|\^/| 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(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;
> end;
exact_soln_y := proc(x)
return c(1.0)/((c(x) - c(6.0))*(c(x) - c(6.0))*(c(x) - c(6.0))*
(c(x) - c(6.0))*(c(x) - c(6.0)))
end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> 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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, 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_5D0,
> array_const_6D0,
#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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> 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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, 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_5D0,
> array_const_6D0,
#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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> 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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, 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_5D0,
> array_const_6D0,
#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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> 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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, 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_5D0,
> array_const_6D0,
#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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> 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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, 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_5D0,
> array_const_6D0,
#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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> 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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, 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_5D0,
> array_const_6D0,
#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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> 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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, 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_5D0,
> array_const_6D0,
#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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> 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_5D0[1]);
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_x[1] - array_const_6D0[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp1[1] / array_tmp2[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp3[1] / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp5[1] / array_tmp6[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp8[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp9[1] := array_tmp7[1] / array_tmp8[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp10[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp11[1] := array_tmp9[1] / array_tmp10[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp12[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp13[1] := array_tmp11[1] / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp14[1] := array_const_0D0[1] + array_tmp13[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_tmp14[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 sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_x[2];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := neg(array_tmp3[1])* array_tmp2[2] / array_tmp2[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 3
> #emit pre div CONST - LINEAR $eq_no = 1 i = 4
> #emit pre div CONST - LINEAR $eq_no = 1 i = 5
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - array_tmp7[1] * array_tmp6[2]) / array_tmp6[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp8[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - array_tmp9[1] * array_tmp8[2]) / array_tmp8[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp10[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp11[2] := (array_tmp9[2] - array_tmp11[1] * array_tmp10[2]) / array_tmp10[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp12[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp13[2] := (array_tmp11[2] - array_tmp13[1] * array_tmp12[2]) / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp14[2] := array_tmp13[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_tmp14[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> array_tmp3[3] := neg(array_tmp3[2])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - array_tmp5[2] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - array_tmp7[2] * array_tmp6[2]) / array_tmp6[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - array_tmp9[2] * array_tmp8[2]) / array_tmp8[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp11[3] := (array_tmp9[3] - array_tmp11[2] * array_tmp10[2]) / array_tmp10[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp13[3] := (array_tmp11[3] - array_tmp13[2] * array_tmp12[2]) / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp14[3] := array_tmp13[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_tmp14[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> array_tmp3[4] := neg(array_tmp3[3])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - array_tmp5[3] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - array_tmp7[3] * array_tmp6[2]) / array_tmp6[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - array_tmp9[3] * array_tmp8[2]) / array_tmp8[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp11[4] := (array_tmp9[4] - array_tmp11[3] * array_tmp10[2]) / array_tmp10[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp13[4] := (array_tmp11[4] - array_tmp13[3] * array_tmp12[2]) / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp14[4] := array_tmp13[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_tmp14[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> array_tmp3[5] := neg(array_tmp3[4])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - array_tmp5[4] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - array_tmp7[4] * array_tmp6[2]) / array_tmp6[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - array_tmp9[4] * array_tmp8[2]) / array_tmp8[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp11[5] := (array_tmp9[5] - array_tmp11[4] * array_tmp10[2]) / array_tmp10[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp13[5] := (array_tmp11[5] - array_tmp13[4] * array_tmp12[2]) / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp14[5] := array_tmp13[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_tmp14[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit div CONST LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp3[kkk] := array_tmp1[1] * array_tmp2[kkk];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp7[kkk] := neg(ats(kkk,array_tmp6,array_tmp7,2)) / array_tmp6[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp9[kkk] := neg(ats(kkk,array_tmp8,array_tmp9,2)) / array_tmp8[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp11[kkk] := neg(ats(kkk,array_tmp10,array_tmp11,2)) / array_tmp10[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp13[kkk] := neg(ats(kkk,array_tmp12,array_tmp13,2)) / array_tmp12[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp14[kkk] := array_tmp13[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_tmp14[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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, 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_5D0[1]);
array_tmp2[1] := array_x[1] - array_const_6D0[1];
array_tmp3[1] := array_tmp1[1]/array_tmp2[1];
array_tmp4[1] := array_x[1] - array_const_6D0[1];
array_tmp5[1] := array_tmp3[1]/array_tmp4[1];
array_tmp6[1] := array_x[1] - array_const_6D0[1];
array_tmp7[1] := array_tmp5[1]/array_tmp6[1];
array_tmp8[1] := array_x[1] - array_const_6D0[1];
array_tmp9[1] := array_tmp7[1]/array_tmp8[1];
array_tmp10[1] := array_x[1] - array_const_6D0[1];
array_tmp11[1] := array_tmp9[1]/array_tmp10[1];
array_tmp12[1] := array_x[1] - array_const_6D0[1];
array_tmp13[1] := array_tmp11[1]/array_tmp12[1];
array_tmp14[1] := array_const_0D0[1] + array_tmp13[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[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_x[2];
array_tmp3[2] := neg(array_tmp3[1])*array_tmp2[2]/array_tmp2[1];
array_tmp4[2] := array_x[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp3[2])/array_tmp4[1];
array_tmp6[2] := array_x[2];
array_tmp7[2] :=
(-array_tmp6[2]*array_tmp7[1] + array_tmp5[2])/array_tmp6[1];
array_tmp8[2] := array_x[2];
array_tmp9[2] :=
(-array_tmp8[2]*array_tmp9[1] + array_tmp7[2])/array_tmp8[1];
array_tmp10[2] := array_x[2];
array_tmp11[2] :=
(-array_tmp10[2]*array_tmp11[1] + array_tmp9[2])/array_tmp10[1];
array_tmp12[2] := array_x[2];
array_tmp13[2] :=
(-array_tmp12[2]*array_tmp13[1] + array_tmp11[2])/array_tmp12[1];
array_tmp14[2] := array_tmp13[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := neg(array_tmp3[2])*array_tmp2[2]/array_tmp2[1];
array_tmp5[3] :=
(-array_tmp4[2]*array_tmp5[2] + array_tmp3[3])/array_tmp4[1];
array_tmp7[3] :=
(-array_tmp6[2]*array_tmp7[2] + array_tmp5[3])/array_tmp6[1];
array_tmp9[3] :=
(-array_tmp8[2]*array_tmp9[2] + array_tmp7[3])/array_tmp8[1];
array_tmp11[3] :=
(-array_tmp10[2]*array_tmp11[2] + array_tmp9[3])/array_tmp10[1];
array_tmp13[3] :=
(-array_tmp12[2]*array_tmp13[2] + array_tmp11[3])/array_tmp12[1];
array_tmp14[3] := array_tmp13[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[4] := neg(array_tmp3[3])*array_tmp2[2]/array_tmp2[1];
array_tmp5[4] :=
(-array_tmp4[2]*array_tmp5[3] + array_tmp3[4])/array_tmp4[1];
array_tmp7[4] :=
(-array_tmp6[2]*array_tmp7[3] + array_tmp5[4])/array_tmp6[1];
array_tmp9[4] :=
(-array_tmp8[2]*array_tmp9[3] + array_tmp7[4])/array_tmp8[1];
array_tmp11[4] :=
(-array_tmp10[2]*array_tmp11[3] + array_tmp9[4])/array_tmp10[1];
array_tmp13[4] :=
(-array_tmp12[2]*array_tmp13[3] + array_tmp11[4])/array_tmp12[1];
array_tmp14[4] := array_tmp13[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[5] := neg(array_tmp3[4])*array_tmp2[2]/array_tmp2[1];
array_tmp5[5] :=
(-array_tmp4[2]*array_tmp5[4] + array_tmp3[5])/array_tmp4[1];
array_tmp7[5] :=
(-array_tmp6[2]*array_tmp7[4] + array_tmp5[5])/array_tmp6[1];
array_tmp9[5] :=
(-array_tmp8[2]*array_tmp9[4] + array_tmp7[5])/array_tmp8[1];
array_tmp11[5] :=
(-array_tmp10[2]*array_tmp11[4] + array_tmp9[5])/array_tmp10[1];
array_tmp13[5] :=
(-array_tmp12[2]*array_tmp13[4] + array_tmp11[5])/array_tmp12[1];
array_tmp14[5] := array_tmp13[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := array_tmp1[1]*array_tmp2[kkk];
array_tmp5[kkk] :=
neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[kkk] :=
neg(ats(kkk, array_tmp6, array_tmp7, 2))/array_tmp6[1];
array_tmp9[kkk] :=
neg(ats(kkk, array_tmp8, array_tmp9, 2))/array_tmp8[1];
array_tmp11[kkk] :=
neg(ats(kkk, array_tmp10, array_tmp11, 2))/array_tmp10[1];
array_tmp13[kkk] :=
neg(ats(kkk, array_tmp12, array_tmp13, 2))/array_tmp12[1];
array_tmp14[kkk] := array_tmp13[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_tmp14[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_5D0,
> array_const_6D0,
> #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_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 20;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=64;
> max_terms:=20;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(20),[]);
> array_norms:= Array(0..(20),[]);
> array_fact_1:= Array(0..(20),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(20),[]);
> array_x:= Array(0..(20),[]);
> array_tmp0:= Array(0..(20),[]);
> array_tmp1:= Array(0..(20),[]);
> array_tmp2:= Array(0..(20),[]);
> array_tmp3:= Array(0..(20),[]);
> array_tmp4:= Array(0..(20),[]);
> array_tmp5:= Array(0..(20),[]);
> array_tmp6:= Array(0..(20),[]);
> array_tmp7:= Array(0..(20),[]);
> array_tmp8:= Array(0..(20),[]);
> array_tmp9:= Array(0..(20),[]);
> array_tmp10:= Array(0..(20),[]);
> array_tmp11:= Array(0..(20),[]);
> array_tmp12:= Array(0..(20),[]);
> array_tmp13:= Array(0..(20),[]);
> array_tmp14:= Array(0..(20),[]);
> array_m1:= Array(0..(20),[]);
> array_y_higher := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(20) ,(0..20+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 20) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp8[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp9[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp10[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp11[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp12[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp13[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp14[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=20) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_tmp8);
> zero_ats_ar(array_tmp9);
> zero_ats_ar(array_tmp10);
> zero_ats_ar(array_tmp11);
> zero_ats_ar(array_tmp12);
> zero_ats_ar(array_tmp13);
> zero_ats_ar(array_tmp14);
> 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_5D0);
> array_const_5D0[1] := c(5.0);
> zero_ats_ar(array_const_6D0);
> array_const_6D0[1] := c(6.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 20;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sing7postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> omniout_str(ALWAYS,"max_terms:=20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 2.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(6.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(1.0)/ (c( x) - c(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 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_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(6.0);
> #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 ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:25:13-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing7")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"sing7 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing7 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_5D0,
array_const_6D0, 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_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 20;
Digits := 64;
max_terms := 20;
glob_html_log := true;
array_y_init := Array(0 .. 20, []);
array_norms := Array(0 .. 20, []);
array_fact_1 := Array(0 .. 20, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 20, []);
array_x := Array(0 .. 20, []);
array_tmp0 := Array(0 .. 20, []);
array_tmp1 := Array(0 .. 20, []);
array_tmp2 := Array(0 .. 20, []);
array_tmp3 := Array(0 .. 20, []);
array_tmp4 := Array(0 .. 20, []);
array_tmp5 := Array(0 .. 20, []);
array_tmp6 := Array(0 .. 20, []);
array_tmp7 := Array(0 .. 20, []);
array_tmp8 := Array(0 .. 20, []);
array_tmp9 := Array(0 .. 20, []);
array_tmp10 := Array(0 .. 20, []);
array_tmp11 := Array(0 .. 20, []);
array_tmp12 := Array(0 .. 20, []);
array_tmp13 := Array(0 .. 20, []);
array_tmp14 := Array(0 .. 20, []);
array_m1 := Array(0 .. 20, []);
array_y_higher := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []);
array_y_set_initial := Array(0 .. 2, 0 .. 21, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 20, 0 .. 21, []);
term := 1;
while term <= 20 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 20 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp8[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp9[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp10[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_tmp11[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_tmp12[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_tmp13[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_tmp14[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 20 do
term := 1;
while term <= 20 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_tmp8);
zero_ats_ar(array_tmp9);
zero_ats_ar(array_tmp10);
zero_ats_ar(array_tmp11);
zero_ats_ar(array_tmp12);
zero_ats_ar(array_tmp13);
zero_ats_ar(array_tmp14);
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_5D0);
array_const_5D0[1] := c(5.0);
zero_ats_ar(array_const_6D0);
array_const_6D0[1] := c(6.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 20;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sing7postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 5.0 ) / \
( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / \
( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
omniout_str(ALWAYS, "max_terms:=20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 2.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(6.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(1.0)/ (c( x) - c(6.0) ) / ( c(x) - c(6.\
0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;\
");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 2.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(6.0);
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 ( 5.0 ) /\
( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 \
) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.\
0 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:25:13-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing7");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) \
/ ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.\
0 ) / ( x - 6.0 ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file,
"sing7 diffeq.mxt");
logitem_str(html_log_file,
"sing7 maple results")
;
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sing7postcpx.cpx#################
diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 2.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(6.0);
#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(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
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0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 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) = -0.00109745309618 -0.000141443751858
y[1] (closed_form) = -0.00109745309618 -0.000141443751858
absolute error = 0
relative error = 0 %
Correct digits = 62
Radius of convergence (given) for eq 1 = 3.901
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.876
Order of pole (three term test) = 2.129e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = -0.00109648526043 -0.00014846960244
y[1] (closed_form) = -0.00109647988071 -0.000148468707555
absolute error = 5.454e-09
relative error = 0.0004929 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.901
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.342
Order of pole (three term test) = 1.399e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1002 0.108
h = 0.001 0.001
y[1] (numeric) = -0.0010959249123 -0.000152689072378
y[1] (closed_form) = -0.00109592599547 -0.000152689219717
absolute error = 1.093e-09
relative error = 9.879e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.901
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.838
Order of pole (three term test) = 1.689e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1012 0.109
h = 0.001 0.003
y[1] (numeric) = -0.0010970852661 -0.000154324883332
y[1] (closed_form) = -0.0010970896869 -0.000154324470353
absolute error = 4.440e-09
relative error = 0.0004008 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.721
Order of pole (three term test) = 5.481e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = -0.00109777141307 -0.000158766799124
y[1] (closed_form) = -0.00109776896988 -0.000158767239398
absolute error = 2.483e-09
relative error = 0.0002238 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.934
Order of pole (three term test) = 4.635e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1023 0.116
h = 0.003 0.006
y[1] (numeric) = -0.00109692212406 -0.000164397903458
y[1] (closed_form) = -0.0010969160783 -0.000164393679628
absolute error = 7.375e-09
relative error = 0.0006649 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.537
Order of pole (three term test) = 1.839e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=37.7MB, alloc=40.3MB, time=0.49
x[1] = 2.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = -0.00109957749474 -0.000173561281554
y[1] (closed_form) = -0.00109956246065 -0.000173581348371
absolute error = 2.507e-08
relative error = 0.002252 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.905
Order of pole (three term test) = 9.376e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = -0.00109834811733 -0.000180613772333
y[1] (closed_form) = -0.00109834174103 -0.000180619327025
absolute error = 8.456e-09
relative error = 0.0007597 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 0 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) = 1.341e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1055 0.13
h = 0.001 0.001
y[1] (numeric) = -0.00109763926234 -0.000184841703592
y[1] (closed_form) = -0.00109763935592 -0.000184848567469
absolute error = 6.865e-09
relative error = 0.0006167 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 0 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) = 5.055e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1065 0.131
h = 0.001 0.003
y[1] (numeric) = -0.00109875105849 -0.000186528054295
y[1] (closed_form) = -0.00109875453731 -0.000186534487462
absolute error = 7.314e-09
relative error = 0.0006562 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.896
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.711
Order of pole (three term test) = 1.751e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = -0.00109928916121 -0.000191022616913
y[1] (closed_form) = -0.00109928569018 -0.000191029634426
absolute error = 7.829e-09
relative error = 0.0007017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.928
Order of pole (three term test) = 8.883e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1076 0.138
h = 0.003 0.006
y[1] (numeric) = -0.00109824088813 -0.000196661221465
y[1] (closed_form) = -0.00109823397472 -0.000196663395436
absolute error = 7.247e-09
relative error = 0.0006496 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.53
Order of pole (three term test) = 6.804e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = -0.00110059862309 -0.000205975141125
y[1] (closed_form) = -0.00110058167959 -0.000206001425412
absolute error = 3.127e-08
relative error = 0.002793 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.892
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.902
Order of pole (three term test) = 4.020e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = -0.00109911871876 -0.000213030580662
y[1] (closed_form) = -0.0010991110799 -0.000213042593776
absolute error = 1.424e-08
relative error = 0.001272 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.892
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.336
Order of pole (three term test) = 1.286e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1108 0.152
h = 0.001 0.001
y[1] (numeric) = -0.00109825991299 -0.000217261076349
y[1] (closed_form) = -0.0010982587388 -0.000217274668165
absolute error = 1.364e-08
relative error = 0.001219 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.892
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.834
Order of pole (three term test) = 1.212e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=83.8MB, alloc=44.3MB, time=1.07
x[1] = 2.1118 0.153
h = 0.001 0.003
y[1] (numeric) = -0.00109932076298 -0.000218996392707
y[1] (closed_form) = -0.00109932301607 -0.000219009686689
absolute error = 1.348e-08
relative error = 0.001203 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.891
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.701
Order of pole (three term test) = 7.510e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = -0.00109970760951 -0.000223538048611
y[1] (closed_form) = -0.00109970283855 -0.000223551651846
absolute error = 1.442e-08
relative error = 0.001285 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.922
Order of pole (three term test) = 8.565e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1129 0.16
h = 0.003 0.006
y[1] (numeric) = -0.00109845858317 -0.000229176216256
y[1] (closed_form) = -0.0010984505396 -0.000229184802386
absolute error = 1.177e-08
relative error = 0.001048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.522
Order of pole (three term test) = 6.954e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = -0.00110051045381 -0.000238629825302
y[1] (closed_form) = -0.00110049133807 -0.000238662292039
absolute error = 3.768e-08
relative error = 0.003346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.888
Order of pole (given) = 0 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) = 5.458e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.116 0.171
h = 0.0001 0.003
y[1] (numeric) = -0.00109877808456 -0.000245678157783
y[1] (closed_form) = -0.00109876891453 -0.000245696626034
absolute error = 2.062e-08
relative error = 0.001831 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.888
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.333
Order of pole (three term test) = 1.259e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1161 0.174
h = 0.001 0.001
y[1] (numeric) = -0.00109776814323 -0.000249905206027
y[1] (closed_form) = -0.00109776542022 -0.000249925524443
absolute error = 2.050e-08
relative error = 0.001821 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.888
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.832
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1171 0.175
h = 0.001 0.003
y[1] (numeric) = -0.00109877571127 -0.000251687791215
y[1] (closed_form) = -0.00109877645179 -0.000251707947684
absolute error = 2.017e-08
relative error = 0.001789 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.691
Order of pole (three term test) = 1.803e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = -0.00109900831865 -0.000256270793509
y[1] (closed_form) = -0.00109900197297 -0.000256290978497
absolute error = 2.116e-08
relative error = 0.001875 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.886
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.917
Order of pole (three term test) = 1.229e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1182 0.182
h = 0.003 0.006
y[1] (numeric) = -0.00109755712049 -0.000261900440846
y[1] (closed_form) = -0.00109754768134 -0.000261915441586
absolute error = 1.772e-08
relative error = 0.001571 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.886
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.515
Order of pole (three term test) = 1.048e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=129.7MB, alloc=44.3MB, time=1.64
x[1] = 2.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = -0.00109929533058 -0.000271482420425
y[1] (closed_form) = -0.00109927377946 -0.000271521022232
absolute error = 4.421e-08
relative error = 0.003904 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.895
Order of pole (three term test) = 7.432e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = -0.00109730900609 -0.00027851341988
y[1] (closed_form) = -0.00109729803422 -0.000278538327599
absolute error = 2.722e-08
relative error = 0.002404 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.331
Order of pole (three term test) = 1.187e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1214 0.196
h = 0.001 0.001
y[1] (numeric) = -0.00109614701182 -0.000282730906222
y[1] (closed_form) = -0.00109614245666 -0.00028275793689
absolute error = 2.741e-08
relative error = 0.002421 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.884
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.83
Order of pole (three term test) = 6.716e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = -0.00109709902165 -0.00028455894232
y[1] (closed_form) = -0.00109709796032 -0.000284585949664
absolute error = 2.703e-08
relative error = 0.002385 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.99
Order of pole (three term test) = 1.083e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1225 0.201
h = 0.003 0.006
y[1] (numeric) = -0.00109548171459 -0.000290175210509
y[1] (closed_form) = -0.00109546918392 -0.000290193945988
absolute error = 2.254e-08
relative error = 0.001989 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.509
Order of pole (three term test) = 1.495e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = -0.00109694270661 -0.000299854426401
y[1] (closed_form) = -0.00109691717689 -0.000299896469877
absolute error = 4.919e-08
relative error = 0.004325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.893
Order of pole (three term test) = 7.192e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = -0.00109473731864 -0.000306859162916
y[1] (closed_form) = -0.00109472290206 -0.000306887807022
absolute error = 3.207e-08
relative error = 0.002821 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.329
Order of pole (three term test) = 1.151e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1257 0.215
h = 0.001 0.001
y[1] (numeric) = -0.00109344413215 -0.000311061632654
y[1] (closed_form) = -0.00109343609266 -0.000311092634505
absolute error = 3.203e-08
relative error = 0.002817 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.828
Order of pole (three term test) = 1.086e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1267 0.216
h = 0.001 0.003
y[1] (numeric) = -0.00109434603734 -0.000312926547217
y[1] (closed_form) = -0.00109434151112 -0.0003129576473
absolute error = 3.143e-08
relative error = 0.002761 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.674
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = -0.00109428421391 -0.000317568660723
y[1] (closed_form) = -0.00109427252278 -0.000317599253544
absolute error = 3.275e-08
relative error = 0.002874 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.907
Order of pole (three term test) = 3.819e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=175.6MB, alloc=44.3MB, time=2.20
x[1] = 2.1278 0.223
h = 0.003 0.006
y[1] (numeric) = -0.00109245462512 -0.000323158078206
y[1] (closed_form) = -0.00109244019963 -0.000323183197094
absolute error = 2.897e-08
relative error = 0.002543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.503
Order of pole (three term test) = 1.072e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = -0.00109358884295 -0.000332943345384
y[1] (closed_form) = -0.0010935603904 -0.000332991399375
absolute error = 5.585e-08
relative error = 0.004885 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.89
Order of pole (three term test) = 4.898e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = -0.00109112808635 -0.000339911338458
y[1] (closed_form) = -0.00109111136159 -0.000339946355962
absolute error = 3.881e-08
relative error = 0.003396 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 0 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) = 7.762e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.131 0.237
h = 0.001 0.001
y[1] (numeric) = -0.00108968195243 -0.000344092637519
y[1] (closed_form) = -0.00108967155047 -0.000344130286118
absolute error = 3.906e-08
relative error = 0.003418 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.826
Order of pole (three term test) = 3.138e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.132 0.238
h = 0.001 0.003
y[1] (numeric) = -0.00109052427057 -0.000345999280135
y[1] (closed_form) = -0.00109051740051 -0.000346037169833
absolute error = 3.851e-08
relative error = 0.003366 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.665
Order of pole (three term test) = 9.420e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.133 0.241
h = 0.0001 0.004
y[1] (numeric) = -0.00109030112009 -0.000350665300346
y[1] (closed_form) = -0.00109028705962 -0.000350702389349
absolute error = 3.966e-08
relative error = 0.003463 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.902
Order of pole (three term test) = 8.228e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1331 0.245
h = 0.003 0.006
y[1] (numeric) = -0.00108826743051 -0.000356222417255
y[1] (closed_form) = -0.00108825083998 -0.000356253886615
absolute error = 3.557e-08
relative error = 0.003107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.496
Order of pole (three term test) = 4.623e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = -0.00108906847162 -0.000366101195196
y[1] (closed_form) = -0.00108903683585 -0.000366155176455
absolute error = 6.257e-08
relative error = 0.005446 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.887
Order of pole (three term test) = 6.678e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = -0.00108635220424 -0.000373021861173
y[1] (closed_form) = -0.00108633289848 -0.00037306319992
absolute error = 4.562e-08
relative error = 0.003972 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.324
Order of pole (three term test) = 6.416e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=221.6MB, alloc=44.3MB, time=2.77
x[1] = 2.1363 0.259
h = 0.001 0.001
y[1] (numeric) = -0.00108475301108 -0.000377175658717
y[1] (closed_form) = -0.00108473996077 -0.000377219901338
absolute error = 4.613e-08
relative error = 0.004016 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.824
Order of pole (three term test) = 2.422e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1373 0.26
h = 0.001 0.003
y[1] (numeric) = -0.00108553367499 -0.000379121878705
y[1] (closed_form) = -0.00108552416872 -0.000379166507166
absolute error = 4.563e-08
relative error = 0.003968 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.657
Order of pole (three term test) = 2.796e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = -0.00108514720902 -0.000383805417643
y[1] (closed_form) = -0.00108513050028 -0.000383848948717
absolute error = 4.663e-08
relative error = 0.004051 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.898
Order of pole (three term test) = 3.550e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1384 0.267
h = 0.003 0.006
y[1] (numeric) = -0.00108290944712 -0.000389321755646
y[1] (closed_form) = -0.00108289042081 -0.000389359529817
absolute error = 4.230e-08
relative error = 0.003675 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.49
Order of pole (three term test) = 4.461e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = -0.00108337144452 -0.000399281117853
y[1] (closed_form) = -0.00108333636732 -0.000399340930532
absolute error = 6.934e-08
relative error = 0.006006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.884
Order of pole (three term test) = 6.446e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = -0.00108040001425 -0.000406143791994
y[1] (closed_form) = -0.00108037785516 -0.000406191386817
absolute error = 5.250e-08
relative error = 0.004549 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.322
Order of pole (three term test) = 2.065e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1416 0.281
h = 0.001 0.001
y[1] (numeric) = -0.00107864794292 -0.00041026370779
y[1] (closed_form) = -0.00107863195881 -0.000410314478007
absolute error = 5.323e-08
relative error = 0.004612 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.823
