0.685935613726
y[1] (closed_form) = -4.44815620057 0.685940436805
absolute error = 4.828e-06
relative error = 0.0001073 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = -4.44826847202 0.689948948623
y[1] (closed_form) = -4.44826858685 0.689953440478
absolute error = 4.493e-06
relative error = 9.982e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2798 0.864
h = 0.001 0.001
y[1] (numeric) = -4.44830450099 0.692358353197
y[1] (closed_form) = -4.44830448156 0.692362835359
absolute error = 4.482e-06
relative error = 9.956e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = -4.44754147667 0.693199031991
y[1] (closed_form) = -4.44754139321 0.693203486981
absolute error = 4.456e-06
relative error = 9.899e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.09
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2809 0.869
h = 0.003 0.006
y[1] (numeric) = -4.44761658387 0.696410580612
y[1] (closed_form) = -4.44761677418 0.696414972196
absolute error = 4.396e-06
relative error = 9.764e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = -4.44544528327 0.70133925875
y[1] (closed_form) = -4.44544552699 0.701344177515
absolute error = 4.925e-06
relative error = 0.0001094 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.284 0.88
h = 0.0001 0.003
y[1] (numeric) = -4.44556195917 0.705353807331
y[1] (closed_form) = -4.44556211027 0.705358394868
absolute error = 4.590e-06
relative error = 0.000102 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.39
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2841 0.883
h = 0.001 0.001
y[1] (numeric) = -4.4456004971 0.707763974421
y[1] (closed_form) = -4.44560051397 0.707768552154
absolute error = 4.578e-06
relative error = 0.0001017 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2851 0.884
h = 0.001 0.003
y[1] (numeric) = -4.44483809049 0.70860572316
y[1] (closed_form) = -4.44483804337 0.708610273672
absolute error = 4.551e-06
relative error = 0.0001011 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.87
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = -4.44415495331 0.711051819559
y[1] (closed_form) = -4.44415503881 0.711056420212
absolute error = 4.601e-06
relative error = 0.0001022 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.22
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2862 0.891
h = 0.003 0.006
y[1] (numeric) = -4.44423411747 0.714264582416
y[1] (closed_form) = -4.44423429771 0.714269108327
absolute error = 4.529e-06
relative error = 0.0001006 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.39
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = -4.44206784538 0.719197848464
y[1] (closed_form) = -4.44206807851 0.719202901461
absolute error = 5.058e-06
relative error = 0.0001124 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = -4.4421893738 0.723213878282
y[1] (closed_form) = -4.44218951466 0.723218600053
absolute error = 4.724e-06
relative error = 0.000105 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.39
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2894 0.905
h = 0.001 0.001
y[1] (numeric) = -4.44223081214 0.725624973796
y[1] (closed_form) = -4.44223081881 0.725629685634
absolute error = 4.712e-06
relative error = 0.0001047 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2904 0.906
h = 0.001 0.003
y[1] (numeric) = -4.4414691045 0.72646797556
y[1] (closed_form) = -4.44146904723 0.726472660123
absolute error = 4.685e-06
relative error = 0.0001041 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.88
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = -4.44078861813 0.728915878911
y[1] (closed_form) = -4.44078869339 0.72892061373
absolute error = 4.735e-06
relative error = 0.0001052 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.23
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2915 0.913
h = 0.003 0.006
y[1] (numeric) = -4.44087165792 0.732129848006
y[1] (closed_form) = -4.44087182797 0.732134508196
absolute error = 4.663e-06
relative error = 0.0001036 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.4
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = -4.43871040848 0.737067705597
y[1] (closed_form) = -4.43871063089 0.737072892779
absolute error = 5.192e-06
relative error = 0.0001154 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=384.7MB, alloc=52.3MB, time=4.48
x[1] = 20.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = -4.43883678662 0.741085220974
y[1] (closed_form) = -4.43883691711 0.741090076932
absolute error = 4.858e-06
relative error = 0.0001079 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.39
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2947 0.927
h = 0.001 0.001
y[1] (numeric) = -4.43888112365 0.743497247484
y[1] (closed_form) = -4.43888112 0.743502093381
absolute error = 4.846e-06
relative error = 0.0001077 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2957 0.928
h = 0.001 0.003
y[1] (numeric) = -4.43812011358 0.744341502607
y[1] (closed_form) = -4.43812004602 0.744346321174
absolute error = 4.819e-06
relative error = 0.0001071 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.9
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = -4.43744227551 0.746791214993
y[1] (closed_form) = -4.43744234041 0.746796083931
absolute error = 4.869e-06
relative error = 0.0001082 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.24
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2968 0.935
h = 0.003 0.006
y[1] (numeric) = -4.43752918869 0.75000639377
y[1] (closed_form) = -4.43752934842 0.750011188192
absolute error = 4.797e-06
relative error = 0.0001066 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.41
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = -4.43537295602 0.754948846526
y[1] (closed_form) = -4.43537316757 0.754954167844
absolute error = 5.326e-06
relative error = 0.0001184 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = -4.43550418109 0.758967851777
y[1] (closed_form) = -4.43550430107 0.758972841874
absolute error = 4.992e-06
relative error = 0.0001109 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.4
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3 0.949
h = 0.001 0.001
y[1] (numeric) = -4.4355514151 0.761380811849
y[1] (closed_form) = -4.43555140098 0.761385791757
absolute error = 4.980e-06
relative error = 0.0001107 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.301 0.95
h = 0.001 0.003
y[1] (numeric) = -4.43479110116 0.762226320662
y[1] (closed_form) = -4.4347910232 0.762231273185
absolute error = 4.953e-06
relative error = 0.0001101 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.91
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.302 0.953
h = 0.0001 0.004
y[1] (numeric) = -4.4341159089 0.764677844161
y[1] (closed_form) = -4.4341159633 0.76468284717
absolute error = 5.003e-06
relative error = 0.0001112 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.24
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3021 0.957
h = 0.003 0.006
y[1] (numeric) = -4.4342066932 0.767894236058
y[1] (closed_form) = -4.43420684248 0.767899164664
absolute error = 4.931e-06
relative error = 0.0001096 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = -4.43205547142 0.772841287585
y[1] (closed_form) = -4.432055672 0.772846742991
absolute error = 5.459e-06
relative error = 0.0001213 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = -4.43219154061 0.776861787017
y[1] (closed_form) = -4.43219164997 0.776866911205
absolute error = 5.125e-06
relative error = 0.0001139 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.4
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3053 0.971
h = 0.001 0.001
y[1] (numeric) = -4.43224166988 0.779275683213
y[1] (closed_form) = -4.43224164518 0.779280797084
absolute error = 5.114e-06
relative error = 0.0001136 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = -4.43148205067 0.780122446043
y[1] (closed_form) = -4.43148196217 0.780127532475
absolute error = 5.087e-06
relative error = 0.0001131 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3064 0.976
h = 0.003 0.006
y[1] (numeric) = -4.43157600101 0.783339826542
y[1] (closed_form) = -4.43157618621 0.783344850952
absolute error = 5.028e-06
relative error = 0.0001117 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = -4.42942914256 0.788290779824
y[1] (closed_form) = -4.42942937861 0.788296330955
absolute error = 5.556e-06
relative error = 0.0001235 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = -4.42956939703 0.792312511181
y[1] (closed_form) = -4.42956954215 0.792317731094
absolute error = 5.222e-06
relative error = 0.000116 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.4
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3096 0.99
h = 0.001 0.001
y[1] (numeric) = -4.42962202825 0.794727180749
y[1] (closed_form) = -4.42962203936 0.794732390234
absolute error = 5.209e-06
relative error = 0.0001158 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3106 0.991
h = 0.001 0.003
y[1] (numeric) = -4.42886302085 0.795575015003
y[1] (closed_form) = -4.42886296819 0.795580197002
absolute error = 5.182e-06
relative error = 0.0001152 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.94
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = -4.42819276678 0.798029882622
y[1] (closed_form) = -4.42819284633 0.798035115322
absolute error = 5.233e-06
relative error = 0.0001163 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.26
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3117 0.998
h = 0.003 0.006
y[1] (numeric) = -4.42829076285 0.801248494933
y[1] (closed_form) = -4.42829093736 0.80125365344
absolute error = 5.161e-06
relative error = 0.0001147 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = -4.42614890439 0.806204053733
y[1] (closed_form) = -4.42614912922 0.806209738862
absolute error = 5.690e-06
relative error = 0.0001265 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = -4.42629399779 0.810227287297
y[1] (closed_form) = -4.42629413204 0.810232641213
absolute error = 5.356e-06
relative error = 0.000119 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.41
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3149 1.012
h = 0.001 0.001
y[1] (numeric) = -4.42634952109 0.812642897763
y[1] (closed_form) = -4.42634952138 0.812648241125
absolute error = 5.343e-06
relative error = 0.0001187 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3159 1.013
h = 0.001 0.003
y[1] (numeric) = -4.42559120578 0.813491986654
y[1] (closed_form) = -4.42559114234 0.813497302475
absolute error = 5.316e-06
relative error = 0.0001181 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.95
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = -4.42492359038 0.815948671325
memory used=429.0MB, alloc=52.3MB, time=5.00
y[1] (closed_form) = -4.42492365906 0.815954037961
absolute error = 5.367e-06
relative error = 0.0001193 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.317 1.02
h = 0.003 0.006
y[1] (numeric) = -4.4250254511 0.819168506584
y[1] (closed_form) = -4.4250256148 0.819173799141
absolute error = 5.295e-06
relative error = 0.0001177 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.32 1.026
h = 0.0001 0.005
y[1] (numeric) = -4.42288858674 0.824128674472
y[1] (closed_form) = -4.42288880023 0.824134493551
absolute error = 5.823e-06
relative error = 0.0001294 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = -4.42303851625 0.828153414527
y[1] (closed_form) = -4.42303863951 0.828158902399
absolute error = 5.489e-06
relative error = 0.000122 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.41
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3202 1.034
h = 0.001 0.001
y[1] (numeric) = -4.42309692989 0.83056996844
y[1] (closed_form) = -4.42309691924 0.83057544563
absolute error = 5.477e-06
relative error = 0.0001217 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3212 1.035
h = 0.001 0.003
y[1] (numeric) = -4.42233930527 0.831420312287
y[1] (closed_form) = -4.42233923093 0.831425761881
absolute error = 5.450e-06
relative error = 0.0001211 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = -4.42167432601 0.833878816064
y[1] (closed_form) = -4.42167438371 0.833884316588
absolute error = 5.501e-06
relative error = 0.0001223 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3223 1.042
h = 0.003 0.006
y[1] (numeric) = -4.42178004913 0.837099877685
y[1] (closed_form) = -4.42178020188 0.837105304243
absolute error = 5.429e-06
relative error = 0.0001206 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = -4.41964817296 0.842064658215
y[1] (closed_form) = -4.41964837498 0.842070611195
absolute error = 5.956e-06
relative error = 0.0001324 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = -4.41980293575 0.846090909038
y[1] (closed_form) = -4.41980304789 0.846096530816
absolute error = 5.623e-06
relative error = 0.000125 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.41
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3255 1.056
h = 0.001 0.001
y[1] (numeric) = -4.41986423801 0.848508408941
y[1] (closed_form) = -4.41986421628 0.848514019911
absolute error = 5.611e-06
relative error = 0.0001247 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3265 1.057
h = 0.001 0.003
y[1] (numeric) = -4.41910730264 0.84936000806
y[1] (closed_form) = -4.41910721728 0.84936559138
absolute error = 5.584e-06
relative error = 0.0001241 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.98
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = -4.41844495702 0.851820332992
y[1] (closed_form) = -4.4184450036 0.851825967355
absolute error = 5.635e-06
relative error = 0.0001252 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3276 1.064
h = 0.003 0.006
y[1] (numeric) = -4.41855454024 0.855042624382
y[1] (closed_form) = -4.41855468192 0.855048184893
absolute error = 5.562e-06
relative error = 0.0001236 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = -4.41642764638 0.860012021097
y[1] (closed_form) = -4.4164278368 0.860018107928
absolute error = 6.090e-06
relative error = 0.0001353 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = -4.4165872396 0.864039786955
y[1] (closed_form) = -4.41658734049 0.864045542591
absolute error = 5.757e-06
relative error = 0.0001279 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3308 1.078
h = 0.001 0.001
y[1] (numeric) = -4.41665142873 0.866458235388
y[1] (closed_form) = -4.41665139581 0.866463980088
absolute error = 5.745e-06
relative error = 0.0001276 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = -4.41589518121 0.867311090091
y[1] (closed_form) = -4.4158950847 0.867316807089
absolute error = 5.718e-06
relative error = 0.0001271 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.26
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3319 1.083
h = 0.003 0.006
y[1] (numeric) = -4.41600792147 0.870534383694
y[1] (closed_form) = -4.41600809857 0.870540040047
absolute error = 5.659e-06
relative error = 0.0001257 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = -4.41388536653 0.875507697438
y[1] (closed_form) = -4.41388559192 0.87551388003
absolute error = 6.187e-06
relative error = 0.0001375 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.335 1.094
h = 0.0001 0.003
y[1] (numeric) = -4.41404913347 0.879536713308
y[1] (closed_form) = -4.41404926963 0.879542564707
absolute error = 5.853e-06
relative error = 0.00013 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3351 1.097
h = 0.001 0.001
y[1] (numeric) = -4.41411581747 0.881955945871
y[1] (closed_form) = -4.41411581985 0.881961786224
absolute error = 5.840e-06
relative error = 0.0001297 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3361 1.098
h = 0.001 0.003
y[1] (numeric) = -4.41336017586 0.882809873419
y[1] (closed_form) = -4.41336011468 0.882815686022
absolute error = 5.813e-06
relative error = 0.0001292 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.01
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = -4.41270274587 0.885273561224
y[1] (closed_form) = -4.41270281647 0.885279425083
absolute error = 5.864e-06
relative error = 0.0001303 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.3
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3372 1.105
h = 0.003 0.006
y[1] (numeric) = -4.41281952047 0.888498104059
y[1] (closed_form) = -4.41281968627 0.888503894275
absolute error = 5.793e-06
relative error = 0.0001287 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = -4.4107019369 0.893476040612
