|\^/| 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(1.0) / (c(x) * c(x) + c(0.000001))) ;
> end;
exact_soln_y := proc(x) return c(1.0)/(c(x)*c(x) + c(0.1*10^(-5))) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre neg ID_CONST $eq_no = 1
> array_tmp1[1] := neg(array_const_2D0[1]);
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] * array_x[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_0D000001[1];
> #emit pre div LINEAR - FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp2[1] / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp6[1] + array_const_0D000001[1];
> #emit pre div FULL - FULL $eq_no = 1 i = 1
> array_tmp8[1] := (array_tmp5[1] / (array_tmp7[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp9[1] := array_const_0D0[1] + array_tmp8[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_tmp9[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_tmp2[2] := array_tmp1[1] * array_x[2];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre div LINEAR - FULL $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp2[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp6[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp6[2];
> #emit pre div FULL - FULL $eq_no = 1 i = 2
> array_tmp8[2] := ((array_tmp5[2] - ats(2,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp9[2] := array_tmp8[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_tmp9[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 mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre div LINEAR FULL $eq_no = 1 i = 3
> array_tmp5[3] := neg( ats(3,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp6[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp6[3];
> #emit pre div FULL - FULL $eq_no = 1 i = 3
> array_tmp8[3] := ((array_tmp5[3] - ats(3,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp9[3] := array_tmp8[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_tmp9[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 add FULL CONST $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre div LINEAR FULL $eq_no = 1 i = 4
> array_tmp5[4] := neg( ats(4,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp6[4];
> #emit pre div FULL - FULL $eq_no = 1 i = 4
> array_tmp8[4] := ((array_tmp5[4] - ats(4,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp9[4] := array_tmp8[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_tmp9[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 add FULL CONST $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre div LINEAR FULL $eq_no = 1 i = 5
> array_tmp5[5] := neg( ats(5,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp6[5];
> #emit pre div FULL - FULL $eq_no = 1 i = 5
> array_tmp8[5] := ((array_tmp5[5] - ats(5,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp9[5] := array_tmp8[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_tmp9[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 mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit div LINEAR FULL $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp7[kkk] := array_tmp6[kkk];
> #emit div FULL FULL $eq_no = 1
> array_tmp8[kkk] := ((array_tmp5[kkk] - ats(kkk,array_tmp7,array_tmp8,2)) /array_tmp7[1]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp9[kkk] := array_tmp8[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_tmp9[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := neg(array_const_2D0[1]);
array_tmp2[1] := array_tmp1[1]*array_x[1];
array_tmp3[1] := array_x[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_0D000001[1];
array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
array_tmp6[1] := array_x[1]*array_x[1];
array_tmp7[1] := array_tmp6[1] + array_const_0D000001[1];
array_tmp8[1] := array_tmp5[1]/array_tmp7[1];
array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp2[2] := array_tmp1[1]*array_x[2];
array_tmp3[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp2[2])/array_tmp4[1];
array_tmp6[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp7[2] := array_tmp6[2];
array_tmp8[2] :=
(array_tmp5[2] - ats(2, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[2] := array_tmp8[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[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] := array_x[2]*array_x[2];
array_tmp4[3] := array_tmp3[3];
array_tmp5[3] := neg(ats(3, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[3] := array_x[2]*array_x[2];
array_tmp7[3] := array_tmp6[3];
array_tmp8[3] :=
(array_tmp5[3] - ats(3, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[3] := array_tmp8[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[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_tmp4[4] := array_tmp3[4];
array_tmp5[4] := neg(ats(4, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[4] := array_tmp6[4];
array_tmp8[4] :=
(array_tmp5[4] - ats(4, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[4] := array_tmp8[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[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_tmp4[5] := array_tmp3[5];
array_tmp5[5] := neg(ats(5, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[5] := array_tmp6[5];
array_tmp8[5] :=
(array_tmp5[5] - ats(5, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[5] := array_tmp8[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[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_tmp4[kkk] := array_tmp3[kkk];
array_tmp5[kkk] :=
neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[kkk] := array_tmp6[kkk];
array_tmp8[kkk] := (
array_tmp5[kkk] - ats(kkk, array_tmp7, array_tmp8, 2))/
array_tmp7[1];
array_tmp9[kkk] := array_tmp8[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_tmp9[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> 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_tmp5:= Array(0..(30),[]);
> array_tmp6:= Array(0..(30),[]);
> array_tmp7:= Array(0..(30),[]);
> array_tmp8:= Array(0..(30),[]);
> array_tmp9:= 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_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp8[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp9[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_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_tmp8);
> zero_ats_ar(array_tmp9);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_0D000001);
> array_const_0D000001[1] := c(0.000001);
> 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/sing1postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -2.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.001);");
> omniout_str(ALWAYS,"glob_min_h := c(0.001);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 2;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.000);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.001);");
> 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,"return(c(1.0) / (c(x) * c(x) + c(0.000001))) ;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -2.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.001);
> glob_min_h := c(0.001);
> glob_type_given_pole := 2;
> array_given_rad_poles[1,1] := c(0.000);
> array_given_rad_poles[1,2] := c(0.001);
> 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 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:22:07-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing1")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ")
> ;
> 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,"sing1 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing1 maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, 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_tmp5 := Array(0 .. 30, []);
array_tmp6 := Array(0 .. 30, []);
array_tmp7 := Array(0 .. 30, []);
array_tmp8 := Array(0 .. 30, []);
array_tmp9 := 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_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp8[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp9[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_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_tmp8);
zero_ats_ar(array_tmp9);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_0D000001);
array_const_0D000001[1] := c(0.1*10^(-5));
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/sing1postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 2.0 ) * \
x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) \
; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -2.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.001);");
omniout_str(ALWAYS, "glob_min_h := c(0.001);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 2;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.000);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.001);");
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, "return(c(1.0) / (c(x) * c(x) + c(0.000001))) ;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
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omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -2.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.001);
glob_min_h := c(0.001);
glob_type_given_pole := 2;
array_given_rad_poles[1, 1] := c(0.);
array_given_rad_poles[1, 2] := c(0.001);
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 ) = neg ( 2.0 ) *\
x / ( x * x + 0.000001 ) / ( x * x + 0.000\
001 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:22:07-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing1");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 2.0 ) * x / ( x * x + 0.000001 ) / ( \
x * x + 0.000001 ) ; ");
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,
"sing1 diffeq.mxt");
logitem_str(html_log_file,
"sing1 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=3.8MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sing1postcpx.cpx#################
diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -2.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.001);
glob_min_h := c(0.001);
glob_type_given_pole := 2;
array_given_rad_poles[1,1] := c(0.000);
array_given_rad_poles[1,2] := c(0.001);
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(1.0) / (c(x) * c(x) + c(0.000001))) ;
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -2.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.225220563566 0.0214983216363
y[1] (closed_form) = 0.225220563566 0.0214983216363
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.628
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0999 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.225085732122 0.0225661191913
y[1] (closed_form) = 0.225084976155 0.0225659847173
absolute error = 7.678e-07
relative error = 0.0003394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.262
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0998 0.108
h = 0.001 0.001
y[1] (numeric) = 0.225008336309 0.0232072991538
y[1] (closed_form) = 0.225008488302 0.0232073220286
absolute error = 1.537e-07
relative error = 6.795e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9906
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0988 0.109
h = 0.001 0.003
y[1] (numeric) = 0.225187377689 0.0234533277373
y[1] (closed_form) = 0.225188000387 0.0234532773415
absolute error = 6.247e-07
relative error = 0.0002759 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.699
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0978 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.225299591123 0.0241258275231
y[1] (closed_form) = 0.22529924619 0.0241258855636
absolute error = 3.498e-07
relative error = 0.0001544 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.658
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0977 0.116
h = 0.003 0.006
y[1] (numeric) = 0.225181470354 0.0249813627985
y[1] (closed_form) = 0.225180626619 0.0249807580455
absolute error = 1.038e-06
relative error = 0.0004582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.522
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=38.3MB, alloc=40.3MB, time=0.50
x[1] = -2.0947 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.225602173426 0.0263655394882
y[1] (closed_form) = 0.225600020066 0.0263683362271
absolute error = 3.530e-06
relative error = 0.001554 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.564
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0946 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.225430480834 0.0274366264903
y[1] (closed_form) = 0.225429574221 0.0274373982225
absolute error = 1.191e-06
relative error = 0.0005243 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.26
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0945 0.13
h = 0.001 0.001
y[1] (numeric) = 0.225332172902 0.028078725424
y[1] (closed_form) = 0.225332173733 0.0280796943613
absolute error = 9.689e-07
relative error = 0.0004267 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9887
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0935 0.131
h = 0.001 0.003
y[1] (numeric) = 0.225504288338 0.0283317745361
y[1] (closed_form) = 0.225504766205 0.0283326898145
absolute error = 1.033e-06
relative error = 0.0004543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.69
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0925 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.225595570554 0.0290114057659
y[1] (closed_form) = 0.225595069592 0.0290123888481
absolute error = 1.103e-06
relative error = 0.0004851 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.653
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0924 0.138
h = 0.003 0.006
y[1] (numeric) = 0.225449437628 0.0298676105345
y[1] (closed_form) = 0.225448462871 0.0298679050474
absolute error = 1.018e-06
relative error = 0.0004478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.516
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0894 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.225827973479 0.0312723662567
y[1] (closed_form) = 0.225825534887 0.0312760286581
absolute error = 4.400e-06
relative error = 0.00193 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.561
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0893 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.225621033618 0.0323433302655
y[1] (closed_form) = 0.225619936645 0.032345008
absolute error = 2.005e-06
relative error = 0.0008795 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.257
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0892 0.152
h = 0.001 0.001
y[1] (numeric) = 0.225501635949 0.032985459595
y[1] (closed_form) = 0.225501443766 0.0329873746815
absolute error = 1.925e-06
relative error = 0.0008445 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9869
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0882 0.153
h = 0.001 0.003
y[1] (numeric) = 0.225666479539 0.0332452790392
y[1] (closed_form) = 0.225666769722 0.0332471605736
absolute error = 1.904e-06
relative error = 0.0008346 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.682
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=84.8MB, alloc=44.3MB, time=1.12
x[1] = -2.0872 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.225736387584 0.0339311923945
y[1] (closed_form) = 0.225735689831 0.0339331001781
absolute error = 2.031e-06
relative error = 0.0008899 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.648
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0871 0.16
h = 0.003 0.006
y[1] (numeric) = 0.225562031937 0.0347868708859
y[1] (closed_form) = 0.225560886974 0.0347880654644
absolute error = 1.655e-06
relative error = 0.000725 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.509
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0841 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.225897249093 0.0362105308359
y[1] (closed_form) = 0.225894486702 0.0362150511649
absolute error = 5.298e-06
relative error = 0.002316 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.559
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.084 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.225654846623 0.0372798575032
y[1] (closed_form) = 0.22565351927 0.0372824389084
absolute error = 2.903e-06
relative error = 0.001269 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.255
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0839 0.174
h = 0.001 0.001
y[1] (numeric) = 0.225514227904 0.0379211122766
y[1] (closed_form) = 0.225513800509 0.0379239713359
absolute error = 2.891e-06
relative error = 0.001264 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9852
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0829 0.175
h = 0.001 0.003
y[1] (numeric) = 0.22567146452 0.0381874313821
y[1] (closed_form) = 0.22567152378 0.038190277431
absolute error = 2.847e-06
relative error = 0.001244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.674
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0819 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.225719597652 0.038878747259
y[1] (closed_form) = 0.225718662036 0.0388815772072
absolute error = 2.981e-06
relative error = 0.001301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.644
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0818 0.182
h = 0.003 0.006
y[1] (numeric) = 0.22551687137 0.0397326833588
y[1] (closed_form) = 0.225515516648 0.0397347767177
absolute error = 2.493e-06
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.504
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0788 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.225807699761 0.0411734984225
y[1] (closed_form) = 0.225804575194 0.0411788668267
absolute error = 6.211e-06
relative error = 0.002706 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0787 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.22552969931 0.0422396508151
y[1] (closed_form) = 0.225528101382 0.0422431313929
absolute error = 3.830e-06
relative error = 0.001669 %
Correct digits = 5
memory used=131.5MB, alloc=44.3MB, time=1.72
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.253
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0786 0.196
h = 0.001 0.001
y[1] (numeric) = 0.225367775985 0.0428791125535
y[1] (closed_form) = 0.225367070978 0.0428829111034
absolute error = 3.863e-06
relative error = 0.001684 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9837
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0776 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.22551708269 0.0431516406972
y[1] (closed_form) = 0.22551686755 0.0431554471492
absolute error = 3.813e-06
relative error = 0.00166 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.905
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0775 0.201
h = 0.003 0.006
y[1] (numeric) = 0.225291095051 0.044003192723
y[1] (closed_form) = 0.225289298795 0.0440058025305
absolute error = 3.168e-06
relative error = 0.00138 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.499
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0745 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.22554274968 0.0454567758992
y[1] (closed_form) = 0.225539054497 0.0454626084658
absolute error = 6.905e-06
relative error = 0.003001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.554
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0744 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.225234124935 0.0465185269811
y[1] (closed_form) = 0.225232032816 0.0465225209887
absolute error = 4.509e-06
relative error = 0.00196 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0743 0.215
h = 0.001 0.001
y[1] (numeric) = 0.225053870234 0.0471554474926
y[1] (closed_form) = 0.225052662721 0.0471597939603
absolute error = 4.511e-06
relative error = 0.001962 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9825
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0733 0.216
h = 0.001 0.003
y[1] (numeric) = 0.225196033976 0.047432973236
y[1] (closed_form) = 0.225195317952 0.0474373458729
absolute error = 4.431e-06
relative error = 0.001925 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.661
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0723 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.225202698206 0.0481316390105
y[1] (closed_form) = 0.225200980913 0.0481359150708
absolute error = 4.608e-06
relative error = 0.002001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.637
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0722 0.223
h = 0.003 0.006
y[1] (numeric) = 0.224947064796 0.0489787037208
y[1] (closed_form) = 0.224944984727 0.0489822037531
absolute error = 4.071e-06
relative error = 0.001769 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.494
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=178.1MB, alloc=44.3MB, time=2.33
x[1] = -2.0692 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.2251525974 0.0504459955964
y[1] (closed_form) = 0.225148469778 0.050452651827
absolute error = 7.832e-06
relative error = 0.003394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0691 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.224808361273 0.0515016704218
y[1] (closed_form) = 0.224805923917 0.0515065488961
absolute error = 5.453e-06
relative error = 0.002365 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.25
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.069 0.237
h = 0.001 0.001
y[1] (numeric) = 0.224606788901 0.0521350635372
y[1] (closed_form) = 0.224605224977 0.0521403344101
absolute error = 5.498e-06
relative error = 0.002384 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9812
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.068 0.238
h = 0.001 0.003
y[1] (numeric) = 0.224740462983 0.0524182032428
y[1] (closed_form) = 0.22473939167 0.0524235216934
absolute error = 5.425e-06
relative error = 0.002351 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.655
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.067 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.224724470451 0.0531196079712
y[1] (closed_form) = 0.224722397482 0.0531247860084
absolute error = 5.578e-06
relative error = 0.002415 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.633
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0669 0.245
h = 0.003 0.006
y[1] (numeric) = 0.224440419483 0.0539613752354
y[1] (closed_form) = 0.224438015755 0.0539657580394
absolute error = 4.999e-06
relative error = 0.002165 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.489
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0639 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.224599022714 0.0554404425112
y[1] (closed_form) = 0.224594425603 0.0554479065316
absolute error = 8.766e-06
relative error = 0.003789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.55
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0638 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.224219279042 0.056488468839
y[1] (closed_form) = 0.224216456561 0.0564942209616
absolute error = 6.407e-06
relative error = 0.002771 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.248
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0637 0.259
h = 0.001 0.001
y[1] (numeric) = 0.223996448267 0.0571173948754
y[1] (closed_form) = 0.223994485819 0.0571235789364
absolute error = 6.488e-06
relative error = 0.002807 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9799
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0627 0.26
h = 0.001 0.003
y[1] (numeric) = 0.224121352361 0.0574058049129
y[1] (closed_form) = 0.224119882489 0.0574120581313
absolute error = 6.424e-06
relative error = 0.002777 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.649
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=224.5MB, alloc=44.3MB, time=2.93
x[1] = -2.0617 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.224082485679 0.0581089775653
y[1] (closed_form) = 0.224080016142 0.0581150462878
absolute error = 6.552e-06
relative error = 0.00283 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.63
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0616 0.267
h = 0.003 0.006
y[1] (numeric) = 0.223770125859 0.0589441914117
y[1] (closed_form) = 0.223767358785 0.0589494473381
absolute error = 5.940e-06
relative error = 0.002567 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.485
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0586 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.223881093021 0.0604330469172
y[1] (closed_form) = 0.223875990093 0.0604413007901
absolute error = 9.704e-06
relative error = 0.004185 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.548
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0585 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.223466031609 0.0614718502496
y[1] (closed_form) = 0.223462784491 0.0614784629824
absolute error = 7.367e-06
relative error = 0.003179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.247
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0584 0.281
h = 0.001 0.001
y[1] (numeric) = 0.22322205302 0.0620953681299
y[1] (closed_form) = 0.223219650324 0.062102451795
absolute error = 7.480e-06
relative error = 0.003228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9788
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0574 0.282
h = 0.001 0.003
y[1] (numeric) = 0.223337924098 0.0623886879772
y[1] (closed_form) = 0.223336012771 0.062395862476
absolute error = 7.425e-06
relative error = 0.003202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.644
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0564 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.223276017591 0.0630926409967
y[1] (closed_form) = 0.223273110998 0.0630995868253
absolute error = 7.529e-06
relative error = 0.003245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.627
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0563 0.289
h = 0.003 0.006
y[1] (numeric) = 0.22293552642 0.0639200454007
y[1] (closed_form) = 0.222932356615 0.0639261626002
absolute error = 6.890e-06
relative error = 0.002971 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.481
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0533 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.222998255538 0.0654166543594
y[1] (closed_form) = 0.222992611327 0.0654256781241
absolute error = 1.064e-05
relative error = 0.00458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.546
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0532 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.222548152765 0.0664446635466
y[1] (closed_form) = 0.222544442024 0.066452121644
absolute error = 8.330e-06
relative error = 0.003587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=271.1MB, alloc=44.3MB, time=3.52
x[1] = -2.0531 0.303
h = 0.001 0.001
y[1] (numeric) = 0.222283188628 0.0670618341431
y[1] (closed_form) = 0.222280304512 0.0670698014734
absolute error = 8.473e-06
relative error = 0.003649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9778
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0521 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.222389782155 0.067359687429
y[1] (closed_form) = 0.222387387014 0.0673677672898
absolute error = 8.427e-06
relative error = 0.003627 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.869
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.052 0.308
h = 0.003 0.006
y[1] (numeric) = 0.222026479764 0.0681797320597
y[1] (closed_form) = 0.22202275683 0.0681862757481
absolute error = 7.529e-06
relative error = 0.003241 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.479
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.049 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.222047229152 0.0696807717126
y[1] (closed_form) = 0.222040917323 0.069690135403
absolute error = 1.129e-05
relative error = 0.004852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.545
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0489 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.221567405373 0.0706978269541
y[1] (closed_form) = 0.221563089825 0.0707056944194
absolute error = 8.973e-06
relative error = 0.003858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0488 0.322
h = 0.001 0.001
y[1] (numeric) = 0.221284637781 0.0713085395934
y[1] (closed_form) = 0.221281131373 0.0713169483464
absolute error = 9.111e-06
relative error = 0.003919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9771
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0478 0.323
h = 0.001 0.003
y[1] (numeric) = 0.221383016997 0.0716098683504
y[1] (closed_form) = 0.221379996292 0.0716184082191
absolute error = 9.058e-06
relative error = 0.003893 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.636
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0468 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.221277999369 0.072312325614
y[1] (closed_form) = 0.221273998564 0.0723205550304
absolute error = 9.150e-06
relative error = 0.003931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.622
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0467 0.33
h = 0.003 0.006
y[1] (numeric) = 0.220885999618 0.0731215472002
y[1] (closed_form) = 0.220881802166 0.073128923833
absolute error = 8.487e-06
relative error = 0.003648 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.476
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0437 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.220857706848 0.0746264461595
y[1] (closed_form) = 0.22085079078 0.074636537
absolute error = 1.223e-05
relative error = 0.005248 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=317.7MB, alloc=44.3MB, time=4.12
x[1] = -2.0436 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.220343605058 0.0756298178408
y[1] (closed_form) = 0.22033875548 0.0756384960723
absolute error = 9.941e-06
relative error = 0.004267 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0435 0.344
h = 0.001 0.001
y[1] (numeric) = 0.220040302539 0.0762324558941
y[1] (closed_form) = 0.220036240355 0.0762417120126
absolute error = 1.011e-05
relative error = 0.004341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9763
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0425 0.345
h = 0.001 0.003
y[1] (numeric) = 0.220129007034 0.0765375771941
y[1] (closed_form) = 0.220125425943 0.0765469859422
absolute error = 1.007e-05
relative error = 0.00432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.632
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0415 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.220000784336 0.0772379285407
y[1] (closed_form) = 0.219996234481 0.077246983302
absolute error = 1.013e-05
relative error = 0.004346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.62
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0414 0.352
h = 0.003 0.006
y[1] (numeric) = 0.219581557177 0.0780357924825
y[1] (closed_form) = 0.219576847511 0.0780439839988
absolute error = 9.449e-06
relative error = 0.004055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.473
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0384 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.219503938441 0.0795424186811
y[1] (closed_form) = 0.21949638588 0.0795532112488
absolute error = 1.317e-05
relative error = 0.005642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0383 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.218956081925 0.0805305777329
y[1] (closed_form) = 0.218950661661 0.08054004535
absolute error = 1.091e-05
relative error = 0.004676 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0382 0.366
h = 0.001 0.001
y[1] (numeric) = 0.218632554112 0.0811242270283
y[1] (closed_form) = 0.218627897443 0.0811343080283
absolute error = 1.110e-05
relative error = 0.004762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9756
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0372 0.367
h = 0.001 0.003
y[1] (numeric) = 0.218711398272 0.081432726016
y[1] (closed_form) = 0.218707216902 0.0814429809567
absolute error = 1.107e-05
relative error = 0.004745 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.629
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0362 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.21856001488 0.0821299526362
y[1] (closed_form) = 0.218554878487 0.0821398105774
absolute error = 1.112e-05
relative error = 0.004761 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.619
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=364.1MB, alloc=44.3MB, time=4.72
x[1] = -2.0361 0.374
h = 0.003 0.006
y[1] (numeric) = 0.218114003352 0.0829152460101
y[1] (closed_form) = 0.218108744637 0.0829242322368
absolute error = 1.041e-05
relative error = 0.004462 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.471