Order of pole (three term test) = 6.821e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1426 0.282
h = 0.001 0.003
y[1] (numeric) = -0.00107936497081 -0.000412247243606
y[1] (closed_form) = -0.00107935253623 -0.000412298545958
absolute error = 5.279e-08
relative error = 0.004569 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.648
Order of pole (three term test) = 5.400e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = -0.00107881348352 -0.000416941776561
y[1] (closed_form) = -0.00107879384811 -0.00041699168225
absolute error = 5.363e-08
relative error = 0.004637 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.893
Order of pole (three term test) = 6.858e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=267.7MB, alloc=44.3MB, time=3.34
x[1] = 2.1437 0.289
h = 0.003 0.006
y[1] (numeric) = -0.00107637207152 -0.000422408800047
y[1] (closed_form) = -0.00107635033884 -0.000422452820515
absolute error = 4.909e-08
relative error = 0.004246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.483
Order of pole (three term test) = 4.310e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = -0.00107648971804 -0.000432435459044
y[1] (closed_form) = -0.00107645094408 -0.000432500994718
absolute error = 7.615e-08
relative error = 0.006564 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.881
Order of pole (three term test) = 1.322e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = -0.00107326397083 -0.000439229420527
y[1] (closed_form) = -0.00107323868721 -0.000439283193173
absolute error = 5.942e-08
relative error = 0.005124 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.32
Order of pole (three term test) = 2.232e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1469 0.303
h = 0.001 0.001
y[1] (numeric) = -0.00107135950009 -0.000443309039888
y[1] (closed_form) = -0.00107134029781 -0.000443366257493
absolute error = 6.035e-08
relative error = 0.005205 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.821
Order of pole (three term test) = 3.768e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = -0.00107201100197 -0.00044532752276
y[1] (closed_form) = -0.00107199534797 -0.000445385420011
absolute error = 5.998e-08
relative error = 0.005167 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.93
Order of pole (three term test) = 9.116e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.148 0.308
h = 0.003 0.006
y[1] (numeric) = -0.00106940373035 -0.000450747535338
y[1] (closed_form) = -0.00106937811005 -0.000450794734268
absolute error = 5.370e-08
relative error = 0.004628 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.479
Order of pole (three term test) = 9.387e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.151 0.314
h = 0.0001 0.005
y[1] (numeric) = -0.00106922058565 -0.000460817047856
y[1] (closed_form) = -0.0010691770929 -0.000460885260412
absolute error = 8.090e-08
relative error = 0.006948 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.862
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.879
Order of pole (three term test) = 6.786e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = -0.00106577798627 -0.00046754024864
y[1] (closed_form) = -0.00106574845654 -0.000467597119891
absolute error = 6.408e-08
relative error = 0.005506 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.862
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.318
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1512 0.322
h = 0.001 0.001
y[1] (numeric) = -0.00106374353311 -0.000471578228466
y[1] (closed_form) = -0.00106371999044 -0.000471638773278
absolute error = 6.496e-08
relative error = 0.005583 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.862
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.82
Order of pole (three term test) = 9.182e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1522 0.323
h = 0.001 0.003
y[1] (numeric) = -0.00106433681772 -0.000473624007501
y[1] (closed_form) = -0.00106431681495 -0.000473685359514
absolute error = 6.453e-08
relative error = 0.005539 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.634
Order of pole (three term test) = 1.799e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=313.7MB, alloc=44.3MB, time=3.90
x[1] = 2.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = -0.00106347478815 -0.000478319221473
y[1] (closed_form) = -0.00106344762843 -0.000478378615884
absolute error = 6.531e-08
relative error = 0.005601 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.885
Order of pole (three term test) = 4.806e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1533 0.33
h = 0.003 0.006
y[1] (numeric) = -0.001060657756 -0.000483669257205
y[1] (closed_form) = -0.00106062892958 -0.000483722555866
absolute error = 6.059e-08
relative error = 0.005198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.473
Order of pole (three term test) = 3.577e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = -0.00106012212004 -0.000493780426706
y[1] (closed_form) = -0.00106007446698 -0.000493854124359
absolute error = 8.776e-08
relative error = 0.007504 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.876
Order of pole (three term test) = 2.939e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = -0.00105642825294 -0.000500414929361
y[1] (closed_form) = -0.00105639510081 -0.000500477794729
absolute error = 7.107e-08
relative error = 0.00608 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.859
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.316
Order of pole (three term test) = 9.424e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1565 0.344
h = 0.001 0.001
y[1] (numeric) = -0.00105424317308 -0.000504400651837
y[1] (closed_form) = -0.00105421588999 -0.000504467454662
absolute error = 7.216e-08
relative error = 0.006174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.859
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.818
Order of pole (three term test) = 8.897e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1575 0.345
h = 0.001 0.003
y[1] (numeric) = -0.00105476771168 -0.00050647667926
y[1] (closed_form) = -0.00105474395434 -0.00050654443805
absolute error = 7.180e-08
relative error = 0.006137 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.627
Order of pole (three term test) = 6.165e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = -0.00105373750335 -0.000511163583937
y[1] (closed_form) = -0.00105370663105 -0.000511229082548
absolute error = 7.241e-08
relative error = 0.006183 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.881
Order of pole (three term test) = 1.401e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1586 0.352
h = 0.003 0.006
y[1] (numeric) = -0.00105072035414 -0.000516439774219
y[1] (closed_form) = -0.00105068805531 -0.000516499076972
absolute error = 6.753e-08
relative error = 0.005768 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.467
Order of pole (three term test) = 5.572e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = -0.00104982864686 -0.000526578440261
y[1] (closed_form) = -0.00104977659022 -0.000526657479176
absolute error = 9.464e-08
relative error = 0.008058 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.874
Order of pole (three term test) = 1.203e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=359.6MB, alloc=44.3MB, time=4.47
x[1] = 2.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = -0.00104588581375 -0.000533113513383
y[1] (closed_form) = -0.00104584877534 -0.000533182257151
absolute error = 7.809e-08
relative error = 0.006652 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.314
Order of pole (three term test) = 9.321e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1618 0.366
h = 0.001 0.001
y[1] (numeric) = -0.00104355145624 -0.000537040554765
y[1] (closed_form) = -0.00104352015583 -0.000537113495911
absolute error = 7.937e-08
relative error = 0.006763 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.856
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.817
Order of pole (three term test) = 1.221e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1628 0.367
h = 0.001 0.003
y[1] (numeric) = -0.00104400565663 -0.000539144180001
y[1] (closed_form) = -0.0010439778608 -0.000539218226075
absolute error = 7.909e-08
relative error = 0.006731 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.619
Order of pole (three term test) = 3.588e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = -0.00104280673601 -0.000543815861216
y[1] (closed_form) = -0.0010427718816 -0.000543887344746
absolute error = 7.953e-08
relative error = 0.006762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.876
Order of pole (three term test) = 6.080e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1639 0.374
h = 0.003 0.006
y[1] (numeric) = -0.00103959145732 -0.000549009647709
y[1] (closed_form) = -0.00103955542259 -0.000549074845924
absolute error = 7.449e-08
relative error = 0.006336 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.462
Order of pole (three term test) = 3.824e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = -0.00103834073912 -0.000559161400116
y[1] (closed_form) = -0.00103828404111 -0.000559245624367
absolute error = 1.015e-07
relative error = 0.008609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.872
Order of pole (three term test) = 6.188e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.167 0.385
h = 0.0001 0.003
y[1] (numeric) = -0.00103415175672 -0.000565586358287
y[1] (closed_form) = -0.00103411057199 -0.000565660851739
absolute error = 8.512e-08
relative error = 0.007221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.312
Order of pole (three term test) = 1.795e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1671 0.388
h = 0.001 0.001
y[1] (numeric) = -0.0010316697785 -0.000569448321344
y[1] (closed_form) = -0.00103163418786 -0.00056952726741
absolute error = 8.660e-08
relative error = 0.007349 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.815
Order of pole (three term test) = 9.373e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1681 0.389
h = 0.001 0.003
y[1] (numeric) = -0.00103205216338 -0.00057157680438
y[1] (closed_form) = -0.00103202004905 -0.000571657004172
absolute error = 8.639e-08
relative error = 0.007323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.612
Order of pole (three term test) = 1.251e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=405.6MB, alloc=44.3MB, time=5.05
x[1] = 2.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = -0.00103068431723 -0.000576226283857
y[1] (closed_form) = -0.00103064521517 -0.000576303619708
absolute error = 8.666e-08
relative error = 0.007339 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.873
Order of pole (three term test) = 5.907e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1692 0.396
h = 0.003 0.006
y[1] (numeric) = -0.00102727330809 -0.00058132915313
y[1] (closed_form) = -0.00102723327746 -0.000581400125244
absolute error = 8.148e-08
relative error = 0.006903 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.457
Order of pole (three term test) = 1.895e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = -0.00102566129697 -0.000591479364126
y[1] (closed_form) = -0.00102559972594 -0.00059156860592
absolute error = 1.084e-07
relative error = 0.009157 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.869
Order of pole (three term test) = 2.690e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = -0.00102122949772 -0.000597783595322
y[1] (closed_form) = -0.00102118391123 -0.000597863696868
absolute error = 9.216e-08
relative error = 0.007789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.31
Order of pole (three term test) = 2.590e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1724 0.41
h = 0.001 0.001
y[1] (numeric) = -0.00101860186417 -0.000601574125716
y[1] (closed_form) = -0.00101856171513 -0.000601658929718
absolute error = 9.383e-08
relative error = 0.007931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.814
Order of pole (three term test) = 1.337e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = -0.00101891107651 -0.000603724642611
y[1] (closed_form) = -0.0010188743684 -0.000603810848595
absolute error = 9.370e-08
relative error = 0.007911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.89
Order of pole (three term test) = 1.411e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1735 0.415
h = 0.003 0.006
y[1] (numeric) = -0.00101534222556 -0.000608746583386
y[1] (closed_form) = -0.00101529762898 -0.000608819988472
absolute error = 8.589e-08
relative error = 0.007255 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.453
Order of pole (three term test) = 7.275e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = -0.00101341817051 -0.000618879284342
y[1] (closed_form) = -0.00101335131295 -0.000618970262036
absolute error = 1.129e-07
relative error = 0.009508 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.868
Order of pole (three term test) = 5.268e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = -0.00100878203253 -0.000625068347558
y[1] (closed_form) = -0.00100873153748 -0.000625150718669
absolute error = 9.662e-08
relative error = 0.008141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.309
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1767 0.429
h = 0.001 0.001
y[1] (numeric) = -0.00100603178545 -0.000628790650185
y[1] (closed_form) = -0.00100598658015 -0.000628877931885
absolute error = 9.829e-08
relative error = 0.008285 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 0 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) = 8.025e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=451.6MB, alloc=44.3MB, time=5.61
x[1] = 2.1777 0.43
h = 0.001 0.003
y[1] (numeric) = -0.00100627680701 -0.000630956920703
y[1] (closed_form) = -0.00100623500472 -0.000631045730741
absolute error = 9.816e-08
relative error = 0.008264 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.601
Order of pole (three term test) = 2.238e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = -0.0010045956434 -0.000635544361373
y[1] (closed_form) = -0.00100454702728 -0.000635629753108
absolute error = 9.826e-08
relative error = 0.008266 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.866
Order of pole (three term test) = 1.126e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1788 0.437
h = 0.003 0.006
y[1] (numeric) = -0.00100082953831 -0.000640453396521
y[1] (closed_form) = -0.00100078047552 -0.000640532312292
absolute error = 9.292e-08
relative error = 0.00782 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.448
Order of pole (three term test) = 5.010e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = -0.000998541924385 -0.000650556865078
y[1] (closed_form) = -0.000998469783637 -0.000650652514878
absolute error = 1.198e-07
relative error = 0.01005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.866
Order of pole (three term test) = 7.697e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = -0.000993670662069 -0.000656605799032
y[1] (closed_form) = -0.000993615306529 -0.00065669347821
absolute error = 1.037e-07
relative error = 0.008706 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.307
Order of pole (three term test) = 1.647e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.182 0.451
h = 0.001 0.001
y[1] (numeric) = -0.000990779308962 -0.000660245047851
y[1] (closed_form) = -0.000990729063556 -0.000660337875422
absolute error = 1.056e-07
relative error = 0.008865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.845
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.811
Order of pole (three term test) = 9.076e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.183 0.452
h = 0.001 0.003
y[1] (numeric) = -0.000990949006042 -0.000662427881916
y[1] (closed_form) = -0.00099090211502 -0.00066252238398
absolute error = 1.055e-07
relative error = 0.00885 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.595
Order of pole (three term test) = 1.079e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.184 0.455
h = 0.0001 0.004
y[1] (numeric) = -0.000989100203522 -0.000666972963449
y[1] (closed_form) = -0.000989046610873 -0.00066706375302
absolute error = 1.054e-07
relative error = 0.008837 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.863
Order of pole (three term test) = 1.669e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1841 0.459
h = 0.003 0.006
y[1] (numeric) = -0.00098514759654 -0.000671767216362
y[1] (closed_form) = -0.000985093821552 -0.000671851485022
absolute error = 9.996e-08
relative error = 0.008384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.444
Order of pole (three term test) = 4.885e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=497.8MB, alloc=44.3MB, time=6.18
x[1] = 2.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = -0.000982496102692 -0.000681826398499
y[1] (closed_form) = -0.000982418468369 -0.000681926520345
absolute error = 1.267e-07
relative error = 0.01059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.864
Order of pole (three term test) = 5.596e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = -0.000977394511632 -0.000687724960105
y[1] (closed_form) = -0.000977334057232 -0.000687817770058
absolute error = 1.108e-07
relative error = 0.009268 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.306
Order of pole (three term test) = 1.136e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1873 0.473
h = 0.001 0.001
y[1] (numeric) = -0.000974364893015 -0.000691275018464