y[1] (closed_form) = -4.41070215045 0.893482356964
absolute error = 6.320e-06
relative error = 0.0001404 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = -4.41087052903 0.897506579473
y[1] (closed_form) = -4.4108706537 0.89751256464
absolute error = 5.986e-06
relative error = 0.000133 %
Correct digits = 6
memory used=473.2MB, alloc=52.3MB, time=5.52
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3404 1.119
h = 0.001 0.001
y[1] (numeric) = -4.41094009668 0.899926765296
y[1] (closed_form) = -4.41094008763 0.899932739291
absolute error = 5.974e-06
relative error = 0.0001327 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3414 1.12
h = 0.001 0.003
y[1] (numeric) = -4.41018514029 0.900781949022
y[1] (closed_form) = -4.41018506772 0.900787895213
absolute error = 5.947e-06
relative error = 0.0001321 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.02
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = -4.40953033675 0.903247463838
y[1] (closed_form) = -4.40953039588 0.903253461398
absolute error = 5.998e-06
relative error = 0.0001333 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.31
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3425 1.127
h = 0.003 0.006
y[1] (numeric) = -4.40965096493 0.906473246182
y[1] (closed_form) = -4.40965111929 0.906479170213
absolute error = 5.926e-06
relative error = 0.0001316 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = -4.40753834681 0.911455809048
y[1] (closed_form) = -4.4075385484 0.91146225911
absolute error = 6.453e-06
relative error = 0.0001434 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = -4.40771176127 0.915487875146
y[1] (closed_form) = -4.40771187433 0.915493994031
absolute error = 6.120e-06
relative error = 0.0001359 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3457 1.141
h = 0.001 0.001
y[1] (numeric) = -4.40778421083 0.917909016754
y[1] (closed_form) = -4.40778419021 0.917915124341
absolute error = 6.108e-06
relative error = 0.0001357 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3467 1.142
h = 0.001 0.003
y[1] (numeric) = -4.40702993824 0.918765456963
y[1] (closed_form) = -4.40702985416 0.918771536693
absolute error = 6.080e-06
relative error = 0.0001351 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.03
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = -4.40637775862 0.921232800814
y[1] (closed_form) = -4.40637780615 0.921238932025
absolute error = 6.131e-06
relative error = 0.0001362 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.31
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3478 1.149
h = 0.003 0.006
y[1] (numeric) = -4.40650223807 0.92445982605
y[1] (closed_form) = -4.40650238088 0.924465883846
absolute error = 6.059e-06
relative error = 0.0001346 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = -4.4043945795 0.929447018719
y[1] (closed_form) = -4.40439476901 0.929453602441
absolute error = 6.586e-06
relative error = 0.0001463 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = -4.40457281342 0.933480616291
y[1] (closed_form) = -4.40457291474 0.933486868846
absolute error = 6.253e-06
relative error = 0.0001389 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.351 1.163
h = 0.001 0.001
y[1] (numeric) = -4.40464814314 0.935902716205
y[1] (closed_form) = -4.40464811083 0.935908957335
absolute error = 6.241e-06
relative error = 0.0001386 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.352 1.164
h = 0.001 0.003
y[1] (numeric) = -4.40389455294 0.936760413198
y[1] (closed_form) = -4.40389445721 0.936766626417
absolute error = 6.214e-06
relative error = 0.000138 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.05
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.353 1.167
h = 0.0001 0.004
y[1] (numeric) = -4.40324499472 0.939229588103
y[1] (closed_form) = -4.40324503051 0.939235852916
absolute error = 6.265e-06
relative error = 0.0001391 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.32
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3531 1.171
h = 0.003 0.006
y[1] (numeric) = -4.40337332312 0.942457859607
y[1] (closed_form) = -4.40337345424 0.942464051119
absolute error = 6.193e-06
relative error = 0.0001375 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = -4.40127061818 0.947449685556
y[1] (closed_form) = -4.40127079548 0.947456402887
absolute error = 6.720e-06
relative error = 0.0001493 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = -4.4014536687 0.951484818832
y[1] (closed_form) = -4.40145375816 0.951491205006
absolute error = 6.387e-06
relative error = 0.0001418 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3563 1.185
h = 0.001 0.001
y[1] (numeric) = -4.40153187681 0.953907879566
y[1] (closed_form) = -4.40153183269 0.953914254189
absolute error = 6.375e-06
relative error = 0.0001415 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = -4.40077896758 0.954766833644
y[1] (closed_form) = -4.40077886009 0.954773180303
absolute error = 6.348e-06
relative error = 0.000141 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.34
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3574 1.19
h = 0.003 0.006
y[1] (numeric) = -4.40091044392 0.957996120848
y[1] (closed_form) = -4.40091060995 0.958002408237
absolute error = 6.290e-06
relative error = 0.0001396 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = -4.3988120534 0.962991878831
y[1] (closed_form) = -4.39881226517 0.962998691953
absolute error = 6.816e-06
relative error = 0.0001514 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = -4.39899926595 0.967028280042
y[1] (closed_form) = -4.39899939017 0.967034762013
absolute error = 6.483e-06
relative error = 0.0001439 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3606 1.204
h = 0.001 0.001
y[1] (numeric) = -4.39907996176 0.96945213557
y[1] (closed_form) = -4.39907995244 0.96945860588
absolute error = 6.470e-06
relative error = 0.0001436 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3616 1.205
h = 0.001 0.003
y[1] (numeric) = -4.39832765254 0.970312163852
y[1] (closed_form) = -4.39832757989 0.970318606152
absolute error = 6.443e-06
relative error = 0.000143 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.07
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = -4.39768298727 0.972784720118
y[1] (closed_form) = -4.39768304597 0.972791214223
absolute error = 6.494e-06
relative error = 0.0001442 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.34
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=517.5MB, alloc=52.3MB, time=6.04
x[1] = 20.3627 1.212
h = 0.003 0.006
y[1] (numeric) = -4.39781848645 0.976015273819
y[1] (closed_form) = -4.39781864056 0.976021694832
absolute error = 6.423e-06
relative error = 0.0001426 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = -4.39572503859 0.981015671584
y[1] (closed_form) = -4.39572523792 0.981022618223
absolute error = 6.949e-06
relative error = 0.0001543 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = -4.39591706243 0.985053616384
y[1] (closed_form) = -4.39591717455 0.985060231882
absolute error = 6.616e-06
relative error = 0.0001469 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3659 1.226
h = 0.001 0.001
y[1] (numeric) = -4.39600063338 0.98747843742
y[1] (closed_form) = -4.39600061201 0.987485041132
absolute error = 6.604e-06
relative error = 0.0001466 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3669 1.227
h = 0.001 0.003
y[1] (numeric) = -4.39524900251 0.988339723352
y[1] (closed_form) = -4.39524891785 0.988346299
absolute error = 6.576e-06
relative error = 0.000146 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.09
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = -4.39460695141 0.990814116444
y[1] (closed_form) = -4.39460699803 0.990820744008
absolute error = 6.628e-06
relative error = 0.0001471 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.35
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.368 1.234
h = 0.003 0.006
y[1] (numeric) = -4.39474629296 0.994045926064
y[1] (closed_form) = -4.39474643502 0.994052480651
absolute error = 6.556e-06
relative error = 0.0001455 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.371 1.24
h = 0.0001 0.005
y[1] (numeric) = -4.39265778183 0.99905096705
y[1] (closed_form) = -4.39265796859 0.999058047154
absolute error = 7.083e-06
relative error = 0.0001572 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = -4.39285461406 1.00309045964
y[1] (closed_form) = -4.39285471396 1.00309720862
absolute error = 6.750e-06
relative error = 0.0001498 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3712 1.248
h = 0.001 0.001
y[1] (numeric) = -4.39294105839 1.00551624869
y[1] (closed_form) = -4.39294102485 1.00552298575
absolute error = 6.737e-06
relative error = 0.0001495 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3722 1.249
h = 0.001 0.003
y[1] (numeric) = -4.39219010445 1.00637879256
y[1] (closed_form) = -4.39219000766 1.00638550151
absolute error = 6.710e-06
relative error = 0.0001489 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.1
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = -4.391550665 1.00885502448
y[1] (closed_form) = -4.3915506994 1.00886178545
absolute error = 6.761e-06
relative error = 0.00015 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.35
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3733 1.256
h = 0.003 0.006
y[1] (numeric) = -4.39169384656 1.01208809337
y[1] (closed_form) = -4.39169397645 1.01209478148
absolute error = 6.689e-06
relative error = 0.0001484 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = -4.38961026625 1.017097781
y[1] (closed_form) = -4.38961044031 1.01710499452
absolute error = 7.216e-06
relative error = 0.0001601 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = -4.38981190398 1.02113882559
y[1] (closed_form) = -4.38981199152 1.02114570799
absolute error = 6.883e-06
relative error = 0.0001527 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3765 1.27
h = 0.001 0.001
y[1] (numeric) = -4.3899012199 1.02356558514
y[1] (closed_form) = -4.38990117406 1.0235724555
absolute error = 6.871e-06
relative error = 0.0001524 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3775 1.271
h = 0.001 0.003
y[1] (numeric) = -4.38915094148 1.02442938724
y[1] (closed_form) = -4.38915083244 1.02443622943
absolute error = 6.843e-06
relative error = 0.0001518 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.12
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = -4.38851411114 1.02690745996
y[1] (closed_form) = -4.3885141332 1.0269143543
absolute error = 6.894e-06
relative error = 0.000153 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3786 1.278
h = 0.003 0.006
y[1] (numeric) = -4.38866113039 1.03014179147
y[1] (closed_form) = -4.38866124798 1.03014861306
absolute error = 6.823e-06
relative error = 0.0001513 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = -4.38658247495 1.03515612916
y[1] (closed_form) = -4.38658263619 1.03516347604
absolute error = 7.349e-06
relative error = 0.000163 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = -4.38678891528 1.03919872993
y[1] (closed_form) = -4.38678899035 1.03920574571
absolute error = 7.016e-06
relative error = 0.0001556 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3818 1.292
h = 0.001 0.001
y[1] (numeric) = -4.38688110103 1.04162646248
y[1] (closed_form) = -4.38688104277 1.04163346609
absolute error = 7.004e-06
relative error = 0.0001553 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = -4.38613149671 1.0424915231
y[1] (closed_form) = -4.3861313753 1.04249849849
absolute error = 6.976e-06
relative error = 0.0001547 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3829 1.297
h = 0.003 0.006
y[1] (numeric) = -4.38628165469 1.04572688367
y[1] (closed_form) = -4.38628180669 1.04573380116
absolute error = 6.919e-06
relative error = 0.0001534 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = -4.38420728912 1.05074516812
y[1] (closed_form) = -4.38420748432 1.05075261082
absolute error = 7.445e-06
relative error = 0.0001651 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.386 1.308
h = 0.0001 0.003
y[1] (numeric) = -4.38441787964 1.05478905459
y[1] (closed_form) = -4.38441798897 1.0547961662
absolute error = 7.112e-06
relative error = 0.0001577 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3861 1.311
h = 0.001 0.001
y[1] (numeric) = -4.38451254584 1.0572175925
y[1] (closed_form) = -4.38451252188 1.05722469183
absolute error = 7.099e-06
relative error = 0.0001574 %
Correct digits = 6
memory used=562.0MB, alloc=52.3MB, time=6.56
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3871 1.312
h = 0.001 0.003
y[1] (numeric) = -4.38376353564 1.05808372862
y[1] (closed_form) = -4.38376344856 1.05809079969
absolute error = 7.072e-06
relative error = 0.0001568 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.14
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = -4.38313157545 1.06056520093
y[1] (closed_form) = -4.38313161931 1.06057232434
absolute error = 7.124e-06
relative error = 0.000158 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3882 1.319
h = 0.003 0.006
y[1] (numeric) = -4.38328574464 1.0638018451
y[1] (closed_form) = -4.3832858841 1.06380889598
absolute error = 7.052e-06
relative error = 0.0001564 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = -4.38121629294 1.068824786
y[1] (closed_form) = -4.38121647509 1.06883236196
absolute error = 7.578e-06
relative error = 0.000168 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = -4.38143168069 1.07287023646
y[1] (closed_form) = -4.38143177732 1.07287748135
absolute error = 7.246e-06
relative error = 0.0001606 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3914 1.333
h = 0.001 0.001
y[1] (numeric) = -4.38152921343 1.07529975201
y[1] (closed_form) = -4.38152917682 1.0753069845
absolute error = 7.233e-06
relative error = 0.0001603 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3924 1.334
h = 0.001 0.003
y[1] (numeric) = -4.38078087471 1.07616714719
y[1] (closed_form) = -4.38078077502 1.07617435136
absolute error = 7.205e-06
relative error = 0.0001597 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.16
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = -4.38015151638 1.07865046599
y[1] (closed_form) = -4.38015154753 1.07865772262
absolute error = 7.257e-06
relative error = 0.0001609 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3935 1.341
h = 0.003 0.006
y[1] (numeric) = -4.38030951658 1.08188838235
y[1] (closed_form) = -4.38030964339 1.08189556655
absolute error = 7.185e-06
relative error = 0.0001593 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = -4.37824497282 1.08691598305
y[1] (closed_form) = -4.37824514179 1.08692369223
absolute error = 7.711e-06
relative error = 0.0001709 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = -4.37846515488 1.09096300168
y[1] (closed_form) = -4.37846523867 1.0909703798
absolute error = 7.379e-06
relative error = 0.0001635 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3967 1.355
h = 0.001 0.001
y[1] (numeric) = -4.37856555237 1.09339349735
y[1] (closed_form) = -4.37856550297 1.09340086294
absolute error = 7.366e-06
relative error = 0.0001632 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3977 1.356
h = 0.001 0.003
y[1] (numeric) = -4.37781788371 1.09426215186
y[1] (closed_form) = -4.37781777129 1.09426948908
absolute error = 7.338e-06
relative error = 0.0001626 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = -4.37719112469 1.09674731912
y[1] (closed_form) = -4.37719114302 1.09675470891
absolute error = 7.390e-06
relative error = 0.0001638 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.39
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.3988 1.363
h = 0.003 0.006
y[1] (numeric) = -4.37735295355 1.09998651098
y[1] (closed_form) = -4.37735306757 1.09999382845
absolute error = 7.318e-06
relative error = 0.0001621 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = -4.37529331178 1.10501877485
y[1] (closed_form) = -4.37529346745 1.10502661719
absolute error = 7.844e-06
relative error = 0.0001738 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = -4.37551828522 1.1090673658
y[1] (closed_form) = -4.37551835606 1.1090748771
absolute error = 7.512e-06
relative error = 0.0001664 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.402 1.377
h = 0.001 0.001
y[1] (numeric) = -4.37562154567 1.11149884406
y[1] (closed_form) = -4.37562148337 1.11150634271