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0331 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.217986890661 0.0844214468773
y[1] (closed_form) = 0.217978670708 0.0844329139764
absolute error = 1.411e-05
relative error = 0.006036 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.542
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.033 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.217405887495 0.0853928895881
y[1] (closed_form) = 0.217399860969 0.085403123157
absolute error = 1.188e-05
relative error = 0.005085 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.242
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0329 0.388
h = 0.001 0.001
y[1] (numeric) = 0.217062494623 0.085976651023
y[1] (closed_form) = 0.217057205912 0.0859875322307
absolute error = 1.210e-05
relative error = 0.005182 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9751
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0319 0.389
h = 0.001 0.003
y[1] (numeric) = 0.217131315145 0.0862881018766
y[1] (closed_form) = 0.217126494762 0.0862991780548
absolute error = 1.208e-05
relative error = 0.00517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.626
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0309 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.21695687125 0.0869811853791
y[1] (closed_form) = 0.216951111962 0.0869918222261
absolute error = 1.210e-05
relative error = 0.005175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.617
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0308 0.396
h = 0.003 0.006
y[1] (numeric) = 0.216484585575 0.0877527172386
y[1] (closed_form) = 0.216478741974 0.0877624759401
absolute error = 1.137e-05
relative error = 0.004869 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.469
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0278 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.216307928338 0.0892563272566
y[1] (closed_form) = 0.216299011566 0.0892684400066
absolute error = 1.504e-05
relative error = 0.006428 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0277 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.215694469885 0.0902095808916
y[1] (closed_form) = 0.215687802738 0.0902205549918
absolute error = 1.284e-05
relative error = 0.005492 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0276 0.41
h = 0.001 0.001
y[1] (numeric) = 0.21533162189 0.0907825737809
y[1] (closed_form) = 0.215325664875 0.0907942284039
absolute error = 1.309e-05
relative error = 0.005601 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9746
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=410.8MB, alloc=44.3MB, time=5.32
x[1] = -2.0266 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.215390278535 0.0910965411581
y[1] (closed_form) = 0.21538478172 0.0911084114229
absolute error = 1.308e-05
relative error = 0.005594 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.851
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0265 0.415
h = 0.003 0.006
y[1] (numeric) = 0.21489695441 0.0918559128312
y[1] (closed_form) = 0.214890470514 0.0918659791681
absolute error = 1.197e-05
relative error = 0.005124 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.468
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0235 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.214677766821 0.0933549656402
y[1] (closed_form) = 0.214668120487 0.0933672706333
absolute error = 1.564e-05
relative error = 0.006679 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0234 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.21403722758 0.0942910372288
y[1] (closed_form) = 0.21402987394 0.094302288353
absolute error = 1.344e-05
relative error = 0.005747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0233 0.429
h = 0.001 0.001
y[1] (numeric) = 0.213658140769 0.0948538479667
y[1] (closed_form) = 0.213651471607 0.0948658063651
absolute error = 1.369e-05
relative error = 0.005857 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9745
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0223 0.43
h = 0.001 0.003
y[1] (numeric) = 0.213707931707 0.0951695038108
y[1] (closed_form) = 0.213701714598 0.0951816951835
absolute error = 1.369e-05
relative error = 0.00585 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.623
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0213 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.213491113221 0.0958519148787
y[1] (closed_form) = 0.21348399385 0.0958635907551
absolute error = 1.368e-05
relative error = 0.005844 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.616
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0212 0.437
h = 0.003 0.006
y[1] (numeric) = 0.212971715828 0.0965944681461
y[1] (closed_form) = 0.212964583816 0.0966052599142
absolute error = 1.294e-05
relative error = 0.005532 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.467
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0182 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.212703230867 0.0980868952581
y[1] (closed_form) = 0.212692837631 0.0980997877116
absolute error = 1.656e-05
relative error = 0.00707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0181 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.212031753916 0.0990021490469
y[1] (closed_form) = 0.212023699767 0.0990140880163
absolute error = 1.440e-05
relative error = 0.006154 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=457.5MB, alloc=44.3MB, time=5.92
x[1] = -2.018 0.451
h = 0.001 0.001
y[1] (numeric) = 0.211634112723 0.0995526189088
y[1] (closed_form) = 0.21162671209 0.0995652951334
absolute error = 1.468e-05
relative error = 0.006276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9742
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.017 0.452
h = 0.001 0.003
y[1] (numeric) = 0.211673547736 0.0998699600675
y[1] (closed_form) = 0.211666588944 0.0998828890556
absolute error = 1.468e-05
relative error = 0.006273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.622
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.016 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.211434274799 0.100545353188
y[1] (closed_form) = 0.211426436375 0.100557727177
absolute error = 1.465e-05
relative error = 0.006256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.615
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0159 0.459
h = 0.003 0.006
y[1] (numeric) = 0.210890433381 0.101270907266
y[1] (closed_form) = 0.210882621045 0.101282396715
absolute error = 1.389e-05
relative error = 0.005939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.466
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0129 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.210572939735 0.102754550249
y[1] (closed_form) = 0.210561774973 0.102767997047
absolute error = 1.748e-05
relative error = 0.007459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0128 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.209871441941 0.103647632919
y[1] (closed_form) = 0.209862657138 0.10366022911
absolute error = 1.536e-05
relative error = 0.006561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0127 0.473
h = 0.001 0.001
y[1] (numeric) = 0.209455790878 0.104184952252
y[1] (closed_form) = 0.209447627006 0.104198313967
absolute error = 1.566e-05
relative error = 0.006693 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9741
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0117 0.474
h = 0.001 0.003
y[1] (numeric) = 0.209484798939 0.104503524921
y[1] (closed_form) = 0.209477065619 0.104517158617
absolute error = 1.567e-05
relative error = 0.006695 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.621
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0107 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.209223385123 0.105170918342
y[1] (closed_form) = 0.209214796949 0.105183958803
absolute error = 1.561e-05
relative error = 0.006668 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.615
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0106 0.481
h = 0.003 0.006
y[1] (numeric) = 0.208655853176 0.105878408549
y[1] (closed_form) = 0.208647329815 0.105890566158
absolute error = 1.485e-05
relative error = 0.006346 %
Correct digits = 4
memory used=504.0MB, alloc=44.3MB, time=6.52
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.466
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0076 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.208289757481 0.107351125986
y[1] (closed_form) = 0.208277798417 0.107365092745
absolute error = 1.839e-05
relative error = 0.007847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0075 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.207559229145 0.108220735496
y[1] (closed_form) = 0.207549685235 0.108233956652
absolute error = 1.631e-05
relative error = 0.006966 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0074 0.495
h = 0.001 0.001
y[1] (numeric) = 0.20712615655 0.108744125156
y[1] (closed_form) = 0.207117199477 0.108758138289
absolute error = 1.663e-05
relative error = 0.007109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9741
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0064 0.496
h = 0.001 0.003
y[1] (numeric) = 0.207144691524 0.109063472068
y[1] (closed_form) = 0.207136152677 0.109077775759
absolute error = 1.666e-05
relative error = 0.007116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.622
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0054 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.206861503855 0.10972190213
y[1] (closed_form) = 0.206852136994 0.109735575753
absolute error = 1.657e-05
relative error = 0.007078 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.615
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0053 0.503
h = 0.003 0.006
y[1] (numeric) = 0.206271092368 0.110410306151
y[1] (closed_form) = 0.206261828897 0.110423100727
absolute error = 1.580e-05
relative error = 0.006752 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.466
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0023 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.205856917923 0.111869981356
y[1] (closed_form) = 0.205844143708 0.111884432551
absolute error = 1.929e-05
relative error = 0.008233 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0022 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.20509841929 0.112714871687
y[1] (closed_form) = 0.205088089615 0.112728684031
absolute error = 1.725e-05
relative error = 0.00737 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0021 0.517
h = 0.001 0.001
y[1] (numeric) = 0.204648555246 0.113223585859
y[1] (closed_form) = 0.204638776931 0.113238214721
absolute error = 1.760e-05
relative error = 0.007524 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9742
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=550.6MB, alloc=44.3MB, time=7.13
x[1] = -2.0011 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.204656596075 0.113543247923
y[1] (closed_form) = 0.204647222665 0.113558185211
absolute error = 1.763e-05
relative error = 0.007535 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.848
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.001 0.522
h = 0.003 0.006
y[1] (numeric) = 0.204048145749 0.114215282038
y[1] (closed_form) = 0.204038187774 0.114228244897
absolute error = 1.635e-05
relative error = 0.00699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.467
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.998 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.203593282534 0.115661498338
y[1] (closed_form) = 0.203579757892 0.115675982716
absolute error = 1.982e-05
relative error = 0.008463 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9979 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.202811921111 0.116483844741
y[1] (closed_form) = 0.202800860287 0.116497783519
absolute error = 1.779e-05
relative error = 0.007608 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9978 0.536
h = 0.001 0.001
y[1] (numeric) = 0.202348324521 0.116979167849
y[1] (closed_form) = 0.202337783246 0.116993942231
absolute error = 1.815e-05
relative error = 0.007765 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9745
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9968 0.537
h = 0.001 0.003
y[1] (numeric) = 0.202347338353 0.117298608502
y[1] (closed_form) = 0.20233718956 0.117313705902
absolute error = 1.819e-05
relative error = 0.007778 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.624
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9958 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.202024921804 0.117937624738
y[1] (closed_form) = 0.202014000482 0.117952028093
absolute error = 1.808e-05
relative error = 0.007727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.616
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9957 0.544
h = 0.003 0.006
y[1] (numeric) = 0.201394533856 0.118587705949
y[1] (closed_form) = 0.201383786744 0.118601243363
absolute error = 1.728e-05
relative error = 0.007396 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.468
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9927 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.200892893487 0.120017042516
y[1] (closed_form) = 0.200878520686 0.120031942441
absolute error = 2.070e-05
relative error = 0.008847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9926 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.200085720445 0.120812529746
y[1] (closed_form) = 0.200073829796 0.120826992975
absolute error = 1.872e-05
relative error = 0.008011 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.242
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=597.2MB, alloc=44.3MB, time=7.73
x[1] = -1.9925 0.558
h = 0.001 0.001
y[1] (numeric) = 0.199606615793 0.121291895816
y[1] (closed_form) = 0.19959520701 0.121307215401
absolute error = 1.910e-05
relative error = 0.008178 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9749
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9915 0.559
h = 0.001 0.003
y[1] (numeric) = 0.199595168572 0.121610798606
y[1] (closed_form) = 0.199584137246 0.121626457585
absolute error = 1.915e-05
relative error = 0.008195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.625
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9905 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.199252321186 0.122238231597
y[1] (closed_form) = 0.19924054948 0.12225316444
absolute error = 1.901e-05
relative error = 0.008134 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.617
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9904 0.566
h = 0.003 0.006
y[1] (numeric) = 0.198601674384 0.122866579712
y[1] (closed_form) = 0.198590114268 0.12288065635
absolute error = 1.822e-05
relative error = 0.0078 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.469
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9874 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.198054101048 0.124277033271
y[1] (closed_form) = 0.198038865086 0.124292310701
absolute error = 2.158e-05
relative error = 0.009228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.542
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9873 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.197222353562 0.125044599783
y[1] (closed_form) = 0.197209612079 0.125059550053
absolute error = 1.964e-05
relative error = 0.008412 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.242
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9872 0.58
h = 0.001 0.001
y[1] (numeric) = 0.196728476563 0.125507372762
y[1] (closed_form) = 0.196716178262 0.125523198015
absolute error = 2.004e-05
relative error = 0.008589 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9753
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9862 0.581
h = 0.001 0.003
y[1] (numeric) = 0.196706618793 0.125825282767
y[1] (closed_form) = 0.196694682088 0.125841462914
absolute error = 2.011e-05
relative error = 0.008611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.627
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9852 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.196343899202 0.126440270799
y[1] (closed_form) = 0.1963312559 0.126455694585
absolute error = 1.994e-05
relative error = 0.00854 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.618
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9851 0.588
h = 0.003 0.006
y[1] (numeric) = 0.195673996303 0.127046060035
y[1] (closed_form) = 0.195661601301 0.127060639356
absolute error = 1.914e-05
relative error = 0.008202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.471
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=643.8MB, alloc=44.3MB, time=8.33
x[1] = -1.9821 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.195081440442 0.128435680251
y[1] (closed_form) = 0.195065328439 0.128451296528
absolute error = 2.244e-05
relative error = 0.009607 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.982 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.194226409036 0.129174335882
y[1] (closed_form) = 0.194212797823 0.129189734769
absolute error = 2.055e-05
relative error = 0.008811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9819 0.602
h = 0.001 0.001
y[1] (numeric) = 0.193718527274 0.12961992219
y[1] (closed_form) = 0.193705319702 0.129636212505
absolute error = 2.097e-05
relative error = 0.008998 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9759
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9809 0.603
h = 0.001 0.003
y[1] (numeric) = 0.193686334038 0.129936388976
y[1] (closed_form) = 0.193673471422 0.129953048758
absolute error = 2.105e-05
relative error = 0.009024 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.63
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9799 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.193304345681 0.130538104077
y[1] (closed_form) = 0.193290811756 0.130553979239
absolute error = 2.086e-05
relative error = 0.008944 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.62
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9798 0.61
h = 0.003 0.006
y[1] (numeric) = 0.192616230465 0.131120566532
y[1] (closed_form) = 0.192602980756 0.131135610915
absolute error = 2.005e-05
relative error = 0.008604 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.473
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9768 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.191979744805 0.132487462692
y[1] (closed_form) = 0.191962746028 0.132503378675
absolute error = 2.329e-05
relative error = 0.009984 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9767 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.191102768418 0.133196291777
y[1] (closed_form) = 0.191088270743 0.133212099983
absolute error = 2.145e-05
relative error = 0.009208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9766 0.624
h = 0.001 0.001
y[1] (numeric) = 0.190581678403 0.133624142164
y[1] (closed_form) = 0.190567544121 0.133640856017
absolute error = 2.189e-05
relative error = 0.009404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9766
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9756 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.19053924894 0.133938721367
y[1] (closed_form) = 0.190525442258 0.133955818287
absolute error = 2.198e-05
relative error = 0.009436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.863
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=690.4MB, alloc=44.3MB, time=8.94
x[1] = -1.9755 0.629
h = 0.003 0.006
y[1] (numeric) = 0.189837078489 0.13450155251
y[1] (closed_form) = 0.189823118094 0.134516616435
absolute error = 2.054e-05
relative error = 0.008828 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.476
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9725 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.189163997434 0.13584692032
y[1] (closed_form) = 0.189146269668 0.13586271252
absolute error = 2.374e-05
relative error = 0.01019 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.545
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9724 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.188269605597 0.136529162466
y[1] (closed_form) = 0.188254373135 0.136544940722
absolute error = 2.193e-05
relative error = 0.00943 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9723 0.643
h = 0.001 0.001
y[1] (numeric) = 0.187738023335 0.136941197636
y[1] (closed_form) = 0.187723119034 0.136957891485
absolute error = 2.238e-05
relative error = 0.009631 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9774
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9713 0.644
h = 0.001 0.003
y[1] (numeric) = 0.187686909925 0.137253682116
y[1] (closed_form) = 0.187672317622 0.137270769712
absolute error = 2.247e-05
relative error = 0.009664 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.637
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9703 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.187270995769 0.137828411933
y[1] (closed_form) = 0.187255801633 0.137844668302
absolute error = 2.225e-05
relative error = 0.00957 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.624
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9702 0.651
h = 0.003 0.006
y[1] (numeric) = 0.186552190104 0.138365446781
y[1] (closed_form) = 0.186537344269 0.138380903199
absolute error = 2.143e-05
relative error = 0.009227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.479
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9672 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.185837415316 0.139684767663
y[1] (closed_form) = 0.185818787045 0.139700785882
absolute error = 2.457e-05
relative error = 0.01057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.546
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9671 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.184923689766 0.14033570381
y[1] (closed_form) = 0.184907546109 0.140351816299
absolute error = 2.281e-05
relative error = 0.009825 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.246
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.967 0.665
h = 0.001 0.001
y[1] (numeric) = 0.184380453046 0.14072911454
y[1] (closed_form) = 0.184364596406 0.140746152622
absolute error = 2.328e-05
relative error = 0.01003 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9783
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=737.0MB, alloc=44.3MB, time=9.54
x[1] = -1.966 0.666
h = 0.001 0.003
y[1] (numeric) = 0.184319355471 0.141038907787
y[1] (closed_form) = 0.184303792343 0.141056351297
absolute error = 2.338e-05
relative error = 0.01007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.642
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.965 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.183886131951 0.141598214843
y[1] (closed_form) = 0.183870005784 0.14161480494
absolute error = 2.314e-05
relative error = 0.009969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.626
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9649 0.673
h = 0.003 0.006
y[1] (numeric) = 0.183152296783 0.142110079249
y[1] (closed_form) = 0.183136551883 0.142125888261
absolute error = 2.231e-05
relative error = 0.009625 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.482
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9619 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.182397146529 0.14340166772
y[1] (closed_form) = 0.182377613219 0.143417872252
absolute error = 2.538e-05
relative error = 0.01094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.548
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9618 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.18146553479 0.144020609325
y[1] (closed_form) = 0.18144846962 0.14403701509
absolute error = 2.367e-05
relative error = 0.01022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.247
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9617 0.687
h = 0.001 0.001
y[1] (numeric) = 0.180911505085 0.144394981506
y[1] (closed_form) = 0.180894685509 0.144412320578
absolute error = 2.416e-05
relative error = 0.01044 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9793
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9607 0.688
h = 0.001 0.003
y[1] (numeric) = 0.180840588189 0.144701665072
y[1] (closed_form) = 0.180824043125 0.144719420182
absolute error = 2.427e-05
relative error = 0.01048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.646
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9597 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.180390806674 0.145244875931
y[1] (closed_form) = 0.180373738315 0.145261757681
absolute error = 2.401e-05
relative error = 0.01037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.629
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9596 0.695
h = 0.003 0.006
y[1] (numeric) = 0.179643104628 0.14573104497
y[1] (closed_form) = 0.179626449269 0.145747166156
absolute error = 2.318e-05
relative error = 0.01002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.486
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9566 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.178848979851 0.146993297318
y[1] (closed_form) = 0.178828539112 0.147009648523
absolute error = 2.618e-05
relative error = 0.01131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.549
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=783.8MB, alloc=44.3MB, time=10.14
x[1] = -1.9565 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.177900957195 0.147579638487
y[1] (closed_form) = 0.177882962468 0.14759629627
absolute error = 2.452e-05
relative error = 0.01061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.248
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9564 0.709
h = 0.001 0.001
y[1] (numeric) = 0.177337012617 0.147934607185
y[1] (closed_form) = 0.177319221931 0.147952203708
absolute error = 2.502e-05
relative error = 0.01084 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9804
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9554 0.71
h = 0.001 0.003
y[1] (numeric) = 0.177256462696 0.148237774291
y[1] (closed_form) = 0.177238927084 0.148255796363
absolute error = 2.515e-05
relative error = 0.01088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.652
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9544 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.17679090586 0.148764260525
y[1] (closed_form) = 0.176772887494 0.148781391569
absolute error = 2.486e-05
relative error = 0.01076 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.632
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9543 0.717
h = 0.003 0.006
y[1] (numeric) = 0.176030519979 0.149224275487
y[1] (closed_form) = 0.176012945018 0.149240668052
absolute error = 2.403e-05
relative error = 0.01041 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.49
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9513 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.175198898332 0.15045567444
y[1] (closed_form) = 0.175177549897 0.150472132878
absolute error = 2.696e-05
relative error = 0.01167 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.551
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9512 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.174235962204 0.151008893016
y[1] (closed_form) = 0.174217032154 0.151025761409
absolute error = 2.536e-05
relative error = 0.011 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.25
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9511 0.731
h = 0.001 0.001
y[1] (numeric) = 0.173662994185 0.151344143127
y[1] (closed_form) = 0.173644226642 0.15136195342
absolute error = 2.587e-05
relative error = 0.01123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9816
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9501 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.173573018053 0.151643399939
y[1] (closed_form) = 0.17355448578 0.15166164418
absolute error = 2.601e-05
relative error = 0.01128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.893
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.95 0.736
h = 0.003 0.006
y[1] (numeric) = 0.172803190681 0.152081714617
y[1] (closed_form) = 0.172784927627 0.152097980793
absolute error = 2.446e-05
relative error = 0.01062 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.494
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=830.4MB, alloc=44.3MB, time=10.75
x[1] = -1.947 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.171940920632 0.153284988683
y[1] (closed_form) = 0.171918903257 0.153301181234
absolute error = 2.733e-05
relative error = 0.01187 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.553
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9469 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.170966760846 0.15380918966
y[1] (closed_form) = 0.170947132614 0.153825878906
absolute error = 2.576e-05
relative error = 0.0112 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9468 0.75
h = 0.001 0.001
y[1] (numeric) = 0.170386986362 0.154127159828
y[1] (closed_form) = 0.170367485011 0.1541447914
absolute error = 2.629e-05
relative error = 0.01144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.086
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9829
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9458 0.751
h = 0.001 0.003
y[1] (numeric) = 0.170289129681 0.154422637621
y[1] (closed_form) = 0.170269846237 0.154440709226
absolute error = 2.643e-05
relative error = 0.0115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.664
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9448 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.169796610394 0.154916326738
y[1] (closed_form) = 0.169776921371 0.1549334811
absolute error = 2.611e-05
relative error = 0.01136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.639
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9447 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.16901614429 0.155326566641
y[1] (closed_form) = 0.168996951111 0.155343027751
absolute error = 2.529e-05
relative error = 0.01102 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.087
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9446 0.762
h = 0.003 0.006
y[1] (numeric) = 0.168235497117 0.155731097248
y[1] (closed_form) = 0.168216303937 0.155747558357
absolute error = 2.529e-05
relative error = 0.01103 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.502
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9416 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.167334142047 0.156893812414
y[1] (closed_form) = 0.167311233992 0.156910013694
absolute error = 2.806e-05
relative error = 0.01223 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.557
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9415 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.166347227227 0.157377869245
y[1] (closed_form) = 0.166326660429 0.157394681285
absolute error = 2.656e-05
relative error = 0.0116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.254
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9414 0.776
h = 0.001 0.001
y[1] (numeric) = 0.165759690007 0.157671925605
y[1] (closed_form) = 0.165739202027 0.157689677073
absolute error = 2.711e-05
relative error = 0.01185 %
Correct digits = 4
memory used=877.0MB, alloc=44.3MB, time=11.35
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.985
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9404 0.777
h = 0.001 0.003
y[1] (numeric) = 0.165651498969 0.15796164347
y[1] (closed_form) = 0.165631204903 0.15797984148
absolute error = 2.726e-05
relative error = 0.01191 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.674
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9394 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.165144054614 0.158433406592
y[1] (closed_form) = 0.165123404535 0.158450676236
absolute error = 2.692e-05
relative error = 0.01176 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.645
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9393 0.784
h = 0.003 0.006
y[1] (numeric) = 0.164353903094 0.158811550024
y[1] (closed_form) = 0.164333778351 0.158828157919
absolute error = 2.609e-05
relative error = 0.01142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.507
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9363 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.163419995633 0.159939460971
y[1] (closed_form) = 0.163396193491 0.159955652729