y[1] (closed_form) = -0.000974309357156 -0.00069137320724
absolute error = 1.128e-07
relative error = 0.009442 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.81
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1883 0.474
h = 0.001 0.003
y[1] (numeric) = -0.000974458280617 -0.000693471387144
y[1] (closed_form) = -0.000974406043428 -0.000693571394937
absolute error = 1.128e-07
relative error = 0.009434 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.589
Order of pole (three term test) = 1.053e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = -0.000972442903834 -0.000697967045915
y[1] (closed_form) = -0.000972384091552 -0.000698063050988
absolute error = 1.126e-07
relative error = 0.009406 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.859
Order of pole (three term test) = 1.197e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1894 0.481
h = 0.003 0.006
y[1] (numeric) = -0.000968307770288 -0.000702638388263
y[1] (closed_form) = -0.000968249043275 -0.00070272783971
absolute error = 1.070e-07
relative error = 0.008944 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.439
Order of pole (three term test) = 5.395e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = -0.000965292781447 -0.000712638146971
y[1] (closed_form) = -0.000965209451752 -0.000712742530173
absolute error = 1.336e-07
relative error = 0.01113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.862
Order of pole (three term test) = 8.811e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = -0.000959966160313 -0.000718376273456
y[1] (closed_form) = -0.00095990037594 -0.000718474024887
absolute error = 1.178e-07
relative error = 0.009827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.304
Order of pole (three term test) = 7.850e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1926 0.495
h = 0.001 0.001
y[1] (numeric) = -0.000956801417685 -0.000721831111473
y[1] (closed_form) = -0.000956740348609 -0.00072193446412
absolute error = 1.200e-07
relative error = 0.01002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.809
Order of pole (three term test) = 1.659e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1936 0.496
h = 0.001 0.003
y[1] (numeric) = -0.000956817648974 -0.000724037926365
y[1] (closed_form) = -0.000956759815818 -0.000724143240539
absolute error = 1.201e-07
relative error = 0.01001 %
Correct digits = 4
memory used=544.0MB, alloc=44.3MB, time=6.76
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.583
Order of pole (three term test) = 1.455e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = -0.000954637099481 -0.000728477118165
y[1] (closed_form) = -0.000954572831957 -0.00072857814413
absolute error = 1.197e-07
relative error = 0.009971 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.838
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.856
Order of pole (three term test) = 2.630e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1947 0.503
h = 0.003 0.006
y[1] (numeric) = -0.000950323814213 -0.000733017573783
y[1] (closed_form) = -0.000950259902217 -0.000733112025869
absolute error = 1.140e-07
relative error = 0.009502 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.838
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.435
Order of pole (three term test) = 2.307e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = -0.00094694642906 -0.000742942726033
y[1] (closed_form) = -0.000946857211382 -0.000743051149684
absolute error = 1.404e-07
relative error = 0.01167 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.86
Order of pole (three term test) = 1.443e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = -0.000941400572398 -0.000748510562431
y[1] (closed_form) = -0.00094132923486 -0.00074861305437
absolute error = 1.249e-07
relative error = 0.01038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.303
Order of pole (three term test) = 1.086e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1979 0.517
h = 0.001 0.001
y[1] (numeric) = -0.000938104143969 -0.000751864273432
y[1] (closed_form) = -0.000938037307206 -0.000751972580285
absolute error = 1.273e-07
relative error = 0.01059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0 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) = 7.257e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = -0.000938042514048 -0.000754078393704
y[1] (closed_form) = -0.000937978843496 -0.0007541888022
absolute error = 1.275e-07
relative error = 0.01059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.85
Order of pole (three term test) = 1.923e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.199 0.522
h = 0.003 0.006
y[1] (numeric) = -0.000933587278694 -0.000758505738661
y[1] (closed_form) = -0.000933518289827 -0.000758601718251
absolute error = 1.182e-07
relative error = 0.009826 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.432
Order of pole (three term test) = 1.169e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.202 0.528
h = 0.0001 0.005
y[1] (numeric) = -0.000929900518747 -0.000768350220948
y[1] (closed_form) = -0.000929805665121 -0.000768459308391
absolute error = 1.446e-07
relative error = 0.01198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.859
Order of pole (three term test) = 3.674e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = -0.000924173147493 -0.000773761255918
y[1] (closed_form) = -0.00092409642818 -0.000773865032499
absolute error = 1.291e-07
relative error = 0.01071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0 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) = 3.023e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=589.9MB, alloc=44.3MB, time=7.32
x[1] = 2.2022 0.536
h = 0.001 0.001
y[1] (numeric) = -0.000920767641976 -0.00077702178883
y[1] (closed_form) = -0.000920695227676 -0.000777131554093
absolute error = 1.315e-07
relative error = 0.01091 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.807
Order of pole (three term test) = 1.429e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2032 0.537
h = 0.001 0.003
y[1] (numeric) = -0.000920638502858 -0.000779238711393
y[1] (closed_form) = -0.000920569187643 -0.000779350695757
absolute error = 1.317e-07
relative error = 0.01092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.574
Order of pole (three term test) = 9.907e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = -0.000918156359724 -0.000783552311792
y[1] (closed_form) = -0.000918080912324 -0.000783659494037
absolute error = 1.311e-07
relative error = 0.01086 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.851
Order of pole (three term test) = 2.521e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2043 0.544
h = 0.003 0.006
y[1] (numeric) = -0.000913526335717 -0.00078782661995
y[1] (closed_form) = -0.00091345175143 -0.000787927227702
absolute error = 1.252e-07
relative error = 0.01038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.429
Order of pole (three term test) = 6.354e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = -0.000909481321534 -0.000797568283789
y[1] (closed_form) = -0.000909380250818 -0.000797680972982
absolute error = 1.514e-07
relative error = 0.01251 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.857
Order of pole (three term test) = 6.519e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = -0.000903546895557 -0.00080279141937
y[1] (closed_form) = -0.000903464233786 -0.000802899530307
absolute error = 1.361e-07
relative error = 0.01126 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.301
Order of pole (three term test) = 9.086e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2075 0.558
h = 0.001 0.001
y[1] (numeric) = -0.000900016939063 -0.000805940266786
y[1] (closed_form) = -0.000899938348049 -0.000806054562133
absolute error = 1.387e-07
relative error = 0.01148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.806
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2085 0.559
h = 0.001 0.003
y[1] (numeric) = -0.000899809054691 -0.000808158531758
y[1] (closed_form) = -0.000899733480422 -0.00080827518078
absolute error = 1.390e-07
relative error = 0.01149 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.57
Order of pole (three term test) = 9.906e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = -0.000897167690657 -0.000812395811657
y[1] (closed_form) = -0.000897086164241 -0.000812507391027
absolute error = 1.382e-07
relative error = 0.01142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.849
Order of pole (three term test) = 1.261e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=636.0MB, alloc=44.3MB, time=7.89
x[1] = 2.2096 0.566
h = 0.003 0.006
y[1] (numeric) = -0.000892374262161 -0.000816517517304
y[1] (closed_form) = -0.000892293872908 -0.000816622538531
absolute error = 1.323e-07
relative error = 0.01093 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.425
Order of pole (three term test) = 9.348e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = -0.00088797415681 -0.000826141265954
y[1] (closed_form) = -0.00088786670586 -0.000826257309487
absolute error = 1.582e-07
relative error = 0.01304 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.856
Order of pole (three term test) = 3.198e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = -0.000881839831138 -0.000831167395919
y[1] (closed_form) = -0.000881751030045 -0.000831279609127
absolute error = 1.431e-07
relative error = 0.01181 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.299
Order of pole (three term test) = 7.998e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2128 0.58
h = 0.001 0.001
y[1] (numeric) = -0.000878189676202 -0.000834199095826
y[1] (closed_form) = -0.000878104701629 -0.00083431767873
absolute error = 1.459e-07
relative error = 0.01204 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.805
Order of pole (three term test) = 2.081e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2138 0.581
h = 0.001 0.003
y[1] (numeric) = -0.000877902765313 -0.000836415455291
y[1] (closed_form) = -0.000877820718532 -0.000836536522977
absolute error = 1.462e-07
relative error = 0.01206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.565
Order of pole (three term test) = 1.027e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = -0.000875104876834 -0.000840569618451
y[1] (closed_form) = -0.000875017071143 -0.000840685356621
absolute error = 1.453e-07
relative error = 0.01197 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.846
Order of pole (three term test) = 1.001e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2149 0.588
h = 0.003 0.006
y[1] (numeric) = -0.000870153887757 -0.000844531539556
y[1] (closed_form) = -0.00087006749335 -0.000844640748929
absolute error = 1.393e-07
relative error = 0.01148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.422
Order of pole (three term test) = 3.060e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = -0.00086540257705 -0.00085402237774
y[1] (closed_form) = -0.000865288593978 -0.000854141519916
absolute error = 1.649e-07
relative error = 0.01356 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.854
Order of pole (three term test) = 9.160e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.218 0.599
h = 0.0001 0.003
y[1] (numeric) = -0.000859075959062 -0.000858842705946
y[1] (closed_form) = -0.000858980832111 -0.000858958779307
absolute error = 1.501e-07
relative error = 0.01235 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.298
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2181 0.602
h = 0.001 0.001
y[1] (numeric) = -0.000855310129074 -0.000861751980669
y[1] (closed_form) = -0.000855218574947 -0.000861874598006
absolute error = 1.530e-07
relative error = 0.0126 %
Correct digits = 4
memory used=682.0MB, alloc=44.3MB, time=8.46
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 0 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) = 6.893e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2191 0.603
h = 0.001 0.003
y[1] (numeric) = -0.000854944062964 -0.00086396316368
y[1] (closed_form) = -0.000854855341225 -0.000864088393079
absolute error = 1.535e-07
relative error = 0.01263 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.561
Order of pole (three term test) = 1.009e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = -0.000851992675697 -0.000868027520893
y[1] (closed_form) = -0.00085189840112 -0.000868147169304
absolute error = 1.523e-07
relative error = 0.01252 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.844
Order of pole (three term test) = 4.773e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2202 0.61
h = 0.003 0.006
y[1] (numeric) = -0.000846890326573 -0.000871822730418
y[1] (closed_form) = -0.000846797736781 -0.000871935892418
absolute error = 1.462e-07
relative error = 0.01203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.419
Order of pole (three term test) = 8.510e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = -0.000841792416029 -0.000881165803068
y[1] (closed_form) = -0.000841671760666 -0.000881287780475
absolute error = 1.716e-07
relative error = 0.01408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.853
Order of pole (three term test) = 4.886e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = -0.000835281550377 -0.000885771868496
y[1] (closed_form) = -0.000835179921928 -0.000885891550376
absolute error = 1.570e-07
relative error = 0.0129 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.297
Order of pole (three term test) = 1.988e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2234 0.624
h = 0.001 0.001
y[1] (numeric) = -0.000831404830613 -0.00088855363967
y[1] (closed_form) = -0.000831306512389 -0.000888680028265
absolute error = 1.601e-07
relative error = 0.01316 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = -0.000830959634831 -0.000890756360293
y[1] (closed_form) = -0.000830864047327 -0.000890885484048
absolute error = 1.607e-07
relative error = 0.01319 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.83
Order of pole (three term test) = 1.288e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2245 0.629
h = 0.003 0.006
y[1] (numeric) = -0.000825738621257 -0.000894410056199
y[1] (closed_form) = -0.000825640652303 -0.000894523723738
absolute error = 1.501e-07
relative error = 0.01233 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.417
Order of pole (three term test) = 9.411e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = -0.00082034860031 -0.000903610136524
y[1] (closed_form) = -0.000820222210327 -0.00090373163245
absolute error = 1.753e-07
relative error = 0.01436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.852
Order of pole (three term test) = 3.057e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=728.1MB, alloc=44.3MB, time=9.02
x[1] = 2.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = -0.000813688586726 -0.000908023213562
y[1] (closed_form) = -0.000813581332341 -0.000908143089042
absolute error = 1.609e-07
relative error = 0.01319 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.297
Order of pole (three term test) = 1.556e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2277 0.643
h = 0.001 0.001
y[1] (numeric) = -0.000809722038483 -0.000910690091521
y[1] (closed_form) = -0.000809617859868 -0.000910816800907
absolute error = 1.640e-07
relative error = 0.01346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 6.583e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2287 0.644
h = 0.001 0.003
y[1] (numeric) = -0.000809209023847 -0.000912881952014
y[1] (closed_form) = -0.000809107482186 -0.000913011497597
absolute error = 1.646e-07
relative error = 0.01349 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.555
Order of pole (three term test) = 9.130e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = -0.000805982423023 -0.000916760110068
y[1] (closed_form) = -0.000805875747426 -0.000916883634275
absolute error = 1.632e-07
relative error = 0.01337 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.84
Order of pole (three term test) = 1.344e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2298 0.651
h = 0.003 0.006
y[1] (numeric) = -0.000800618267151 -0.000920226013878
y[1] (closed_form) = -0.000800513780354 -0.000920343168444
absolute error = 1.570e-07
relative error = 0.01287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.414
Order of pole (three term test) = 1.582e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = -0.0007948922829 -0.000929251267212
y[1] (closed_form) = -0.000794758995788 -0.00092937508847
absolute error = 1.819e-07
relative error = 0.01488 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.851
Order of pole (three term test) = 1.066e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = -0.000788064187002 -0.000933435419076
y[1] (closed_form) = -0.000787950138347 -0.00093355840967
absolute error = 1.677e-07
relative error = 0.01373 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 2.170e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.233 0.665
h = 0.001 0.001
y[1] (numeric) = -0.000783996370023 -0.00093596598742
y[1] (closed_form) = -0.000783885119723 -0.000936095951777
absolute error = 1.711e-07
relative error = 0.01401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 1.452e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.234 0.666
h = 0.001 0.003
y[1] (numeric) = -0.000783404726817 -0.00093814326401
y[1] (closed_form) = -0.000783296000769 -0.000938276178903
absolute error = 1.717e-07
relative error = 0.01405 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.552