absolute error = 7.499e-06
relative error = 0.0001661 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.403 1.378
h = 0.001 0.003
y[1] (numeric) = -4.37487454567 1.11236875818
y[1] (closed_form) = -4.37487442039 1.1123762284
absolute error = 7.471e-06
relative error = 0.0001655 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.19
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.404 1.381
h = 0.0001 0.004
y[1] (numeric) = -4.3742503834 1.11485577587
y[1] (closed_form) = -4.37425038878 1.11486329877
absolute error = 7.523e-06
relative error = 0.0001667 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.4
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4041 1.385
h = 0.003 0.006
y[1] (numeric) = -4.37441603856 1.11809624653
y[1] (closed_form) = -4.37441613967 1.11810369723
absolute error = 7.451e-06
relative error = 0.000165 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = -4.37236129285 1.12313317692
y[1] (closed_form) = -4.37236143509 1.12314115237
absolute error = 7.977e-06
relative error = 0.0001767 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = -4.37259105473 1.12718334435
y[1] (closed_form) = -4.37259111248 1.12719098877
absolute error = 7.645e-06
relative error = 0.0001693 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4073 1.399
h = 0.001 0.001
y[1] (numeric) = -4.37269717635 1.12961580767
y[1] (closed_form) = -4.37269710101 1.12962343932
absolute error = 7.632e-06
relative error = 0.000169 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4083 1.4
h = 0.003 0.006
y[1] (numeric) = -4.37195084359 1.13048698165
y[1] (closed_form) = -4.37195070532 1.13049458483
absolute error = 7.604e-06
relative error = 0.0001684 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 106.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = -4.36989888963 1.13552713838
y[1] (closed_form) = -4.36989924721 1.135535375
absolute error = 8.244e-06
relative error = 0.0001826 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=606.4MB, alloc=52.3MB, time=7.06
x[1] = 20.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = -4.37013190389 1.13957851319
y[1] (closed_form) = -4.37013217721 1.13958641879
absolute error = 7.910e-06
relative error = 0.0001752 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4115 1.414
h = 0.001 0.001
y[1] (numeric) = -4.37023996773 1.14201172757
y[1] (closed_form) = -4.370240108 1.14201962032
absolute error = 7.894e-06
relative error = 0.0001748 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4125 1.415
h = 0.001 0.003
y[1] (numeric) = -4.3694940614 1.14288378513
y[1] (closed_form) = -4.36949413877 1.14289164937
absolute error = 7.865e-06
relative error = 0.0001741 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.22
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = -4.36887422965 1.14537399583
y[1] (closed_form) = -4.36887443753 1.14538191293
absolute error = 7.920e-06
relative error = 0.0001754 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4136 1.422
h = 0.003 0.006
y[1] (numeric) = -4.36904630539 1.14861672874
y[1] (closed_form) = -4.36904660907 1.14862457383
absolute error = 7.851e-06
relative error = 0.0001738 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = -4.36699969243 1.15366166623
y[1] (closed_form) = -4.36700003637 1.15367003587
absolute error = 8.377e-06
relative error = 0.0001855 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = -4.36723749006 1.15771462443
y[1] (closed_form) = -4.36723775009 1.15772266307
absolute error = 8.043e-06
relative error = 0.000178 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4168 1.436
h = 0.001 0.001
y[1] (numeric) = -4.36734841196 1.16014882798
y[1] (closed_form) = -4.36734853899 1.16015685364
absolute error = 8.027e-06
relative error = 0.0001776 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4178 1.437
h = 0.001 0.003
y[1] (numeric) = -4.36660317049 1.16102214583
y[1] (closed_form) = -4.36660323467 1.16103014293
absolute error = 7.997e-06
relative error = 0.000177 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.23
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = -4.36598592858 1.16351421213
y[1] (closed_form) = -4.36598612318 1.1635222622
absolute error = 8.052e-06
relative error = 0.0001782 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4189 1.444
h = 0.003 0.006
y[1] (numeric) = -4.36616182416 1.16675823266
y[1] (closed_form) = -4.3661621146 1.16676621084
absolute error = 7.983e-06
relative error = 0.0001766 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = -4.36412009117 1.17180784545
y[1] (closed_form) = -4.36412042136 1.17181634805
absolute error = 8.509e-06
relative error = 0.0001883 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.422 1.455
h = 0.0001 0.003
y[1] (numeric) = -4.36436266924 1.17586239117
y[1] (closed_form) = -4.36436291585 1.17587056279
absolute error = 8.175e-06
relative error = 0.0001809 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4221 1.458
h = 0.001 0.001
y[1] (numeric) = -4.3644764474 1.17829758634
y[1] (closed_form) = -4.36447656107 1.17830574486
absolute error = 8.159e-06
relative error = 0.0001805 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4231 1.459
h = 0.001 0.003
y[1] (numeric) = -4.36373186937 1.17917216474
y[1] (closed_form) = -4.36373192023 1.17918029465
absolute error = 8.130e-06
relative error = 0.0001799 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.25
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = -4.36311721474 1.18166608857
y[1] (closed_form) = -4.36311739594 1.18167427156
absolute error = 8.185e-06
relative error = 0.0001811 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4242 1.466
h = 0.003 0.006
y[1] (numeric) = -4.36329692779 1.18491140002
y[1] (closed_form) = -4.36329720486 1.18491951124
absolute error = 8.116e-06
relative error = 0.0001795 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = -4.36126006882 1.1899656914
y[1] (closed_form) = -4.36126038512 1.18997432692
absolute error = 8.641e-06
relative error = 0.0001912 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = -4.36150742435 1.19402182876
y[1] (closed_form) = -4.36150765743 1.19403013332
absolute error = 8.308e-06
relative error = 0.0001837 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4274 1.48
h = 0.001 0.001
y[1] (numeric) = -4.36162405696 1.196458018
y[1] (closed_form) = -4.36162415715 1.19646630933
absolute error = 8.292e-06
relative error = 0.0001833 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = -4.36088014097 1.19733385722
y[1] (closed_form) = -4.36088017839 1.19734211988
absolute error = 8.263e-06
relative error = 0.0001827 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4285 1.485
h = 0.003 0.006
y[1] (numeric) = -4.36106297621 1.20058022087
y[1] (closed_form) = -4.36106328682 1.20058842803
absolute error = 8.213e-06
relative error = 0.0001816 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = -4.35903036364 1.20563848409
y[1] (closed_form) = -4.35903071303 1.20564721545
absolute error = 8.738e-06
relative error = 0.0001932 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = -4.35928184812 1.20969593791
y[1] (closed_form) = -4.35928211458 1.20970433833
absolute error = 8.405e-06
relative error = 0.0001858 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4317 1.499
h = 0.001 0.001
y[1] (numeric) = -4.35940094818 1.2121329508
y[1] (closed_form) = -4.35940108179 1.21214133788
absolute error = 8.388e-06
relative error = 0.0001854 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4327 1.5
h = 0.001 0.003
y[1] (numeric) = -4.35865761593 1.21300986763
y[1] (closed_form) = -4.35865768682 1.213018226
absolute error = 8.359e-06
relative error = 0.0001848 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=650.8MB, alloc=52.3MB, time=7.58
x[1] = 20.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = -4.358047791 1.21550722228
y[1] (closed_form) = -4.35804799206 1.21551563394
absolute error = 8.414e-06
relative error = 0.000186 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4338 1.507
h = 0.003 0.006
y[1] (numeric) = -4.35823461657 1.21875489916
y[1] (closed_form) = -4.35823491359 1.21876323925
absolute error = 8.345e-06
relative error = 0.0001844 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = -4.35620686698 1.22381784713
y[1] (closed_form) = -4.35620720226 1.22382671131
absolute error = 8.871e-06
relative error = 0.000196 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = -4.35646312346 1.22787690028
y[1] (closed_form) = -4.35646337615 1.22788543352
absolute error = 8.537e-06
relative error = 0.0001886 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.437 1.521
h = 0.001 0.001
y[1] (numeric) = -4.35658507462 1.2303149118
y[1] (closed_form) = -4.35658519452 1.23032343159
absolute error = 8.521e-06
relative error = 0.0001882 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.438 1.522
h = 0.001 0.003
y[1] (numeric) = -4.35584240179 1.23119308994
y[1] (closed_form) = -4.35584245901 1.23120158097
absolute error = 8.491e-06
relative error = 0.0001876 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.29
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.439 1.525
h = 0.0001 0.004
y[1] (numeric) = -4.35523515684 1.23369230767
y[1] (closed_form) = -4.35523534413 1.23370085209
absolute error = 8.546e-06
relative error = 0.0001888 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4391 1.529
h = 0.003 0.006
y[1] (numeric) = -4.35542579308 1.23694128486
y[1] (closed_form) = -4.35542607637 1.23694975783
absolute error = 8.478e-06
relative error = 0.0001872 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = -4.35340290049 1.24200892085
y[1] (closed_form) = -4.35340322153 1.24201791778
absolute error = 9.003e-06
relative error = 0.0001989 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = -4.353663926 1.24606957742
y[1] (closed_form) = -4.3536641648 1.24607824345
absolute error = 8.669e-06
relative error = 0.0001914 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4423 1.543
h = 0.001 0.001
y[1] (numeric) = -4.35378872645 1.24850859002
y[1] (closed_form) = -4.3537888325 1.24851724246
absolute error = 8.653e-06
relative error = 0.000191 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4433 1.544
h = 0.001 0.003
y[1] (numeric) = -4.35304671162 1.24938802972
y[1] (closed_form) = -4.35304675505 1.24939665335
absolute error = 8.624e-06
relative error = 0.0001904 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.3
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = -4.35244204408 1.25188911243
y[1] (closed_form) = -4.35244221749 1.25189778957
absolute error = 8.679e-06
relative error = 0.0001916 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4444 1.551
h = 0.003 0.006
y[1] (numeric) = -4.35263648858 1.2551393932
y[1] (closed_form) = -4.35263675803 1.255147999
absolute error = 8.610e-06
relative error = 0.0001901 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = -4.35061844703 1.26021172045
y[1] (closed_form) = -4.35061875372 1.26022085009
absolute error = 9.135e-06
relative error = 0.0002017 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = -4.3508842386 1.26427398453
y[1] (closed_form) = -4.35088446338 1.26428278329
absolute error = 8.802e-06
relative error = 0.0001943 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4476 1.565
h = 0.001 0.001
y[1] (numeric) = -4.35101188651 1.26671400063
y[1] (closed_form) = -4.3510119786 1.26672278569
absolute error = 8.786e-06
relative error = 0.0001939 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4486 1.566
h = 0.001 0.003
y[1] (numeric) = -4.35027052827 1.26759470214
y[1] (closed_form) = -4.35027055779 1.26760345833
absolute error = 8.756e-06
relative error = 0.0001932 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.32
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = -4.34966843557 1.27009765175
y[1] (closed_form) = -4.34966859498 1.27010646155
absolute error = 8.811e-06
relative error = 0.0001945 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4497 1.573
h = 0.003 0.006
y[1] (numeric) = -4.34986668595 1.27334923937
y[1] (closed_form) = -4.34986694142 1.27335797794
absolute error = 8.742e-06
relative error = 0.0001929 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = -4.34785348947 1.2784262611
y[1] (closed_form) = -4.34785378167 1.2784355234
absolute error = 9.267e-06
relative error = 0.0002045 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.78
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = -4.3481240441 1.28249013677
y[1] (closed_form) = -4.34812425474 1.2824990682
absolute error = 8.934e-06
relative error = 0.0001971 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4529 1.587
h = 0.001 0.001
y[1] (numeric) = -4.34825453765 1.28493115881
y[1] (closed_form) = -4.34825461565 1.28494007641
absolute error = 8.918e-06
relative error = 0.0001967 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = -4.3475138346 1.28581312237
y[1] (closed_form) = -4.34751385007 1.28582201106
absolute error = 8.889e-06
relative error = 0.0001961 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.454 1.592
h = 0.003 0.006
y[1] (numeric) = -4.34771519769 1.2890657752
y[1] (closed_form) = -4.34771548621 1.28907460974
absolute error = 8.839e-06
relative error = 0.0001949 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.457 1.598
h = 0.0001 0.005
y[1] (numeric) = -4.34570622288 1.29414678276
y[1] (closed_form) = -4.34570654768 1.29415614091
absolute error = 9.364e-06
relative error = 0.0002065 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.78
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = -4.34598089426 1.29821199221
y[1] (closed_form) = -4.34598113779 1.29822101952
absolute error = 9.031e-06
relative error = 0.0001991 %
Correct digits = 6
memory used=695.0MB, alloc=52.3MB, time=8.08
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4572 1.606
h = 0.001 0.001
y[1] (numeric) = -4.3461138478 1.30065384818
y[1] (closed_form) = -4.34611395874 1.30066286156
absolute error = 9.014e-06
relative error = 0.0001987 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4582 1.607
h = 0.001 0.003
y[1] (numeric) = -4.34537372262 1.3015368905
y[1] (closed_form) = -4.34537377107 1.30154587491
absolute error = 8.985e-06
relative error = 0.0001981 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.35
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = -4.34477643655 1.30404328842
y[1] (closed_form) = -4.34477661472 1.30405232665
absolute error = 9.040e-06
relative error = 0.0001993 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4593 1.614
h = 0.003 0.006
y[1] (numeric) = -4.34498177799 1.30729727114
y[1] (closed_form) = -4.34498205231 1.30730623835
absolute error = 8.971e-06
relative error = 0.0001977 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = -4.34297763718 1.31238297924
y[1] (closed_form) = -4.34297794727 1.31239246994
absolute error = 9.496e-06
relative error = 0.0002093 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = -4.3432570661 1.31644980789
y[1] (closed_form) = -4.34325729527 1.31645896777
absolute error = 9.163e-06
relative error = 0.0002019 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4625 1.628
h = 0.001 0.001
y[1] (numeric) = -4.34339286191 1.31889267431
y[1] (closed_form) = -4.34339295853 1.31890182014
absolute error = 9.146e-06
relative error = 0.0002015 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4635 1.629
h = 0.001 0.003
y[1] (numeric) = -4.34265338929 1.31977697915
y[1] (closed_form) = -4.34265342347 1.31978609596
absolute error = 9.117e-06
relative error = 0.0002009 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = -4.34205867072 1.32228524943
y[1] (closed_form) = -4.34205883453 1.32229442016
absolute error = 9.172e-06
relative error = 0.0002021 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4646 1.636
h = 0.003 0.006
y[1] (numeric) = -4.34226781117 1.3255405483
y[1] (closed_form) = -4.34226807117 1.32554964813
absolute error = 9.104e-06
relative error = 0.0002005 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = -4.34026849838 1.33063096012
y[1] (closed_form) = -4.34026879364 1.33064058332
absolute error = 9.628e-06
relative error = 0.0002121 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = -4.34055268184 1.33469941204
y[1] (closed_form) = -4.34055289651 1.33470870444
absolute error = 9.295e-06
relative error = 0.0002047 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4678 1.65