absolute error = 2.879e-05
relative error = 0.01259 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.559
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9362 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.162422799329 0.160389403009
y[1] (closed_form) = 0.162401295471 0.160406300729
absolute error = 2.735e-05
relative error = 0.01198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.256
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9361 0.798
h = 0.001 0.001
y[1] (numeric) = 0.161828997108 0.160663137105
y[1] (closed_form) = 0.16180753157 0.160680970732
absolute error = 2.791e-05
relative error = 0.01224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9866
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9351 0.799
h = 0.001 0.003
y[1] (numeric) = 0.161712138473 0.160947854218
y[1] (closed_form) = 0.161690846452 0.160966139345
absolute error = 2.807e-05
relative error = 0.0123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.681
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9341 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.161192347534 0.161400887297
y[1] (closed_form) = 0.161170741579 0.161418235779
absolute error = 2.771e-05
relative error = 0.01215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.649
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.934 0.806
h = 0.003 0.006
y[1] (numeric) = 0.16039440824 0.161751768065
y[1] (closed_form) = 0.160373351803 0.161768482036
absolute error = 2.688e-05
relative error = 0.0118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.513
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.931 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.159429664788 0.162843745449
y[1] (closed_form) = 0.159404976362 0.16285989044
absolute error = 2.950e-05
relative error = 0.01294 %
Correct digits = 4
memory used=923.9MB, alloc=44.3MB, time=11.96
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.562
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9309 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.158423713303 0.163259390519
y[1] (closed_form) = 0.158401275556 0.16327633348
absolute error = 2.812e-05
relative error = 0.01236 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.096
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.258
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9308 0.82
h = 0.001 0.001
y[1] (numeric) = 0.15782455523 0.163512689581
y[1] (closed_form) = 0.157802115884 0.163530562819
absolute error = 2.869e-05
relative error = 0.01262 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9883
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9298 0.821
h = 0.001 0.003
y[1] (numeric) = 0.157699306552 0.163792076296
y[1] (closed_form) = 0.157677020265 0.163810404866
absolute error = 2.886e-05
relative error = 0.01269 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.689
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9288 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.157168057131 0.164225997547
y[1] (closed_form) = 0.157145499014 0.1642433835
absolute error = 2.848e-05
relative error = 0.01253 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.654
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9287 0.828
h = 0.003 0.006
y[1] (numeric) = 0.156363545399 0.164549494309
y[1] (closed_form) = 0.156341559303 0.164566274
absolute error = 2.766e-05
relative error = 0.01218 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.099
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.519
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9257 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.155369725531 0.165604510532
y[1] (closed_form) = 0.155344160477 0.16562057232
absolute error = 3.019e-05
relative error = 0.0133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.564
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9256 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.154356539733 0.165985759011
y[1] (closed_form) = 0.154333173378 0.166002707332
absolute error = 2.887e-05
relative error = 0.01274 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.261
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9255 0.842
h = 0.001 0.001
y[1] (numeric) = 0.153752931867 0.166218559411
y[1] (closed_form) = 0.153729524701 0.166236430333
absolute error = 2.945e-05
relative error = 0.01301 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9901
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9245 0.843
h = 0.001 0.003
y[1] (numeric) = 0.153619585331 0.166492304029
y[1] (closed_form) = 0.153596310772 0.166510632995
absolute error = 2.963e-05
relative error = 0.01308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.698
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=970.3MB, alloc=44.3MB, time=12.56
x[1] = -1.9235 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.153077776799 0.166906782399
y[1] (closed_form) = 0.153054272394 0.166924165057
absolute error = 2.923e-05
relative error = 0.01291 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.659
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9234 0.85
h = 0.003 0.006
y[1] (numeric) = 0.152267902078 0.167202839189
y[1] (closed_form) = 0.152244990477 0.167219644726
absolute error = 2.841e-05
relative error = 0.01256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.525
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9204 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.151246801581 0.168219969875
y[1] (closed_form) = 0.151220371329 0.168235912943
absolute error = 3.087e-05
relative error = 0.01365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.567
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9203 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.150227891749 0.168566803325
y[1] (closed_form) = 0.150203604117 0.168583717808
absolute error = 2.960e-05
relative error = 0.01311 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.104
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9202 0.864
h = 0.001 0.001
y[1] (numeric) = 0.149620733997 0.16877908976
y[1] (closed_form) = 0.149596367163 0.168796917193
absolute error = 3.019e-05
relative error = 0.01339 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9921
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9192 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.149479595096 0.169046899223
y[1] (closed_form) = 0.149455340497 0.169065186311
absolute error = 3.038e-05
relative error = 0.01346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.956
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9191 0.869
h = 0.003 0.006
y[1] (numeric) = 0.14866626864 0.169320512735
y[1] (closed_form) = 0.148642746013 0.169337032237
absolute error = 2.874e-05
relative error = 0.01276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.106
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.532
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9161 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.147623610749 0.170304076809
y[1] (closed_form) = 0.147596628568 0.170319614026
absolute error = 3.114e-05
relative error = 0.01382 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.106
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.57
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.916 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.146601380269 0.170621288895
y[1] (closed_form) = 0.146576488426 0.170637866758
absolute error = 2.991e-05
relative error = 0.0133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.108
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.266
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9159 0.883
h = 0.001 0.001
y[1] (numeric) = 0.145992124362 0.170815913614
y[1] (closed_form) = 0.145967121165 0.170833394154
absolute error = 3.051e-05
relative error = 0.01358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9939
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1016.9MB, alloc=44.3MB, time=13.16
x[1] = -1.9149 0.884
h = 0.001 0.003
y[1] (numeric) = 0.145844606946 0.171078306643
y[1] (closed_form) = 0.145819698561 0.171096247116
absolute error = 3.070e-05
relative error = 0.01365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.716
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9139 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.14528580734 0.171455798929
y[1] (closed_form) = 0.145260746416 0.171472792652
absolute error = 3.028e-05
relative error = 0.01347 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.669
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9138 0.891
h = 0.003 0.006
y[1] (numeric) = 0.144469460909 0.171700835652
y[1] (closed_form) = 0.144445026403 0.171717308637
absolute error = 2.947e-05
relative error = 0.01313 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.111
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.539
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9108 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.143402944542 0.172645093845
y[1] (closed_form) = 0.143375123263 0.172660449196
absolute error = 3.178e-05
relative error = 0.01416 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.574
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9107 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.142377753273 0.172928083935
y[1] (closed_form) = 0.142351959442 0.172944557393
absolute error = 3.061e-05
relative error = 0.01366 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.112
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.268
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9106 0.905
h = 0.001 0.001
y[1] (numeric) = 0.141766594456 0.173102301589
y[1] (closed_form) = 0.141740652732 0.173119664624
absolute error = 3.122e-05
relative error = 0.01395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.114
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.996
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9096 0.906
h = 0.001 0.003
y[1] (numeric) = 0.141611886865 0.173358269658
y[1] (closed_form) = 0.141586019919 0.173376092244
absolute error = 3.141e-05
relative error = 0.01403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.113
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.726
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9086 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.141045135485 0.173715662638
y[1] (closed_form) = 0.14101915685 0.173732541062
absolute error = 3.098e-05
relative error = 0.01385 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.114
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.675
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9085 0.913
h = 0.003 0.006
y[1] (numeric) = 0.140226816103 0.17393346219
y[1] (closed_form) = 0.140201479586 0.173949850881
absolute error = 3.017e-05
relative error = 0.01351 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.115
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.547
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9055 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.139138301085 0.174837789057
y[1] (closed_form) = 0.139109656728 0.174852930168
absolute error = 3.240e-05
relative error = 0.0145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.115
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.577
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1063.7MB, alloc=44.3MB, time=13.77
x[1] = -1.9054 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.138111601401 0.175086759931
y[1] (closed_form) = 0.138084918351 0.175103092407
absolute error = 3.128e-05
relative error = 0.01403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.117
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.271
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9053 0.927
h = 0.001 0.001
y[1] (numeric) = 0.137499405556 0.175240686949
y[1] (closed_form) = 0.137472539199 0.175257894167
absolute error = 3.190e-05
relative error = 0.01432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.118
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9983
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9043 0.928
h = 0.001 0.003
y[1] (numeric) = 0.137337843616 0.175489993318
y[1] (closed_form) = 0.137311032267 0.175507658674
absolute error = 3.211e-05
relative error = 0.01441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.118
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.737
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9033 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.13676405187 0.175827150253
y[1] (closed_form) = 0.136737169048 0.175843876118
absolute error = 3.166e-05
relative error = 0.01421 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.118
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.681
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9032 0.935
h = 0.003 0.006
y[1] (numeric) = 0.135944909023 0.176017895065
y[1] (closed_form) = 0.135918682217 0.176034162631
absolute error = 3.086e-05
relative error = 0.01388 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.555
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9002 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.134836264861 0.17688176913
y[1] (closed_form) = 0.134806814877 0.176896664874
absolute error = 3.300e-05
relative error = 0.01484 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.581
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9001 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.133809480605 0.177096996239
y[1] (closed_form) = 0.133781922842 0.17711315226
absolute error = 3.194e-05
relative error = 0.01439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.122
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.274
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9 0.949
h = 0.001 0.001
y[1] (numeric) = 0.133197096792 0.177230792335
y[1] (closed_form) = 0.133169321524 0.177247806628
absolute error = 3.257e-05
relative error = 0.01469 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.001
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.899 0.95
h = 0.001 0.003
y[1] (numeric) = 0.133029024347 0.17747322057
y[1] (closed_form) = 0.133001284643 0.177490690587
absolute error = 3.278e-05
relative error = 0.01478 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.748
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.898 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.13244909928 0.177790053525
y[1] (closed_form) = 0.132421327562 0.177806590736
absolute error = 3.232e-05
relative error = 0.01458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.687
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1110.3MB, alloc=44.3MB, time=14.37
x[1] = -1.8979 0.957
h = 0.003 0.006
y[1] (numeric) = 0.131630258507 0.17795398306
y[1] (closed_form) = 0.131603154908 0.177970093713
absolute error = 3.153e-05
relative error = 0.01424 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.125
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.564
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8949 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.130503357818 0.17877698583
y[1] (closed_form) = 0.130473120987 0.178791606387
absolute error = 3.359e-05
relative error = 0.01517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.125
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8948 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.129477880251 0.178958814401
y[1] (closed_form) = 0.129449463927 0.178974759693
absolute error = 3.258e-05
relative error = 0.01475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.127
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8947 0.971
h = 0.001 0.001
y[1] (numeric) = 0.128866138299 0.179072680863
y[1] (closed_form) = 0.128837471568 0.179089466423
absolute error = 3.322e-05
relative error = 0.01506 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.129
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.003
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8937 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.128691905838 0.179308035014
y[1] (closed_form) = 0.12866325561 0.179325272918
absolute error = 3.344e-05
relative error = 0.01515 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.128
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.022
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8936 0.976
h = 0.003 0.006
y[1] (numeric) = 0.127874170406 0.179450253573
y[1] (closed_form) = 0.127846546808 0.179465976684
absolute error = 3.178e-05
relative error = 0.01442 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.572
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8906 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.126733544059 0.180237630967
y[1] (closed_form) = 0.126702869848 0.180251768276
absolute error = 3.378e-05
relative error = 0.01533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8905 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.125710668681 0.180391076052
y[1] (closed_form) = 0.12568175069 0.180406589053
absolute error = 3.282e-05
relative error = 0.01493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.132
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.28
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8904 0.99
h = 0.001 0.001
y[1] (numeric) = 0.125100360788 0.180488000011
y[1] (closed_form) = 0.125071165402 0.180504336262
absolute error = 3.346e-05
relative error = 0.01523 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.133
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.005
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8894 0.991
h = 0.001 0.003
y[1] (numeric) = 0.124921197779 0.180717056209
y[1] (closed_form) = 0.124892002888 0.180733840935
absolute error = 3.368e-05
relative error = 0.01533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.133
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.771
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1157.0MB, alloc=44.3MB, time=14.97
x[1] = -1.8884 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.124332489413 0.180995951708
y[1] (closed_form) = 0.124303333411 0.18101182159
absolute error = 3.320e-05
relative error = 0.01512 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.7
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8883 0.998
h = 0.003 0.006
y[1] (numeric) = 0.123517421696 0.181110840854
y[1] (closed_form) = 0.123488951206 0.18112634377
absolute error = 3.242e-05
relative error = 0.01479 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.135
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.581
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8853 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.122362012051 0.181856859172
y[1] (closed_form) = 0.122330589444 0.181870669746
absolute error = 3.432e-05
relative error = 0.01566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.592
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8852 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.121342926855 0.18197773845
y[1] (closed_form) = 0.121313184759 0.181992980644
absolute error = 3.342e-05
relative error = 0.01528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.138
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.283
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8851 1.012
h = 0.001 0.001
y[1] (numeric) = 0.120734742737 0.182055220786
y[1] (closed_form) = 0.12070469296 0.182071265666
absolute error = 3.407e-05
relative error = 0.01559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8841 1.013
h = 0.001 0.003
y[1] (numeric) = 0.120550086672 0.182276897281
y[1] (closed_form) = 0.120520019186 0.182293385574
absolute error = 3.429e-05
relative error = 0.01569 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.783
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8831 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.119957789125 0.182535487104
y[1] (closed_form) = 0.119927797213 0.182551072525
absolute error = 3.380e-05
relative error = 0.01547 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.707
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.883 1.02
h = 0.003 0.006
y[1] (numeric) = 0.119146079158 0.182624551175
y[1] (closed_form) = 0.119116779801 0.182639801613
absolute error = 3.303e-05
relative error = 0.01515 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.141
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.59
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.88 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.1179777321 0.183329076921
y[1] (closed_form) = 0.117945583098 0.183342534991
absolute error = 3.485e-05
relative error = 0.01599 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.141
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.597
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8799 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.116963714672 0.183417916759
y[1] (closed_form) = 0.116933168745 0.183432857739
absolute error = 3.400e-05
relative error = 0.01563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.287
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1203.7MB, alloc=44.3MB, time=15.57
x[1] = -1.8798 1.034
h = 0.001 0.001
y[1] (numeric) = 0.116358416962 0.183476266747
y[1] (closed_form) = 0.116327534548 0.183491988619
absolute error = 3.465e-05
relative error = 0.01595 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.145
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.011
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8788 1.035
h = 0.001 0.003
y[1] (numeric) = 0.116168629638 0.18369042629
y[1] (closed_form) = 0.116137711832 0.183706585671
absolute error = 3.489e-05
relative error = 0.01605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.145
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.796
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8778 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.115573606185 0.183928799389
y[1] (closed_form) = 0.115542799496 0.183944069545
absolute error = 3.438e-05
relative error = 0.01583 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.145
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.715
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8777 1.042
h = 0.003 0.006
y[1] (numeric) = 0.114766259191 0.183992473816
y[1] (closed_form) = 0.114736150385 0.184007440854
absolute error = 3.362e-05
relative error = 0.01551 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.6
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8747 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.113586800437 0.184655468575
y[1] (closed_form) = 0.113553947967 0.18466854986
absolute error = 3.536e-05
relative error = 0.01631 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.601
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8746 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.112579082952 0.184712851969
y[1] (closed_form) = 0.112547754708 0.184727462791
absolute error = 3.457e-05
relative error = 0.01598 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.291
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8745 1.056
h = 0.001 0.001
y[1] (numeric) = 0.111977407421 0.184752412665
y[1] (closed_form) = 0.111945715409 0.184767781471
absolute error = 3.522e-05
relative error = 0.0163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.014
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8735 1.057
h = 0.001 0.003
y[1] (numeric) = 0.11178285216 0.184958938237
y[1] (closed_form) = 0.111751107637 0.18497473785
absolute error = 3.546e-05
relative error = 0.01641 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.81
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8725 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.111185948751 0.185177225661
y[1] (closed_form) = 0.111154349666 0.185192151271
absolute error = 3.495e-05
relative error = 0.01618 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.723
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8724 1.064
h = 0.003 0.006
y[1] (numeric) = 0.110383933027 0.185215989863
y[1] (closed_form) = 0.110353035477 0.185230644002
absolute error = 3.420e-05
relative error = 0.01586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.153
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.611
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1250.2MB, alloc=44.3MB, time=16.17
x[1] = -1.8694 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.109195162764 0.185837507377
y[1] (closed_form) = 0.109161630577 0.185850189106
absolute error = 3.585e-05
relative error = 0.01663 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.153
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.606
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8693 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.108194929419 0.185864070181
y[1] (closed_form) = 0.108162841499 0.185878323418
absolute error = 3.511e-05
relative error = 0.01633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.156
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.294
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8692 1.078
h = 0.001 0.001
y[1] (numeric) = 0.107597583435 0.185885216192
y[1] (closed_form) = 0.107565106033 0.1859002035
absolute error = 3.577e-05
relative error = 0.01665 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.157
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.017
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8682 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.107398623841 0.186084010724
y[1] (closed_form) = 0.107366077409 0.186099421387
absolute error = 3.601e-05
relative error = 0.01676 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.157
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.104
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8681 1.083
h = 0.003 0.006
y[1] (numeric) = 0.106601697897 0.186102798082
y[1] (closed_form) = 0.106570387609 0.186116992974
absolute error = 3.438e-05
relative error = 0.01603 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.159
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.62
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8651 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.105406822478 0.186688642066
y[1] (closed_form) = 0.105372974412 0.186700796728
absolute error = 3.596e-05
relative error = 0.01678 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.159
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.865 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.104414297114 0.186689329634
y[1] (closed_form) = 0.104381823406 0.186703087252
absolute error = 3.527e-05
relative error = 0.01649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.162
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.298
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8649 1.097
h = 0.001 0.001
y[1] (numeric) = 0.103821434365 0.18669500976
y[1] (closed_form) = 0.103788550616 0.186709479865
absolute error = 3.593e-05
relative error = 0.01682 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.163
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.019
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8639 1.098
h = 0.001 0.003
y[1] (numeric) = 0.103619067469 0.186887040316
y[1] (closed_form) = 0.103586101076 0.186901926615
absolute error = 3.617e-05
relative error = 0.01693 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.163
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.837
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8629 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.103021082765 0.187068438773
y[1] (closed_form) = 0.102988321962 0.187082483605
absolute error = 3.564e-05
relative error = 0.01669 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.163
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.738
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1296.9MB, alloc=44.3MB, time=16.77
x[1] = -1.8628 1.105
h = 0.003 0.006
y[1] (numeric) = 0.102231711428 0.187062353751
y[1] (closed_form) = 0.10219965428 0.187076185093
absolute error = 3.491e-05
relative error = 0.01638 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.165
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.631
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8598 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.101030786197 0.187607074955
y[1] (closed_form) = 0.100996304673 0.187618792074
absolute error = 3.642e-05
relative error = 0.01709 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.166
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.615
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8597 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.100047804406 0.187578265185
y[1] (closed_form) = 0.100014616059 0.187591618632
absolute error = 3.577e-05
relative error = 0.01683 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.168
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.302
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8596 1.119
h = 0.001 0.001
y[1] (numeric) = 0.0994605021594 0.18756631135
y[1] (closed_form) = 0.0994268810513 0.18758035182
absolute error = 3.644e-05
relative error = 0.01716 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.023
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8586 1.12
h = 0.001 0.003
y[1] (numeric) = 0.0992544048285 0.187750486328
y[1] (closed_form) = 0.0992206857651 0.187764934289
absolute error = 3.668e-05
relative error = 0.01727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.852
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8576 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.0986568424705 0.187912398995
y[1] (closed_form) = 0.0986233594437 0.187926024627
absolute error = 3.615e-05
relative error = 0.01703 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.747
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8575 1.127
h = 0.003 0.006
y[1] (numeric) = 0.0978753449378 0.187883000722
y[1] (closed_form) = 0.0978425646914 0.187896443359
absolute error = 3.543e-05
relative error = 0.01672 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.172
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.643
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8545 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.0966700694363 0.18838689721
y[1] (closed_form) = 0.0966349799681 0.188398158424
absolute error = 3.685e-05
relative error = 0.0174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.173
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.62
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8544 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.0956976663054 0.188329354988
y[1] (closed_form) = 0.0956637885554 0.188342281366
absolute error = 3.626e-05
relative error = 0.01716 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.175
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.306
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8543 1.141
h = 0.001 0.001
y[1] (numeric) = 0.0951165436204 0.188300218903
y[1] (closed_form) = 0.0950822120162 0.188313806153
absolute error = 3.692e-05
relative error = 0.0175 %
Correct digits = 4
memory used=1343.6MB, alloc=44.3MB, time=17.37
Radius of convergence (given) for eq 1 = 2.177
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.026
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8533 1.142
h = 0.001 0.003
y[1] (numeric) = 0.0949070736348 0.188476496016
y[1] (closed_form) = 0.0948726294471 0.188490481453
absolute error = 3.718e-05
relative error = 0.01762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.176
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.868
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8523 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.0943106931676 0.188619198196
y[1] (closed_form) = 0.0942765140145 0.188632381608
absolute error = 3.663e-05
relative error = 0.01737 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.177
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.755
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8522 1.149
h = 0.003 0.006
y[1] (numeric) = 0.0935378787531 0.188567106477
y[1] (closed_form) = 0.0935044000308 0.188580136828
absolute error = 3.593e-05
relative error = 0.01707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.179
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.654
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8492 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.0923299094904 0.189030554496