Order of pole (three term test) = 9.006e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=774.3MB, alloc=44.3MB, time=9.59
x[1] = 2.235 0.669
h = 0.0001 0.004
y[1] (numeric) = -0.000780035128369 -0.000941913278281
y[1] (closed_form) = -0.000779921508637 -0.000942039948301
absolute error = 1.702e-07
relative error = 0.01391 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.838
Order of pole (three term test) = 7.254e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2351 0.673
h = 0.003 0.006
y[1] (numeric) = -0.000774539273965 -0.000945194322707
y[1] (closed_form) = -0.000774428110759 -0.000945314702623
absolute error = 1.639e-07
relative error = 0.01341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.412
Order of pole (three term test) = 9.959e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = -0.000768483950254 -0.000954030516207
y[1] (closed_form) = -0.000768343661718 -0.000954156380912
absolute error = 1.885e-07
relative error = 0.01538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.85
Order of pole (three term test) = 3.156e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = -0.000761496966017 -0.000957978375671
y[1] (closed_form) = -0.000761375981573 -0.000958104205831
absolute error = 1.746e-07
relative error = 0.01426 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.295
Order of pole (three term test) = 6.774e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2383 0.687
h = 0.001 0.001
y[1] (numeric) = -0.000757333354293 -0.000960368207003
y[1] (closed_form) = -0.000757214883664 -0.000960501137899
absolute error = 1.781e-07
relative error = 0.01456 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 6.413e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2393 0.688
h = 0.001 0.003
y[1] (numeric) = -0.000756663554292 -0.000962527618142
y[1] (closed_form) = -0.000756547489597 -0.000962663608779
absolute error = 1.788e-07
relative error = 0.0146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.549
Order of pole (three term test) = 1.885e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = -0.000753155199197 -0.000966183381326
y[1] (closed_form) = -0.000753034492082 -0.000966312914578
absolute error = 1.771e-07
relative error = 0.01445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 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) = 2.266e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2404 0.695
h = 0.003 0.006
y[1] (numeric) = -0.000747535091787 -0.000969273806082
y[1] (closed_form) = -0.000747417105616 -0.000969397141587
absolute error = 1.707e-07
relative error = 0.01394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.41
Order of pole (three term test) = 6.394e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = -0.000741157738406 -0.000977906994709
y[1] (closed_form) = -0.000741010357341 -0.000978034615745
absolute error = 1.950e-07
relative error = 0.01589 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.849
Order of pole (three term test) = 1.470e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = -0.000734021424763 -0.000981611617578
y[1] (closed_form) = -0.000733893375795 -0.00098174000455
absolute error = 1.813e-07
relative error = 0.01479 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.294
Order of pole (three term test) = 1.340e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=820.4MB, alloc=44.3MB, time=10.16
x[1] = 2.2436 0.709
h = 0.001 0.001
y[1] (numeric) = -0.000729767711118 -0.00098385653639
y[1] (closed_form) = -0.000729641884977 -0.000983992137785
absolute error = 1.850e-07
relative error = 0.0151 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 6.341e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2446 0.71
h = 0.001 0.003
y[1] (numeric) = -0.000729020382295 -0.00098599481748
y[1] (closed_form) = -0.000728896838417 -0.000986133582381
absolute error = 1.858e-07
relative error = 0.01515 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.546
Order of pole (three term test) = 9.833e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = -0.000725377807847 -0.000989530413189
y[1] (closed_form) = -0.000725249883259 -0.000989662519785
absolute error = 1.839e-07
relative error = 0.01499 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.835
Order of pole (three term test) = 5.012e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2457 0.717
h = 0.003 0.006
y[1] (numeric) = -0.000719641177733 -0.000992424801629
y[1] (closed_form) = -0.000719516234513 -0.000992550815498
absolute error = 1.775e-07
relative error = 0.01448 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.408
Order of pole (three term test) = 6.326e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = -0.000712949776272 -0.0010008413652
y[1] (closed_form) = -0.000712795225052 -0.00100097045092
absolute error = 2.014e-07
relative error = 0.01639 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.848
Order of pole (three term test) = 1.646e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = -0.000705674035139 -0.00100429625046
y[1] (closed_form) = -0.000705538806105 -0.00100442690496
absolute error = 1.880e-07
relative error = 0.01532 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.294
Order of pole (three term test) = 6.630e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2489 0.731
h = 0.001 0.001
y[1] (numeric) = -0.000701336118148 -0.00100639234519
y[1] (closed_form) = -0.000701202815204 -0.00100653031415
absolute error = 1.918e-07
relative error = 0.01564 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 7.321e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = -0.000700512044005 -0.00100850625694
y[1] (closed_form) = -0.000700380894585 -0.00100864748743
absolute error = 1.927e-07
relative error = 0.0157 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.81
Order of pole (three term test) = 7.692e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.25 0.736
h = 0.003 0.006
y[1] (numeric) = -0.000694686364436 -0.00101123638789
y[1] (closed_form) = -0.000694555976704 -0.00101136182373
absolute error = 1.809e-07
relative error = 0.01475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.407
Order of pole (three term test) = 8.895e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=866.5MB, alloc=44.3MB, time=10.73
x[1] = 2.253 0.742
h = 0.0001 0.005
y[1] (numeric) = -0.000687734327636 -0.00101945225659
y[1] (closed_form) = -0.000687574208962 -0.00101957970871
absolute error = 2.047e-07
relative error = 0.01664 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.848
Order of pole (three term test) = 1.476e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = -0.000680349817559 -0.00102268582811
y[1] (closed_form) = -0.000680208972484 -0.00102281553969
absolute error = 1.915e-07
relative error = 0.01559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 1.979e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2532 0.75
h = 0.001 0.001
y[1] (numeric) = -0.000675946122525 -0.00102464999378
y[1] (closed_form) = -0.000675806943097 -0.00102478709113
absolute error = 1.954e-07
relative error = 0.01591 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 6.346e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2542 0.751
h = 0.001 0.003
y[1] (numeric) = -0.000675057076041 -0.00102673946211
y[1] (closed_form) = -0.000674919934423 -0.00102687989897
absolute error = 1.963e-07
relative error = 0.01597 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.543
Order of pole (three term test) = 3.466e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = -0.000671179388445 -0.00103003496995
y[1] (closed_form) = -0.000671038380845 -0.0010301684108
absolute error = 1.941e-07
relative error = 0.01579 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 1.608e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = -0.000665249881855 -0.00103255024696
y[1] (closed_form) = -0.000665112325652 -0.00103267782647
absolute error = 1.876e-07
relative error = 0.01527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.821
Order of pole (three term test) = 7.839e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2554 0.762
h = 0.003 0.006
y[1] (numeric) = -0.000659314898608 -0.00103502024518
y[1] (closed_form) = -0.000659177342405 -0.00103514782469
absolute error = 1.876e-07
relative error = 0.01529 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.407
Order of pole (three term test) = 2.807e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = -0.000652024368669 -0.00104294154526
y[1] (closed_form) = -0.000651857009092 -0.00104306969312
absolute error = 2.108e-07
relative error = 0.01714 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.848
Order of pole (three term test) = 2.890e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = -0.000644509858715 -0.00104586490275
y[1] (closed_form) = -0.000644361644481 -0.00104599624578
absolute error = 1.980e-07
relative error = 0.01612 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 6.588e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=912.6MB, alloc=44.3MB, time=11.30
x[1] = 2.2586 0.776
h = 0.001 0.001
y[1] (numeric) = -0.000640027389287 -0.00104764407795
y[1] (closed_form) = -0.000639880479818 -0.00104778288041
absolute error = 2.021e-07
relative error = 0.01646 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 1.303e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2596 0.777
h = 0.001 0.003
y[1] (numeric) = -0.000639051884687 -0.00104969495995
y[1] (closed_form) = -0.000638906848529 -0.00104983719762
absolute error = 2.031e-07
relative error = 0.01653 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.542
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = -0.00063503960429 -0.00105282633866
y[1] (closed_form) = -0.000634891046505 -0.00105296139948
absolute error = 2.008e-07
relative error = 0.01633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 2.207e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2607 0.784
h = 0.003 0.006
y[1] (numeric) = -0.000629009813766 -0.00105509237576
y[1] (closed_form) = -0.000628864988758 -0.0010552217495
absolute error = 1.942e-07
relative error = 0.01581 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.405
Order of pole (three term test) = 2.788e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = -0.000621433976797 -0.00106275858683
y[1] (closed_form) = -0.000621259311165 -0.00106288729287
absolute error = 2.170e-07
relative error = 0.01762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.847
Order of pole (three term test) = 2.030e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = -0.000613812167392 -0.00106541591782
y[1] (closed_form) = -0.000613656521868 -0.00106554861478
absolute error = 2.045e-07
relative error = 0.01663 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 6.546e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2639 0.798
h = 0.001 0.001
y[1] (numeric) = -0.000609264643972 -0.00106703644808
y[1] (closed_form) = -0.000609109994238 -0.00106717666116
absolute error = 2.087e-07
relative error = 0.01699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 6.202e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2649 0.799
h = 0.001 0.003
y[1] (numeric) = -0.000608215859026 -0.00106905343842
y[1] (closed_form) = -0.000608062940715 -0.00106919716554
absolute error = 2.099e-07
relative error = 0.01706 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.541
Order of pole (three term test) = 8.605e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = -0.000604090693854 -0.0010720433241
y[1] (closed_form) = -0.000603934550605 -0.00107217972602
absolute error = 2.073e-07
relative error = 0.01685 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 3.103e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.266 0.806
h = 0.003 0.006
y[1] (numeric) = -0.000597978253134 -0.00107409569863
y[1] (closed_form) = -0.000597826079621 -0.00107422656682
absolute error = 2.007e-07
relative error = 0.01633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.404
Order of pole (three term test) = 3.920e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=958.6MB, alloc=44.3MB, time=11.86
x[1] = 2.269 0.812
h = 0.0001 0.005
y[1] (numeric) = -0.000590127588833 -0.00108149489728
y[1] (closed_form) = -0.000589945596043 -0.00108162385964
absolute error = 2.231e-07
relative error = 0.0181 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.847
Order of pole (three term test) = 5.712e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = -0.00058240949324 -0.00108388167696
y[1] (closed_form) = -0.000582246357558 -0.00108401542018
absolute error = 2.110e-07
relative error = 0.01714 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 6.513e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2692 0.82
h = 0.001 0.001
y[1] (numeric) = -0.000577803482196 -0.00108534082834
y[1] (closed_form) = -0.000577641030607 -0.00108548212972
absolute error = 2.153e-07
relative error = 0.01751 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 2.225e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2702 0.821
h = 0.001 0.003
y[1] (numeric) = -0.000576682807888 -0.00108732088068
y[1] (closed_form) = -0.000576521942086 -0.00108746576821
absolute error = 2.165e-07
relative error = 0.01759 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.54
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = -0.00057245060661 -0.00109016456134
y[1] (closed_form) = -0.000572286819615 -0.00109030198937
absolute error = 2.138e-07
relative error = 0.01736 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.832
Order of pole (three term test) = 2.442e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2713 0.828
h = 0.003 0.006
y[1] (numeric) = -0.000566264368773 -0.00109199981106
y[1] (closed_form) = -0.000566104781206 -0.00109213186994
absolute error = 2.071e-07
relative error = 0.01684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.404
Order of pole (three term test) = 8.917e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = -0.000558149923347 -0.00109912056922
y[1] (closed_form) = -0.000557960596556 -0.00109924948522
absolute error = 2.291e-07
relative error = 0.01858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 2.021e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = -0.00055034676975 -0.00110123279514
y[1] (closed_form) = -0.000550176099618 -0.0011013672741
absolute error = 2.173e-07
relative error = 0.01765 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 1.451e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2745 0.842
h = 0.001 0.001
y[1] (numeric) = -0.000545688966895 -0.00110252814508
y[1] (closed_form) = -0.000545518667219 -0.00110267020947
absolute error = 2.218e-07
relative error = 0.01803 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 6.149e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1004.8MB, alloc=44.3MB, time=12.44
x[1] = 2.2755 0.843
h = 0.001 0.003
y[1] (numeric) = -0.000544497938554 -0.00110446827915
y[1] (closed_form) = -0.000544329075636 -0.00110461399487
absolute error = 2.230e-07
relative error = 0.01811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.539
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = -0.000540164772973 -0.00110716132041
y[1] (closed_form) = -0.000539993298914 -0.00110729945677
absolute error = 2.202e-07
relative error = 0.01787 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.831
Order of pole (three term test) = 4.867e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2766 0.85
h = 0.003 0.006
y[1] (numeric) = -0.000533913754347 -0.00110877640329
y[1] (closed_form) = -0.000533746701545 -0.00110890934595
absolute error = 2.135e-07
relative error = 0.01735 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.403
Order of pole (three term test) = 9.919e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = -0.000525547113998 -0.00111560781836
y[1] (closed_form) = -0.000525350460653 -0.00111573638525
absolute error = 2.350e-07
relative error = 0.01905 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = -0.000517670317561 -0.00111744202173
y[1] (closed_form) = -0.000517492083412 -0.00111757692387
absolute error = 2.235e-07
relative error = 0.01815 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 1.309e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2798 0.864
h = 0.001 0.001
y[1] (numeric) = -0.000512967531502 -0.00111857146585
y[1] (closed_form) = -0.000512789353018 -0.00111871396581
absolute error = 2.282e-07
relative error = 0.01854 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.799
Order of pole (three term test) = 8.675e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = -0.00051170782522 -0.00112046877516
y[1] (closed_form) = -0.000511530931448 -0.00112061498454
absolute error = 2.295e-07
relative error = 0.01863 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 1.189e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2809 0.869
h = 0.003 0.006
y[1] (numeric) = -0.000505410971854 -0.00112190176159
y[1] (closed_form) = -0.000505238746923 -0.00112203279158
absolute error = 2.164e-07
relative error = 0.01759 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.403
Order of pole (three term test) = 2.753e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = -0.000496840532927 -0.00112847300471
y[1] (closed_form) = -0.000496638888134 -0.00112859860606
absolute error = 2.376e-07
relative error = 0.01927 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 5.679e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.284 0.88
h = 0.0001 0.003
y[1] (numeric) = -0.000488912967728 -0.00113006484316