h = 0.001 0.001
y[1] (numeric) = -4.34069131807 1.33714329132
y[1] (closed_form) = -4.34069140026 1.33715256954
absolute error = 9.279e-06
relative error = 0.0002043 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4688 1.651
h = 0.001 0.003
y[1] (numeric) = -4.33995249662 1.33802885893
y[1] (closed_form) = -4.3399525164 1.33803810808
absolute error = 9.249e-06
relative error = 0.0002037 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = -4.33936034297 1.34053900343
y[1] (closed_form) = -4.3393604923 1.34054830662
absolute error = 9.304e-06
relative error = 0.0002049 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4699 1.658
h = 0.003 0.006
y[1] (numeric) = -4.33957328 1.34379562169
y[1] (closed_form) = -4.33957352556 1.34380485409
absolute error = 9.236e-06
relative error = 0.0002033 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = -4.33757878926 1.34889074042
y[1] (closed_form) = -4.33757906956 1.34890049606
absolute error = 9.760e-06
relative error = 0.0002149 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.8
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.473 1.669
h = 0.0001 0.003
y[1] (numeric) = -4.33786772425 1.35296081965
y[1] (closed_form) = -4.33786792431 1.35297024451
absolute error = 9.427e-06
relative error = 0.0002075 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4731 1.672
h = 0.001 0.001
y[1] (numeric) = -4.33800919906 1.3554057142
y[1] (closed_form) = -4.33800926669 1.35541512476
absolute error = 9.411e-06
relative error = 0.0002071 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4741 1.673
h = 0.001 0.003
y[1] (numeric) = -4.33727102736 1.3562925448
y[1] (closed_form) = -4.33727103263 1.35630192625
absolute error = 9.381e-06
relative error = 0.0002064 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.39
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = -4.33668143606 1.35880456542
y[1] (closed_form) = -4.33668157079 1.35881400101
absolute error = 9.437e-06
relative error = 0.0002076 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4752 1.68
h = 0.003 0.006
y[1] (numeric) = -4.33689816725 1.36206250629
y[1] (closed_form) = -4.33689839824 1.3620718712
absolute error = 9.368e-06
relative error = 0.0002061 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = -4.33490849257 1.36716233509
y[1] (closed_form) = -4.33490875779 1.36717222312
absolute error = 9.892e-06
relative error = 0.0002176 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.8
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = -4.33520217607 1.37123404567
y[1] (closed_form) = -4.33520236139 1.37124360295
absolute error = 9.559e-06
relative error = 0.0002102 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4784 1.694
h = 0.001 0.001
y[1] (numeric) = -4.33534648762 1.37367995789
y[1] (closed_form) = -4.33534654057 1.37368950075
absolute error = 9.543e-06
relative error = 0.0002098 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = -4.33460896427 1.37456805173
y[1] (closed_form) = -4.33460895491 1.37457756541
absolute error = 9.514e-06
relative error = 0.0002092 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.78
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=739.3MB, alloc=52.3MB, time=8.60
x[1] = 20.4795 1.699
h = 0.003 0.006
y[1] (numeric) = -4.3348287986 1.3778270707
y[1] (closed_form) = -4.33482906214 1.37783653158
absolute error = 9.465e-06
relative error = 0.0002081 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = -4.33284332079 1.38293089904
y[1] (closed_form) = -4.33284361812 1.38294088293
absolute error = 9.988e-06
relative error = 0.0002196 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.81
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = -4.33314110874 1.38700396054
y[1] (closed_form) = -4.33314132646 1.3870136137
absolute error = 9.656e-06
relative error = 0.0002122 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4827 1.713
h = 0.001 0.001
y[1] (numeric) = -4.33328787275 1.3894507169
y[1] (closed_form) = -4.33328795814 1.38946035553
absolute error = 9.639e-06
relative error = 0.0002118 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4837 1.714
h = 0.001 0.003
y[1] (numeric) = -4.33255092139 1.39033989056
y[1] (closed_form) = -4.33255094452 1.39034949998
absolute error = 9.609e-06
relative error = 0.0002112 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = -4.33196611356 1.39285537672
y[1] (closed_form) = -4.33196626596 1.39286504048
absolute error = 9.665e-06
relative error = 0.0002124 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4848 1.721
h = 0.003 0.006
y[1] (numeric) = -4.33218991416 1.39611574209
y[1] (closed_form) = -4.3321901629 1.39612533539
absolute error = 9.597e-06
relative error = 0.0002108 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.81
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = -4.33020924131 1.40122428643
y[1] (closed_form) = -4.33020952334 1.4012344026
absolute error = 1.012e-05
relative error = 0.0002224 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.81
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = -4.33051177219 1.40529898682
y[1] (closed_form) = -4.33051197495 1.40530877229
absolute error = 9.788e-06
relative error = 0.000215 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.488 1.735
h = 0.001 0.001
y[1] (numeric) = -4.33066136954 1.40774676532
y[1] (closed_form) = -4.33066144002 1.40775653614
absolute error = 9.771e-06
relative error = 0.0002146 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.489 1.736
h = 0.001 0.003
y[1] (numeric) = -4.32992506391 1.40863720266
y[1] (closed_form) = -4.32992507217 1.40864694422
absolute error = 9.742e-06
relative error = 0.0002139 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.49 1.739
h = 0.0001 0.004
y[1] (numeric) = -4.32934281106 1.41115457029
y[1] (closed_form) = -4.32934294851 1.4111643663
absolute error = 9.797e-06
relative error = 0.0002152 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4901 1.743
h = 0.003 0.006
y[1] (numeric) = -4.32957039888 1.4144162675
y[1] (closed_form) = -4.32957063271 1.41442599315
absolute error = 9.728e-06
relative error = 0.0002136 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.82
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = -4.32759452502 1.41952953096
y[1] (closed_form) = -4.32759479162 1.41953977937
absolute error = 1.025e-05
relative error = 0.0002251 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.82
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = -4.32790179581 1.42360587426
y[1] (closed_form) = -4.32790198347 1.42361579199
absolute error = 9.920e-06
relative error = 0.0002177 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4933 1.757
h = 0.001 0.001
y[1] (numeric) = -4.32805422463 1.42605467729
y[1] (closed_form) = -4.32805428008 1.42606458025
absolute error = 9.903e-06
relative error = 0.0002173 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4943 1.758
h = 0.001 0.003
y[1] (numeric) = -4.32731856333 1.42694637853
y[1] (closed_form) = -4.32731855661 1.42695625218
absolute error = 9.874e-06
relative error = 0.0002167 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = -4.32673886287 1.4294656295
y[1] (closed_form) = -4.32673898525 1.4294755577
absolute error = 9.929e-06
relative error = 0.0002179 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4954 1.765
h = 0.003 0.006
y[1] (numeric) = -4.32697023548 1.43272866174
y[1] (closed_form) = -4.32697045427 1.4327385197
absolute error = 9.860e-06
relative error = 0.0002163 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.83
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = -4.3249991546 1.43784664745
y[1] (closed_form) = -4.32499940565 1.43785702803
absolute error = 1.038e-05
relative error = 0.0002278 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.57
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.82
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = -4.32531116226 1.44192463766
y[1] (closed_form) = -4.32531133472 1.44193468759
absolute error = 1.005e-05
relative error = 0.0002205 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.57
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4986 1.779
h = 0.001 0.001
y[1] (numeric) = -4.3254664207 1.44437446761
y[1] (closed_form) = -4.325466461 1.44438450264
absolute error = 1.004e-05
relative error = 0.0002201 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.57
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.4996 1.78
h = 0.001 0.003
y[1] (numeric) = -4.32473140232 1.44526743297
y[1] (closed_form) = -4.3247313805 1.44527743864
absolute error = 1.001e-05
relative error = 0.0002194 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.57
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.47
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = -4.32415425168 1.44778856913
y[1] (closed_form) = -4.32415435885 1.44779862946
absolute error = 1.006e-05
relative error = 0.0002206 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.57
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5007 1.787
h = 0.003 0.006
y[1] (numeric) = -4.32438940662 1.45105293958
y[1] (closed_form) = -4.32438961024 1.45106292979
absolute error = 9.992e-06
relative error = 0.0002191 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.57
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.84
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = -4.32242311274 1.45617565064
y[1] (closed_form) = -4.32242334812 1.45618616333
absolute error = 1.052e-05
relative error = 0.0002305 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.83
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = -4.32273985421 1.46025529177
y[1] (closed_form) = -4.32274001135 1.46026547384
absolute error = 1.018e-05
relative error = 0.0002232 %
Correct digits = 6
memory used=783.8MB, alloc=52.3MB, time=9.11
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5039 1.801
h = 0.001 0.001
y[1] (numeric) = -4.32289794042 1.46270615101
y[1] (closed_form) = -4.32289796545 1.46271631806
absolute error = 1.017e-05
relative error = 0.0002228 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = -4.32216356356 1.4636003807
y[1] (closed_form) = -4.32216352651 1.46361051835
absolute error = 1.014e-05
relative error = 0.0002222 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.88
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.505 1.806
h = 0.003 0.006
y[1] (numeric) = -4.32240181199 1.46686584203
y[1] (closed_form) = -4.32240204766 1.46687592822
absolute error = 1.009e-05
relative error = 0.000221 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.85
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.508 1.812
h = 0.0001 0.005
y[1] (numeric) = -4.32043969013 1.47199256605
y[1] (closed_form) = -4.32043995713 1.47200317462
absolute error = 1.061e-05
relative error = 0.0002325 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.83
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = -4.32076052362 1.4760735751
y[1] (closed_form) = -4.32076071266 1.47608385306
absolute error = 1.028e-05
relative error = 0.0002251 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.55
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5082 1.82
h = 0.001 0.001
y[1] (numeric) = -4.32092105468 1.47852528856
y[1] (closed_form) = -4.32092111165 1.4785355514
absolute error = 1.026e-05
relative error = 0.0002247 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5092 1.821
h = 0.001 0.003
y[1] (numeric) = -4.32018724395 1.47942059911
y[1] (closed_form) = -4.32018723889 1.4794308325
absolute error = 1.023e-05
relative error = 0.0002241 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.5
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = -4.31961485351 1.48194521776
y[1] (closed_form) = -4.31961497729 1.48195550601
absolute error = 1.029e-05
relative error = 0.0002253 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5103 1.828
h = 0.003 0.006
y[1] (numeric) = -4.31985705599 1.48521204183
y[1] (closed_form) = -4.31985727628 1.48522226016
absolute error = 1.022e-05
relative error = 0.0002237 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.86
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = -4.31789971002 1.490343497
y[1] (closed_form) = -4.31789996112 1.49035423758
absolute error = 1.074e-05
relative error = 0.0002352 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.59
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.84
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = -4.31822527169 1.49442616443
y[1] (closed_form) = -4.31822544518 1.49443657443
absolute error = 1.041e-05
relative error = 0.0002278 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.59
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5135 1.842
h = 0.001 0.001
y[1] (numeric) = -4.31838862708 1.49687891161
y[1] (closed_form) = -4.31838866855 1.49688930638
absolute error = 1.039e-05
relative error = 0.0002274 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.59
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5145 1.843
h = 0.001 0.003
y[1] (numeric) = -4.31765545526 1.49777548692
y[1] (closed_form) = -4.31765543474 1.49778585218
absolute error = 1.037e-05
relative error = 0.0002268 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.59
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.51
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = -4.31708560723 1.50030199604
y[1] (closed_form) = -4.31708571546 1.50031241626
absolute error = 1.042e-05
relative error = 0.000228 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.59
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5156 1.85
h = 0.003 0.006
y[1] (numeric) = -4.31733158505 1.50357016747
y[1] (closed_form) = -4.31733178983 1.50358051789
absolute error = 1.035e-05
relative error = 0.0002264 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.59
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.88
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = -4.31537900895 1.50870635685
y[1] (closed_form) = -4.31537924404 1.50871722938
absolute error = 1.088e-05
relative error = 0.0002379 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.59
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.84
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = -4.31570929576 1.51279068663
y[1] (closed_form) = -4.31570945357 1.51280122862
absolute error = 1.054e-05
relative error = 0.0002305 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.56
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5188 1.864
h = 0.001 0.001
y[1] (numeric) = -4.3158754736 1.5152444699
y[1] (closed_form) = -4.31587549946 1.51525499653
absolute error = 1.053e-05
relative error = 0.0002301 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5198 1.865
h = 0.001 0.003
y[1] (numeric) = -4.31514293928 1.51614231018
y[1] (closed_form) = -4.3151429032 1.51615280725
absolute error = 1.050e-05
relative error = 0.0002295 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = -4.31457563108 1.51867071159
y[1] (closed_form) = -4.31457572364 1.51868126373
absolute error = 1.055e-05
relative error = 0.0002307 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5209 1.872
h = 0.003 0.006
y[1] (numeric) = -4.31482538177 1.52194023354
y[1] (closed_form) = -4.31482557093 1.52195071599
absolute error = 1.048e-05
relative error = 0.0002291 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.89
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = -4.31287756955 1.52708116018
y[1] (closed_form) = -4.31287778851 1.52709216461
absolute error = 1.101e-05
relative error = 0.0002406 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.85
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.524 1.883
h = 0.0001 0.003
y[1] (numeric) = -4.31321257843 1.53116715629
y[1] (closed_form) = -4.31321272045 1.53117783021
absolute error = 1.067e-05
relative error = 0.0002332 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5241 1.886
h = 0.001 0.001
y[1] (numeric) = -4.31338157685 1.533621978
y[1] (closed_form) = -4.31338158697 1.53363263644
absolute error = 1.066e-05
relative error = 0.0002328 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5251 1.887
h = 0.001 0.003
y[1] (numeric) = -4.31264967863 1.53452108345
y[1] (closed_form) = -4.31264962686 1.53453171229
absolute error = 1.063e-05
relative error = 0.0002322 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.54