y[1] (closed_form) = 0.0922942380221 0.189041342981
absolute error = 3.727e-05
relative error = 0.01772 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8491 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.0913690652104 0.188945082356
y[1] (closed_form) = 0.091334523993 0.188957560381
absolute error = 3.673e-05
relative error = 0.0175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.182
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.31
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.849 1.163
h = 0.001 0.001
y[1] (numeric) = 0.0907947086166 0.18889923826
y[1] (closed_form) = 0.0907596940848 0.188912350431
absolute error = 3.739e-05
relative error = 0.01784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.848 1.164
h = 0.001 0.003
y[1] (numeric) = 0.0905822197378 0.189067593377
y[1] (closed_form) = 0.090547078698 0.189081093878
absolute error = 3.765e-05
relative error = 0.01796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.884
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.847 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.0899877543562 0.189191392719
y[1] (closed_form) = 0.0899529058625 0.189204112559
absolute error = 3.710e-05
relative error = 0.01771 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.764
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8469 1.171
h = 0.003 0.006
y[1] (numeric) = 0.089224388356 0.189117256171
y[1] (closed_form) = 0.0891902365319 0.189129852254
absolute error = 3.640e-05
relative error = 0.01741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.186
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.666
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1390.3MB, alloc=44.3MB, time=17.97
x[1] = -1.8439 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.0880153351383 0.189540706031
y[1] (closed_form) = 0.0879791079446 0.189551006498
absolute error = 3.766e-05
relative error = 0.01802 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.187
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.631
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8438 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.0870669739521 0.189428140171
y[1] (closed_form) = 0.0870317957927 0.189440150185
absolute error = 3.717e-05
relative error = 0.01783 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.315
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8437 1.185
h = 0.001 0.001
y[1] (numeric) = 0.0864999368175 0.189366082473
y[1] (closed_form) = 0.0864642675156 0.189378699438
absolute error = 3.783e-05
relative error = 0.01817 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.033
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8427 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.0862847778176 0.189526509004
y[1] (closed_form) = 0.086248968804 0.189539503946
absolute error = 3.809e-05
relative error = 0.01829 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.2
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8426 1.19
h = 0.003 0.006
y[1] (numeric) = 0.0855297089469 0.189434859929
y[1] (closed_form) = 0.0854952579722 0.189446955971
absolute error = 3.651e-05
relative error = 0.01757 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.193
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.677
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8396 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.0843214415443 0.189824306959
y[1] (closed_form) = 0.0842850171784 0.189834067813
absolute error = 3.771e-05
relative error = 0.01816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.194
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8395 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.0833848308534 0.189689274743
y[1] (closed_form) = 0.0833493858328 0.189700757994
absolute error = 3.726e-05
relative error = 0.01798 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.196
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.319
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8394 1.204
h = 0.001 0.001
y[1] (numeric) = 0.0828246963203 0.18961376603
y[1] (closed_form) = 0.0827887464416 0.189625832341
absolute error = 3.792e-05
relative error = 0.01833 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.198
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.036
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8384 1.205
h = 0.001 0.003
y[1] (numeric) = 0.0826076080168 0.189767349265
y[1] (closed_form) = 0.0825715077787 0.189779784137
absolute error = 3.818e-05
relative error = 0.01845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.198
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.915
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8374 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.082018777096 0.189856937346
y[1] (closed_form) = 0.0819830162651 0.189868634039
absolute error = 3.763e-05
relative error = 0.01819 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.198
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.782
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1436.9MB, alloc=44.3MB, time=18.57
x[1] = -1.8373 1.212
h = 0.003 0.006
y[1] (numeric) = 0.0812751187674 0.189743724363
y[1] (closed_form) = 0.0812400437525 0.189755349833
absolute error = 3.695e-05
relative error = 0.0179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.69
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8343 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.0800686202837 0.190094211298
y[1] (closed_form) = 0.0800316897866 0.190103460021
absolute error = 3.807e-05
relative error = 0.01846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.201
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.641
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8342 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.0791460504768 0.189933726834
y[1] (closed_form) = 0.0791100192684 0.189944710146
absolute error = 3.767e-05
relative error = 0.01831 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.204
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.323
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8341 1.226
h = 0.001 0.001
y[1] (numeric) = 0.0785941690439 0.189842975814
y[1] (closed_form) = 0.078557618162 0.18985451441
absolute error = 3.833e-05
relative error = 0.01865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.039
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8331 1.227
h = 0.001 0.003
y[1] (numeric) = 0.0783750428905 0.189988666564
y[1] (closed_form) = 0.0783383298229 0.190000562587
absolute error = 3.859e-05
relative error = 0.01878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.205
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.932
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8321 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.0777900631479 0.190060398236
y[1] (closed_form) = 0.0777537126012 0.190071579857
absolute error = 3.803e-05
relative error = 0.01852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.792
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.832 1.234
h = 0.003 0.006
y[1] (numeric) = 0.0770577851489 0.189927134254
y[1] (closed_form) = 0.077022113006 0.189938271776
absolute error = 3.737e-05
relative error = 0.01823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.208
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.703
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.829 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.0758545140829 0.190239298682
y[1] (closed_form) = 0.075817104154 0.190248024263
absolute error = 3.841e-05
relative error = 0.01876 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.209
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.647
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8289 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.0749467458934 0.190054272146
y[1] (closed_form) = 0.0749101561133 0.190064740488
absolute error = 3.806e-05
relative error = 0.01863 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.212
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.328
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8288 1.248
h = 0.001 0.001
y[1] (numeric) = 0.0744035739636 0.189948817685
y[1] (closed_form) = 0.0743664512843 0.189959813356
absolute error = 3.872e-05
relative error = 0.01898 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.213
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.043
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1483.5MB, alloc=44.3MB, time=19.17
x[1] = -1.8278 1.249
h = 0.001 0.003
y[1] (numeric) = 0.0741827395121 0.190086655648
y[1] (closed_form) = 0.0741454435683 0.190097997262
absolute error = 3.898e-05
relative error = 0.0191 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.213
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.95
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8268 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.0736022312953 0.190140942114
y[1] (closed_form) = 0.0735653194293 0.190151593749
absolute error = 3.842e-05
relative error = 0.01884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.214
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.802
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8267 1.256
h = 0.003 0.006
y[1] (numeric) = 0.0728819238151 0.18998835713
y[1] (closed_form) = 0.0728456818006 0.18999899093
absolute error = 3.777e-05
relative error = 0.01856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.216
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.717
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8237 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.0716832812833 0.190262893683
y[1] (closed_form) = 0.0716454186115 0.190271086553
absolute error = 3.874e-05
relative error = 0.01905 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.217
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.653
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8236 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.0707910181485 0.190054254
y[1] (closed_form) = 0.0707538976081 0.190064193929
absolute error = 3.843e-05
relative error = 0.01895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.333
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8235 1.27
h = 0.001 0.001
y[1] (numeric) = 0.070256978131 0.189934646284
y[1] (closed_form) = 0.0702193130296 0.189945085498
absolute error = 3.908e-05
relative error = 0.0193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.222
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.047
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8225 1.271
h = 0.001 0.003
y[1] (numeric) = 0.070034756835 0.190064685915
y[1] (closed_form) = 0.06999690814 0.190075459289
absolute error = 3.935e-05
relative error = 0.01943 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.221
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.968
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8215 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.0694593093892 0.190101959797
y[1] (closed_form) = 0.0694218647715 0.190112068157
absolute error = 3.879e-05
relative error = 0.01916 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.222
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.813
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8214 1.278
h = 0.003 0.006
y[1] (numeric) = 0.0687515170853 0.189930797681
y[1] (closed_form) = 0.0687147327014 0.189940913568
absolute error = 3.815e-05
relative error = 0.01889 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.224
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.73
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8184 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.0675588449224 0.190168453497
y[1] (closed_form) = 0.0675205561076 0.190176105497
absolute error = 3.905e-05
relative error = 0.01935 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.225
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1530.2MB, alloc=44.3MB, time=19.77
x[1] = -1.8183 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.0666827332512 0.189937144685
y[1] (closed_form) = 0.0666451098635 0.18994654432
absolute error = 3.878e-05
relative error = 0.01926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.228
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8182 1.292
h = 0.001 0.001
y[1] (numeric) = 0.066158213712 0.189803943054
y[1] (closed_form) = 0.0661200356336 0.189813813932
absolute error = 3.943e-05
relative error = 0.01962 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8172 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.0659349182868 0.189926252771
y[1] (closed_form) = 0.065896547035 0.189936445774
absolute error = 3.970e-05
relative error = 0.01975 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.31
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8171 1.297
h = 0.003 0.006
y[1] (numeric) = 0.0652377613372 0.18974047888
y[1] (closed_form) = 0.0652007888676 0.189750082768
absolute error = 3.820e-05
relative error = 0.01904 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.232
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.743
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8141 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.0640516826819 0.189947115756
y[1] (closed_form) = 0.0640133050412 0.189954242044
absolute error = 3.903e-05
relative error = 0.01947 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.233
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.814 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.0631902026192 0.189697260797
y[1] (closed_form) = 0.0631524256177 0.189706131469
absolute error = 3.880e-05
relative error = 0.01941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.236
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.342
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8139 1.311
h = 0.001 0.001
y[1] (numeric) = 0.0626743162466 0.189552930401
y[1] (closed_form) = 0.0626359773666 0.189562248149
absolute error = 3.945e-05
relative error = 0.01976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.237
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.054
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8129 1.312
h = 0.001 0.003
y[1] (numeric) = 0.0624504302925 0.189668643413
y[1] (closed_form) = 0.0624118907368 0.189678272659
absolute error = 3.972e-05
relative error = 0.01989 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.237
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.004
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8119 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.0618860492817 0.189675551705
y[1] (closed_form) = 0.0618479465899 0.189684563695
absolute error = 3.915e-05
relative error = 0.01962 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.238
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.833
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8118 1.319
h = 0.003 0.006
y[1] (numeric) = 0.0612030396913 0.189471999655
y[1] (closed_form) = 0.0611655764851 0.189481063686
absolute error = 3.854e-05
relative error = 0.01936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.757
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1576.9MB, alloc=44.3MB, time=20.38
x[1] = -1.8088 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.0600252552303 0.189643284528
y[1] (closed_form) = 0.0599865005134 0.189649858683
absolute error = 3.931e-05
relative error = 0.01976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.242
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.672
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8087 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.059180968021 0.189372551327
y[1] (closed_form) = 0.0591427401779 0.189380863971
absolute error = 3.912e-05
relative error = 0.01972 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.244
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.348
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8086 1.333
h = 0.001 0.001
y[1] (numeric) = 0.0586752293348 0.189215688735
y[1] (closed_form) = 0.0586364322317 0.189224420656
absolute error = 3.977e-05
relative error = 0.02007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.246
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.059
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8076 1.334
h = 0.001 0.003
y[1] (numeric) = 0.058450824812 0.189323836955
y[1] (closed_form) = 0.0584118188367 0.189332868006
absolute error = 4.004e-05
relative error = 0.02021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.246
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.023
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8066 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.0578930090474 0.189315074397
y[1] (closed_form) = 0.0578544555321 0.189323514155
absolute error = 3.947e-05
relative error = 0.01994 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.247
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.844
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8065 1.341
h = 0.003 0.006
y[1] (numeric) = 0.0572238154104 0.189095129296
y[1] (closed_form) = 0.0571858891446 0.189103643668
absolute error = 3.887e-05
relative error = 0.01968 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.249
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.772
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8035 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.0560554895091 0.18923193382
y[1] (closed_form) = 0.0560163836507 0.189237951481
absolute error = 3.957e-05
relative error = 0.02005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.678
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8034 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.0552288818447 0.188941289863
y[1] (closed_form) = 0.0551902308675 0.188949036874
absolute error = 3.942e-05
relative error = 0.02003 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.253
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.353
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8033 1.355
h = 0.001 0.001
y[1] (numeric) = 0.054733584577 0.188772468892
y[1] (closed_form) = 0.0546943583735 0.188780607613
absolute error = 4.006e-05
relative error = 0.02038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.255
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.063
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8023 1.356
h = 0.001 0.003
y[1] (numeric) = 0.0545089461529 0.188873156012
y[1] (closed_form) = 0.0544695036108 0.188881581374
absolute error = 4.033e-05
relative error = 0.02052 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.255
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.043
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1623.5MB, alloc=44.3MB, time=20.97
x[1] = -1.8013 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.0539581615399 0.18884921683
y[1] (closed_form) = 0.0539191855542 0.18885707704
absolute error = 3.976e-05
relative error = 0.02024 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.256
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.855
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8012 1.363
h = 0.003 0.006
y[1] (numeric) = 0.053303156885 0.188613649572
y[1] (closed_form) = 0.0532647951393 0.188621605949
absolute error = 3.918e-05
relative error = 0.01999 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.258
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.787
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7982 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.0521453904972 0.18871688061
y[1] (closed_form) = 0.0521059590819 0.188722338652
absolute error = 3.981e-05
relative error = 0.02033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.259
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.685
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7981 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.0513368951268 0.188407295604
y[1] (closed_form) = 0.0512978485044 0.188414470792
absolute error = 3.970e-05
relative error = 0.02033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.262
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.358
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.798 1.377
h = 0.001 0.001
y[1] (numeric) = 0.0508523009641 0.188227091574
y[1] (closed_form) = 0.0508126745171 0.188234631208
absolute error = 4.034e-05
relative error = 0.02069 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.264
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.067
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.797 1.378
h = 0.001 0.003
y[1] (numeric) = 0.0506277027487 0.188320432041
y[1] (closed_form) = 0.0505878532146 0.188328245751
absolute error = 4.061e-05
relative error = 0.02082 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.264
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.064
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.796 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.0500843832001 0.188281821372
y[1] (closed_form) = 0.0500450128471 0.188289096161
absolute error = 4.004e-05
relative error = 0.02055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.265
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.867
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7959 1.385
h = 0.003 0.006
y[1] (numeric) = 0.0494438979777 0.188031403774
y[1] (closed_form) = 0.0494051281558 0.18803879525
absolute error = 3.947e-05
relative error = 0.0203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.267
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.802
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7929 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.0482977283148 0.188101999091
y[1] (closed_form) = 0.0482579965206 0.188106895581
absolute error = 4.003e-05
relative error = 0.02061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.269
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7928 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.0475077252764 0.18777444199
y[1] (closed_form) = 0.0474683102081 0.187781040536
absolute error = 3.996e-05
relative error = 0.02063 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.272
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.364
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1670.3MB, alloc=44.3MB, time=21.57
x[1] = -1.7927 1.399
h = 0.001 0.001
y[1] (numeric) = 0.0470340645822 0.187583429965
y[1] (closed_form) = 0.0469940664079 0.18759036606
absolute error = 4.060e-05
relative error = 0.02099 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.273
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.071
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7917 1.4
h = 0.003 0.006
y[1] (numeric) = 0.0468097698134 0.18766954814
y[1] (closed_form) = 0.0467695425079 0.187676745708
absolute error = 4.087e-05
relative error = 0.02113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.273
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) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7887 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.0456694894494 0.187719370813
y[1] (closed_form) = 0.0456302364553 0.187722635777
absolute error = 3.939e-05
relative error = 0.02039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.275
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.696
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7886 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.0448919769647 0.187379535827
y[1] (closed_form) = 0.04485299464 0.187384492537
absolute error = 3.930e-05
relative error = 0.02039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.278
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7885 1.414
h = 0.001 0.001
y[1] (numeric) = 0.0444256999148 0.187181140498
y[1] (closed_form) = 0.0443861322987 0.187186416547
absolute error = 3.992e-05
relative error = 0.02075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.279
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7875 1.415
h = 0.001 0.003
y[1] (numeric) = 0.0442015829196 0.187262352293
y[1] (closed_form) = 0.0441617820975 0.187267881276
absolute error = 4.018e-05
relative error = 0.02088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.279
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.098
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7865 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.0436714182521 0.187199938213
y[1] (closed_form) = 0.0436321153327 0.187204972297
absolute error = 3.962e-05
relative error = 0.02061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.886
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7864 1.422
h = 0.003 0.006
y[1] (numeric) = 0.0430557426374 0.186925820172
y[1] (closed_form) = 0.0430170161872 0.186931003577
absolute error = 3.907e-05
relative error = 0.02037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.283
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.828
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7834 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.0419305534471 0.18694318573
y[1] (closed_form) = 0.0418910415205 0.18694588782
absolute error = 3.960e-05
relative error = 0.02067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.284
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7833 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.0411720832428 0.186586997898
y[1] (closed_form) = 0.0411327774923 0.18659137213
absolute error = 3.955e-05
relative error = 0.0207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.287
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1717.0MB, alloc=44.3MB, time=22.18
x[1] = -1.7832 1.436
h = 0.001 0.001
y[1] (numeric) = 0.0407170740738 0.186378755871
y[1] (closed_form) = 0.0406771818635 0.186383423272
absolute error = 4.016e-05
relative error = 0.02105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.289
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.079
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7822 1.437
h = 0.001 0.003
y[1] (numeric) = 0.0404936831133 0.186452969439
y[1] (closed_form) = 0.0404535528051 0.186457877178
absolute error = 4.043e-05
relative error = 0.02119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.289
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.119
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7812 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.0399720065934 0.186377272041
y[1] (closed_form) = 0.0399323830239 0.186381711005
absolute error = 3.987e-05
relative error = 0.02092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.898
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7811 1.444
h = 0.003 0.006
y[1] (numeric) = 0.0393715550402 0.186090360238
y[1] (closed_form) = 0.039332492684 0.186094966228
absolute error = 3.933e-05
relative error = 0.02068 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.292
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.844
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7781 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.0382604604529 0.186077710643
y[1] (closed_form) = 0.0382207134625 0.186079850873
absolute error = 3.980e-05
relative error = 0.02095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.294
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.71
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.778 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.0375212778595 0.185706124676
y[1] (closed_form) = 0.0374816748202 0.185709915046
absolute error = 3.978e-05
relative error = 0.021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.297
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.379
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7779 1.458
h = 0.001 0.001
y[1] (numeric) = 0.037077686844 0.185488603045
y[1] (closed_form) = 0.0370374973467 0.185492660935
absolute error = 4.039e-05
relative error = 0.02135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.299
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.083
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7769 1.459
h = 0.001 0.003
y[1] (numeric) = 0.036855255028 0.185555965583
y[1] (closed_form) = 0.0368148231986 0.185560251277
absolute error = 4.066e-05
relative error = 0.02149 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.299
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.141
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7759 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.0363423854117 0.185467514311
y[1] (closed_form) = 0.0363024678217 0.185471357167
absolute error = 4.010e-05
relative error = 0.02122 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.911
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7758 1.466
h = 0.003 0.006
y[1] (numeric) = 0.0357573408281 0.185168565957
y[1] (closed_form) = 0.0357179687582 0.185172592492
absolute error = 3.958e-05
relative error = 0.02099 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.302
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.861
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1763.7MB, alloc=44.3MB, time=22.78
x[1] = -1.7728 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.0346611448783 0.185126919159
y[1] (closed_form) = 0.034621186118 0.185128499535
absolute error = 3.999e-05
relative error = 0.02123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.304
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.718
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7727 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.0339414481602 0.184740879475
y[1] (closed_form) = 0.0339015734592 0.184744085774
absolute error = 4.000e-05
relative error = 0.0213 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.307
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.385
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7726 1.48
h = 0.001 0.001
y[1] (numeric) = 0.0335093975679 0.184514639397
y[1] (closed_form) = 0.0334689375225 0.184518088135
absolute error = 4.061e-05
relative error = 0.02165 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.309
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.088
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7716 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.0332881464673 0.184575305004
y[1] (closed_form) = 0.0332474404925 0.184578969106
absolute error = 4.087e-05
relative error = 0.02179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.308
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.533
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7715 1.485
h = 0.003 0.006
y[1] (numeric) = 0.0327158290899 0.184267093671
y[1] (closed_form) = 0.0326764387372 0.184270642564
absolute error = 3.955e-05
relative error = 0.02113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.311
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.875
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7685 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.03163338261 0.184201501055
y[1] (closed_form) = 0.0315934871571 0.184202624824
absolute error = 3.991e-05
relative error = 0.02136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.313
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.724
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7684 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.0309307399299 0.183804001386
y[1] (closed_form) = 0.0308908792126 0.183806727919
absolute error = 3.995e-05
relative error = 0.02144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.316
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.39
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7683 1.499
h = 0.001 0.001
y[1] (numeric) = 0.0305087951498 0.183570839583
y[1] (closed_form) = 0.0304683511808 0.183573787485
absolute error = 4.055e-05
relative error = 0.02179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.318
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7673 1.5
h = 0.001 0.003
y[1] (numeric) = 0.0302888061133 0.183625886225
y[1] (closed_form) = 0.0302481137577 0.18362903885
absolute error = 4.081e-05
relative error = 0.02193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.317
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.183
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7663 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.0297932069456 0.183515230914
y[1] (closed_form) = 0.0297530390886 0.183517988302
absolute error = 4.026e-05
relative error = 0.02166 %
Correct digits = 4