y[1] (closed_form) = -0.000488729499506 -0.00113019743173
absolute error = 2.264e-07
relative error = 0.01838 %
Correct digits = 4
memory used=1050.8MB, alloc=44.3MB, time=13.00
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 6.497e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2841 0.883
h = 0.001 0.001
y[1] (numeric) = -0.000484178991665 -0.00113104961949
y[1] (closed_form) = -0.000483995307927 -0.00113118980081
absolute error = 2.311e-07
relative error = 0.01878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.799
Order of pole (three term test) = 1.347e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2851 0.884
h = 0.001 0.003
y[1] (numeric) = -0.000482862172103 -0.00113290701267
y[1] (closed_form) = -0.000482679639496 -0.00113305094577
absolute error = 2.325e-07
relative error = 0.01887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.539
Order of pole (three term test) = 1.705e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = -0.000478359902982 -0.00113530792373
y[1] (closed_form) = -0.000478175351298 -0.00113544409775
absolute error = 2.294e-07
relative error = 0.01862 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.831
Order of pole (three term test) = 7.844e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2862 0.891
h = 0.003 0.006
y[1] (numeric) = -0.000472015492907 -0.00113650619278
y[1] (closed_form) = -0.000471835750002 -0.00113663752935
absolute error = 2.226e-07
relative error = 0.01809 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.403
Order of pole (three term test) = 9.919e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = -0.000463215871159 -0.0011427694525
y[1] (closed_form) = -0.000463006955185 -0.00114289414434
absolute error = 2.433e-07
relative error = 0.01973 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 4.014e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = -0.000455236329302 -0.00114407840588
y[1] (closed_form) = -0.000455045285295 -0.00114421083331
absolute error = 2.325e-07
relative error = 0.01888 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 6.480e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2894 0.905
h = 0.001 0.001
y[1] (numeric) = -0.000450470296716 -0.00114489431008
y[1] (closed_form) = -0.000450278722555 -0.00114503431488
absolute error = 2.373e-07
relative error = 0.01929 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.799
Order of pole (three term test) = 7.499e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2904 0.906
h = 0.001 0.003
y[1] (numeric) = -0.000449088310758 -0.0011467037156
y[1] (closed_form) = -0.000448897731169 -0.00114684751664
absolute error = 2.387e-07
relative error = 0.01939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.539
Order of pole (three term test) = 8.695e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = -0.00044450358422 -0.0011489430164
y[1] (closed_form) = -0.000444311309131 -0.00114907898148
absolute error = 2.355e-07
relative error = 0.01911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.831
Order of pole (three term test) = 1.754e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1097.1MB, alloc=44.3MB, time=13.57
x[1] = 2.2915 0.913
h = 0.003 0.006
y[1] (numeric) = -0.00043812090408 -0.00114991491923
y[1] (closed_form) = -0.000437933633913 -0.00115004625075
absolute error = 2.287e-07
relative error = 0.01859 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.403
Order of pole (three term test) = 2.096e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = -0.000429105061344 -0.00115586095309
y[1] (closed_form) = -0.000428888922249 -0.00115598443685
absolute error = 2.489e-07
relative error = 0.02019 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 1.004e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = -0.000421085326574 -0.00115688512782
y[1] (closed_form) = -0.000420886719735 -0.0011570170802
absolute error = 2.384e-07
relative error = 0.01937 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 6.486e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2947 0.927
h = 0.001 0.001
y[1] (numeric) = -0.000416294269588 -0.00115753099496
y[1] (closed_form) = -0.000416094819081 -0.00115767049443
absolute error = 2.434e-07
relative error = 0.01979 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 2.461e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2957 0.928
h = 0.001 0.003
y[1] (numeric) = -0.000414849171113 -0.00115928975916
y[1] (closed_form) = -0.000414650556712 -0.00115943309187
absolute error = 2.449e-07
relative error = 0.01989 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.539
Order of pole (three term test) = 2.561e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = -0.000410188770929 -0.00116136419152
y[1] (closed_form) = -0.000409988787831 -0.00116149962681
absolute error = 2.415e-07
relative error = 0.01961 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.832
Order of pole (three term test) = 2.179e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2968 0.935
h = 0.003 0.006
y[1] (numeric) = -0.000403777247001 -0.00116210837703
y[1] (closed_form) = -0.000403582455044 -0.00116223939169
absolute error = 2.348e-07
relative error = 0.01908 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.403
Order of pole (three term test) = 1.378e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = -0.000394558566813 -0.00116772856807
y[1] (closed_form) = -0.00039433526663 -0.00116785054803
absolute error = 2.544e-07
relative error = 0.02064 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 4.501e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = -0.000386510496812 -0.00116846663165
y[1] (closed_form) = -0.000386304354948 -0.00116859779608
absolute error = 2.443e-07
relative error = 0.01985 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 6.502e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1143.2MB, alloc=44.3MB, time=14.14
x[1] = 2.3 0.949
h = 0.001 0.001
y[1] (numeric) = -0.000381701492949 -0.00116894163149
y[1] (closed_form) = -0.000381494195816 -0.00116908029793
absolute error = 2.494e-07
relative error = 0.02028 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 1.379e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.301 0.95
h = 0.001 0.003
y[1] (numeric) = -0.000380195458608 -0.00117064720172
y[1] (closed_form) = -0.00037998883761 -0.00117078973082
absolute error = 2.510e-07
relative error = 0.02039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.54
Order of pole (three term test) = 1.211e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.302 0.953
h = 0.0001 0.004
y[1] (numeric) = -0.000375466313276 -0.00117255383349
y[1] (closed_form) = -0.000375258652782 -0.0011726884193
absolute error = 2.475e-07
relative error = 0.0201 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.832
Order of pole (three term test) = 6.911e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3021 0.957
h = 0.003 0.006
y[1] (numeric) = -0.000369035421977 -0.00117306939916
y[1] (closed_form) = -0.000368833128457 -0.00117319978573
absolute error = 2.407e-07
relative error = 0.01957 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.404
Order of pole (three term test) = 6.183e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = -0.000359627675536 -0.00117835577729
y[1] (closed_form) = -0.000359397290088 -0.00117847596131
absolute error = 2.598e-07
relative error = 0.02109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.847
Order of pole (three term test) = 4.039e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = -0.00035156317188 -0.0011788069612
y[1] (closed_form) = -0.000351349537571 -0.00117893702654
absolute error = 2.501e-07
relative error = 0.02033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 9.228e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3053 0.971
h = 0.001 0.001
y[1] (numeric) = -0.000346743326149 -0.00117911059999
y[1] (closed_form) = -0.000346528227669 -0.0011792481076
absolute error = 2.553e-07
relative error = 0.02077 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 6.190e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = -0.000345178649749 -0.00118076053098
y[1] (closed_form) = -0.000344964066333 -0.00118090192306
absolute error = 2.570e-07
relative error = 0.02089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.81
Order of pole (three term test) = 7.590e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3064 0.976
h = 0.003 0.006
y[1] (numeric) = -0.000338739333638 -0.00118108876294
y[1] (closed_form) = -0.000338532349764 -0.00118121624446
absolute error = 2.431e-07
relative error = 0.01978 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.405
Order of pole (three term test) = 6.636e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = -0.000329184236025 -0.00118607990962
y[1] (closed_form) = -0.000328949575762 -0.00118619620668
absolute error = 2.619e-07
relative error = 0.02128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.847
Order of pole (three term test) = 6.427e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1189.3MB, alloc=44.3MB, time=14.71
x[1] = 2.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = -0.000321118547808 -0.00118628397051
y[1] (closed_form) = -0.000320900254443 -0.00118641072685
absolute error = 2.524e-07
relative error = 0.02054 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 1.314e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3096 0.99
h = 0.001 0.001
y[1] (numeric) = -0.000316297109957 -0.0011864399557
y[1] (closed_form) = -0.000316077090228 -0.00118657408764
absolute error = 2.577e-07
relative error = 0.02098 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3106 0.991
h = 0.001 0.003
y[1] (numeric) = -0.000314684578589 -0.00118803946329
y[1] (closed_form) = -0.000314464934574 -0.00118817749041
absolute error = 2.594e-07
relative error = 0.02111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.542
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = -0.000309848442639 -0.00118962658017
y[1] (closed_form) = -0.000309628375317 -0.00118975662434
absolute error = 2.556e-07
relative error = 0.02079 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 6.987e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3117 0.998
h = 0.003 0.006
y[1] (numeric) = -0.000303409534493 -0.00118971591481
y[1] (closed_form) = -0.000303195129397 -0.00118984219406
absolute error = 2.488e-07
relative error = 0.02027 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.406
Order of pole (three term test) = 8.111e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = -0.000293691981814 -0.00119436037773
y[1] (closed_form) = -0.000293450416613 -0.00119447434849
absolute error = 2.671e-07
relative error = 0.02172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.848
Order of pole (three term test) = 2.123e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = -0.000285632012877 -0.00119427777412
y[1] (closed_form) = -0.000285406348777 -0.00119440286081
absolute error = 2.580e-07
relative error = 0.02101 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 6.608e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3149 1.012
h = 0.001 0.001
y[1] (numeric) = -0.000280812961917 -0.00119426246136
y[1] (closed_form) = -0.000280585269795 -0.00119439483717
absolute error = 2.634e-07
relative error = 0.02147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3159 1.013
h = 0.001 0.003
y[1] (numeric) = -0.000279146373665 -0.00119580211602
y[1] (closed_form) = -0.000278918895318 -0.00119593839453
absolute error = 2.652e-07
relative error = 0.02159 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.544
Order of pole (three term test) = 5.223e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1235.5MB, alloc=44.3MB, time=15.28
x[1] = 2.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = -0.000274261974556 -0.00119721499022
y[1] (closed_form) = -0.000274034404156 -0.00119734328481
absolute error = 2.612e-07
relative error = 0.02127 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.834
Order of pole (three term test) = 8.017e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.317 1.02
h = 0.003 0.006
y[1] (numeric) = -0.000267830863664 -0.00119707572299
y[1] (closed_form) = -0.000267609099284 -0.00119720049493
absolute error = 2.545e-07
relative error = 0.02074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.407
Order of pole (three term test) = 1.126e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.32 1.026
h = 0.0001 0.005
y[1] (numeric) = -0.000257965529675 -0.00120136748521
y[1] (closed_form) = -0.000257717173335 -0.00120147885184
absolute error = 2.722e-07
relative error = 0.02215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.848
Order of pole (three term test) = 4.602e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = -0.000249923134168 -0.00120099906144
y[1] (closed_form) = -0.000249690183279 -0.00120112217693
absolute error = 2.635e-07
relative error = 0.02148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.294
Order of pole (three term test) = 1.372e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3202 1.034
h = 0.001 0.001
y[1] (numeric) = -0.000245113550559 -0.00120081291958
y[1] (closed_form) = -0.000244878274863 -0.00120094322368
absolute error = 2.689e-07
relative error = 0.02194 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 6.316e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3212 1.035
h = 0.001 0.003
y[1] (numeric) = -0.000243395498746 -0.00120229061617
y[1] (closed_form) = -0.000243160274958 -0.00120242482282
absolute error = 2.708e-07
relative error = 0.02208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.545
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = -0.000238470150937 -0.00120352763193
y[1] (closed_form) = -0.000238235165518 -0.00120365386936
absolute error = 2.667e-07
relative error = 0.02174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.835
Order of pole (three term test) = 1.120e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3223 1.042
h = 0.003 0.006
y[1] (numeric) = -0.000232056276817 -0.00120316059544
y[1] (closed_form) = -0.000231827229376 -0.00120328355863
absolute error = 2.600e-07
relative error = 0.02121 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.408
Order of pole (three term test) = 4.013e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = -0.000222058081446 -0.00120709434908
y[1] (closed_form) = -0.000221803060443 -0.00120720284
absolute error = 2.771e-07
relative error = 0.02258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.849
Order of pole (three term test) = 6.226e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = -0.000214045041582 -0.00120644150766
y[1] (closed_form) = -0.00021380490188 -0.00120656235516
absolute error = 2.688e-07
relative error = 0.02194 %
Correct digits = 4
memory used=1281.6MB, alloc=44.3MB, time=15.86
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.294
Order of pole (three term test) = 3.356e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3255 1.056
h = 0.001 0.001
y[1] (numeric) = -0.000209251964178 -0.00120608533877
y[1] (closed_form) = -0.000209009208489 -0.00120621326062
absolute error = 2.744e-07
relative error = 0.02241 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 2.548e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3265 1.057
h = 0.001 0.003
y[1] (numeric) = -0.000207485134377 -0.0012074991005
y[1] (closed_form) = -0.000207242269206 -0.00120763091712
absolute error = 2.763e-07
relative error = 0.02255 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.547
Order of pole (three term test) = 1.032e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = -0.000202526208361 -0.00120855899216
y[1] (closed_form) = -0.00020228391032 -0.00120868286982
absolute error = 2.721e-07
relative error = 0.02221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 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) = 5.055e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3276 1.064
h = 0.003 0.006
y[1] (numeric) = -0.000196138944494 -0.00120796546266
y[1] (closed_form) = -0.000195902704265 -0.00120808631997
absolute error = 2.654e-07
relative error = 0.02168 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.41
Order of pole (three term test) = 1.181e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = -0.000186023015372 -0.0012115366197
y[1] (closed_form) = -0.000185761468475 -0.00121164197023
absolute error = 2.820e-07
relative error = 0.023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.849
Order of pole (three term test) = 2.963e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = -0.000178051011995 -0.00121060131561
y[1] (closed_form) = -0.000177803795193 -0.00121071960378
absolute error = 2.741e-07
relative error = 0.0224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.295
Order of pole (three term test) = 6.778e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3308 1.078
h = 0.001 0.001
y[1] (numeric) = -0.00017328142049 -0.0012100762516
y[1] (closed_form) = -0.000173031302833 -0.00121020148652
absolute error = 2.797e-07
relative error = 0.02288 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 7.854e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = -0.000171468583394 -0.00121142423448
y[1] (closed_form) = -0.000171218195748 -0.00121155334877
absolute error = 2.817e-07
relative error = 0.02302 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.82
Order of pole (three term test) = 7.893e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3319 1.083
h = 0.003 0.006