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = -4.31208490764 1.53705137899
y[1] (closed_form) = -4.31208498443 1.53706206299
absolute error = 1.068e-05
relative error = 0.0002334 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=828.3MB, alloc=52.3MB, time=9.62
x[1] = 20.5262 1.894
h = 0.003 0.006
y[1] (numeric) = -4.31233842874 1.54032225461
y[1] (closed_form) = -4.31233860215 1.54033286904
absolute error = 1.062e-05
relative error = 0.0002318 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.9
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = -4.31039537441 1.54546792156
y[1] (closed_form) = -4.31039557711 1.54547905783
absolute error = 1.114e-05
relative error = 0.0002432 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.86
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = -4.31073510228 1.54955558795
y[1] (closed_form) = -4.31073522838 1.54956639375
absolute error = 1.081e-05
relative error = 0.0002359 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5294 1.908
h = 0.001 0.001
y[1] (numeric) = -4.31090691941 1.55201145046
y[1] (closed_form) = -4.31090691367 1.55202224065
absolute error = 1.079e-05
relative error = 0.0002355 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = -4.31017565588 1.55291182129
y[1] (closed_form) = -4.31017558829 1.55292258182
absolute error = 1.076e-05
relative error = 0.0002349 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5305 1.913
h = 0.003 0.006
y[1] (numeric) = -4.31043226072 1.55618380042
y[1] (closed_form) = -4.31043246568 1.55619451083
absolute error = 1.071e-05
relative error = 0.0002338 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.91
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = -4.30849335351 1.5613334935
y[1] (closed_form) = -4.30849358733 1.56134472564
absolute error = 1.123e-05
relative error = 0.0002452 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.86
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = -4.30883716084 1.56542254463
y[1] (closed_form) = -4.30883731835 1.56543344631
absolute error = 1.090e-05
relative error = 0.0002378 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5337 1.927
h = 0.001 0.001
y[1] (numeric) = -4.30901141515 1.56787927135
y[1] (closed_form) = -4.30901144086 1.56789015732
absolute error = 1.089e-05
relative error = 0.0002374 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5347 1.928
h = 0.001 0.003
y[1] (numeric) = -4.3082807119 1.568780724
y[1] (closed_form) = -4.30828067581 1.56879158028
absolute error = 1.086e-05
relative error = 0.0002368 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = -4.30772067778 1.57131451871
y[1] (closed_form) = -4.30772077008 1.57132543036
absolute error = 1.091e-05
relative error = 0.000238 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5358 1.935
h = 0.003 0.006
y[1] (numeric) = -4.30798122434 1.57458787677
y[1] (closed_form) = -4.30798141333 1.57459871905
absolute error = 1.084e-05
relative error = 0.0002364 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.92
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = -4.30604706388 1.57974231583
y[1] (closed_form) = -4.30604728122 1.57975367971
absolute error = 1.137e-05
relative error = 0.0002478 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.86
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = -4.30639558452 1.58383304463
y[1] (closed_form) = -4.30639572589 1.58384407808
absolute error = 1.103e-05
relative error = 0.0002405 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.539 1.949
h = 0.001 0.001
y[1] (numeric) = -4.30657265406 1.58629081653
y[1] (closed_form) = -4.30657266369 1.58630183416
absolute error = 1.102e-05
relative error = 0.0002401 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.54 1.95
h = 0.001 0.003
y[1] (numeric) = -4.3058425829 1.58719353496
y[1] (closed_form) = -4.30584253078 1.58720452284
absolute error = 1.099e-05
relative error = 0.0002394 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.541 1.953
h = 0.0001 0.004
y[1] (numeric) = -4.30528507859 1.58972922899
y[1] (closed_form) = -4.30528515475 1.58974027234
absolute error = 1.104e-05
relative error = 0.0002406 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5411 1.957
h = 0.003 0.006
y[1] (numeric) = -4.3055493885 1.59300394976
y[1] (closed_form) = -4.30554956139 1.59301492387
absolute error = 1.098e-05
relative error = 0.0002391 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.93
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = -4.30361996876 1.5981631378
y[1] (closed_form) = -4.30362016951 1.59817463336
absolute error = 1.150e-05
relative error = 0.0002504 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.87
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = -4.30397319963 1.60225554822
y[1] (closed_form) = -4.30397332474 1.60226671338
absolute error = 1.117e-05
relative error = 0.0002431 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5443 1.971
h = 0.001 0.001
y[1] (numeric) = -4.30415308252 1.60471436764
y[1] (closed_form) = -4.30415307595 1.60472551686
absolute error = 1.115e-05
relative error = 0.0002427 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5453 1.972
h = 0.001 0.003
y[1] (numeric) = -4.30342364205 1.60561835203
y[1] (closed_form) = -4.30342357377 1.60562947145
absolute error = 1.112e-05
relative error = 0.0002421 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = -4.30286866493 1.60815594718
y[1] (closed_form) = -4.30286872485 1.60816712217
absolute error = 1.118e-05
relative error = 0.0002433 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5464 1.979
h = 0.003 0.006
y[1] (numeric) = -4.30313673571 1.6114320338
y[1] (closed_form) = -4.30313689239 1.61144313967
absolute error = 1.111e-05
relative error = 0.0002417 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.94
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = -4.30121205069 1.61659597381
y[1] (closed_form) = -4.30121223472 1.61660760099
absolute error = 1.163e-05
relative error = 0.0002531 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.88
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = -4.3015699887 1.62069006977
y[1] (closed_form) = -4.30157009743 1.62070136659
absolute error = 1.130e-05
relative error = 0.0002458 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=872.5MB, alloc=52.3MB, time=10.13
x[1] = 20.5496 1.993
h = 0.001 0.001
y[1] (numeric) = -4.30175268305 1.62314993904
y[1] (closed_form) = -4.30175266016 1.62316121979
absolute error = 1.128e-05
relative error = 0.0002454 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5506 1.994
h = 0.001 0.003
y[1] (numeric) = -4.30102387187 1.6240551896
y[1] (closed_form) = -4.30102378731 1.6240664405
absolute error = 1.125e-05
relative error = 0.0002447 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = -4.30047141934 1.62659468765
y[1] (closed_form) = -4.30047146289 1.62660599423
absolute error = 1.131e-05
relative error = 0.0002459 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5517 2.001
h = 0.003 0.006
y[1] (numeric) = -4.30074324848 1.62987214325
y[1] (closed_form) = -4.30074338883 1.62988338082
absolute error = 1.124e-05
relative error = 0.0002444 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.96
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = -4.29882329217 1.6350408382
y[1] (closed_form) = -4.29882345937 1.63505259694
absolute error = 1.176e-05
relative error = 0.0002557 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.88
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = -4.29918593422 1.63913662362
y[1] (closed_form) = -4.29918602645 1.63914805203
absolute error = 1.143e-05
relative error = 0.0002484 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5549 2.015
h = 0.001 0.001
y[1] (numeric) = -4.29937143814 1.64159754507
y[1] (closed_form) = -4.2993713988 1.6416089573
absolute error = 1.141e-05
relative error = 0.000248 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = -4.29864325485 1.64250406198
y[1] (closed_form) = -4.2986431539 1.64251544431
absolute error = 1.138e-05
relative error = 0.0002474 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.07
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.556 2.02
h = 0.003 0.006
y[1] (numeric) = -4.29891815789 1.64578263359
y[1] (closed_form) = -4.29891832931 1.64579396714
absolute error = 1.133e-05
relative error = 0.0002462 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.559 2.026
h = 0.0001 0.005
y[1] (numeric) = -4.29700232378 1.65095536757
y[1] (closed_form) = -4.2970025216 1.65096722218
absolute error = 1.186e-05
relative error = 0.0002576 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.89
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = -4.29736903261 1.65505255438
y[1] (closed_form) = -4.29736915576 1.65506407868
absolute error = 1.152e-05
relative error = 0.0002503 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5592 2.034
h = 0.001 0.001
y[1] (numeric) = -4.29755696596 1.65751434993
y[1] (closed_form) = -4.2975569576 1.65752585794
absolute error = 1.151e-05
relative error = 0.0002498 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5602 2.035
h = 0.001 0.003
y[1] (numeric) = -4.2968293371 1.65842194957
y[1] (closed_form) = -4.29682926717 1.65843342765
absolute error = 1.148e-05
relative error = 0.0002492 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = -4.29628159802 1.66096496323
y[1] (closed_form) = -4.29628165601 1.66097649718
absolute error = 1.153e-05
relative error = 0.0002504 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5613 2.042
h = 0.003 0.006
y[1] (numeric) = -4.29656043036 1.66424492978
y[1] (closed_form) = -4.29656058521 1.66425639493
absolute error = 1.147e-05
relative error = 0.0002489 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.98
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = -4.29464931379 1.66942242427
y[1] (closed_form) = -4.29464949456 1.66943441033
absolute error = 1.199e-05
relative error = 0.0002602 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.89
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = -4.29502072093 1.67352130784
y[1] (closed_form) = -4.29502082736 1.67353296363
absolute error = 1.166e-05
relative error = 0.0002529 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5645 2.056
h = 0.001 0.001
y[1] (numeric) = -4.29521146035 1.67598415992
y[1] (closed_form) = -4.29521143532 1.6759957993
absolute error = 1.164e-05
relative error = 0.0002524 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5655 2.057
h = 0.001 0.003
y[1] (numeric) = -4.29448445678 1.67689302628
y[1] (closed_form) = -4.29448437023 1.67690463568
absolute error = 1.161e-05
relative error = 0.0002518 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = -4.29393923484 1.67943794795
y[1] (closed_form) = -4.29393927612 1.67944961333
absolute error = 1.167e-05
relative error = 0.000253 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5666 2.064
h = 0.003 0.006
y[1] (numeric) = -4.29422181843 1.68271929244
y[1] (closed_form) = -4.29422195661 1.68273088912
absolute error = 1.160e-05
relative error = 0.0002515 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.99
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = -4.29231541341 1.68790155036
y[1] (closed_form) = -4.29231557699 1.68791366781
absolute error = 1.212e-05
relative error = 0.0002627 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.9
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = -4.29269151573 1.6920021346
y[1] (closed_form) = -4.29269160532 1.69201392183
absolute error = 1.179e-05
relative error = 0.0002555 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.6
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5698 2.078
h = 0.001 0.001
y[1] (numeric) = -4.29288505932 1.69446604551
y[1] (closed_form) = -4.29288501751 1.69447781621
absolute error = 1.177e-05
relative error = 0.000255 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5708 2.079
h = 0.001 0.003
y[1] (numeric) = -4.29215867964 1.69537617878
y[1] (closed_form) = -4.29215857635 1.69538791945
absolute error = 1.174e-05
relative error = 0.0002544 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = -4.29161597223 1.69792301024
y[1] (closed_form) = -4.29161599669 1.69793480698
absolute error = 1.180e-05
relative error = 0.0002556 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5719 2.086
h = 0.003 0.006
y[1] (numeric) = -4.29190230456 1.70120573575
y[1] (closed_form) = -4.29190242595 1.70121746391
absolute error = 1.173e-05
relative error = 0.000254 %
Correct digits = 6
memory used=916.8MB, alloc=52.3MB, time=10.64
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = -4.29000060506 1.70639276003
y[1] (closed_form) = -4.29000075135 1.70640500882
absolute error = 1.225e-05
relative error = 0.0002653 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.9
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.575 2.097
h = 0.0001 0.003
y[1] (numeric) = -4.29038139946 1.71049504883
y[1] (closed_form) = -4.29038147209 1.71050696743
absolute error = 1.192e-05
relative error = 0.0002581 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5751 2.1
h = 0.001 0.001
y[1] (numeric) = -4.29057774531 1.71296002088
y[1] (closed_form) = -4.2905776866 1.71297192283
absolute error = 1.190e-05
relative error = 0.0002576 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5761 2.101
h = 0.001 0.003
y[1] (numeric) = -4.28985198812 1.71387142124
y[1] (closed_form) = -4.28985186797 1.71388329311
absolute error = 1.187e-05
relative error = 0.000257 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = -4.28931179263 1.71642016424
y[1] (closed_form) = -4.28931180014 1.71643209229
absolute error = 1.193e-05
relative error = 0.0002582 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5772 2.108
h = 0.003 0.006
y[1] (numeric) = -4.28960187119 1.71970427387
y[1] (closed_form) = -4.28960197566 1.71971613346
absolute error = 1.186e-05
relative error = 0.0002566 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.68
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.02
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = -4.28770487118 1.72489606741
y[1] (closed_form) = -4.28770500006 1.72490844748
absolute error = 1.238e-05
relative error = 0.0002679 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.68
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.91
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = -4.28809035453 1.72900006465
y[1] (closed_form) = -4.28809041009 1.72901211457
absolute error = 1.205e-05
relative error = 0.0002606 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.68
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.61
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5804 2.122
h = 0.001 0.001
y[1] (numeric) = -4.28828950074 1.73146610015
y[1] (closed_form) = -4.28828942501 1.7314781333
absolute error = 1.203e-05
relative error = 0.0002602 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.68
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = -4.28756436464 1.73237876777
y[1] (closed_form) = -4.28756422753 1.73239077079
absolute error = 1.200e-05
relative error = 0.0002596 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.68
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5815 2.127
h = 0.003 0.006
y[1] (numeric) = -4.28785750719 1.73566400579
y[1] (closed_form) = -4.28785764223 1.73567596135
absolute error = 1.196e-05
relative error = 0.0002585 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.68
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.03
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = -4.28596460439 1.74085985099
y[1] (closed_form) = -4.28596476341 1.74087232691
absolute error = 1.248e-05
relative error = 0.0002697 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.91
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = -4.28635414174 1.7449652661
y[1] (closed_form) = -4.28635422772 1.74497741189
absolute error = 1.215e-05
relative error = 0.0002625 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5847 2.141
h = 0.001 0.001
y[1] (numeric) = -4.28655570958 1.74743218549
y[1] (closed_form) = -4.28655566432 1.74744431442
absolute error = 1.213e-05
relative error = 0.000262 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5857 2.142
h = 0.001 0.003
y[1] (numeric) = -4.28583112207 1.74834593669
y[1] (closed_form) = -4.28583101548 1.74835803545
absolute error = 1.210e-05