memory used=1810.4MB, alloc=44.3MB, time=23.38
Radius of convergence (given) for eq 1 = 2.319
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.935
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7662 1.507
h = 0.003 0.006
y[1] (numeric) = 0.0292373150063 0.183196056328
y[1] (closed_form) = 0.0291976623607 0.183199025399
absolute error = 3.976e-05
relative error = 0.02143 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.321
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.892
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7632 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.0281710868094 0.183103398656
y[1] (closed_form) = 0.0281310212369 0.183103969011
absolute error = 4.007e-05
relative error = 0.02163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.323
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.732
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7631 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.0274881689914 0.182693169046
y[1] (closed_form) = 0.0274480827537 0.182695314331
absolute error = 4.014e-05
relative error = 0.02173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.326
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.396
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.763 1.521
h = 0.001 0.001
y[1] (numeric) = 0.0270779148105 0.182452313552
y[1] (closed_form) = 0.0270372483378 0.182454656303
absolute error = 4.073e-05
relative error = 0.02208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.328
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.097
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.762 1.522
h = 0.001 0.003
y[1] (numeric) = 0.0268594859464 0.182500968023
y[1] (closed_form) = 0.0268185686135 0.182503503318
absolute error = 4.100e-05
relative error = 0.02222 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.328
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.206
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.761 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.026373435607 0.182379082743
y[1] (closed_form) = 0.0263330467162 0.182381247851
absolute error = 4.045e-05
relative error = 0.02195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.329
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.948
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7609 1.529
h = 0.003 0.006
y[1] (numeric) = 0.0258332662703 0.182049984412
y[1] (closed_form) = 0.0257933760171 0.182052374878
absolute error = 3.996e-05
relative error = 0.02173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.331
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.91
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7579 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.0247838860271 0.181931304958
y[1] (closed_form) = 0.0247436717989 0.181931326425
absolute error = 4.021e-05
relative error = 0.0219 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.333
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.74
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7578 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.0241207670315 0.181509248523
y[1] (closed_form) = 0.0240804791839 0.181510815377
absolute error = 4.032e-05
relative error = 0.02202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.336
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.403
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1857.0MB, alloc=44.3MB, time=23.98
x[1] = -1.7577 1.543
h = 0.001 0.001
y[1] (numeric) = 0.0237222517049 0.181261236448
y[1] (closed_form) = 0.0236813875798 0.18126297754
absolute error = 4.090e-05
relative error = 0.02237 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.338
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.102
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7567 1.544
h = 0.001 0.003
y[1] (numeric) = 0.0235055714185 0.181303668208
y[1] (closed_form) = 0.0234644545303 0.181305589841
absolute error = 4.116e-05
relative error = 0.02252 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.338
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.23
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7557 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.0230292766681 0.181171081953
y[1] (closed_form) = 0.0229886910178 0.18117265804
absolute error = 4.062e-05
relative error = 0.02224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.339
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.961
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7556 1.551
h = 0.003 0.006
y[1] (numeric) = 0.022504878533 0.180832774009
y[1] (closed_form) = 0.0224647747514 0.180834588116
absolute error = 4.014e-05
relative error = 0.02203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.342
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.927
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7526 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.0214729174177 0.180689118773
y[1] (closed_form) = 0.021432575314 0.180688596654
absolute error = 4.035e-05
relative error = 0.02217 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.344
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.748
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7525 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.0208296314346 0.180256120957
y[1] (closed_form) = 0.0207891652216 0.180257113146
absolute error = 4.048e-05
relative error = 0.02231 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.347
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.409
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7524 1.565
h = 0.001 0.001
y[1] (numeric) = 0.0204428795178 0.180001479073
y[1] (closed_form) = 0.0204018418656 0.180002622974
absolute error = 4.105e-05
relative error = 0.02266 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.349
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.107
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7514 1.566
h = 0.001 0.003
y[1] (numeric) = 0.0202281247527 0.180037861596
y[1] (closed_form) = 0.0201868329808 0.180039174233
absolute error = 4.131e-05
relative error = 0.0228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.349
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.253
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7504 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.0197617653502 0.179895099846
y[1] (closed_form) = 0.0197210065165 0.179896091124
absolute error = 4.077e-05
relative error = 0.02253 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.974
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7503 1.573
h = 0.003 0.006
y[1] (numeric) = 0.0192531559294 0.179548281953
y[1] (closed_form) = 0.0192128620567 0.179549522918
absolute error = 4.031e-05
relative error = 0.02232 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.353
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.945
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1903.5MB, alloc=44.3MB, time=24.58
x[1] = -1.7473 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.0182391281064 0.17938069665
y[1] (closed_form) = 0.0181986782046 0.179379636967
absolute error = 4.046e-05
relative error = 0.02244 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.354
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.756
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7472 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.0176156715516 0.178937623725
y[1] (closed_form) = 0.017575049523 0.178938045898
absolute error = 4.062e-05
relative error = 0.02259 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.358
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.416
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7471 1.587
h = 0.001 0.001
y[1] (numeric) = 0.0172406850792 0.178676867568
y[1] (closed_form) = 0.0171994972704 0.178677419656
absolute error = 4.119e-05
relative error = 0.02295 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.112
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7461 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.0170280214374 0.178707377654
y[1] (closed_form) = 0.0169865786734 0.178708086894
absolute error = 4.145e-05
relative error = 0.02309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.678
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.746 1.592
h = 0.003 0.006
y[1] (numeric) = 0.0165323284087 0.17835413362
y[1] (closed_form) = 0.0164920916482 0.178354938857
absolute error = 4.024e-05
relative error = 0.02247 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.362
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.961
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.743 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.0155343745179 0.178167006111
y[1] (closed_form) = 0.0154940493743 0.178165544308
absolute error = 4.035e-05
relative error = 0.02256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.364
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.763
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7429 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.014928062605 0.177716174412
y[1] (closed_form) = 0.0148875263864 0.177716165025
absolute error = 4.054e-05
relative error = 0.02273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.367
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.421
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7428 1.606
h = 0.001 0.001
y[1] (numeric) = 0.0145632534479 0.177450698741
y[1] (closed_form) = 0.0145221571801 0.177450801183
absolute error = 4.110e-05
relative error = 0.02308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.369
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.117
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7418 1.607
h = 0.001 0.003
y[1] (numeric) = 0.0143525808767 0.177476325049
y[1] (closed_form) = 0.0143112294661 0.177476574861
absolute error = 4.135e-05
relative error = 0.02322 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.369
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.299
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7408 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.0139052053724 0.177316132698
y[1] (closed_form) = 0.0138643870587 0.177316104797
absolute error = 4.082e-05
relative error = 0.02295 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.37
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1950.2MB, alloc=44.3MB, time=25.18
x[1] = -1.7407 1.614
h = 0.003 0.006
y[1] (numeric) = 0.0134260042866 0.176955474953
y[1] (closed_form) = 0.0133856191709 0.176955715675
absolute error = 4.039e-05
relative error = 0.02276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.373
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.98
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7377 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.0124467819818 0.176746357492
y[1] (closed_form) = 0.0124063843925 0.176744371281
absolute error = 4.045e-05
relative error = 0.02283 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.375
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.771
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7376 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.0118601894868 0.176287006118
y[1] (closed_form) = 0.0118195374035 0.176286437773
absolute error = 4.066e-05
relative error = 0.02301 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.378
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.428
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7375 1.628
h = 0.001 0.001
y[1] (numeric) = 0.0115070879156 0.17601634235
y[1] (closed_form) = 0.011465882804 0.176015865449
absolute error = 4.121e-05
relative error = 0.02336 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.122
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7365 1.629
h = 0.001 0.003
y[1] (numeric) = 0.0112987828151 0.176036433503
y[1] (closed_form) = 0.011257322623 0.176036092851
absolute error = 4.146e-05
relative error = 0.0235 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.38
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.324
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7355 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.010861710273 0.175867539878
y[1] (closed_form) = 0.0108207820484 0.175866944173
absolute error = 4.093e-05
relative error = 0.02323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.382
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.014
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7354 1.636
h = 0.003 0.006
y[1] (numeric) = 0.0103981829698 0.175500283259
y[1] (closed_form) = 0.010357670933 0.175499965126
absolute error = 4.051e-05
relative error = 0.02304 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.384
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.998
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7324 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.00943805270495 0.175270205146
y[1] (closed_form) = 0.00939760066157 0.175267702302
absolute error = 4.053e-05
relative error = 0.02309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.386
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.779
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7323 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.00887107942008 0.174803138321
y[1] (closed_form) = 0.00883033190366 0.174802017869
absolute error = 4.076e-05
relative error = 0.02329 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.435
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7322 1.65
h = 0.001 0.001
y[1] (numeric) = 0.00852962980027 0.174527765548
y[1] (closed_form) = 0.0084883369305 0.174526716927
absolute error = 4.131e-05
relative error = 0.02364 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.392
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.127
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1996.8MB, alloc=44.3MB, time=25.78
x[1] = -1.7312 1.651
h = 0.001 0.003
y[1] (numeric) = 0.00832382627865 0.174542504224
y[1] (closed_form) = 0.00828227883754 0.174541581003
absolute error = 4.156e-05
relative error = 0.02378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.392
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.349
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7302 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.00789714138203 0.17436541008
y[1] (closed_form) = 0.00785612389286 0.174364253873
absolute error = 4.103e-05
relative error = 0.02351 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.393
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.029
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7301 1.658
h = 0.003 0.006
y[1] (numeric) = 0.00744920060735 0.173992188506
y[1] (closed_form) = 0.00740858234543 0.17399131792
absolute error = 4.063e-05
relative error = 0.02333 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.396
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.017
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7271 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.00650847263109 0.173742168879
y[1] (closed_form) = 0.00646798338482 0.173739157697
absolute error = 4.060e-05
relative error = 0.02335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.398
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.788
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.727 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.00596098838899 0.173268167394
y[1] (closed_form) = 0.0059201651042 0.173266502345
absolute error = 4.086e-05
relative error = 0.02357 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.401
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.442
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7269 1.672
h = 0.001 0.001
y[1] (numeric) = 0.00563111718431 0.172988550913
y[1] (closed_form) = 0.00558975681913 0.172986938866
absolute error = 4.139e-05
relative error = 0.02392 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.403
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.132
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7259 1.673
h = 0.001 0.003
y[1] (numeric) = 0.00542793878198 0.172998120764
y[1] (closed_form) = 0.00538632477566 0.17299662355
absolute error = 4.164e-05
relative error = 0.02406 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.403
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.375
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7249 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.00501170406899 0.172813318154
y[1] (closed_form) = 0.00497061716673 0.172811609407
absolute error = 4.112e-05
relative error = 0.02379 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.404
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.043
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7248 1.68
h = 0.003 0.006
y[1] (numeric) = 0.0045792392807 0.17243474671
y[1] (closed_form) = 0.00453853473661 0.17243333076
absolute error = 4.073e-05
relative error = 0.02361 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.407
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.037
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7218 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.00365817558301 0.172165792433
y[1] (closed_form) = 0.00361766564244 0.172162281673
absolute error = 4.066e-05
relative error = 0.02361 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.409
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.797
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2043.4MB, alloc=44.3MB, time=26.38
x[1] = -1.7217 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.00313002225285 0.17168561289
y[1] (closed_form) = 0.00308914208826 0.171683411362
absolute error = 4.094e-05
relative error = 0.02384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.413
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.448
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7216 1.694
h = 0.001 0.001
y[1] (numeric) = 0.00281163920606 0.171402203758
y[1] (closed_form) = 0.00277023077735 0.171400037187
absolute error = 4.147e-05
relative error = 0.02419 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.415
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.138
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7206 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.002611199158 0.171406788876
y[1] (closed_form) = 0.00256953841358 0.171404726868
absolute error = 4.171e-05
relative error = 0.02433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.415
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.834
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7205 1.699
h = 0.003 0.006
y[1] (numeric) = 0.00219130059218 0.171024309426
y[1] (closed_form) = 0.00215071169029 0.171022508435
absolute error = 4.063e-05
relative error = 0.02375 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.417
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.054
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7175 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.00128754716317 0.170740089932
y[1] (closed_form) = 0.00124720601857 0.170736235444
absolute error = 4.052e-05
relative error = 0.02373 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.419
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.804
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7174 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.000775948502874 0.17025540669
y[1] (closed_form) = 0.000735208310028 0.170252828864
absolute error = 4.082e-05
relative error = 0.02398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.423
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.455
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7173 1.713
h = 0.001 0.001
y[1] (numeric) = 0.000467408035395 0.169969218107
y[1] (closed_form) = 0.000426147763798 0.169966660451
absolute error = 4.134e-05
relative error = 0.02432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.425
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.143
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7163 1.714
h = 0.001 0.003
y[1] (numeric) = 0.000269464481846 0.169969694186
y[1] (closed_form) = 0.000227953449759 0.169967232517
absolute error = 4.158e-05
relative error = 0.02447 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.425
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.424
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7153 1.717
h = 0.0001 0.004
y[1] (numeric) = -0.000127151407049 0.169771949744
y[1] (closed_form) = -0.000168142903306 0.169769314694
absolute error = 4.108e-05
relative error = 0.0242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.426
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.071
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7152 1.721
h = 0.003 0.006
y[1] (numeric) = -0.000531139070343 0.169385174003
y[1] (closed_form) = -0.000571779286874 0.16938284269
absolute error = 4.071e-05
relative error = 0.02403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.429
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.074
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2090.2MB, alloc=44.3MB, time=26.98
x[1] = -1.7122 1.727
h = 0.0001 0.005
y[1] (numeric) = -0.00141487385559 0.169083856099
y[1] (closed_form) = -0.00145520706442 0.169079519589
absolute error = 4.057e-05
relative error = 0.02399 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.431
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.813
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7121 1.732
h = 0.0001 0.003
y[1] (numeric) = -0.00190751186246 0.168594333704
y[1] (closed_form) = -0.00194827598307 0.168591236126
absolute error = 4.088e-05
relative error = 0.02425 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.435
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.462
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.712 1.735
h = 0.001 0.001
y[1] (numeric) = -0.00220477760312 0.16830515116
y[1] (closed_form) = -0.00224605212461 0.168302057184
absolute error = 4.139e-05
relative error = 0.02459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.437
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.148
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.711 1.736
h = 0.001 0.003
y[1] (numeric) = -0.0023998007287 0.168300985619
y[1] (closed_form) = -0.00244132402136 0.168297977936
absolute error = 4.163e-05
relative error = 0.02473 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.437
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.45
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.71 1.739
h = 0.0001 0.004
y[1] (numeric) = -0.00278590573431 0.16809688545
y[1] (closed_form) = -0.0028269144179 0.168093723962
absolute error = 4.113e-05
relative error = 0.02447 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.438
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.086
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7099 1.743
h = 0.003 0.006
y[1] (numeric) = -0.00317485475712 0.167706408762
y[1] (closed_form) = -0.00321552855636 0.167703555866
absolute error = 4.077e-05
relative error = 0.02431 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.441
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.094
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7069 1.749
h = 0.0001 0.005
y[1] (numeric) = -0.00403843560395 0.167388953633
y[1] (closed_form) = -0.00407874648584 0.167384144928
absolute error = 4.060e-05
relative error = 0.02425 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.443
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.822
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7068 1.754
h = 0.0001 0.003
y[1] (numeric) = -0.00451234002875 0.16689527629
y[1] (closed_form) = -0.00455311143648 0.166891668502
absolute error = 4.093e-05
relative error = 0.02452 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.447
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.469
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7067 1.757
h = 0.001 0.001
y[1] (numeric) = -0.00479846258976 0.166603508146
y[1] (closed_form) = -0.00483973432434 0.166599888176
absolute error = 4.143e-05
relative error = 0.02486 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.154
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7057 1.758
h = 0.001 0.003
y[1] (numeric) = -0.0049904799024 0.16659488358
y[1] (closed_form) = -0.00503199809577 0.166591340528
absolute error = 4.167e-05
relative error = 0.025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.477
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2136.8MB, alloc=44.3MB, time=27.58
x[1] = -1.7047 1.761
h = 0.0001 0.004
y[1] (numeric) = -0.00536608683149 0.166384879175
y[1] (closed_form) = -0.00540709597188 0.166381201216
absolute error = 4.117e-05
relative error = 0.02473 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.45
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.101
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7046 1.765
h = 0.003 0.006
y[1] (numeric) = -0.00574018284167 0.165991239398
y[1] (closed_form) = -0.00578087326929 0.165987874134
absolute error = 4.083e-05
relative error = 0.02458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.453
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.114
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7016 1.771
h = 0.0001 0.005
y[1] (numeric) = -0.00658351482403 0.165658589469
y[1] (closed_form) = -0.00662378971506 0.165653318688
absolute error = 4.062e-05
relative error = 0.0245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.455
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.831
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7015 1.776
h = 0.0001 0.003
y[1] (numeric) = -0.00703893331054 0.165161415541
y[1] (closed_form) = -0.00707969614659 0.165157307485
absolute error = 4.097e-05
relative error = 0.02478 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.459
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.476
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7014 1.779
h = 0.001 0.001
y[1] (numeric) = -0.00731405658312 0.164867454903
y[1] (closed_form) = -0.0073553093237 0.164863319662
absolute error = 4.146e-05
relative error = 0.02512 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.461
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7004 1.78
h = 0.001 0.003
y[1] (numeric) = -0.00750299182043 0.164854552601
y[1] (closed_form) = -0.00754448840865 0.164850485227
absolute error = 4.170e-05
relative error = 0.02527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.461
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.504
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6994 1.783
h = 0.0001 0.004
y[1] (numeric) = -0.00786813043221 0.164639083645
y[1] (closed_form) = -0.00790912410288 0.164634899574
absolute error = 4.121e-05
relative error = 0.025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.462
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.117
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6993 1.787
h = 0.003 0.006
y[1] (numeric) = -0.00822757494009 0.16424279805
y[1] (closed_form) = -0.00826826581831 0.164238930062
absolute error = 4.087e-05
relative error = 0.02486 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.465
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.134
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6963 1.793
h = 0.0001 0.005
y[1] (numeric) = -0.0090506014269 0.163895875712
y[1] (closed_form) = -0.00909082738126 0.163890153224
absolute error = 4.063e-05
relative error = 0.02475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.468
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.84
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6962 1.798
h = 0.0001 0.003
y[1] (numeric) = -0.00948780039084 0.163395837559
y[1] (closed_form) = -0.00952853957319 0.163391239534
absolute error = 4.100e-05
relative error = 0.02505 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.471
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.484
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2183.4MB, alloc=44.3MB, time=28.18
x[1] = -1.6961 1.801
h = 0.001 0.001
y[1] (numeric) = -0.00975207954311 0.163100062175
y[1] (closed_form) = -0.00979329790524 0.163095422733
absolute error = 4.148e-05
relative error = 0.02539 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.473
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.166
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6951 1.802
h = 0.0001 0.004
y[1] (numeric) = -0.00993786523013 0.163083061747
y[1] (closed_form) = -0.00997932455366 0.163078481449
absolute error = 4.171e-05
relative error = 0.02553 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.473
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.695 1.806
h = 0.003 0.006
y[1] (numeric) = -0.0102854843025 0.162685004534
y[1] (closed_form) = -0.0103260171864 0.162680806107
absolute error = 4.075e-05
relative error = 0.025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.476
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.152
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.692 1.812
h = 0.0001 0.005
y[1] (numeric) = -0.0110908594057 0.162326761598
y[1] (closed_form) = -0.0111308880093 0.162320753576
absolute error = 4.048e-05
relative error = 0.02488 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.478
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.848
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6919 1.817
h = 0.0001 0.003
y[1] (numeric) = -0.0115125776426 0.161824956895
y[1] (closed_form) = -0.0115531391185 0.161820040152
absolute error = 4.086e-05
relative error = 0.02519 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.482
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.49
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6918 1.82
h = 0.001 0.001
y[1] (numeric) = -0.0117676388581 0.161528036641
y[1] (closed_form) = -0.0118086699164 0.161523066974
absolute error = 4.133e-05
relative error = 0.02552 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.484
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.171
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6908 1.821
h = 0.001 0.003
y[1] (numeric) = -0.0119506199985 0.161507689427
y[1] (closed_form) = -0.0119918892326 0.161502771696
absolute error = 4.156e-05
relative error = 0.02566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.484
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.556
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6898 1.824
h = 0.0001 0.004
y[1] (numeric) = -0.0122963591183 0.161283303492
y[1] (closed_form) = -0.0123371384254 0.161278301019
absolute error = 4.108e-05
relative error = 0.0254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.486
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.146
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6897 1.828
h = 0.003 0.006
y[1] (numeric) = -0.0126291075299 0.16088356875
y[1] (closed_form) = -0.0126696129386 0.160878886683
absolute error = 4.078e-05
relative error = 0.02527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.489
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.173
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6867 1.834
h = 0.0001 0.005
y[1] (numeric) = -0.0134141769861 0.160512712371
y[1] (closed_form) = -0.0134541345657 0.160506272604
absolute error = 4.047e-05
relative error = 0.02513 %
Correct digits = 4
memory used=2230.2MB, alloc=44.3MB, time=28.78
Radius of convergence (given) for eq 1 = 2.491
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.858
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6866 1.839
h = 0.0001 0.003
y[1] (numeric) = -0.0138182222688 0.160009147175
y[1] (closed_form) = -0.0138587341976 0.160003760573
absolute error = 4.087e-05
relative error = 0.02545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.495
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6865 1.842
h = 0.001 0.001
y[1] (numeric) = -0.0140627586588 0.159711071985
y[1] (closed_form) = -0.0141037290064 0.159705619639
absolute error = 4.133e-05
relative error = 0.02578 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.497
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.177
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6855 1.843
h = 0.001 0.003
y[1] (numeric) = -0.0142424889797 0.159686955802
y[1] (closed_form) = -0.0142836941698 0.159681547285
absolute error = 4.156e-05
relative error = 0.02592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.497