y[1] (numeric) = -0.000165110330737 -0.00121064679187
y[1] (closed_form) = -0.000164870092587 -0.00121076388918
absolute error = 2.673e-07
relative error = 0.02187 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.412
Order of pole (three term test) = 8.688e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1327.7MB, alloc=44.3MB, time=16.42
x[1] = 2.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = -0.000154909684027 -0.00121390156567
y[1] (closed_form) = -0.000154644762385 -0.00121400230227
absolute error = 2.834e-07
relative error = 0.02316 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.85
Order of pole (three term test) = 8.992e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.335 1.094
h = 0.0001 0.003
y[1] (numeric) = -0.000146985581283 -0.00121272578473
y[1] (closed_form) = -0.000146734488299 -0.00121283992979
absolute error = 2.758e-07
relative error = 0.02258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 9.700e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3351 1.097
h = 0.001 0.001
y[1] (numeric) = -0.000142243724349 -0.00121205688798
y[1] (closed_form) = -0.000141989492617 -0.00121217785623
absolute error = 2.815e-07
relative error = 0.02307 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 1.428e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3361 1.098
h = 0.001 0.003
y[1] (numeric) = -0.000140394374861 -0.00121334637666
y[1] (closed_form) = -0.000140139736296 -0.00121347120314
absolute error = 2.836e-07
relative error = 0.02322 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.553
Order of pole (three term test) = 1.344e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = -0.000135394827198 -0.00121407432752
y[1] (closed_form) = -0.000135141359494 -0.00121419131609
absolute error = 2.792e-07
relative error = 0.02285 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.84
Order of pole (three term test) = 3.269e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3372 1.105
h = 0.003 0.006
y[1] (numeric) = -0.000129084345391 -0.00121306481754
y[1] (closed_form) = -0.00012883712225 -0.00121317927161
absolute error = 2.724e-07
relative error = 0.02233 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.414
Order of pole (three term test) = 1.657e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = -0.000118794567128 -0.00121595058494
y[1] (closed_form) = -0.000118523412007 -0.00121604771109
absolute error = 2.880e-07
relative error = 0.02357 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.851
Order of pole (three term test) = 4.796e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = -0.000110932829157 -0.00121449755783
y[1] (closed_form) = -0.000110674905587 -0.00121460862017
absolute error = 2.808e-07
relative error = 0.02302 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 1.552e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3404 1.119
h = 0.001 0.001
y[1] (numeric) = -0.000106227206747 -0.00121366281519
y[1] (closed_form) = -0.00010596587326 -0.00121378054936
absolute error = 2.866e-07
relative error = 0.02353 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1373.9MB, alloc=44.3MB, time=17.00
x[1] = 2.3414 1.12
h = 0.001 0.003
y[1] (numeric) = -0.000104337224803 -0.00121488349566
y[1] (closed_form) = -0.000104075326763 -0.0012150050588
absolute error = 2.887e-07
relative error = 0.02368 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.556
Order of pole (three term test) = 1.295e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = -9.93253264139e-05 -0.00121543273477
y[1] (closed_form) = -9.90649185762e-05 -0.00121554653377
absolute error = 2.842e-07
relative error = 0.0233 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.841
Order of pole (three term test) = 1.194e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3425 1.127
h = 0.003 0.006
y[1] (numeric) = -9.30676660418e-05 -0.00121420288886
y[1] (closed_form) = -9.28135866526e-05 -0.00121431441911
absolute error = 2.775e-07
relative error = 0.02278 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.416
Order of pole (three term test) = 2.966e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = -8.27042531093e-05 -0.00121671716085
y[1] (closed_form) = -8.24270359247e-05 -0.00121681043507
absolute error = 2.925e-07
relative error = 0.02398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.852
Order of pole (three term test) = 1.536e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = -7.49161065999e-05 -0.00121499037409
y[1] (closed_form) = -7.46515013405e-05 -0.00121509808204
absolute error = 2.857e-07
relative error = 0.02347 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.297
Order of pole (three term test) = 1.407e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3457 1.141
h = 0.001 0.001
y[1] (numeric) = -7.02534311856e-05 -0.00121399183229
y[1] (closed_form) = -6.99851530396e-05 -0.00121410604854
absolute error = 2.916e-07
relative error = 0.02398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0 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) = 6.682e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3467 1.142
h = 0.001 0.003
y[1] (numeric) = -6.83257879205e-05 -0.00121514226179
y[1] (closed_form) = -6.80567895045e-05 -0.00121526027044
absolute error = 2.937e-07
relative error = 0.02413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.559
Order of pole (three term test) = 1.312e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = -6.33089452062e-05 -0.00121551288158
y[1] (closed_form) = -6.30417515865e-05 -0.0012156232146
absolute error = 2.891e-07
relative error = 0.02375 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.843
Order of pole (three term test) = 2.477e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3478 1.149
h = 0.003 0.006
y[1] (numeric) = -5.71130048671e-05 -0.00121406562735
y[1] (closed_form) = -5.68522107346e-05 -0.00121417396025
absolute error = 2.824e-07
relative error = 0.02323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.419
Order of pole (three term test) = 1.068e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = -4.66915101465e-05 -0.00121620665412
y[1] (closed_form) = -4.64084128092e-05 -0.00121629584406
absolute error = 2.968e-07
relative error = 0.02439 %
Correct digits = 4
memory used=1419.9MB, alloc=44.3MB, time=17.56
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.854
Order of pole (three term test) = 3.117e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = -3.89879722044e-05 -0.00121421010867
y[1] (closed_form) = -3.87168463546e-05 -0.00121431419863
absolute error = 2.904e-07
relative error = 0.0239 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.298
Order of pole (three term test) = 7.138e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.351 1.163
h = 0.001 0.001
y[1] (numeric) = -3.43748325115e-05 -0.00121305012185
y[1] (closed_form) = -3.40997796060e-05 -0.0012131605449
absolute error = 2.964e-07
relative error = 0.02442 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.804
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.352 1.164
h = 0.001 0.003
y[1] (numeric) = -3.24125546968e-05 -0.00121412900329
y[1] (closed_form) = -3.21366281866e-05 -0.00121424317501
absolute error = 2.986e-07
relative error = 0.02458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.562
Order of pole (three term test) = 9.419e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.353 1.167
h = 0.0001 0.004
y[1] (numeric) = -2.73981391867e-05 -0.00121432144429
y[1] (closed_form) = -2.71243265608e-05 -0.00121442804332
absolute error = 2.938e-07
relative error = 0.02419 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.845
Order of pole (three term test) = 3.407e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3531 1.171
h = 0.003 0.006
y[1] (numeric) = -2.12726426342e-05 -0.00121266011578
y[1] (closed_form) = -2.10052875983e-05 -0.00121276498549
absolute error = 2.872e-07
relative error = 0.02368 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.422
Order of pole (three term test) = 6.829e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = -1.08086356405e-05 -0.00121442688614
y[1] (closed_form) = -1.05198500203e-05 -0.00121451176906
absolute error = 3.010e-07
relative error = 0.02478 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0 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) = 4.477e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = -3.20048758948e-06 -0.00121216508383
y[1] (closed_form) = -2.92301396246e-06 -0.00121226530089
absolute error = 2.950e-07
relative error = 0.02434 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.299
Order of pole (three term test) = 7.288e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 1.35666704851e-06 -0.00121084630548
y[1] (closed_form) = 1.63831252633e-06 -0.00121095266929
absolute error = 3.011e-07
relative error = 0.02486 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.805
Order of pole (three term test) = 1.541e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 3.35050497901e-06 -0.0012118524897
y[1] (closed_form) = 3.63317464833e-06 -0.00121196255142
absolute error = 3.033e-07
relative error = 0.02503 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.84
Order of pole (three term test) = 6.576e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1466.1MB, alloc=44.3MB, time=18.14
x[1] = 2.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 9.41172303536e-06 -0.00121001896906
y[1] (closed_form) = 9.68221588807e-06 -0.00121011940906
absolute error = 2.885e-07
relative error = 0.02384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.425
Order of pole (three term test) = 4.391e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 1.98954108578e-05 -0.00121146308967
y[1] (closed_form) = 2.01865452862e-05 -0.00121154286338
absolute error = 3.019e-07
relative error = 0.02491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.856
Order of pole (three term test) = 5.091e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 2.74099380176e-05 -0.00120897824555
y[1] (closed_form) = 2.76903466435e-05 -0.00120907369252
absolute error = 2.962e-07
relative error = 0.02449 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.3
Order of pole (three term test) = 7.523e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 3.19120125878e-05 -0.00120752590013
y[1] (closed_form) = 3.21967934680e-05 -0.00120762732219
absolute error = 3.023e-07
relative error = 0.02502 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.806
Order of pole (three term test) = 2.804e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 3.39296422356e-05 -0.00120846837761
y[1] (closed_form) = 3.42155737411e-05 -0.0012085734467
absolute error = 3.046e-07
relative error = 0.0252 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.57
Order of pole (three term test) = 1.089e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 3.89180227265e-05 -0.00120833185202
y[1] (closed_form) = 3.92012839681e-05 -0.00120842958054
absolute error = 2.996e-07
relative error = 0.02478 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 0 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) = 3.523e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 4.48874672341e-05 -0.00120628347399
y[1] (closed_form) = 4.51642005895e-05 -0.00120637998086
absolute error = 2.931e-07
relative error = 0.02428 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.428
Order of pole (three term test) = 1.413e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 5.53847940397e-05 -0.00120735359517
y[1] (closed_form) = 5.56812328030e-05 -0.00120742867714
absolute error = 3.058e-07
relative error = 0.0253 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.857
Order of pole (three term test) = 5.183e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 6.27846500372e-05 -0.00120461327218
y[1] (closed_form) = 6.30710527243e-05 -0.00120470439932
absolute error = 3.006e-07
relative error = 0.02491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.301
Order of pole (three term test) = 7.842e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1512.2MB, alloc=44.3MB, time=18.71
x[1] = 2.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 6.72192006396e-05 -0.00120300791056
y[1] (closed_form) = 6.75102014125e-05 -0.00120310480732
absolute error = 3.067e-07
relative error = 0.02545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.807
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 6.92625609295e-05 -0.0012038759893
y[1] (closed_form) = 6.95548567890e-05 -0.00120397646987
absolute error = 3.091e-07
relative error = 0.02563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.575
Order of pole (three term test) = 1.334e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 7.42277991622e-05 -0.00120356451614
y[1] (closed_form) = 7.45171355367e-05 -0.00120365779806
absolute error = 3.040e-07
relative error = 0.02521 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0 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) = 2.538e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.368 1.234
h = 0.003 0.006
y[1] (numeric) = 8.01030448398e-05 -0.00120131383558
y[1] (closed_form) = 8.03858323571e-05 -0.00120140616891
absolute error = 2.975e-07
relative error = 0.02471 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.431
Order of pole (three term test) = 7.199e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 9.05986166161e-05 -0.00120201103433
y[1] (closed_form) = 9.09001426714e-05 -0.00120208123191
absolute error = 3.096e-07
relative error = 0.02568 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.859
Order of pole (three term test) = 4.725e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 9.78738357928e-05 -0.00119902107557
y[1] (closed_form) = 9.81660293009e-05 -0.00119910765599
absolute error = 3.048e-07
relative error = 0.02533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.303
Order of pole (three term test) = 4.595e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 0.000102234896173 -0.00119726615331
y[1] (closed_form) = 0.000102531902789 -0.0011973582884
absolute error = 3.110e-07
relative error = 0.02588 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0 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) = 8.885e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 0.000104300822791 -0.00119805911548
y[1] (closed_form) = 0.000104599265231 -0.00119815476471
absolute error = 3.134e-07
relative error = 0.02606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.579
Order of pole (three term test) = 1.011e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.000109235853744 -0.00119757443516
y[1] (closed_form) = 0.000109531055658 -0.00119766304046
absolute error = 3.082e-07
relative error = 0.02563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.855
Order of pole (three term test) = 7.321e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 0.000115009042137 -0.00119512623628
y[1] (closed_form) = 0.000115297687113 -0.00119521416557
absolute error = 3.017e-07
relative error = 0.02513 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.838
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.435
Order of pole (three term test) = 3.284e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1558.3MB, alloc=44.3MB, time=19.27
x[1] = 2.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.000125487596414 -0.00119545230433
y[1] (closed_form) = 0.000125793985057 -0.00119551743609
absolute error = 3.132e-07
relative error = 0.02606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.861
Order of pole (three term test) = 1.364e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.000132628540159 -0.00119221898801
y[1] (closed_form) = 0.000132926311698 -0.00119230080551
absolute error = 3.088e-07
relative error = 0.02574 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.304
Order of pole (three term test) = 7.817e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 0.000136910337978 -0.00119031822101
y[1] (closed_form) = 0.000137213126407 -0.00119040536937
absolute error = 3.151e-07
relative error = 0.02629 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.809
Order of pole (three term test) = 1.488e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 0.000138995650248 -0.00119103550061
y[1] (closed_form) = 0.000139300011198 -0.00119112608727
absolute error = 3.176e-07
relative error = 0.02648 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.584
Order of pole (three term test) = 1.033e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.000143893528771 -0.00119037967456
y[1] (closed_form) = 0.000144194376959 -0.00119046338427
absolute error = 3.123e-07
relative error = 0.02604 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.858
Order of pole (three term test) = 8.358e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 0.000149557068329 -0.00118773908278
y[1] (closed_form) = 0.000149851364279 -0.00118782238789
absolute error = 3.059e-07
relative error = 0.02555 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.438
Order of pole (three term test) = 1.677e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.000160003510939 -0.00118769651524
y[1] (closed_form) = 0.000160314530441 -0.00118775641129
absolute error = 3.167e-07
relative error = 0.02643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.862
Order of pole (three term test) = 3.484e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.000167000888494 -0.0011842265347
y[1] (closed_form) = 0.000167304016346 -0.00118430338422
absolute error = 3.127e-07