relative error = 0.0002614 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = -4.28529561653 1.75089821145
y[1] (closed_form) = -4.28529563741 1.75091036658
absolute error = 1.216e-05
relative error = 0.0002626 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5868 2.149
h = 0.003 0.006
y[1] (numeric) = -4.28559267582 1.75418486027
y[1] (closed_form) = -4.28559279373 1.75419694715
absolute error = 1.209e-05
relative error = 0.000261 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.04
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = -4.28370446135 1.75938548019
y[1] (closed_form) = -4.28370460274 1.75939808728
absolute error = 1.261e-05
relative error = 0.0002723 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.92
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = -4.28409868187 1.76349261096
y[1] (closed_form) = -4.28409875055 1.76350488797
absolute error = 1.228e-05
relative error = 0.000265 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.59 2.163
h = 0.001 0.001
y[1] (numeric) = -4.28430304653 1.76596059809
y[1] (closed_form) = -4.28430298404 1.76597285811
absolute error = 1.226e-05
relative error = 0.0002646 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.591 2.164
h = 0.001 0.003
y[1] (numeric) = -4.28357907752 1.7668756169
y[1] (closed_form) = -4.28357895374 1.7668878467
absolute error = 1.223e-05
relative error = 0.0002639 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.592 2.167
h = 0.0001 0.004
y[1] (numeric) = -4.28304607643 1.76942980825
y[1] (closed_form) = -4.28304608003 1.76944209452
absolute error = 1.229e-05
relative error = 0.0002651 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5921 2.171
h = 0.003 0.006
y[1] (numeric) = -4.28334687478 1.77271785004
y[1] (closed_form) = -4.28334697543 1.77273006817
absolute error = 1.222e-05
relative error = 0.0002636 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.05
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = -4.28146334261 1.77792324753
y[1] (closed_form) = -4.28146346625 1.77793598573
absolute error = 1.274e-05
relative error = 0.0002748 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.92
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = -4.28186224316 1.78203209784
y[1] (closed_form) = -4.28186229442 1.78204450599
absolute error = 1.241e-05
relative error = 0.0002675 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5953 2.185
h = 0.001 0.001
y[1] (numeric) = -4.28206940273 1.78450115499
y[1] (closed_form) = -4.28206932288 1.78451354604
absolute error = 1.239e-05
relative error = 0.0002671 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=961.2MB, alloc=52.3MB, time=11.14
x[1] = 20.5963 2.186
h = 0.001 0.003
y[1] (numeric) = -4.28134605082 1.78541744158
y[1] (closed_form) = -4.28134590972 1.78542980236
absolute error = 1.236e-05
relative error = 0.0002665 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = -4.28081555156 1.78797355124
y[1] (closed_form) = -4.28081553775 1.7879859686
absolute error = 1.242e-05
relative error = 0.0002677 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.5974 2.193
h = 0.003 0.006
y[1] (numeric) = -4.28112008643 1.79126298907
y[1] (closed_form) = -4.28112016971 1.7912753384
absolute error = 1.235e-05
relative error = 0.0002661 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.06
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = -4.27924123054 1.796473167
y[1] (closed_form) = -4.2792413363 1.79648603625
absolute error = 1.287e-05
relative error = 0.0002773 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.93
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = -4.27964480797 1.80058374068
y[1] (closed_form) = -4.2796448417 1.80059627993
absolute error = 1.254e-05
relative error = 0.0002701 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6006 2.207
h = 0.001 0.001
y[1] (numeric) = -4.27985476053 1.80305387015
y[1] (closed_form) = -4.2798546632 1.80306639217
absolute error = 1.252e-05
relative error = 0.0002696 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6016 2.208
h = 0.001 0.003
y[1] (numeric) = -4.27913202432 1.80397142469
y[1] (closed_form) = -4.2791318658 1.80398391639
absolute error = 1.249e-05
relative error = 0.000269 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.78
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = -4.27860402427 1.80652945439
y[1] (closed_form) = -4.27860399294 1.80654200277
absolute error = 1.255e-05
relative error = 0.0002702 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6027 2.215
h = 0.003 0.006
y[1] (numeric) = -4.27891229313 1.80982029132
y[1] (closed_form) = -4.27891235892 1.8098327718
absolute error = 1.248e-05
relative error = 0.0002686 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.08
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = -4.27703810749 1.81503525253
y[1] (closed_form) = -4.27703819527 1.81504825277
absolute error = 1.300e-05
relative error = 0.0002798 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.93
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = -4.27744635865 1.81914755343
y[1] (closed_form) = -4.27744637473 1.81916022371
absolute error = 1.267e-05
relative error = 0.0002726 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6059 2.229
h = 0.001 0.001
y[1] (numeric) = -4.27765910228 1.82161875749
y[1] (closed_form) = -4.27765898736 1.82163141043
absolute error = 1.265e-05
relative error = 0.0002722 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = -4.27693698039 1.82253758014
y[1] (closed_form) = -4.27693680432 1.82255020271
absolute error = 1.262e-05
relative error = 0.0002715 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.607 2.234
h = 0.003 0.006
y[1] (numeric) = -4.27724830324 1.82582955771
y[1] (closed_form) = -4.27724839912 1.82584213414
absolute error = 1.258e-05
relative error = 0.0002704 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.09
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.61 2.24
h = 0.0001 0.005
y[1] (numeric) = -4.27537818978 1.83104858293
y[1] (closed_form) = -4.27537830722 1.83106167901
absolute error = 1.310e-05
relative error = 0.0002816 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.94
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = -4.27579048205 1.83516231801
y[1] (closed_form) = -4.27579052808 1.83517508415
absolute error = 1.277e-05
relative error = 0.0002744 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6102 2.248
h = 0.001 0.001
y[1] (numeric) = -4.27600563944 1.83763441565
y[1] (closed_form) = -4.27600555451 1.83764716435
absolute error = 1.275e-05
relative error = 0.0002739 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6112 2.249
h = 0.001 0.003
y[1] (numeric) = -4.27528406031 1.83855432267
y[1] (closed_form) = -4.27528391428 1.83856704097
absolute error = 1.272e-05
relative error = 0.0002733 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.81
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = -4.27476072664 1.84111590002
y[1] (closed_form) = -4.27476070762 1.84112867519
absolute error = 1.278e-05
relative error = 0.0002745 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6123 2.256
h = 0.003 0.006
y[1] (numeric) = -4.27507595358 1.84440930408
y[1] (closed_form) = -4.27507603175 1.84442201155
absolute error = 1.271e-05
relative error = 0.0002729 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.1
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = -4.27321049919 1.84963311791
y[1] (closed_form) = -4.27321059842 1.84964634487
absolute error = 1.323e-05
relative error = 0.0002841 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.94
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = -4.27362745936 1.85374858737
y[1] (closed_form) = -4.27362748751 1.85376148443
absolute error = 1.290e-05
relative error = 0.0002769 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6155 2.27
h = 0.001 0.001
y[1] (numeric) = -4.27384540426 1.85622176384
y[1] (closed_form) = -4.27384530152 1.85623464335
absolute error = 1.288e-05
relative error = 0.0002764 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6165 2.271
h = 0.001 0.003
y[1] (numeric) = -4.27312443685 1.85714293929
y[1] (closed_form) = -4.27312427306 1.85715578835
absolute error = 1.285e-05
relative error = 0.0002758 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.83
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = -4.27260359489 1.85970644164
y[1] (closed_form) = -4.27260355801 1.85971934766
absolute error = 1.291e-05
relative error = 0.000277 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6176 2.278
h = 0.003 0.006
y[1] (numeric) = -4.27292254859 1.86300125356
y[1] (closed_form) = -4.27292260893 1.86301409199
absolute error = 1.284e-05
relative error = 0.0002754 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.11
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = -4.27106174723 1.8682298588
y[1] (closed_form) = -4.27106182814 1.86824321658
absolute error = 1.336e-05
relative error = 0.0002865 %
Correct digits = 6
memory used=1005.7MB, alloc=52.3MB, time=11.66
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.95
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = -4.27148337214 1.87234706644
y[1] (closed_form) = -4.27148338231 1.87236009437
absolute error = 1.303e-05
relative error = 0.0002793 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6208 2.292
h = 0.001 0.001
y[1] (numeric) = -4.27170410262 1.87482132403
y[1] (closed_form) = -4.27170398195 1.87483433428
absolute error = 1.301e-05
relative error = 0.0002789 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6218 2.293
h = 0.001 0.003
y[1] (numeric) = -4.27098374554 1.87574376806
y[1] (closed_form) = -4.27098356386 1.87575674781
absolute error = 1.298e-05
relative error = 0.0002783 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.84
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = -4.27046539267 1.87830919711
y[1] (closed_form) = -4.27046533781 1.87832223393
absolute error = 1.304e-05
relative error = 0.0002794 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6229 2.3
h = 0.003 0.006
y[1] (numeric) = -4.27078807057 1.88160541993
y[1] (closed_form) = -4.27078811297 1.88161838927
absolute error = 1.297e-05
relative error = 0.0002779 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.12
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = -4.26893191621 1.88683881936
y[1] (closed_form) = -4.26893197868 1.8868523079
absolute error = 1.349e-05
relative error = 0.000289 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.96
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.626 2.311
h = 0.0001 0.003
y[1] (numeric) = -4.2693582027 1.89095776901
y[1] (closed_form) = -4.26935819475 1.89097092774
absolute error = 1.316e-05
relative error = 0.0002818 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6261 2.314
h = 0.001 0.001
y[1] (numeric) = -4.26958171682 1.89343310995
y[1] (closed_form) = -4.26958157811 1.89344625089
absolute error = 1.314e-05
relative error = 0.0002814 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6271 2.315
h = 0.001 0.003
y[1] (numeric) = -4.26886196867 1.89435682272
y[1] (closed_form) = -4.268861769 1.89436993311
absolute error = 1.311e-05
relative error = 0.0002808 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.86
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = -4.26834610225 1.89692418018
y[1] (closed_form) = -4.26834602931 1.89693734773
absolute error = 1.317e-05
relative error = 0.0002819 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.78
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6282 2.322
h = 0.003 0.006
y[1] (numeric) = -4.26867250181 1.90022181692
y[1] (closed_form) = -4.26867252615 1.90023491712
absolute error = 1.310e-05
relative error = 0.0002804 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.14
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = -4.26682098841 1.90546001334
y[1] (closed_form) = -4.26682103233 1.90547363257
absolute error = 1.362e-05
relative error = 0.0002914 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.96
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = -4.2672519333 1.90958070878
y[1] (closed_form) = -4.26725190713 1.90959399825
absolute error = 1.329e-05
relative error = 0.0002843 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6314 2.336
h = 0.001 0.001
y[1] (numeric) = -4.26747822913 1.91205713534
y[1] (closed_form) = -4.26747807226 1.9120704069
absolute error = 1.327e-05
relative error = 0.0002838 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = -4.26675908853 1.912982117
y[1] (closed_form) = -4.26675887074 1.91299535796
absolute error = 1.324e-05
relative error = 0.0002832 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.37
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6325 2.341
h = 0.003 0.006
y[1] (numeric) = -4.26708853199 1.9162809065
y[1] (closed_form) = -4.26708858592 1.91629410264
absolute error = 1.320e-05
relative error = 0.0002821 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.15
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = -4.26524106573 1.92152317902
y[1] (closed_form) = -4.26524113882 1.92153689408
absolute error = 1.372e-05
relative error = 0.0002932 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = -4.26567603872 1.92564532478
y[1] (closed_form) = -4.26567604201 1.9256587101
absolute error = 1.339e-05
relative error = 0.000286 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6357 2.355
h = 0.001 0.001
y[1] (numeric) = -4.26590474037 1.9281226545
y[1] (closed_form) = -4.265904613 1.92813602181
absolute error = 1.337e-05
relative error = 0.0002856 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6367 2.356
h = 0.001 0.003
y[1] (numeric) = -4.26518613672 1.92904872128
y[1] (closed_form) = -4.26518594848 1.92906205796
absolute error = 1.334e-05
relative error = 0.0002849 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.89
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = -4.26467491303 1.93161964201
y[1] (closed_form) = -4.26467485135 1.93163303604
absolute error = 1.339e-05
relative error = 0.0002861 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.8
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6378 2.363
h = 0.003 0.006
y[1] (numeric) = -4.26500824784 1.93491987352
y[1] (closed_form) = -4.26500828349 1.9349332004
absolute error = 1.333e-05
relative error = 0.0002846 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.16
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = -4.26316541135 1.94016694823
y[1] (closed_form) = -4.26316546566 1.94018079388
absolute error = 1.385e-05
relative error = 0.0002956 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = -4.26360503685 1.94429084688
y[1] (closed_form) = -4.26360502171 1.94430436283
absolute error = 1.352e-05
relative error = 0.0002884 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.66
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.641 2.377
h = 0.001 0.001
y[1] (numeric) = -4.26383651663 1.94676926641
y[1] (closed_form) = -4.26383637088 1.94678276424
absolute error = 1.350e-05
relative error = 0.000288 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.642 2.378
h = 0.001 0.003
y[1] (numeric) = -4.26311851793 1.94769660238
y[1] (closed_form) = -4.26311831137 1.94771006952
absolute error = 1.347e-05
relative error = 0.0002874 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.91
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1050.1MB, alloc=52.3MB, time=12.17
x[1] = 20.643 2.381
h = 0.0001 0.004
y[1] (numeric) = -4.2626097732 1.95026945637
y[1] (closed_form) = -4.26260969309 1.95028298097
absolute error = 1.352e-05
relative error = 0.0002885 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.81
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6431 2.385
h = 0.003 0.006
y[1] (numeric) = -4.26294682236 1.95357111047
y[1] (closed_form) = -4.26294683962 1.95358456803
absolute error = 1.346e-05
relative error = 0.000287 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = -4.2611086096 1.95882299011
y[1] (closed_form) = -4.26110864502 1.95883696628
absolute error = 1.398e-05
relative error = 0.000298 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.98
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = -4.26155288444 1.96294864541
y[1] (closed_form) = -4.26155285073 1.96296229193
absolute error = 1.365e-05
relative error = 0.0002909 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6463 2.399