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.585
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6845 1.846
h = 0.0001 0.004
y[1] (numeric) = -0.0145779339421 0.159458293611
y[1] (closed_form) = -0.0146186567261 0.159452816573
absolute error = 4.109e-05
relative error = 0.02566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.498
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.162
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6844 1.85
h = 0.003 0.006
y[1] (numeric) = -0.0148966878954 0.159057275707
y[1] (closed_form) = -0.0149371518478 0.159052120596
absolute error = 4.079e-05
relative error = 0.02553 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.501
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.195
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6814 1.856
h = 0.0001 0.005
y[1] (numeric) = -0.0156614929862 0.158674664862
y[1] (closed_form) = -0.0157013685867 0.158667804217
absolute error = 4.046e-05
relative error = 0.02538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.504
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.867
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6813 1.861
h = 0.0001 0.003
y[1] (numeric) = -0.0160481756957 0.158169897001
y[1] (closed_form) = -0.0160886251717 0.158164051598
absolute error = 4.087e-05
relative error = 0.02571 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.507
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.505
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6812 1.864
h = 0.001 0.001
y[1] (numeric) = -0.0162823689141 0.157871000556
y[1] (closed_form) = -0.0163232654625 0.157865077328
absolute error = 4.132e-05
relative error = 0.02604 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.509
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.183
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6802 1.865
h = 0.001 0.003
y[1] (numeric) = -0.0164588041353 0.157843288319
y[1] (closed_form) = -0.0164999319818 0.157837401143
absolute error = 4.155e-05
relative error = 0.02618 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.509
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.613
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2276.9MB, alloc=44.3MB, time=29.38
x[1] = -1.6792 1.868
h = 0.0001 0.004
y[1] (numeric) = -0.0167840402972 0.157610740563
y[1] (closed_form) = -0.0168246936586 0.157604800395
absolute error = 4.109e-05
relative error = 0.02592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.511
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.178
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6791 1.872
h = 0.003 0.006
y[1] (numeric) = -0.0170890495143 0.157208876939
y[1] (closed_form) = -0.0171294587783 0.15720325963
absolute error = 4.080e-05
relative error = 0.0258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.514
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.216
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6761 1.878
h = 0.0001 0.005
y[1] (numeric) = -0.0178336619334 0.156815347037
y[1] (closed_form) = -0.0178734452671 0.156808076493
absolute error = 4.044e-05
relative error = 0.02562 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.516
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.877
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.676 1.883
h = 0.0001 0.003
y[1] (numeric) = -0.0182033048271 0.156309908627
y[1] (closed_form) = -0.0182436796809 0.156303615672
absolute error = 4.086e-05
relative error = 0.02597 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.513
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6759 1.886
h = 0.001 0.001
y[1] (numeric) = -0.0184273440104 0.156010509397
y[1] (closed_form) = -0.0184681544452 0.156004127258
absolute error = 4.131e-05
relative error = 0.02629 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.522
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.189
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6749 1.887
h = 0.001 0.003
y[1] (numeric) = -0.0186004472875 0.155979371179
y[1] (closed_form) = -0.0186414852858 0.155973017644
absolute error = 4.153e-05
relative error = 0.02644 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.522
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.642
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6739 1.89
h = 0.0001 0.004
y[1] (numeric) = -0.0189155720306 0.155743315369
y[1] (closed_form) = -0.0189561438223 0.155736923682
absolute error = 4.107e-05
relative error = 0.02618 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.524
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.195
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6738 1.894
h = 0.003 0.006
y[1] (numeric) = -0.0192070956866 0.155341023102
y[1] (closed_form) = -0.0192474377676 0.155334954649
absolute error = 4.080e-05
relative error = 0.02606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.527
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.238
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6708 1.9
h = 0.0001 0.005
y[1] (numeric) = -0.0199316155721 0.154937385391
y[1] (closed_form) = -0.019971297003 0.154929716003
absolute error = 4.042e-05
relative error = 0.02587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.529
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.886
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6707 1.905
h = 0.0001 0.003
y[1] (numeric) = -0.0202845522843 0.154431783102
y[1] (closed_form) = -0.0203248410683 0.154425053993
absolute error = 4.085e-05
relative error = 0.02622 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.533
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.521
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2323.5MB, alloc=44.3MB, time=29.99
x[1] = -1.6706 1.908
h = 0.001 0.001
y[1] (numeric) = -0.0204986331604 0.15413218449
y[1] (closed_form) = -0.0205393459246 0.154125355546
absolute error = 4.128e-05
relative error = 0.02655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.535
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.195
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6696 1.909
h = 0.0001 0.004
y[1] (numeric) = -0.0206683747314 0.154097787289
y[1] (closed_form) = -0.0207093111545 0.154090979828
absolute error = 4.150e-05
relative error = 0.02669 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.535
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.175
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6695 1.913
h = 0.003 0.006
y[1] (numeric) = -0.0209490682254 0.153695460661
y[1] (closed_form) = -0.0209892244419 0.153689116454
absolute error = 4.065e-05
relative error = 0.02621 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.538
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.257
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6665 1.919
h = 0.0001 0.005
y[1] (numeric) = -0.0216562859002 0.153283990539
y[1] (closed_form) = -0.0216957544228 0.15327609069
absolute error = 4.025e-05
relative error = 0.026 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.541
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.895
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6664 1.924
h = 0.0001 0.003
y[1] (numeric) = -0.0219951226945 0.152778827146
y[1] (closed_form) = -0.0220352103649 0.152771835627
absolute error = 4.069e-05
relative error = 0.02636 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.545
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.528
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6663 1.927
h = 0.001 0.001
y[1] (numeric) = -0.0222007951964 0.152479403851
y[1] (closed_form) = -0.0222412966838 0.15247230402
absolute error = 4.112e-05
relative error = 0.02669 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.547
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.2
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6653 1.928
h = 0.001 0.003
y[1] (numeric) = -0.0223675882624 0.152442373055
y[1] (closed_form) = -0.0224083098467 0.152435288886
absolute error = 4.133e-05
relative error = 0.02683 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.547
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.697
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6643 1.931
h = 0.0001 0.004
y[1] (numeric) = -0.0226641626828 0.152200865979
y[1] (closed_form) = -0.0227044344357 0.152193769357
absolute error = 4.089e-05
relative error = 0.02657 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.548
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.226
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6642 1.935
h = 0.003 0.006
y[1] (numeric) = -0.0229313158814 0.151798970383
y[1] (closed_form) = -0.0229713837161 0.151792196161
absolute error = 4.064e-05
relative error = 0.02647 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.551
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.279
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6612 1.941
h = 0.0001 0.005
y[1] (numeric) = -0.0236187054647 0.15137883425
y[1] (closed_form) = -0.0236580559622 0.151370556336
absolute error = 4.021e-05
relative error = 0.02625 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.554
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.905
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2370.2MB, alloc=44.3MB, time=30.60
x[1] = -1.6611 1.946
h = 0.0001 0.003
y[1] (numeric) = -0.0239414863235 0.150874378993
y[1] (closed_form) = -0.0239814686271 0.150866972929
absolute error = 4.066e-05
relative error = 0.02662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.558
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.536
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.661 1.949
h = 0.001 0.001
y[1] (numeric) = -0.0241375825813 0.150575278977
y[1] (closed_form) = -0.0241779669932 0.15056775522
absolute error = 4.108e-05
relative error = 0.02694 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.206
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.66 1.95
h = 0.001 0.003
y[1] (numeric) = -0.0243009780981 0.15053529124
y[1] (closed_form) = -0.0243415784401 0.150527776625
absolute error = 4.129e-05
relative error = 0.02708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.56
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.726
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.659 1.953
h = 0.0001 0.004
y[1] (numeric) = -0.0245877817288 0.150291280956
y[1] (closed_form) = -0.0246279413139 0.150283766796
absolute error = 4.086e-05
relative error = 0.02683 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.562
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.242
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6589 1.957
h = 0.003 0.006
y[1] (numeric) = -0.0248422369132 0.149890036274
y[1] (closed_form) = -0.0248822059022 0.149882843478
absolute error = 4.061e-05
relative error = 0.02673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.565
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.301
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6559 1.963
h = 0.0001 0.005
y[1] (numeric) = -0.0255099691428 0.149461973765
y[1] (closed_form) = -0.0255491937465 0.149453328902
absolute error = 4.017e-05
relative error = 0.02649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.567
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.915
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6558 1.968
h = 0.0001 0.003
y[1] (numeric) = -0.0258170508555 0.148958662443
y[1] (closed_form) = -0.0258569183183 0.148950853468
absolute error = 4.063e-05
relative error = 0.02687 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.571
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6557 1.971
h = 0.001 0.001
y[1] (numeric) = -0.0260037807231 0.148660147126
y[1] (closed_form) = -0.0260440385663 0.148652211728
absolute error = 4.103e-05
relative error = 0.02719 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.573
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.213
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6547 1.972
h = 0.001 0.003
y[1] (numeric) = -0.026163767208 0.148617359518
y[1] (closed_form) = -0.0262042366973 0.148609427062
absolute error = 4.124e-05
relative error = 0.02733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.573
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.756
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6537 1.975
h = 0.0001 0.004
y[1] (numeric) = -0.0264409351053 0.148371171961
y[1] (closed_form) = -0.0264809731224 0.148363252213
absolute error = 4.081e-05
relative error = 0.02708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.575
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.259
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2416.7MB, alloc=44.3MB, time=31.20
x[1] = -1.6536 1.979
h = 0.003 0.006
y[1] (numeric) = -0.0266829771977 0.147970919137
y[1] (closed_form) = -0.0267228375544 0.14796331928
absolute error = 4.058e-05
relative error = 0.02699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.578
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.324
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6506 1.985
h = 0.0001 0.005
y[1] (numeric) = -0.0273312440919 0.14753564452
y[1] (closed_form) = -0.0273703355149 0.147526643799
absolute error = 4.011e-05
relative error = 0.02673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.581
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.925
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6505 1.99
h = 0.0001 0.003
y[1] (numeric) = -0.0276229891818 0.14703388907
y[1] (closed_form) = -0.0276627329837 0.147025688842
absolute error = 4.058e-05
relative error = 0.02713 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.585
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6504 1.993
h = 0.001 0.001
y[1] (numeric) = -0.0278005660466 0.146736205717
y[1] (closed_form) = -0.0278406885095 0.146727870973
absolute error = 4.098e-05
relative error = 0.02744 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.587
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.219
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6494 1.994
h = 0.001 0.003
y[1] (numeric) = -0.0279571377552 0.146690771576
y[1] (closed_form) = -0.0279974674795 0.146682433881
absolute error = 4.118e-05
relative error = 0.02758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.587
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.786
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6484 1.997
h = 0.0001 0.004
y[1] (numeric) = -0.028224812698 0.14644271942
y[1] (closed_form) = -0.0282647204115 0.146434406043
absolute error = 4.076e-05
relative error = 0.02733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.589
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.276
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6483 2.001
h = 0.003 0.006
y[1] (numeric) = -0.0284547308869 0.146043780567
y[1] (closed_form) = -0.0284944734834 0.146035785205
absolute error = 4.054e-05
relative error = 0.02725 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.592
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.346
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6453 2.007
h = 0.0001 0.005
y[1] (numeric) = -0.0290837440221 0.145601982664
y[1] (closed_form) = -0.0291226955396 0.145592637129
absolute error = 4.006e-05
relative error = 0.02698 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.594
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.935
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6452 2.012
h = 0.0001 0.003
y[1] (numeric) = -0.0293605195807 0.145102171679
y[1] (closed_form) = -0.0294001315358 0.145093591854
absolute error = 4.053e-05
relative error = 0.02738 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.598
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.56
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6451 2.015
h = 0.001 0.001
y[1] (numeric) = -0.0295291596696 0.144805553714
y[1] (closed_form) = -0.0295691386005 0.144796831891
absolute error = 4.092e-05
relative error = 0.02769 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.6
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.226
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2463.4MB, alloc=44.3MB, time=31.82
x[1] = -1.6441 2.016
h = 0.0001 0.004
y[1] (numeric) = -0.0296823162602 0.144757622521
y[1] (closed_form) = -0.0297224979832 0.144748892161
absolute error = 4.112e-05
relative error = 0.02783 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.601
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.36
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.644 2.02
h = 0.003 0.006
y[1] (numeric) = -0.0299025392387 0.144360002933
y[1] (closed_form) = -0.0299420803469 0.144351783829
absolute error = 4.039e-05
relative error = 0.02739 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.604
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.366
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.641 2.026
h = 0.0001 0.005
y[1] (numeric) = -0.0305150954979 0.143913347757
y[1] (closed_form) = -0.0305538289095 0.143903821868
absolute error = 3.989e-05
relative error = 0.02711 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.606
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.944
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6409 2.031
h = 0.0001 0.003
y[1] (numeric) = -0.030779311455 0.143415676567
y[1] (closed_form) = -0.0308187107214 0.143406886893
absolute error = 4.037e-05
relative error = 0.02752 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.567
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6408 2.034
h = 0.001 0.001
y[1] (numeric) = -0.0309404501221 0.143120255146
y[1] (closed_form) = -0.0309802062721 0.14311131765
absolute error = 4.075e-05
relative error = 0.02783 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.613
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.231
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6398 2.035
h = 0.001 0.003
y[1] (numeric) = -0.0310906433068 0.143070331853
y[1] (closed_form) = -0.031130598284 0.143061381305
absolute error = 4.095e-05
relative error = 0.02797 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.613
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.844
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6388 2.038
h = 0.0001 0.004
y[1] (numeric) = -0.0313410432446 0.142819706099
y[1] (closed_form) = -0.0313805942992 0.142810799692
absolute error = 4.054e-05
relative error = 0.02773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.614
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.309
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6387 2.042
h = 0.003 0.006
y[1] (numeric) = -0.0315492060956 0.142424142991
y[1] (closed_form) = -0.0315886142845 0.142415549988
absolute error = 4.033e-05
relative error = 0.02765 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.617
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.39
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6357 2.048
h = 0.0001 0.005
y[1] (numeric) = -0.0321429561887 0.141972175633
y[1] (closed_form) = -0.03218153874 0.141962325346
absolute error = 3.982e-05
relative error = 0.02736 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.954
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6356 2.053
h = 0.0001 0.003
y[1] (numeric) = -0.0323928981337 0.141477107338
y[1] (closed_form) = -0.0324321520775 0.141467959739
absolute error = 4.031e-05
relative error = 0.02777 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.624
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.575
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2510.1MB, alloc=44.3MB, time=32.42
x[1] = -1.6355 2.056
h = 0.001 0.001
y[1] (numeric) = -0.0325455101266 0.141183147297
y[1] (closed_form) = -0.0325851094008 0.14117384548
absolute error = 4.068e-05
relative error = 0.02808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.626
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.238
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6345 2.057
h = 0.001 0.003
y[1] (numeric) = -0.0326923024857 0.141130994394
y[1] (closed_form) = -0.0327320960031 0.141121674491
absolute error = 4.087e-05
relative error = 0.02821 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.627
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.875
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6335 2.06
h = 0.0001 0.004
y[1] (numeric) = -0.0329336568522 0.140879324419
y[1] (closed_form) = -0.0329730562365 0.140870058504
absolute error = 4.047e-05
relative error = 0.02798 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.628
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.327
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6334 2.064
h = 0.003 0.006
y[1] (numeric) = -0.0331305418822 0.140485893145
y[1] (closed_form) = -0.0331698098014 0.140476937758
absolute error = 4.028e-05
relative error = 0.0279 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.631
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.413
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6304 2.07
h = 0.0001 0.005
y[1] (numeric) = -0.033705744072 0.140029229768
y[1] (closed_form) = -0.0337441705364 0.140019065875
absolute error = 3.975e-05
relative error = 0.0276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.634
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.964
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6303 2.075
h = 0.0001 0.003
y[1] (numeric) = -0.0339417860783 0.139537089344
y[1] (closed_form) = -0.0339808882138 0.139527595324
absolute error = 4.024e-05
relative error = 0.02802 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.638
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.584
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6302 2.078
h = 0.001 0.001
y[1] (numeric) = -0.0340860921202 0.139244786342
y[1] (closed_form) = -0.0341255281299 0.139235132261
absolute error = 4.060e-05
relative error = 0.02832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6292 2.079
h = 0.001 0.003
y[1] (numeric) = -0.0342294969316 0.139190541762
y[1] (closed_form) = -0.0342691225566 0.139180864846
absolute error = 4.079e-05
relative error = 0.02846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.641
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.906
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6282 2.082
h = 0.0001 0.004
y[1] (numeric) = -0.0344619710664 0.13893809025
y[1] (closed_form) = -0.0345012124114 0.138928476582
absolute error = 4.040e-05
relative error = 0.02822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.642
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.344
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6281 2.086
h = 0.003 0.006
y[1] (numeric) = -0.0346478756943 0.138547044411
y[1] (closed_form) = -0.0346869965751 0.138537738097
absolute error = 4.021e-05
relative error = 0.02816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.645
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.436
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2556.8MB, alloc=44.3MB, time=33.03
x[1] = -1.6251 2.092
h = 0.0001 0.005
y[1] (numeric) = -0.0352048017348 0.138086276189
y[1] (closed_form) = -0.0352430673707 0.138075809362
absolute error = 3.967e-05
relative error = 0.02784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.648
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.975
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.625 2.097
h = 0.0001 0.003
y[1] (numeric) = -0.0354273185804 0.137597367584
y[1] (closed_form) = -0.0354662629755 0.137587538554
absolute error = 4.017e-05
relative error = 0.02827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.652
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.592
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6249 2.1
h = 0.001 0.001
y[1] (numeric) = -0.0355635399304 0.137306904785
y[1] (closed_form) = -0.0356028068591 0.137296910383
absolute error = 4.052e-05
relative error = 0.02857 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.654
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.251
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6239 2.101
h = 0.001 0.003
y[1] (numeric) = -0.0357035746502 0.137250702337
y[1] (closed_form) = -0.0357430265352 0.137240680631
absolute error = 4.070e-05
relative error = 0.0287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.655
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.938
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6229 2.104
h = 0.0001 0.004
y[1] (numeric) = -0.0359273381021 0.136997719508
y[1] (closed_form) = -0.0359664155985 0.136987769738
absolute error = 4.032e-05
relative error = 0.02847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.656
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.362
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6228 2.108
h = 0.003 0.006
y[1] (numeric) = -0.0361025601027 0.136609296162
y[1] (closed_form) = -0.0361415277374 0.136599650298
absolute error = 4.014e-05
relative error = 0.02841 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.659
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.46
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6198 2.114
h = 0.0001 0.005
y[1] (numeric) = -0.0366414938246 0.136144989551
y[1] (closed_form) = -0.0366795943554 0.136134230329
absolute error = 3.959e-05
relative error = 0.02808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.662
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.985
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6197 2.119
h = 0.0001 0.003
y[1] (numeric) = -0.036850860146 0.135659596332
y[1] (closed_form) = -0.0368896414011 0.135649443592
absolute error = 4.009e-05
relative error = 0.02852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.666
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.601
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6196 2.122
h = 0.001 0.001
y[1] (numeric) = -0.0369792180938 0.135371144791
y[1] (closed_form) = -0.0370183106744 0.135360821877
absolute error = 4.043e-05
relative error = 0.02881 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.669
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.258
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6186 2.123
h = 0.0001 0.004
y[1] (numeric) = -0.0371159040616 0.13531311413
y[1] (closed_form) = -0.0371551769197 0.135302759712
absolute error = 4.061e-05
relative error = 0.02895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.669
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.553
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2603.4MB, alloc=44.3MB, time=33.63
x[1] = -1.6185 2.127
h = 0.003 0.006
y[1] (numeric) = -0.0372826152295 0.134927016399
y[1] (closed_form) = -0.037321375594 0.134917194346
absolute error = 3.999e-05
relative error = 0.02856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.672
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.481
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6155 2.133
h = 0.0001 0.005
y[1] (numeric) = -0.0378062638509 0.134460308555
y[1] (closed_form) = -0.0378441489253 0.134449413138
absolute error = 3.942e-05
relative error = 0.02822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.675
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.995
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6154 2.138
h = 0.0001 0.003
y[1] (numeric) = -0.0380046560561 0.13397830386
y[1] (closed_form) = -0.0380432223365 0.133967988587
absolute error = 3.992e-05
relative error = 0.02867 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.679
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6153 2.141
h = 0.001 0.001
y[1] (numeric) = -0.038126448842 0.133691801646
y[1] (closed_form) = -0.0381653168687 0.133681312589
absolute error = 4.026e-05
relative error = 0.02896 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.681
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.264
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6143 2.142
h = 0.001 0.003
y[1] (numeric) = -0.0382602524043 0.133632337438
y[1] (closed_form) = -0.0382992966282 0.133621813528
absolute error = 4.044e-05
relative error = 0.02909 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.681
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.998
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6133 2.145
h = 0.0001 0.004
y[1] (numeric) = -0.0384682705618 0.133379089069
y[1] (closed_form) = -0.0385069589152 0.133368651689
absolute error = 4.007e-05
relative error = 0.02887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.683
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.396
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6132 2.149
h = 0.003 0.006
y[1] (numeric) = -0.0386244429161 0.132996240907
y[1] (closed_form) = -0.0386630400368 0.132986100256
absolute error = 3.991e-05
relative error = 0.02882 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.686
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.505
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6102 2.155
h = 0.0001 0.005
y[1] (numeric) = -0.039130660999 0.132526980427
y[1] (closed_form) = -0.039168374302 0.132515811863
absolute error = 3.933e-05
relative error = 0.02846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.689
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.005
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6101 2.16
h = 0.0001 0.003
y[1] (numeric) = -0.0393165996079 0.132048962385
y[1] (closed_form) = -0.0393549941747 0.132038344127
absolute error = 3.984e-05
relative error = 0.02891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.693
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.617
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.61 2.163
h = 0.001 0.001
y[1] (numeric) = -0.0394309409765 0.131764756207
y[1] (closed_form) = -0.0394696263728 0.131753960252
absolute error = 4.016e-05
relative error = 0.0292 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.696
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.27
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2650.1MB, alloc=44.3MB, time=34.24
x[1] = -1.609 2.164
h = 0.001 0.003
y[1] (numeric) = -0.0395614462858 0.13170369359
y[1] (closed_form) = -0.0396003031962 0.131692859065
absolute error = 4.034e-05
relative error = 0.02933 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.696
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.03
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.608 2.167
h = 0.0001 0.004
y[1] (numeric) = -0.0397612591246 0.13145056096
y[1] (closed_form) = -0.0397997700368 0.131439820119
absolute error = 3.998e-05
relative error = 0.02911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.698
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.414
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6079 2.171
h = 0.003 0.006
y[1] (numeric) = -0.0399075992202 0.131070923262
y[1] (closed_form) = -0.0399460283758 0.131060475053
absolute error = 3.982e-05
relative error = 0.02907 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.701
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.529
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6049 2.177
h = 0.0001 0.005
y[1] (numeric) = -0.0403966976364 0.130599607761
y[1] (closed_form) = -0.040434236111 0.130588176136
absolute error = 3.924e-05
relative error = 0.0287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.704
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.016
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6048 2.182
h = 0.0001 0.003
y[1] (numeric) = -0.0405705525345 0.130125805365
y[1] (closed_form) = -0.0406087713906 0.13011489501
absolute error = 3.975e-05
relative error = 0.02916 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.708
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.626
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6047 2.185
h = 0.001 0.001
y[1] (numeric) = -0.0406776612639 0.129844033816
y[1] (closed_form) = -0.0407161602049 0.129832942299
absolute error = 4.006e-05
relative error = 0.02944 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6037 2.186
h = 0.001 0.003
y[1] (numeric) = -0.0408048991764 0.129781490481
y[1] (closed_form) = -0.040843564958 0.129770356924
absolute error = 4.024e-05
relative error = 0.02958 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.062
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6027 2.189