h = 0.001 0.001
y[1] (numeric) = -4.2617871404 1.965428157
y[1] (closed_form) = -4.26178697615 1.96544178528
absolute error = 1.363e-05
relative error = 0.0002904 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6473 2.4
h = 0.001 0.003
y[1] (numeric) = -4.26106974526 1.96635676229
y[1] (closed_form) = -4.26106952025 1.96637035984
absolute error = 1.360e-05
relative error = 0.0002898 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.92
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = -4.26056347684 1.96893155123
y[1] (closed_form) = -4.26056337818 1.96894520634
absolute error = 1.366e-05
relative error = 0.0002909 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.82
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6484 2.407
h = 0.003 0.006
y[1] (numeric) = -4.2609042378 1.97223463093
y[1] (closed_form) = -4.26090423654 1.97224821911
absolute error = 1.359e-05
relative error = 0.0002894 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.18
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = -4.25907064272 1.97749131822
y[1] (closed_form) = -4.25907065914 1.97750542485
absolute error = 1.411e-05
relative error = 0.0003004 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.98
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = -4.2595195637 1.98161873394
y[1] (closed_form) = -4.25951951132 1.98163251097
absolute error = 1.378e-05
relative error = 0.0002933 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6516 2.421
h = 0.001 0.001
y[1] (numeric) = -4.25975659389 1.98409933982
y[1] (closed_form) = -4.25975641103 1.9841130985
absolute error = 1.376e-05
relative error = 0.0002928 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6526 2.422
h = 0.001 0.003
y[1] (numeric) = -4.25903980093 1.98502921458
y[1] (closed_form) = -4.25903955735 1.98504294248
absolute error = 1.373e-05
relative error = 0.0002922 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.94
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = -4.25853600618 1.98760594014
y[1] (closed_form) = -4.25853588887 1.98761972568
absolute error = 1.379e-05
relative error = 0.0002933 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.83
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6537 2.429
h = 0.003 0.006
y[1] (numeric) = -4.25888047636 1.99091044842
y[1] (closed_form) = -4.25888045648 1.99092416716
absolute error = 1.372e-05
relative error = 0.0002918 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.2
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = -4.25705149293 1.99617194608
y[1] (closed_form) = -4.25705149023 1.99618618312
absolute error = 1.424e-05
relative error = 0.0003028 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.99
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = -4.25750505685 2.00030112598
y[1] (closed_form) = -4.25750498568 2.00031503346
absolute error = 1.391e-05
relative error = 0.0002957 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6569 2.443
h = 0.001 0.001
y[1] (numeric) = -4.25774485932 2.00278282839
y[1] (closed_form) = -4.25774465774 2.00279671739
absolute error = 1.389e-05
relative error = 0.0002952 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = -4.25702866715 2.00371397275
y[1] (closed_form) = -4.25702840489 2.00372783093
absolute error = 1.386e-05
relative error = 0.0002946 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.48
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.658 2.448
h = 0.003 0.006
y[1] (numeric) = -4.25737617108 2.00701964577
y[1] (closed_form) = -4.25737618031 2.00703346043
absolute error = 1.381e-05
relative error = 0.0002935 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.21
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.661 2.454
h = 0.0001 0.005
y[1] (numeric) = -4.25555120971 2.01228523137
y[1] (closed_form) = -4.2555512357 2.0122995642
absolute error = 1.433e-05
relative error = 0.0003045 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.99
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = -4.25600878862 2.01641587755
y[1] (closed_form) = -4.25600874643 2.01642988086
absolute error = 1.400e-05
relative error = 0.0002973 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6612 2.462
h = 0.001 0.001
y[1] (numeric) = -4.25625098892 2.0188984926
y[1] (closed_form) = -4.25625081636 2.01891247733
absolute error = 1.399e-05
relative error = 0.0002969 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6622 2.463
h = 0.001 0.003
y[1] (numeric) = -4.2555353279 2.01983072277
y[1] (closed_form) = -4.25553509471 2.01984467664
absolute error = 1.396e-05
relative error = 0.0002963 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = -4.25503615217 2.02241102695
y[1] (closed_form) = -4.25503604507 2.02242503866
absolute error = 1.401e-05
relative error = 0.0002974 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.85
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6633 2.47
h = 0.003 0.006
y[1] (numeric) = -4.25538753459 2.02571815735
y[1] (closed_form) = -4.25538752497 2.02573210246
absolute error = 1.395e-05
relative error = 0.0002959 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.22
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = -4.25356717366 2.03098855841
y[1] (closed_form) = -4.25356718031 2.03100302152
absolute error = 1.446e-05
relative error = 0.0003068 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1094.5MB, alloc=52.3MB, time=12.69
x[1] = 20.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = -4.25402938959 2.03512097578
y[1] (closed_form) = -4.2540293284 2.03513510942
absolute error = 1.413e-05
relative error = 0.0002997 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6665 2.484
h = 0.001 0.001
y[1] (numeric) = -4.25427435855 2.0376046915
y[1] (closed_form) = -4.25427416705 2.03761880646
absolute error = 1.412e-05
relative error = 0.0002993 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6675 2.485
h = 0.001 0.003
y[1] (numeric) = -4.25355929574 2.03853819154
y[1] (closed_form) = -4.25355904366 2.03855227559
absolute error = 1.409e-05
relative error = 0.0002986 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.99
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = -4.25306258616 2.04112043713
y[1] (closed_form) = -4.25306246007 2.04113457911
absolute error = 1.414e-05
relative error = 0.0002998 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.85
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6686 2.492
h = 0.003 0.006
y[1] (numeric) = -4.25341767045 2.04442900468
y[1] (closed_form) = -4.25341764187 2.04444308018
absolute error = 1.408e-05
relative error = 0.0002983 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.23
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = -4.25160190392 2.04970422387
y[1] (closed_form) = -4.25160189112 2.04971881722
absolute error = 1.459e-05
relative error = 0.0003092 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = -4.25206875365 2.05383841616
y[1] (closed_form) = -4.25206867334 2.05385268008
absolute error = 1.426e-05
relative error = 0.0003021 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6718 2.506
h = 0.001 0.001
y[1] (numeric) = -4.25231648932 2.05632323478
y[1] (closed_form) = -4.25231627876 2.05633747989
absolute error = 1.425e-05
relative error = 0.0003016 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6728 2.507
h = 0.001 0.003
y[1] (numeric) = -4.25160202333 2.05725800482
y[1] (closed_form) = -4.25160175224 2.05727221898
absolute error = 1.422e-05
relative error = 0.000301 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.01
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = -4.25110777725 2.05984219345
y[1] (closed_form) = -4.25110763205 2.05985646564
absolute error = 1.427e-05
relative error = 0.0003021 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.86
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6739 2.514
h = 0.003 0.006
y[1] (numeric) = -4.25146656083 2.06315220113
y[1] (closed_form) = -4.25146651318 2.06316640695
absolute error = 1.421e-05
relative error = 0.0003006 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.25
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = -4.24965538265 2.06843224113
y[1] (closed_form) = -4.24965535029 2.06844696463
absolute error = 1.472e-05
relative error = 0.0003115 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.01
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.677 2.525
h = 0.0001 0.003
y[1] (numeric) = -4.25012686297 2.07256821205
y[1] (closed_form) = -4.25012676342 2.07258260618
absolute error = 1.439e-05
relative error = 0.0003044 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6771 2.528
h = 0.001 0.001
y[1] (numeric) = -4.25037736339 2.07505413577
y[1] (closed_form) = -4.25037713366 2.07506851098
absolute error = 1.438e-05
relative error = 0.000304 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6781 2.529
h = 0.001 0.003
y[1] (numeric) = -4.24966349284 2.07599017594
y[1] (closed_form) = -4.24966320262 2.07600452015
absolute error = 1.435e-05
relative error = 0.0003033 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.02
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = -4.24917170762 2.07857630927
y[1] (closed_form) = -4.2491715432 2.0785907116
absolute error = 1.440e-05
relative error = 0.0003045 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.87
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6792 2.536
h = 0.003 0.006
y[1] (numeric) = -4.24953418789 2.08188776004
y[1] (closed_form) = -4.24953412105 2.08190209612
absolute error = 1.434e-05
relative error = 0.000303 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.26
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = -4.24772759202 2.08717262348
y[1] (closed_form) = -4.24772753998 2.08718747709
absolute error = 1.485e-05
relative error = 0.0003138 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.02
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = -4.24820369971 2.09131037677
y[1] (closed_form) = -4.24820358081 2.09132490105
absolute error = 1.452e-05
relative error = 0.0003067 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6824 2.55
h = 0.001 0.001
y[1] (numeric) = -4.24845696291 2.09379740779
y[1] (closed_form) = -4.24845671389 2.09381191303
absolute error = 1.451e-05
relative error = 0.0003063 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = -4.2477436864 2.09473471822
y[1] (closed_form) = -4.24774337695 2.09474919242
absolute error = 1.448e-05
relative error = 0.0003057 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6835 2.555
h = 0.003 0.006
y[1] (numeric) = -4.24810919019 2.09804734558
y[1] (closed_form) = -4.24810915198 2.09806177757
absolute error = 1.443e-05
relative error = 0.0003046 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = -4.24630659127 2.10333630852
y[1] (closed_form) = -4.24630656744 2.1033512579
absolute error = 1.495e-05
relative error = 0.0003155 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.02
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = -4.24678670075 2.1074755439
y[1] (closed_form) = -4.24678661034 2.10749016399
absolute error = 1.462e-05
relative error = 0.0003084 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.7
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6867 2.569
h = 0.001 0.001
y[1] (numeric) = -4.24704235371 2.10996349693
y[1] (closed_form) = -4.24704213324 2.10997809788
absolute error = 1.460e-05
relative error = 0.0003079 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6877 2.57
h = 0.001 0.003
y[1] (numeric) = -4.24632960257 2.11090189381
y[1] (closed_form) = -4.2463293217 2.11091646367
absolute error = 1.457e-05
relative error = 0.0003073 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.06
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = -4.2458424126 2.11349162085
y[1] (closed_form) = -4.24584225735 2.11350624903
absolute error = 1.463e-05
relative error = 0.0003084 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.89
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1138.9MB, alloc=52.3MB, time=13.21
x[1] = 20.6888 2.577
h = 0.003 0.006
y[1] (numeric) = -4.24621178193 2.11680572078
y[1] (closed_form) = -4.24621172431 2.11682028291
absolute error = 1.456e-05
relative error = 0.0003069 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = -4.24441375409 2.12209951214
y[1] (closed_form) = -4.24441371037 2.1221145915
absolute error = 1.508e-05
relative error = 0.0003178 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.03
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = -4.24489848497 2.12624053681
y[1] (closed_form) = -4.244898375 2.12625528693
absolute error = 1.475e-05
relative error = 0.0003107 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.692 2.591
h = 0.001 0.001
y[1] (numeric) = -4.24515689709 2.12872960126
y[1] (closed_form) = -4.24515665711 2.12874433213
absolute error = 1.473e-05
relative error = 0.0003102 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.693 2.592
h = 0.001 0.003
y[1] (numeric) = -4.24444473742 2.12966926863
y[1] (closed_form) = -4.2444444371 2.12968396837
absolute error = 1.470e-05
relative error = 0.0003096 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.07
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.694 2.595
h = 0.0001 0.004
y[1] (numeric) = -4.24396000076 2.13226094506
y[1] (closed_form) = -4.24395982596 2.13227570321
absolute error = 1.476e-05
relative error = 0.0003108 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.9
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6941 2.599
h = 0.003 0.006
y[1] (numeric) = -4.24433305938 2.13557649655
y[1] (closed_form) = -4.24433298224 2.13559118877
absolute error = 1.469e-05
relative error = 0.0003092 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.3
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = -4.24253959659 2.14087511895
y[1] (closed_form) = -4.24253953286 2.14089032823
absolute error = 1.521e-05
relative error = 0.0003201 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.03
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = -4.24302894563 2.14501793659
y[1] (closed_form) = -4.24302881598 2.14503281669
absolute error = 1.488e-05
relative error = 0.000313 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6973 2.613
h = 0.001 0.001
y[1] (numeric) = -4.24329011492 2.14750811464
y[1] (closed_form) = -4.24328985533 2.14752297537
absolute error = 1.486e-05
relative error = 0.0003125 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6983 2.614
h = 0.001 0.003
y[1] (numeric) = -4.24257854534 2.14844905263
y[1] (closed_form) = -4.24257822545 2.14846388219
absolute error = 1.483e-05
relative error = 0.0003119 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.09
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = -4.24209625934 2.15104268007
y[1] (closed_form) = -4.24209606488 2.15105756813
absolute error = 1.489e-05
relative error = 0.000313 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.91
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.6994 2.621
h = 0.003 0.006
y[1] (numeric) = -4.24247300466 2.15435968606
y[1] (closed_form) = -4.24247290788 2.1543745083
absolute error = 1.482e-05
relative error = 0.0003115 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.31
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = -4.24068410086 2.1596631421
y[1] (closed_form) = -4.24068401701 2.15967848124
absolute error = 1.534e-05
relative error = 0.0003223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.04
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = -4.24117806483 2.16380775641
y[1] (closed_form) = -4.24117791538 2.16382276641
absolute error = 1.501e-05
relative error = 0.0003153 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7026 2.635
h = 0.001 0.001
y[1] (numeric) = -4.24144198931 2.16629905024
y[1] (closed_form) = -4.24144170998 2.16631404077
absolute error = 1.499e-05
relative error = 0.0003148 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7036 2.636
h = 0.001 0.003
y[1] (numeric) = -4.24073100844 2.16724125897
y[1] (closed_form) = -4.24073066887 2.16725621827
absolute error = 1.496e-05
relative error = 0.0003142 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.11
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = -4.24025117045 2.16983683902
y[1] (closed_form) = -4.24025095621 2.16985185692
absolute error = 1.502e-05
relative error = 0.0003153 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.92