h = 0.0001 0.004
y[1] (numeric) = -0.0409966868289 0.129528678054
y[1] (closed_form) = -0.0410350164422 0.129517644832
absolute error = 3.989e-05
relative error = 0.02936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.712
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.433
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6026 2.193
h = 0.003 0.006
y[1] (numeric) = -0.0411334879156 0.129152428971
y[1] (closed_form) = -0.0411717448641 0.1291416841
absolute error = 3.974e-05
relative error = 0.02932 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.715
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.554
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5996 2.199
h = 0.0001 0.005
y[1] (numeric) = -0.0416057847697 0.128679532873
y[1] (closed_form) = -0.0416431457478 0.128667848092
absolute error = 3.915e-05
relative error = 0.02895 %
Correct digits = 4
memory used=2696.8MB, alloc=44.3MB, time=34.85
Radius of convergence (given) for eq 1 = 2.718
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.027
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5995 2.204
h = 0.0001 0.003
y[1] (numeric) = -0.0417679230003 0.128210157346
y[1] (closed_form) = -0.0418059625984 0.128198965613
absolute error = 3.965e-05
relative error = 0.02941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.722
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.635
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5994 2.207
h = 0.001 0.001
y[1] (numeric) = -0.0418680162828 0.12793094844
y[1] (closed_form) = -0.0419063254042 0.127919572509
absolute error = 3.996e-05
relative error = 0.02969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.725
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.284
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5984 2.208
h = 0.001 0.003
y[1] (numeric) = -0.0419920204915 0.127867037935
y[1] (closed_form) = -0.042030491799 0.127855616733
absolute error = 4.013e-05
relative error = 0.02982 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.725
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.095
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5974 2.211
h = 0.0001 0.004
y[1] (numeric) = -0.0421759645955 0.127614739029
y[1] (closed_form) = -0.0422141095045 0.127603424328
absolute error = 3.979e-05
relative error = 0.0296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.727
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.451
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5973 2.215
h = 0.003 0.006
y[1] (numeric) = -0.0423035175341 0.127242042764
y[1] (closed_form) = -0.0423415984915 0.127231011966
absolute error = 3.965e-05
relative error = 0.02957 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.578
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5943 2.221
h = 0.0001 0.005
y[1] (numeric) = -0.0427593370638 0.126768017779
y[1] (closed_form) = -0.0427965182478 0.126756089563
absolute error = 3.905e-05
relative error = 0.02919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.733
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.038
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5942 2.226
h = 0.0001 0.003
y[1] (numeric) = -0.0429101222606 0.12630326326
y[1] (closed_form) = -0.0429479794823 0.12629180069
absolute error = 3.955e-05
relative error = 0.02965 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.737
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.643
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5941 2.229
h = 0.001 0.001
y[1] (numeric) = -0.0430034153622 0.12602673484
y[1] (closed_form) = -0.0430415317385 0.126015085441
absolute error = 3.986e-05
relative error = 0.02993 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.291
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5931 2.23
h = 0.0001 0.004
y[1] (numeric) = -0.0431242221518 0.125961566599
y[1] (closed_form) = -0.0431624960868 0.125949868929
absolute error = 4.002e-05
relative error = 0.03006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.754
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2743.5MB, alloc=44.3MB, time=35.46
x[1] = -1.593 2.234
h = 0.003 0.006
y[1] (numeric) = -0.0432444317907 0.125591902278
y[1] (closed_form) = -0.0432823072219 0.125580737411
absolute error = 3.949e-05
relative error = 0.02973 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.743
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.6
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.59 2.24
h = 0.0001 0.005
y[1] (numeric) = -0.0436863252089 0.125117441267
y[1] (closed_form) = -0.0437232992074 0.12510541475
absolute error = 3.888e-05
relative error = 0.02934 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.048
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5899 2.245
h = 0.0001 0.003
y[1] (numeric) = -0.0438276841829 0.124656936693
y[1] (closed_form) = -0.0438653310694 0.124645352936
absolute error = 3.939e-05
relative error = 0.02981 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.651
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5898 2.248
h = 0.001 0.001
y[1] (numeric) = -0.0439153282529 0.124382879994
y[1] (closed_form) = -0.043953225505 0.124371107575
absolute error = 3.968e-05
relative error = 0.03008 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.297
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5888 2.249
h = 0.001 0.003
y[1] (numeric) = -0.0440334003878 0.12431675111
y[1] (closed_form) = -0.0440714512103 0.12430492807
absolute error = 3.985e-05
relative error = 0.03021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.157
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5878 2.252
h = 0.0001 0.004
y[1] (numeric) = -0.0442032472219 0.124065973646
y[1] (closed_form) = -0.0442409896731 0.124054267238
absolute error = 3.952e-05
relative error = 0.03 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.755
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.487
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5877 2.256
h = 0.003 0.006
y[1] (numeric) = -0.0443144019997 0.123700381982
y[1] (closed_form) = -0.0443520956696 0.123688950734
absolute error = 3.939e-05
relative error = 0.02998 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.758
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.625
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5847 2.262
h = 0.0001 0.005
y[1] (numeric) = -0.0447404390085 0.123225569949
y[1] (closed_form) = -0.0447772299701 0.123213317585
absolute error = 3.878e-05
relative error = 0.02958 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.761
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.059
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5846 2.267
h = 0.0001 0.003
y[1] (numeric) = -0.0448711126417 0.122770000277
y[1] (closed_form) = -0.0449085725409 0.122758164811
absolute error = 3.929e-05
relative error = 0.03005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.765
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5845 2.27
h = 0.001 0.001
y[1] (numeric) = -0.0449523520583 0.122498815139
y[1] (closed_form) = -0.0449900523395 0.122486789082
absolute error = 3.957e-05
relative error = 0.03033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.767
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.304
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2790.1MB, alloc=44.3MB, time=36.06
x[1] = -1.5835 2.271
h = 0.001 0.003
y[1] (numeric) = -0.0450673015817 0.122431620847
y[1] (closed_form) = -0.045105150878 0.122419541573
absolute error = 3.973e-05
relative error = 0.03045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.768
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.191
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5825 2.274
h = 0.0001 0.004
y[1] (numeric) = -0.0452298306809 0.122181848963
y[1] (closed_form) = -0.0452673811162 0.1221698912
absolute error = 3.941e-05
relative error = 0.03025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.505
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5824 2.278
h = 0.003 0.006
y[1] (numeric) = -0.0453325538958 0.12182020434
y[1] (closed_form) = -0.0453700632147 0.121808516924
absolute error = 3.929e-05
relative error = 0.03023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.773
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.65
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5794 2.284
h = 0.0001 0.005
y[1] (numeric) = -0.0457430705127 0.121345430898
y[1] (closed_form) = -0.0457796770954 0.121332961837
absolute error = 3.867e-05
relative error = 0.02982 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.776
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.07
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5793 2.289
h = 0.0001 0.003
y[1] (numeric) = -0.0458634098198 0.120894945201
y[1] (closed_form) = -0.0459006807258 0.120882867997
absolute error = 3.918e-05
relative error = 0.0303 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.669
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5792 2.292
h = 0.001 0.001
y[1] (numeric) = -0.045938452617 0.120626722604
y[1] (closed_form) = -0.0459759541354 0.120614453229
absolute error = 3.946e-05
relative error = 0.03057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.783
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.311
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5782 2.293
h = 0.001 0.003
y[1] (numeric) = -0.0460503219187 0.120558560791
y[1] (closed_form) = -0.0460879679434 0.12054623581
absolute error = 3.961e-05
relative error = 0.03069 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.783
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.224
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5772 2.296
h = 0.0001 0.004
y[1] (numeric) = -0.0462057165532 0.120309947707
y[1] (closed_form) = -0.0462430731136 0.120297748701
absolute error = 3.930e-05
relative error = 0.03049 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.785
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.525
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5771 2.3
h = 0.003 0.006
y[1] (numeric) = -0.0463002859457 0.119952365583
y[1] (closed_form) = -0.0463376087032 0.119940432014
absolute error = 3.918e-05
relative error = 0.03047 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.788
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.675
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5741 2.306
h = 0.0001 0.005
y[1] (numeric) = -0.046695620658 0.119477999744
y[1] (closed_form) = -0.0467320418206 0.119465322927
absolute error = 3.856e-05
relative error = 0.03006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.791
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.081
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2836.7MB, alloc=44.3MB, time=36.66
x[1] = -1.574 2.311
h = 0.0001 0.003
y[1] (numeric) = -0.0468059715178 0.119032732617
y[1] (closed_form) = -0.0468430517762 0.119020423435
absolute error = 3.907e-05
relative error = 0.03055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.795
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.678
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5739 2.314
h = 0.001 0.001
y[1] (numeric) = -0.046875022764 0.118767554904
y[1] (closed_form) = -0.0469123240846 0.118755052302
absolute error = 3.934e-05
relative error = 0.03081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.798
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.319
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5729 2.315
h = 0.001 0.003
y[1] (numeric) = -0.0469838559769 0.11869851954
y[1] (closed_form) = -0.0470212973476 0.11868595914
absolute error = 3.949e-05
relative error = 0.03094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.798
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.258
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5719 2.318
h = 0.0001 0.004
y[1] (numeric) = -0.0471322989605 0.118451208883
y[1] (closed_form) = -0.0471694601388 0.118438778525
absolute error = 3.919e-05
relative error = 0.03074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.544
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5718 2.322
h = 0.003 0.006
y[1] (numeric) = -0.0472189881174 0.118097793372
y[1] (closed_form) = -0.0472561224631 0.11808562346
absolute error = 3.908e-05
relative error = 0.03072 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.803
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.701
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5688 2.328
h = 0.0001 0.005
y[1] (numeric) = -0.0475994810733 0.117624184131
y[1] (closed_form) = -0.0476357160586 0.117611308289
absolute error = 3.845e-05
relative error = 0.03031 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.806
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.093
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5687 2.333
h = 0.0001 0.003
y[1] (numeric) = -0.0477001838865 0.117184256345
y[1] (closed_form) = -0.0477370721756 0.117171724728
absolute error = 3.896e-05
relative error = 0.03079 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.811
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.687
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5686 2.336
h = 0.001 0.001
y[1] (numeric) = -0.0477634454781 0.116922197609
y[1] (closed_form) = -0.0478005455031 0.116909471635
absolute error = 3.922e-05
relative error = 0.03105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.813
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.326
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5676 2.337
h = 0.0001 0.004
y[1] (numeric) = -0.0478692882839 0.116852378813
y[1] (closed_form) = -0.0479065239604 0.11683959304
absolute error = 3.937e-05
relative error = 0.03118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.813
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.962
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5675 2.341
h = 0.003 0.006
y[1] (numeric) = -0.047949739729 0.116502452289
y[1] (closed_form) = -0.047986675746 0.116490184636
absolute error = 3.892e-05
relative error = 0.03089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.816
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.723
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2883.4MB, alloc=44.3MB, time=37.27
x[1] = -1.5645 2.347
h = 0.0001 0.005
y[1] (numeric) = -0.0483177447966 0.11602993019
y[1] (closed_form) = -0.0483537846232 0.116016987818
absolute error = 3.829e-05
relative error = 0.03047 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.103
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5644 2.352
h = 0.0001 0.003
y[1] (numeric) = -0.0484104763852 0.115594794477
y[1] (closed_form) = -0.0484471638479 0.115582176904
absolute error = 3.880e-05
relative error = 0.03096 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.824
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.695
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5643 2.355
h = 0.001 0.001
y[1] (numeric) = -0.0484689517586 0.115335539522
y[1] (closed_form) = -0.0485058431048 0.115322727129
absolute error = 3.905e-05
relative error = 0.03122 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.826
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.332
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5633 2.356
h = 0.001 0.003
y[1] (numeric) = -0.048572250207 0.115265150508
y[1] (closed_form) = -0.0486092734472 0.11525227679
absolute error = 3.920e-05
relative error = 0.03134 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.827
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.322
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5623 2.359
h = 0.0001 0.004
y[1] (numeric) = -0.0487082605984 0.115020691858
y[1] (closed_form) = -0.0487450205726 0.115007954641
absolute error = 3.890e-05
relative error = 0.03115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.829
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.58
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5622 2.363
h = 0.003 0.006
y[1] (numeric) = -0.0487810514076 0.114675356215
y[1] (closed_form) = -0.0488177965732 0.114662869919
absolute error = 3.881e-05
relative error = 0.03114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.832
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.749
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5592 2.369
h = 0.0001 0.005
y[1] (numeric) = -0.0491348531532 0.114204184821
y[1] (closed_form) = -0.0491707061915 0.1141910591
absolute error = 3.818e-05
relative error = 0.03071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.114
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5591 2.374
h = 0.0001 0.003
y[1] (numeric) = -0.0492185555933 0.113774574694
y[1] (closed_form) = -0.0492550495575 0.11376175186
absolute error = 3.868e-05
relative error = 0.0312 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.839
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.705
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.559 2.377
h = 0.001 0.001
y[1] (numeric) = -0.0492716086085 0.113518553615
y[1] (closed_form) = -0.049308297558 0.113505535556
absolute error = 3.893e-05
relative error = 0.03146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.842
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.339
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.558 2.378
h = 0.001 0.003
y[1] (numeric) = -0.0493720061189 0.113447538284
y[1] (closed_form) = -0.0494088226851 0.113434457227
absolute error = 3.907e-05
relative error = 0.03158 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.842
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.357
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2930.1MB, alloc=44.3MB, time=37.87
x[1] = -1.557 2.381
h = 0.0001 0.004
y[1] (numeric) = -0.0495015839075 0.113204740785
y[1] (closed_form) = -0.0495381460683 0.113191799253
absolute error = 3.878e-05
relative error = 0.03139 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.844
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.6
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5569 2.385
h = 0.003 0.006
y[1] (numeric) = -0.0495672528261 0.11286380846
y[1] (closed_form) = -0.0496038062133 0.112851112709
absolute error = 3.870e-05
relative error = 0.03139 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.847
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.775
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5539 2.391
h = 0.0001 0.005
y[1] (numeric) = -0.0499071919486 0.112394282831
y[1] (closed_form) = -0.0499428581625 0.112380981869
absolute error = 3.807e-05
relative error = 0.03095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.851
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.126
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5538 2.396
h = 0.0001 0.003
y[1] (numeric) = -0.0499821882873 0.111970283099
y[1] (closed_form) = -0.0500184882801 0.111957263903
absolute error = 3.856e-05
relative error = 0.03145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.855
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.714
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5537 2.399
h = 0.001 0.001
y[1] (numeric) = -0.0500300107461 0.111717548508
y[1] (closed_form) = -0.0500664970575 0.111704333941
absolute error = 3.881e-05
relative error = 0.0317 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.857
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.347
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5527 2.4
h = 0.001 0.003
y[1] (numeric) = -0.0501275564033 0.111645986365
y[1] (closed_form) = -0.0501641661236 0.111632707296
absolute error = 3.894e-05
relative error = 0.03182 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.858
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.392
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5517 2.403
h = 0.0001 0.004
y[1] (numeric) = -0.0502508797475 0.111404959718
y[1] (closed_form) = -0.0502872437665 0.111391822866
absolute error = 3.866e-05
relative error = 0.03164 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.619
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5516 2.407
h = 0.003 0.006
y[1] (numeric) = -0.0503096820295 0.111068495848
y[1] (closed_form) = -0.0503460430002 0.111055599606
absolute error = 3.858e-05
relative error = 0.03164 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.863
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.801
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5486 2.413
h = 0.0001 0.005
y[1] (numeric) = -0.0506360982688 0.110600893365
y[1] (closed_form) = -0.0506715778457 0.110587425056
absolute error = 3.795e-05
relative error = 0.0312 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.866
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.137
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5485 2.418
h = 0.0001 0.003
y[1] (numeric) = -0.0507027051141 0.110182577434
y[1] (closed_form) = -0.050738810927 0.110169370543
absolute error = 3.845e-05
relative error = 0.0317 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.723
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2976.8MB, alloc=44.3MB, time=38.48
x[1] = -1.5484 2.421
h = 0.001 0.001
y[1] (numeric) = -0.0507454850617 0.109933175114
y[1] (closed_form) = -0.0507817687591 0.109919772956
absolute error = 3.868e-05
relative error = 0.03194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.873
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.354
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5474 2.422
h = 0.001 0.003
y[1] (numeric) = -0.0508402288422 0.10986114212
y[1] (closed_form) = -0.0508766318134 0.109847674113
absolute error = 3.881e-05
relative error = 0.03206 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.873
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.427
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5464 2.425
h = 0.0001 0.004
y[1] (numeric) = -0.0509574741139 0.109621988033
y[1] (closed_form) = -0.0509936399254 0.109608664618
absolute error = 3.854e-05
relative error = 0.03188 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.875
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.639
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5463 2.429
h = 0.003 0.006
y[1] (numeric) = -0.0510096598666 0.109290048826
y[1] (closed_form) = -0.051045828055 0.109276960833
absolute error = 3.846e-05
relative error = 0.03189 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.879
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.827
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5433 2.435
h = 0.0001 0.005
y[1] (numeric) = -0.0513228914422 0.108824629811
y[1] (closed_form) = -0.0513581847787 0.108811001827
absolute error = 3.783e-05
relative error = 0.03144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.882
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.149
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5432 2.44
h = 0.0001 0.003
y[1] (numeric) = -0.0513814187932 0.108412060263
y[1] (closed_form) = -0.0514173304659 0.108398674116
absolute error = 3.833e-05
relative error = 0.03194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.886
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.733
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5431 2.443
h = 0.001 0.001
y[1] (numeric) = -0.0514193404139 0.108166029526
y[1] (closed_form) = -0.0514554217699 0.108152448445
absolute error = 3.855e-05
relative error = 0.03219 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.889
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.361
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5421 2.444
h = 0.0001 0.004
y[1] (numeric) = -0.0515113330385 0.10809359818
y[1] (closed_form) = -0.0515475296091 0.108079950053
absolute error = 3.868e-05
relative error = 0.03231 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.889
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.176
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.542 2.448
h = 0.003 0.006
y[1] (numeric) = -0.051558296974 0.10776540493
y[1] (closed_form) = -0.0515942777319 0.107752249812
absolute error = 3.831e-05
relative error = 0.03207 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.892
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.85
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.539 2.454
h = 0.0001 0.005
y[1] (numeric) = -0.0518604788487 0.107302212861
y[1] (closed_form) = -0.0518955913155 0.107288544428
absolute error = 3.768e-05
relative error = 0.03162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.896
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.159
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3023.5MB, alloc=44.3MB, time=39.08
x[1] = -1.5389 2.459
h = 0.0001 0.003
y[1] (numeric) = -0.0519123640036 0.106894723227
y[1] (closed_form) = -0.0519480875279 0.106881280477
absolute error = 3.817e-05
relative error = 0.03212 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.741
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5388 2.462
h = 0.001 0.001
y[1] (numeric) = -0.0519462889009 0.106651676384
y[1] (closed_form) = -0.0519821752433 0.106638039253
absolute error = 3.839e-05
relative error = 0.03236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.902
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.368
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5378 2.463
h = 0.001 0.003
y[1] (numeric) = -0.0520359508718 0.106578989566
y[1] (closed_form) = -0.0520719489853 0.106565284522
absolute error = 3.852e-05
relative error = 0.03248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.903
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.493
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5368 2.466
h = 0.0001 0.004
y[1] (numeric) = -0.0521423735336 0.106343632067
y[1] (closed_form) = -0.0521781499513 0.106330075151
absolute error = 3.826e-05
relative error = 0.0323 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.905
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.677
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5367 2.47
h = 0.003 0.006
y[1] (numeric) = -0.0521829500883 0.106020305183
y[1] (closed_form) = -0.0522187381485 0.106006973965
absolute error = 3.819e-05
relative error = 0.03232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.908
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.877
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5337 2.476
h = 0.0001 0.005
y[1] (numeric) = -0.0524725735139 0.105559733685
y[1] (closed_form) = -0.0525075010736 0.105545919266
absolute error = 3.756e-05
relative error = 0.03186 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.912
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.171
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5336 2.481
h = 0.0001 0.003
y[1] (numeric) = -0.0525169384264 0.105158076538
y[1] (closed_form) = -0.0525524685846 0.105144469612
absolute error = 3.805e-05
relative error = 0.03237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.916
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.751
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5335 2.484
h = 0.001 0.001
y[1] (numeric) = -0.0525463374601 0.10491845627
y[1] (closed_form) = -0.0525820226706 0.104904655681
absolute error = 3.826e-05
relative error = 0.03261 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.918
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.375
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5325 2.485
h = 0.001 0.003
y[1] (numeric) = -0.052633344939 0.10484549648
y[1] (closed_form) = -0.05266913801 0.104831627042
absolute error = 3.839e-05
relative error = 0.03272 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.919
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.528
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5315 2.488
h = 0.0001 0.004
y[1] (numeric) = -0.052734183365 0.104612259201
y[1] (closed_form) = -0.0527697627876 0.10459853945
absolute error = 3.813e-05
relative error = 0.03255 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.921
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.697
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3070.0MB, alloc=44.3MB, time=39.68
x[1] = -1.5314 2.492
h = 0.003 0.006
y[1] (numeric) = -0.0527688297691 0.10429356982
y[1] (closed_form) = -0.0528044254518 0.104280070584
absolute error = 3.807e-05
relative error = 0.03257 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.924
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.904
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5284 2.498
h = 0.0001 0.005
y[1] (numeric) = -0.0530462257323 0.103835833786
y[1] (closed_form) = -0.0530809693029 0.103821880432
absolute error = 3.744e-05
relative error = 0.03211 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.928
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.183
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5283 2.503
h = 0.0001 0.003
y[1] (numeric) = -0.0530833607029 0.103440043948
y[1] (closed_form) = -0.0531186981562 0.103426280619
absolute error = 3.792e-05
relative error = 0.03262 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.932
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.76
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5282 2.506
h = 0.001 0.001
y[1] (numeric) = -0.0531084065216 0.103203872934
y[1] (closed_form) = -0.0531438914926 0.103189916849
absolute error = 3.813e-05
relative error = 0.03285 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.934
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.383
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5272 2.507
h = 0.001 0.003
y[1] (numeric) = -0.0531928115868 0.103130703265
y[1] (closed_form) = -0.0532284005895 0.103116677526
absolute error = 3.825e-05
relative error = 0.03296 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.935
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.564
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5262 2.51
h = 0.0001 0.004
y[1] (numeric) = -0.0532882334003 0.102899660056
y[1] (closed_form) = -0.0533236166239 0.102885785304
absolute error = 3.801e-05
relative error = 0.0328 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.937
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.717
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5261 2.514
h = 0.003 0.006
y[1] (numeric) = -0.0533171788044 0.102585634223
y[1] (closed_form) = -0.0533525826412 0.102571974823
absolute error = 3.795e-05
relative error = 0.03282 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.94
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.931
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5231 2.52
h = 0.0001 0.005
y[1] (numeric) = -0.0535826750164 0.102130933816
y[1] (closed_form) = -0.053617235675 0.102116848363
absolute error = 3.732e-05
relative error = 0.03236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.944
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.195
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.523 2.525
h = 0.0001 0.003
y[1] (numeric) = -0.0536128633435 0.10174103741
y[1] (closed_form) = -0.0536480089433 0.101727125224
absolute error = 3.780e-05
relative error = 0.03287 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.948
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.77
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5229 2.528
h = 0.001 0.001
y[1] (numeric) = -0.0536337244887 0.101508333112
y[1] (closed_form) = -0.0536690103013 0.101494229251
absolute error = 3.800e-05
relative error = 0.0331 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.95
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.39
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3116.7MB, alloc=44.3MB, time=40.28
x[1] = -1.5219 2.529
h = 0.001 0.003
y[1] (numeric) = -0.0537155794762 0.101435013549
y[1] (closed_form) = -0.0537509655749 0.101420839352
absolute error = 3.812e-05
relative error = 0.03321 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.951
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.6
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5209 2.532
h = 0.0001 0.004
y[1] (numeric) = -0.053805749689 0.101206231783
y[1] (closed_form) = -0.0538409376974 0.10119220963
absolute error = 3.788e-05
relative error = 0.03305 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.953
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.737