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7047 2.643
h = 0.003 0.006
y[1] (numeric) = -4.24063159985 2.17315530245
y[1] (closed_form) = -4.24063148332 2.17317025464
absolute error = 1.495e-05
relative error = 0.0003138 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.32
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = -4.23884724899 2.1784635947
y[1] (closed_form) = -4.23884714491 2.17847906364
absolute error = 1.547e-05
relative error = 0.0003246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.04
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = -4.23934582464 2.18261000935
y[1] (closed_form) = -4.23934565529 2.1826251492
absolute error = 1.514e-05
relative error = 0.0003175 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.72
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7079 2.657
h = 0.001 0.001
y[1] (numeric) = -4.23961250234 2.18510242115
y[1] (closed_form) = -4.23961220317 2.18511754141
absolute error = 1.512e-05
relative error = 0.0003171 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = -4.2389021088 2.18604590072
y[1] (closed_form) = -4.23890174944 2.18606098971
absolute error = 1.509e-05
relative error = 0.0003165 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.69
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.709 2.662
h = 0.003 0.006
y[1] (numeric) = -4.2392855514 2.18936555247
y[1] (closed_form) = -4.23928546302 2.18938060054
absolute error = 1.505e-05
relative error = 0.0003154 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.33
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.712 2.668
h = 0.0001 0.005
y[1] (numeric) = -4.23750517238 2.19467795551
y[1] (closed_form) = -4.23750509602 2.19469352018
absolute error = 1.556e-05
relative error = 0.0003262 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.05
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = -4.2380077365 2.19882586788
y[1] (closed_form) = -4.23800759517 2.19884110351
absolute error = 1.524e-05
relative error = 0.0003191 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1183.3MB, alloc=52.3MB, time=13.72
x[1] = 20.7122 2.676
h = 0.001 0.001
y[1] (numeric) = -4.23827679585 2.20131921097
y[1] (closed_form) = -4.23827652475 2.2013344269
absolute error = 1.522e-05
relative error = 0.0003187 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7132 2.677
h = 0.001 0.003
y[1] (numeric) = -4.2375669219 2.20226377755
y[1] (closed_form) = -4.23756659064 2.20227896219
absolute error = 1.519e-05
relative error = 0.000318 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.14
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = -4.23709165534 2.20486296616
y[1] (closed_form) = -4.23709144923 2.20487820957
absolute error = 1.524e-05
relative error = 0.0003192 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.94
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7143 2.684
h = 0.003 0.006
y[1] (numeric) = -4.23747895043 2.20818410549
y[1] (closed_form) = -4.23747884209 2.20819928341
absolute error = 1.518e-05
relative error = 0.0003176 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.35
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = -4.23570311312 2.21350134961
y[1] (closed_form) = -4.23570301632 2.21351704396
absolute error = 1.569e-05
relative error = 0.0003284 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.05
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = -4.23621028292 2.21765106917
y[1] (closed_form) = -4.23621012147 2.21766643453
absolute error = 1.537e-05
relative error = 0.0003214 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7175 2.698
h = 0.001 0.001
y[1] (numeric) = -4.23648209183 2.22014553429
y[1] (closed_form) = -4.23648180067 2.22016087984
absolute error = 1.535e-05
relative error = 0.0003209 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.78
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7185 2.699
h = 0.001 0.003
y[1] (numeric) = -4.23577280263 2.22109137194
y[1] (closed_form) = -4.23577245137 2.22110668615
absolute error = 1.532e-05
relative error = 0.0003203 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.16
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = -4.23529997652 2.22369251777
y[1] (closed_form) = -4.2352997503 2.22370789086
absolute error = 1.537e-05
relative error = 0.0003214 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.95
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7196 2.706
h = 0.003 0.006
y[1] (numeric) = -4.23569094825 2.22701512292
y[1] (closed_form) = -4.23569081983 2.22703043062
absolute error = 1.531e-05
relative error = 0.0003199 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = -4.2339196466 2.23233721066
y[1] (closed_form) = -4.23391952924 2.23235303463
absolute error = 1.582e-05
relative error = 0.0003306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.06
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = -4.23443141881 2.23648874107
y[1] (closed_form) = -4.23443123713 2.2365042361
absolute error = 1.550e-05
relative error = 0.0003236 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7228 2.72
h = 0.001 0.001
y[1] (numeric) = -4.23470597529 2.23898433038
y[1] (closed_form) = -4.23470566396 2.23899980549
absolute error = 1.548e-05
relative error = 0.0003231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.78
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7238 2.721
h = 0.001 0.003
y[1] (numeric) = -4.23399726947 2.2399314392
y[1] (closed_form) = -4.23399689809 2.23994688291
absolute error = 1.545e-05
relative error = 0.0003225 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = -4.23352688115 2.24253454385
y[1] (closed_form) = -4.23352663472 2.24255004654
absolute error = 1.550e-05
relative error = 0.0003236 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.96
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7249 2.728
h = 0.003 0.006
y[1] (numeric) = -4.23392152688 2.24585861771
y[1] (closed_form) = -4.23392137827 2.24587405513
absolute error = 1.544e-05
relative error = 0.0003221 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.37
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = -4.23215475485 2.25118555162
y[1] (closed_form) = -4.23215461682 2.25120150514
absolute error = 1.595e-05
relative error = 0.0003328 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.07
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.728 2.739
h = 0.0001 0.003
y[1] (numeric) = -4.23267112621 2.25533889651
y[1] (closed_form) = -4.23267092418 2.25535452114
absolute error = 1.563e-05
relative error = 0.0003258 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.74
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7281 2.742
h = 0.001 0.001
y[1] (numeric) = -4.23294842828 2.25783561217
y[1] (closed_form) = -4.23294809667 2.25785121677
absolute error = 1.561e-05
relative error = 0.0003253 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7291 2.743
h = 0.001 0.003
y[1] (numeric) = -4.23224030446 2.25878399226
y[1] (closed_form) = -4.23223991285 2.25879956543
absolute error = 1.558e-05
relative error = 0.0003247 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.19
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = -4.23177235127 2.26138905732
y[1] (closed_form) = -4.23177208451 2.26140468955
absolute error = 1.563e-05
relative error = 0.0003258 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.97
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7302 2.75
h = 0.003 0.006
y[1] (numeric) = -4.23217066839 2.26471460279
y[1] (closed_form) = -4.23217049947 2.26473016987
absolute error = 1.557e-05
relative error = 0.0003243 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.39
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = -4.23040841992 2.27004638539
y[1] (closed_form) = -4.2304082611 2.2700624684
absolute error = 1.608e-05
relative error = 0.000335 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.07
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = -4.23092938716 2.27420154839
y[1] (closed_form) = -4.23092916467 2.27421730257
absolute error = 1.576e-05
relative error = 0.000328 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7334 2.764
h = 0.001 0.001
y[1] (numeric) = -4.23120943282 2.27669939256
y[1] (closed_form) = -4.23120908081 2.27671512659
absolute error = 1.574e-05
relative error = 0.0003275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = -4.23050188962 2.27764904403
y[1] (closed_form) = -4.23050147766 2.27766474658
absolute error = 1.571e-05
relative error = 0.0003269 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.8
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7345 2.769
h = 0.003 0.006
y[1] (numeric) = -4.23090320956 2.28097578941
y[1] (closed_form) = -4.23090306832 2.28099145232
absolute error = 1.566e-05
relative error = 0.0003259 %
Correct digits = 5
memory used=1227.7MB, alloc=52.3MB, time=14.23
Radius of convergence (given) for eq 1 = 22.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.4
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = -4.22914490778 2.28631169383
y[1] (closed_form) = -4.22914477622 2.28632787253
absolute error = 1.618e-05
relative error = 0.0003365 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.08
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = -4.2296698501 2.29046837001
y[1] (closed_form) = -4.22966965515 2.29048421993
absolute error = 1.585e-05
relative error = 0.0003295 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7377 2.783
h = 0.001 0.001
y[1] (numeric) = -4.22995226924 2.29296715463
y[1] (closed_form) = -4.22995194482 2.2929829843
absolute error = 1.583e-05
relative error = 0.0003291 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7387 2.784
h = 0.001 0.003
y[1] (numeric) = -4.22924523986 2.29391789363
y[1] (closed_form) = -4.22924485553 2.29393369179
absolute error = 1.580e-05
relative error = 0.0003285 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.22
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = -4.22878183421 2.29652658181
y[1] (closed_form) = -4.22878157456 2.29654243921
absolute error = 1.586e-05
relative error = 0.0003296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.99
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7398 2.791
h = 0.003 0.006
y[1] (numeric) = -4.22918699352 2.29985482964
y[1] (closed_form) = -4.22918683176 2.29987062209
absolute error = 1.579e-05
relative error = 0.0003281 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.41
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = -4.22743320407 2.30519558748
y[1] (closed_form) = -4.22743305151 2.30521189555
absolute error = 1.631e-05
relative error = 0.0003387 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.08
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = -4.22796273622 2.30935408855
y[1] (closed_form) = -4.22796252059 2.30937006789
absolute error = 1.598e-05
relative error = 0.0003317 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.75
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.743 2.805
h = 0.001 0.001
y[1] (numeric) = -4.22824789526 2.31185400569
y[1] (closed_form) = -4.22824755023 2.31186996468
absolute error = 1.596e-05
relative error = 0.0003312 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.744 2.806
h = 0.001 0.003
y[1] (numeric) = -4.22754144394 2.31280601627
y[1] (closed_form) = -4.22754103906 2.31282194369
absolute error = 1.593e-05
relative error = 0.0003306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.24
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.745 2.809
h = 0.0001 0.004
y[1] (numeric) = -4.22708046585 2.31541666937
y[1] (closed_form) = -4.22708018554 2.31543265614
absolute error = 1.599e-05
relative error = 0.0003317 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7451 2.813
h = 0.003 0.006
y[1] (numeric) = -4.22748928903 2.3187463971
y[1] (closed_form) = -4.22748910664 2.31876231902
absolute error = 1.592e-05
relative error = 0.0003302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.42
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = -4.22574000586 2.32409201085
y[1] (closed_form) = -4.22573983219 2.32410844823
absolute error = 1.644e-05
relative error = 0.0003409 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.09
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = -4.22627412456 2.32825234042
y[1] (closed_form) = -4.22627388816 2.32826844912
absolute error = 1.611e-05
relative error = 0.0003339 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7483 2.827
h = 0.001 0.001
y[1] (numeric) = -4.22656202151 2.33075339223
y[1] (closed_form) = -4.22656165577 2.33076948046
absolute error = 1.609e-05
relative error = 0.0003334 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7493 2.828
h = 0.001 0.003
y[1] (numeric) = -4.22585614688 2.33170667446
y[1] (closed_form) = -4.22585572133 2.33172273109
absolute error = 1.606e-05
relative error = 0.0003328 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.26
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = -4.22539759368 2.33431929406
y[1] (closed_form) = -4.2253972926 2.33433541012
absolute error = 1.612e-05
relative error = 0.0003339 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.01
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7504 2.835
h = 0.003 0.006
y[1] (numeric) = -4.2258100781 2.33765050455
y[1] (closed_form) = -4.22580987497 2.33766655589
absolute error = 1.605e-05
relative error = 0.0003324 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = -4.22406529515 2.34300097669
y[1] (closed_form) = -4.22406510026 2.34301754331
absolute error = 1.657e-05
relative error = 0.000343 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.09
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = -4.22460399712 2.34716313836
y[1] (closed_form) = -4.22460373982 2.34717937636
absolute error = 1.624e-05
relative error = 0.000336 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7536 2.849
h = 0.001 0.001
y[1] (numeric) = -4.22489462998 2.34966532696
y[1] (closed_form) = -4.2248942434 2.34968154439
absolute error = 1.622e-05
relative error = 0.0003356 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7546 2.85
h = 0.001 0.003
y[1] (numeric) = -4.22418933066 2.35061988095
y[1] (closed_form) = -4.22418888432 2.35063606671
absolute error = 1.619e-05
relative error = 0.0003349 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = -4.22373319969 2.3532344686
y[1] (closed_form) = -4.22373287773 2.3532507139
absolute error = 1.625e-05
relative error = 0.0003361 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.02
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7557 2.857
h = 0.003 0.006
y[1] (numeric) = -4.2241493427 2.35656716472
y[1] (closed_form) = -4.22414911872 2.3565833454
absolute error = 1.618e-05
relative error = 0.0003345 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.45
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = -4.22240905392 2.36192249771
y[1] (closed_form) = -4.2224088377 2.3619391935
absolute error = 1.670e-05
relative error = 0.0003451 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.94
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.1
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = -4.22295233587 2.36608649507
y[1] (closed_form) = -4.22295205756 2.3661028623
absolute error = 1.637e-05
relative error = 0.0003382 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.94
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.77
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1272.2MB, alloc=52.3MB, time=14.74
x[1] = 20.7589 2.871
h = 0.001 0.001
y[1] (numeric) = -4.22324570263 2.36858982259
y[1] (closed_form) = -4.22324529511 2.36860616914
absolute error = 1.635e-05
relative error = 0.0003377 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.94
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.81
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 20.7599 2.872
h = 0.001 0.003
y[1] (numeric) = -4.22254097724 2.36954564842
y[1] (closed_form) = -4.22254051002 2.36956196326
absolute error = 1.632e-05
relative error = 0.0003371 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 22.94
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.3
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ;
Iterations = 754
Total Elapsed Time = 14 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 14 Seconds
> quit
memory used=1276.7MB, alloc=52.3MB, time=14.79