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5208 2.536
h = 0.003 0.006
y[1] (numeric) = -0.0538292176791 0.100896888749
y[1] (closed_form) = -0.0538644303987 0.100883076811
absolute error = 3.782e-05
relative error = 0.03307 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.956
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.958
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5178 2.542
h = 0.0001 0.005
y[1] (numeric) = -0.0540831382148 0.100445409987
y[1] (closed_form) = -0.0541175171854 0.10043119906
absolute error = 3.720e-05
relative error = 0.03261 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.96
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.207
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5177 2.547
h = 0.0001 0.003
y[1] (numeric) = -0.0541066561484 0.100061424944
y[1] (closed_form) = -0.0541416109231 0.100047371216
absolute error = 3.767e-05
relative error = 0.03312 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.964
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.78
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5176 2.55
h = 0.001 0.001
y[1] (numeric) = -0.0541234970233 0.0998321999064
y[1] (closed_form) = -0.0541585849335 0.0998179557475
absolute error = 3.787e-05
relative error = 0.03335 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.967
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.398
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5166 2.551
h = 0.0001 0.004
y[1] (numeric) = -0.054202854421 0.0997587874209
y[1] (closed_form) = -0.0542380389557 0.0997444723598
absolute error = 3.799e-05
relative error = 0.03346 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.967
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.397
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5165 2.555
h = 0.003 0.006
y[1] (numeric) = -0.0542220124229 0.099453291941
y[1] (closed_form) = -0.0542570508946 0.0994394381445
absolute error = 3.768e-05
relative error = 0.03326 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.97
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.981
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5135 2.561
h = 0.0001 0.005
y[1] (numeric) = -0.0544662666342 0.0990048575576
y[1] (closed_form) = -0.0545004801401 0.0989906271603
absolute error = 3.705e-05
relative error = 0.03279 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.974
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.218
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5134 2.566
h = 0.0001 0.003
y[1] (numeric) = -0.0544843292916 0.0986260443927
y[1] (closed_form) = -0.0545191104208 0.0986119580182
absolute error = 3.753e-05
relative error = 0.0333 %
Correct digits = 3
memory used=3163.4MB, alloc=44.3MB, time=40.88
Radius of convergence (given) for eq 1 = 2.978
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.788
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5133 2.569
h = 0.001 0.001
y[1] (numeric) = -0.0544978796907 0.0983998659942
y[1] (closed_form) = -0.0545327880611 0.0983855904598
absolute error = 3.771e-05
relative error = 0.03353 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.981
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.405
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5123 2.57
h = 0.001 0.003
y[1] (numeric) = -0.0545751290816 0.098326445813
y[1] (closed_form) = -0.0546101309881 0.0983120990202
absolute error = 3.783e-05
relative error = 0.03364 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.981
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.668
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5113 2.573
h = 0.0001 0.004
y[1] (numeric) = -0.054655985596 0.0981020884667
y[1] (closed_form) = -0.0546908032402 0.0980878949966
absolute error = 3.760e-05
relative error = 0.03348 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.983
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.776
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5112 2.577
h = 0.003 0.006
y[1] (numeric) = -0.0546698933299 0.0978015478568
y[1] (closed_form) = -0.0547047426029 0.0977875550933
absolute error = 3.755e-05
relative error = 0.03352 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.987
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.008
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5082 2.583
h = 0.0001 0.005
y[1] (numeric) = -0.0549031659671 0.0973566418327
y[1] (closed_form) = -0.0549372004889 0.0973422977122
absolute error = 3.693e-05
relative error = 0.03304 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.99
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.23
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5081 2.588
h = 0.0001 0.003
y[1] (numeric) = -0.0549150534399 0.0969837501614
y[1] (closed_form) = -0.0549496461648 0.0969695352421
absolute error = 3.740e-05
relative error = 0.03356 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.994
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.798
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.508 2.591
h = 0.001 0.001
y[1] (numeric) = -0.0549248784415 0.0967610604248
y[1] (closed_form) = -0.0549595917486 0.0967466578552
absolute error = 3.758e-05
relative error = 0.03378 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.997
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.412
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.507 2.592
h = 0.001 0.003
y[1] (numeric) = -0.0549997285769 0.096687645007
y[1] (closed_form) = -0.0550345319189 0.0966731708125
absolute error = 3.769e-05
relative error = 0.03388 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.997
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.704
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.506 2.595
h = 0.0001 0.004
y[1] (numeric) = -0.0550757906948 0.0964657068342
y[1] (closed_form) = -0.0551104169371 0.0964513863984
absolute error = 3.747e-05
relative error = 0.03373 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.999
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.796
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3210.2MB, alloc=44.3MB, time=41.48
x[1] = -1.5059 2.599
h = 0.003 0.006
y[1] (numeric) = -0.0550848296821 0.0961698676296
y[1] (closed_form) = -0.0551194909722 0.0961557428773
absolute error = 3.743e-05
relative error = 0.03377 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.003
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.036
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5029 2.605
h = 0.0001 0.005
y[1] (numeric) = -0.055307432584 0.0957286387241
y[1] (closed_form) = -0.0553412897039 0.0957141869101
absolute error = 3.681e-05
relative error = 0.0333 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.007
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.242
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5028 2.61
h = 0.0001 0.003
y[1] (numeric) = -0.0553134008007 0.0953616657661
y[1] (closed_form) = -0.0553478065829 0.0953473289754
absolute error = 3.727e-05
relative error = 0.03381 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.011
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.808
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5027 2.613
h = 0.001 0.001
y[1] (numeric) = -0.0553196528591 0.0951424647867
y[1] (closed_form) = -0.0553541727842 0.0951279419832
absolute error = 3.745e-05
relative error = 0.03403 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.013
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.42
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5017 2.614
h = 0.001 0.003
y[1] (numeric) = -0.0553921561048 0.095069103002
y[1] (closed_form) = -0.0554267626496 0.095054508306
absolute error = 3.756e-05
relative error = 0.03413 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.014
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.741
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5007 2.617
h = 0.0001 0.004
y[1] (numeric) = -0.0554635777086 0.0948496291099
y[1] (closed_form) = -0.0554980141323 0.094835188415
absolute error = 3.734e-05
relative error = 0.03398 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.016
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.817
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5006 2.621
h = 0.003 0.006
y[1] (numeric) = -0.0554679498256 0.0945584879987
y[1] (closed_form) = -0.055502424496 0.0945442380146
absolute error = 3.730e-05
relative error = 0.03403 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.019
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.063
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4976 2.627
h = 0.0001 0.005
y[1] (numeric) = -0.0556801901209 0.094121072998
y[1] (closed_form) = -0.0557138715274 0.0941065193191
absolute error = 3.669e-05
relative error = 0.03355 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.023
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.254
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4975 2.632
h = 0.0001 0.003
y[1] (numeric) = -0.0556804879652 0.0937600095717
y[1] (closed_form) = -0.0557147083962 0.0937455573643
absolute error = 3.715e-05
relative error = 0.03406 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.027
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.818
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4974 2.635
h = 0.001 0.001
y[1] (numeric) = -0.0556833153874 0.0935442935907
y[1] (closed_form) = -0.0557176437384 0.0935296571253
absolute error = 3.732e-05
relative error = 0.03428 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.03
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.428
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3257.0MB, alloc=44.3MB, time=42.09
x[1] = -1.4964 2.636
h = 0.001 0.003
y[1] (numeric) = -0.0557535239175 0.0934710316574
y[1] (closed_form) = -0.0557879355592 0.0934563231247
absolute error = 3.742e-05
relative error = 0.03438 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.03
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.778
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4954 2.639
h = 0.0001 0.004
y[1] (numeric) = -0.0558204558378 0.0932540620419
y[1] (closed_form) = -0.0558547041532 0.0932395075712
absolute error = 3.721e-05
relative error = 0.03424 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.032
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.838
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4953 2.643
h = 0.003 0.006
y[1] (numeric) = -0.0558203573813 0.0929676107187
y[1] (closed_form) = -0.0558546469306 0.0929532420413
absolute error = 3.718e-05
relative error = 0.03428 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.036
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.091
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4923 2.649
h = 0.0001 0.005
y[1] (numeric) = -0.0560225372808 0.092534134969
y[1] (closed_form) = -0.0560560447596 0.0925194850555
absolute error = 3.657e-05
relative error = 0.03381 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.04
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.267
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4922 2.654
h = 0.0001 0.003
y[1] (numeric) = -0.0560174066296 0.0921789659117
y[1] (closed_form) = -0.05605144342 0.0921644045267
absolute error = 3.702e-05
relative error = 0.03432 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.044
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.827
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4921 2.657
h = 0.001 0.001
y[1] (numeric) = -0.0560169535954 0.0919667275668
y[1] (closed_form) = -0.0560510922956 0.0919519837856
absolute error = 3.719e-05
relative error = 0.03453 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.046
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.436
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4911 2.658
h = 0.0001 0.004
y[1] (numeric) = -0.0560849193191 0.0918936091438
y[1] (closed_form) = -0.0561191380673 0.091878793208
absolute error = 3.729e-05
relative error = 0.03463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.047
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.623
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.491 2.662
h = 0.003 0.006
y[1] (numeric) = -0.0560813140008 0.0916109903211
y[1] (closed_form) = -0.0561154436711 0.0915966002281
absolute error = 3.704e-05
relative error = 0.03448 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.05
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.115
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.488 2.668
h = 0.0001 0.005
y[1] (numeric) = -0.0562751211139 0.0911811124052
y[1] (closed_form) = -0.0563084788038 0.0911664595596
absolute error = 3.643e-05
relative error = 0.034 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.054
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.277
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4879 2.673
h = 0.0001 0.003
y[1] (numeric) = -0.0562655760346 0.0908310614866
y[1] (closed_form) = -0.0562994544866 0.090816486619
absolute error = 3.688e-05
relative error = 0.03452 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.058
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.836
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3303.7MB, alloc=44.3MB, time=42.70
x[1] = -1.4878 2.676
h = 0.001 0.001
y[1] (numeric) = -0.0562624528605 0.0906218449207
y[1] (closed_form) = -0.0562964282401 0.0906070894057
absolute error = 3.704e-05
relative error = 0.03472 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.061
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.443
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4868 2.677
h = 0.001 0.003
y[1] (numeric) = -0.0563285317384 0.0905489089818
y[1] (closed_form) = -0.0563625844438 0.0905340813402
absolute error = 3.714e-05
relative error = 0.03483 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.061
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.847
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4858 2.68
h = 0.0001 0.004
y[1] (numeric) = -0.056387530913 0.0903367386404
y[1] (closed_form) = -0.0564214324445 0.0903220646533
absolute error = 3.694e-05
relative error = 0.03469 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.063
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.877
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4857 2.684
h = 0.003 0.006
y[1] (numeric) = -0.0563796726664 0.0900590240637
y[1] (closed_form) = -0.0564136203996 0.0900445268516
absolute error = 3.691e-05
relative error = 0.03474 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.143
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4827 2.69
h = 0.0001 0.005
y[1] (numeric) = -0.0565639692336 0.0896332865074
y[1] (closed_form) = -0.0565971566085 0.089618547366
absolute error = 3.631e-05
relative error = 0.03426 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.29
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4826 2.695
h = 0.0001 0.003
y[1] (numeric) = -0.0565494269395 0.0892890845085
y[1] (closed_form) = -0.056583125284 0.0892744114878
absolute error = 3.675e-05
relative error = 0.03477 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.846
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4825 2.698
h = 0.001 0.001
y[1] (numeric) = -0.0565432805304 0.0890833214989
y[1] (closed_form) = -0.0565770701791 0.0890684698637
absolute error = 3.691e-05
relative error = 0.03498 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.45
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4815 2.699
h = 0.001 0.003
y[1] (numeric) = -0.0566072127148 0.0890106032019
y[1] (closed_form) = -0.0566410766069 0.0889956795003
absolute error = 3.701e-05
relative error = 0.03508 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.885
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4805 2.702
h = 0.0001 0.004
y[1] (numeric) = -0.0566621367039 0.0888010239382
y[1] (closed_form) = -0.0566958556937 0.0887862534958
absolute error = 3.681e-05
relative error = 0.03494 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.08
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.898
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4804 2.706
h = 0.003 0.006
y[1] (numeric) = -0.0566503386949 0.0885279485886
y[1] (closed_form) = -0.0566841063159 0.088513350187
absolute error = 3.679e-05
relative error = 0.035 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.084
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.171
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3350.3MB, alloc=44.3MB, time=43.30
x[1] = -1.4774 2.712
h = 0.0001 0.005
y[1] (numeric) = -0.0568254118278 0.0881064468996
y[1] (closed_form) = -0.0568584309015 0.0880916265459
absolute error = 3.619e-05
relative error = 0.03452 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.087
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.302
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4773 2.717
h = 0.0001 0.003
y[1] (numeric) = -0.0568060944165 0.0877680637987
y[1] (closed_form) = -0.0568396146469 0.0877532982665
absolute error = 3.663e-05
relative error = 0.03503 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.092
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.856
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4772 2.72
h = 0.001 0.001
y[1] (numeric) = -0.0567970572877 0.087565738012
y[1] (closed_form) = -0.0568306634002 0.0875507959783
absolute error = 3.678e-05
relative error = 0.03524 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.094
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.458
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4762 2.721
h = 0.001 0.003
y[1] (numeric) = -0.0568588935516 0.0874932742001
y[1] (closed_form) = -0.0568925709102 0.0874782602327
absolute error = 3.687e-05
relative error = 0.03533 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.095
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.922
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4752 2.724
h = 0.0001 0.004
y[1] (numeric) = -0.0569098809483 0.0872863086671
y[1] (closed_form) = -0.0569434194965 0.0872714474235
absolute error = 3.668e-05
relative error = 0.0352 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.097
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.92
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4751 2.728
h = 0.003 0.006
y[1] (numeric) = -0.0568943182834 0.0870178479967
y[1] (closed_form) = -0.0569279077128 0.0870031541298
absolute error = 3.666e-05
relative error = 0.03526 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.199
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4721 2.734
h = 0.0001 0.005
y[1] (numeric) = -0.0570604496144 0.0866006681749
y[1] (closed_form) = -0.0570933024662 0.0865857715089
absolute error = 3.607e-05
relative error = 0.03478 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.104
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.315
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.472 2.739
h = 0.0001 0.003
y[1] (numeric) = -0.0570365724396 0.0862680694329
y[1] (closed_form) = -0.0570699166314 0.0862532168297
absolute error = 3.650e-05
relative error = 0.03529 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.109
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.866
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4719 2.742
h = 0.001 0.001
y[1] (numeric) = -0.0570247731255 0.0860691618026
y[1] (closed_form) = -0.0570581979744 0.0860541348829
absolute error = 3.665e-05
relative error = 0.03549 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.111
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.466
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4709 2.743
h = 0.001 0.003
y[1] (numeric) = -0.0570845637491 0.0859969871055
y[1] (closed_form) = -0.0571180569309 0.0859818884527
absolute error = 3.674e-05
relative error = 0.03559 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.112
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.96
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3396.9MB, alloc=44.3MB, time=43.90
x[1] = -1.4699 2.746
h = 0.0001 0.004
y[1] (numeric) = -0.0571317499332 0.0857926540253
y[1] (closed_form) = -0.057165110219 0.0857777074304
absolute error = 3.656e-05
relative error = 0.03546 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.114
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.941
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4698 2.75
h = 0.003 0.006
y[1] (numeric) = -0.0571125923888 0.0855287799683
y[1] (closed_form) = -0.0571460056341 0.0855139961587
absolute error = 3.654e-05
relative error = 0.03552 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.117
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.228
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4668 2.756
h = 0.0001 0.005
y[1] (numeric) = -0.0572700579776 0.0851159989713
y[1] (closed_form) = -0.0573027467448 0.0851010307139
absolute error = 3.595e-05
relative error = 0.03504 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.121
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.327
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4667 2.761
h = 0.0001 0.003
y[1] (numeric) = -0.0572418297395 0.0847891458706
y[1] (closed_form) = -0.0572750000416 0.0847742114403
absolute error = 3.638e-05
relative error = 0.03556 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.126
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.877
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4666 2.764
h = 0.001 0.001
y[1] (numeric) = -0.057227392845 0.0845936347991
y[1] (closed_form) = -0.0572606387721 0.0845785283014
absolute error = 3.652e-05
relative error = 0.03575 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.128
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.474
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4656 2.765
h = 0.0001 0.004
y[1] (numeric) = -0.0572851875686 0.0845217817193
y[1] (closed_form) = -0.057318498999 0.0845066037522
absolute error = 3.661e-05
relative error = 0.03585 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.129
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.854
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4655 2.769
h = 0.003 0.006
y[1] (numeric) = -0.0572632196188 0.0842616407838
y[1] (closed_form) = -0.0572964877223 0.0842468517738
absolute error = 3.641e-05
relative error = 0.03573 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.132
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.252
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4625 2.775
h = 0.0001 0.005
y[1] (numeric) = -0.0574134962621 0.0838528000592
y[1] (closed_form) = -0.0574460505919 0.0838378416269
absolute error = 3.583e-05
relative error = 0.03525 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.136
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.339
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4624 2.78
h = 0.0001 0.003
y[1] (numeric) = -0.05738175263 0.083530907228
y[1] (closed_form) = -0.0574147799612 0.083515974334
absolute error = 3.625e-05
relative error = 0.03576 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.885
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4623 2.783
h = 0.001 0.001
y[1] (numeric) = -0.0573651822817 0.0833383301868
y[1] (closed_form) = -0.0573982810852 0.0833232272641
absolute error = 3.638e-05
relative error = 0.03596 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.143
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.481
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3443.5MB, alloc=44.3MB, time=44.50
x[1] = -1.4613 2.784
h = 0.001 0.003
y[1] (numeric) = -0.0574213027084 0.083266801389
y[1] (closed_form) = -0.0574544646497 0.0832516273033
absolute error = 3.647e-05
relative error = 0.03605 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.143
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.031
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4603 2.787
h = 0.0001 0.004
y[1] (numeric) = -0.0574617967265 0.0830674455835
y[1] (closed_form) = -0.0574948363001 0.0830524219352
absolute error = 3.629e-05
relative error = 0.03593 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.146
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.981
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4602 2.791
h = 0.003 0.006
y[1] (numeric) = -0.0574364375695 0.0828120587839
y[1] (closed_form) = -0.0574695334863 0.0827971895593
absolute error = 3.628e-05
relative error = 0.036 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.149
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.281
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4572 2.797
h = 0.0001 0.005
y[1] (numeric) = -0.0575785477593 0.082407734424
y[1] (closed_form) = -0.0576109421648 0.082392712695
absolute error = 3.571e-05
relative error = 0.03552 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.153
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.351
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4571 2.802
h = 0.0001 0.003
y[1] (numeric) = -0.0575428234749 0.0820915028603
y[1] (closed_form) = -0.0575756811413 0.0820764973606
absolute error = 3.612e-05
relative error = 0.03603 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.157
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.896
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.457 2.805
h = 0.001 0.001
y[1] (numeric) = -0.0575238368248 0.0819022747299
y[1] (closed_form) = -0.0575567612787 0.0818871015481
absolute error = 3.625e-05
relative error = 0.03622 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.489
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.456 2.806
h = 0.001 0.003
y[1] (numeric) = -0.0575780526596 0.081831122078
y[1] (closed_form) = -0.057611037575 0.0818158781021
absolute error = 3.634e-05
relative error = 0.03631 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.069
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.455 2.809
h = 0.0001 0.004
y[1] (numeric) = -0.0576151150608 0.0816344310181
y[1] (closed_form) = -0.0576479830255 0.0816193364922
absolute error = 3.617e-05
relative error = 0.0362 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.163
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.003
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4549 2.813
h = 0.003 0.006
y[1] (numeric) = -0.0575866175078 0.0813835316224
y[1] (closed_form) = -0.0576195434452 0.0813685871514
absolute error = 3.616e-05
relative error = 0.03627 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.166
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.31
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4519 2.819
h = 0.0001 0.005
y[1] (numeric) = -0.0577208209146 0.0809837772265
y[1] (closed_form) = -0.0577530576615 0.0809686964316
absolute error = 3.559e-05
relative error = 0.03578 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.364
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3490.3MB, alloc=44.3MB, time=45.10
x[1] = -1.4518 2.824
h = 0.0001 0.003
y[1] (numeric) = -0.0576813061715 0.0806731580665
y[1] (closed_form) = -0.057713996488 0.0806580846656
absolute error = 3.600e-05
relative error = 0.0363 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.174
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.906
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4517 2.827
h = 0.001 0.001
y[1] (numeric) = -0.0576600168846 0.0804872510855
y[1] (closed_form) = -0.0576927694836 0.0804720123931
absolute error = 3.612e-05
relative error = 0.03648 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.177
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.497
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4507 2.828
h = 0.001 0.003
y[1] (numeric) = -0.0577123760825 0.0804165014621
y[1] (closed_form) = -0.0577451865473 0.0804011923957
absolute error = 3.621e-05
relative error = 0.03658 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.177
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.107
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4497 2.831
h = 0.0001 0.004
y[1] (numeric) = -0.0577461298009 0.080222480714
y[1] (closed_form) = -0.0577788285636 0.0802073200131
absolute error = 3.604e-05
relative error = 0.03646 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.024
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4496 2.835
h = 0.003 0.006
y[1] (numeric) = -0.0577146437587 0.0799760295137
y[1] (closed_form) = -0.0577474019802 0.0799610145795
absolute error = 3.604e-05
relative error = 0.03653 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.183
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.338
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4466 2.841
h = 0.0001 0.005
y[1] (numeric) = -0.0578411942878 0.0795808913004
y[1] (closed_form) = -0.0578732756755 0.0795657555071
absolute error = 3.547e-05
relative error = 0.03605 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.187
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.377
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4465 2.846
h = 0.0001 0.003
y[1] (numeric) = -0.0577980730428 0.0792758326641
y[1] (closed_form) = -0.0578305983697 0.079260695887
absolute error = 3.588e-05
relative error = 0.03656 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.192
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.916
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4464 2.849
h = 0.001 0.001
y[1] (numeric) = -0.0577745910948 0.0790932172338
y[1] (closed_form) = -0.0578071743744 0.0790779175934
absolute error = 3.600e-05
relative error = 0.03675 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.194
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.505
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4454 2.85
h = 0.001 0.003
y[1] (numeric) = -0.0578251409317 0.0790228957092
y[1] (closed_form) = -0.0578577795606 0.0790075261621
absolute error = 3.608e-05
relative error = 0.03684 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.195
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.146
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4444 2.853
h = 0.0001 0.004
y[1] (numeric) = -0.0578557057193 0.0788315478971
y[1] (closed_form) = -0.057888237729 0.0788163255417
absolute error = 3.592e-05
relative error = 0.03673 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.197
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.046
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3537.0MB, alloc=44.3MB, time=45.70
x[1] = -1.4443 2.857
h = 0.003 0.006
y[1] (numeric) = -0.0578213761726 0.0785895033409
y[1] (closed_form) = -0.0578539689907 0.0785744225458
absolute error = 3.591e-05
relative error = 0.0368 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.367
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4413 2.863
h = 0.0001 0.005
y[1] (numeric) = -0.0579405219492 0.0781990205421
y[1] (closed_form) = -0.0579724503061 0.0781838336596
absolute error = 3.536e-05
relative error = 0.03633 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.204
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.39
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4412 2.868
h = 0.0001 0.003
y[1] (numeric) = -0.0578939720424 0.0778994677998
y[1] (closed_form) = -0.057926334779 0.0778842719964
absolute error = 3.575e-05
relative error = 0.03683 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.209
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.927
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4411 2.871
h = 0.001 0.001
y[1] (numeric) = -0.057868403789 0.0777201126426
y[1] (closed_form) = -0.057900820319 0.0777047564359
absolute error = 3.587e-05
relative error = 0.03702 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.211
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.513
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4401 2.872
h = 0.001 0.003
y[1] (numeric) = -0.0579171908346 0.0776502425512
y[1] (closed_form) = -0.0579496602754 0.0776348169489
absolute error = 3.595e-05
relative error = 0.03711 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.212
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.184
Order of pole (three term test) = 2 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ;
Iterations = 754
Total Elapsed Time = 45 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 45 Seconds
> quit
memory used=3564.6MB, alloc=44.3MB, time=46.05