relative error = 0.02615 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.305
Order of pole (three term test) = 1.130e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 0.000171197857768 -0.00118218388733
y[1] (closed_form) = 0.000171506194661 -0.00118226583569
absolute error = 3.190e-07
relative error = 0.02671 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.81
Order of pole (three term test) = 1.074e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1604.5MB, alloc=44.3MB, time=19.84
x[1] = 2.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.00017329936673 -0.00118282507013
y[1] (closed_form) = 0.000173609408504 -0.00118291037502
absolute error = 3.216e-07
relative error = 0.0269 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.87
Order of pole (three term test) = 1.189e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 0.000178867505041 -0.00118003135762
y[1] (closed_form) = 0.00017916396511 -0.00118010978194
absolute error = 3.067e-07
relative error = 0.02569 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.442
Order of pole (three term test) = 1.038e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.000189270037046 -0.00117967462939
y[1] (closed_form) = 0.00018958231806 -0.00117972917175
absolute error = 3.170e-07
relative error = 0.02653 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.864
Order of pole (three term test) = 2.518e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.000196133974488 -0.00117600845138
y[1] (closed_form) = 0.000196438997469 -0.00117608014052
absolute error = 3.133e-07
relative error = 0.02628 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.307
Order of pole (three term test) = 8.169e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 0.000200252013825 -0.00117384812983
y[1] (closed_form) = 0.000200562398776 -0.00117392470994
absolute error = 3.197e-07
relative error = 0.02684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.811
Order of pole (three term test) = 7.768e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 0.000202363999954 -0.00117442345353
y[1] (closed_form) = 0.000202676198963 -0.00117450331372
absolute error = 3.223e-07
relative error = 0.02704 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.595
Order of pole (three term test) = 1.080e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.000207172772555 -0.00117345634695
y[1] (closed_form) = 0.000207480979949 -0.00117352967465
absolute error = 3.168e-07
relative error = 0.02658 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.864
Order of pole (three term test) = 8.293e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 0.00021261092401 -0.00117047400498
y[1] (closed_form) = 0.000212912624576 -0.00117054742737
absolute error = 3.105e-07
relative error = 0.0261 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.845
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.446
Order of pole (three term test) = 1.416e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.000222953876347 -0.00116975528198
y[1] (closed_form) = 0.000223270338888 -0.00116980430707
absolute error = 3.202e-07
relative error = 0.02689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.866
Order of pole (three term test) = 8.650e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.000229658041622 -0.00116586602663
y[1] (closed_form) = 0.000229967984693 -0.00116593240007
absolute error = 3.170e-07
relative error = 0.02667 %
Correct digits = 4
memory used=1650.7MB, alloc=44.3MB, time=20.42
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.308
Order of pole (three term test) = 5.021e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 0.000233681537574 -0.0011635718796
y[1] (closed_form) = 0.000233997012143 -0.00116364289864
absolute error = 3.234e-07
relative error = 0.02724 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.812
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 0.000235803791127 -0.00116407077509
y[1] (closed_form) = 0.000236121203242 -0.00116414498217
absolute error = 3.260e-07
relative error = 0.02744 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.601
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.000240556382918 -0.0011629401908
y[1] (closed_form) = 0.000240869559599 -0.00116300806424
absolute error = 3.204e-07
relative error = 0.02698 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.867
Order of pole (three term test) = 6.334e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 0.000245864855474 -0.00115978193263
y[1] (closed_form) = 0.000246171565623 -0.00115985016512
absolute error = 3.142e-07
relative error = 0.0265 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.848
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.451
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.000256133817361 -0.00115870563785
y[1] (closed_form) = 0.000256454213391 -0.00115874901026
absolute error = 3.233e-07
relative error = 0.02724 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.868
Order of pole (three term test) = 9.534e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.00026267002176 -0.00115460106186
y[1] (closed_form) = 0.000262984641422 -0.00115466194852
absolute error = 3.205e-07
relative error = 0.02706 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.31
Order of pole (three term test) = 8.752e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 0.000266594062655 -0.00115217769075
y[1] (closed_form) = 0.000266914370826 -0.00115224297139
absolute error = 3.269e-07
relative error = 0.02764 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.814
Order of pole (three term test) = 1.154e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 0.000268723416655 -0.00115260017289
y[1] (closed_form) = 0.000269045780772 -0.0011526685444
absolute error = 3.295e-07
relative error = 0.02784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.607
Order of pole (three term test) = 2.269e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.000273413494008 -0.00115130932327
y[1] (closed_form) = 0.000273731389725 -0.00115137157003
absolute error = 3.239e-07
relative error = 0.02737 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.87
Order of pole (three term test) = 6.499e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1696.7MB, alloc=44.3MB, time=20.98
x[1] = 2.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 0.000278585871944 -0.00114798142839
y[1] (closed_form) = 0.000278897353432 -0.00114804429489
absolute error = 3.178e-07
relative error = 0.0269 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.455
Order of pole (three term test) = 1.882e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.000288766732775 -0.00114655262528
y[1] (closed_form) = 0.000289090809801 -0.001146590222
absolute error = 3.263e-07
relative error = 0.02759 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.87
Order of pole (three term test) = 1.384e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.000295127202627 -0.00114224081409
y[1] (closed_form) = 0.000295446249029 -0.00114229605535
absolute error = 3.238e-07
relative error = 0.02744 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.312
Order of pole (three term test) = 9.201e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.402 1.377
h = 0.001 0.001
y[1] (numeric) = 0.000298947123362 -0.00113969301743
y[1] (closed_form) = 0.000299272002538 -0.00113975239549
absolute error = 3.303e-07
relative error = 0.02803 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.815
Order of pole (three term test) = 8.550e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.403 1.378
h = 0.001 0.003
y[1] (numeric) = 0.000301080432847 -0.00114003924797
y[1] (closed_form) = 0.000301407481049 -0.00114010161491
absolute error = 3.329e-07
relative error = 0.02823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.613
Order of pole (three term test) = 1.186e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.000305701853968 -0.00113859161782
y[1] (closed_form) = 0.000306024212096 -0.00113864807824
absolute error = 3.273e-07
relative error = 0.02776 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.874
Order of pole (three term test) = 1.267e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 0.00031073205657 -0.00113510062085
y[1] (closed_form) = 0.0003110480645 -0.00113515795748
absolute error = 3.212e-07
relative error = 0.02729 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.853
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.46
Order of pole (three term test) = 1.073e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.000320811037025 -0.00113332499272
y[1] (closed_form) = 0.000321138538779 -0.00113335670328
absolute error = 3.290e-07
relative error = 0.02793 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.853
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.872
Order of pole (three term test) = 1.578e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.000326988427616 -0.00112881433629
y[1] (closed_form) = 0.000327311645254 -0.00112886378618
absolute error = 3.270e-07
relative error = 0.02782 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.314
Order of pole (three term test) = 2.732e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1743.0MB, alloc=44.3MB, time=21.56
x[1] = 2.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 0.000330699818001 -0.00112614709537
y[1] (closed_form) = 0.000331028999745 -0.00112620042002
absolute error = 3.335e-07
relative error = 0.02841 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.816
Order of pole (three term test) = 8.763e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 0.000332833967499 -0.00112641738064
y[1] (closed_form) = 0.000333165425821 -0.00112647358767
absolute error = 3.362e-07
relative error = 0.02862 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.29
Order of pole (three term test) = 1.086e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.000342862505208 -0.00112442003107
y[1] (closed_form) = 0.00034318580152 -0.00112443415681
absolute error = 3.236e-07
relative error = 0.02753 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.873
Order of pole (three term test) = 1.524e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.000348914674474 -0.00111977278825
y[1] (closed_form) = 0.000349234198328 -0.00111980471687
absolute error = 3.211e-07
relative error = 0.02738 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.856
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.314
Order of pole (three term test) = 9.192e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 0.000352551839953 -0.00111702350369
y[1] (closed_form) = 0.000352877417395 -0.00111705912729
absolute error = 3.275e-07
relative error = 0.02796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.817
Order of pole (three term test) = 8.747e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 0.000354686677913 -0.00111724172789
y[1] (closed_form) = 0.000355014605418 -0.00111728016069
absolute error = 3.302e-07
relative error = 0.02816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.856
Order of pole (given) = 0 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) = 2.432e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.000359182595917 -0.00111553604333
y[1] (closed_form) = 0.00035950547993 -0.00111556895244
absolute error = 3.246e-07
relative error = 0.02769 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.88
Order of pole (three term test) = 3.116e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 0.000363963727767 -0.00111178133075
y[1] (closed_form) = 0.000364280389184 -0.00111181554003
absolute error = 3.185e-07
relative error = 0.02722 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.468
Order of pole (three term test) = 3.960e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.000373848884853 -0.0011094315528
y[1] (closed_form) = 0.000374175168757 -0.00110943962791
absolute error = 3.264e-07
relative error = 0.02788 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.876
Order of pole (three term test) = 6.518e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.000379706358564 -0.00110460008694
y[1] (closed_form) = 0.000380029614499 -0.0011046260004
absolute error = 3.243e-07
relative error = 0.02776 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.859
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.316
Order of pole (three term test) = 1.339e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1789.1MB, alloc=44.3MB, time=22.13
x[1] = 2.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 0.000383228013988 -0.00110174004271
y[1] (closed_form) = 0.000383557432788 -0.00110176938221
absolute error = 3.307e-07
relative error = 0.02835 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.819
Order of pole (three term test) = 2.704e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 0.000385358505047 -0.00110188308263
y[1] (closed_form) = 0.00038569037181 -0.00110191511782
absolute error = 3.334e-07
relative error = 0.02856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.631
Order of pole (three term test) = 1.259e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.000389770197153 -0.00110003110088
y[1] (closed_form) = 0.000390096830773 -0.00110005785277
absolute error = 3.277e-07
relative error = 0.02808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 0 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) = 1.637e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 0.000394394366301 -0.00109613183809
y[1] (closed_form) = 0.000394714871378 -0.00109616013273
absolute error = 3.218e-07
relative error = 0.02762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.474
Order of pole (three term test) = 4.082e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.000404142282989 -0.00109345309079
y[1] (closed_form) = 0.00040447129111 -0.00109345503874
absolute error = 3.290e-07
relative error = 0.02822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.878
Order of pole (three term test) = 6.011e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.000409798920853 -0.00108844649775
y[1] (closed_form) = 0.000410125641343 -0.0010884662849
absolute error = 3.273e-07
relative error = 0.02814 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.863
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.318
Order of pole (three term test) = 1.381e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 0.000413201372095 -0.00108548109935
y[1] (closed_form) = 0.000413534351483 -0.00108550404066
absolute error = 3.338e-07
relative error = 0.02873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.82
Order of pole (three term test) = 9.296e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 0.000415324512119 -0.00108554963669
y[1] (closed_form) = 0.000415660031373 -0.00108557515655
absolute error = 3.365e-07
relative error = 0.02895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.863
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.638
Order of pole (three term test) = 1.293e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.000419646641794 -0.00108355574349
y[1] (closed_form) = 0.000419976750819 -0.00108357622731
absolute error = 3.307e-07
relative error = 0.02846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.863
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.888
Order of pole (three term test) = 1.326e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1835.1MB, alloc=44.3MB, time=22.69
x[1] = 2.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 0.000424109081148 -0.00107951924385
y[1] (closed_form) = 0.000424433166115 -0.00107954150675
absolute error = 3.248e-07
relative error = 0.028 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.479
Order of pole (three term test) = 3.791e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.00043370743077 -0.00107651930453
y[1] (closed_form) = 0.000434038898448 -0.00107651506142
absolute error = 3.315e-07
relative error = 0.02856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.881
Order of pole (three term test) = 4.388e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.000439157560088 -0.00107134689125
y[1] (closed_form) = 0.000439487474569 -0.00107136045413
absolute error = 3.302e-07
relative error = 0.02851 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.866
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.32
Order of pole (three term test) = 1.008e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 0.000442437391159 -0.00106828167131
y[1] (closed_form) = 0.000442773647292 -0.00106829811425
absolute error = 3.367e-07
relative error = 0.02911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 0 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) = 1.358e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.000444550231279 -0.00106827652063
y[1] (closed_form) = 0.000444889113053 -0.00106829542169
absolute error = 3.394e-07
relative error = 0.02933 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.866
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.94
Order of pole (three term test) = 8.353e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 0.000448876929144 -0.00106413359296
y[1] (closed_form) = 0.000449201372801 -0.00106415074533
absolute error = 3.249e-07
relative error = 0.02813 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.485
Order of pole (three term test) = 4.364e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.000458333323247 -0.00106086576873
y[1] (closed_form) = 0.000458664185624 -0.00106085633355
absolute error = 3.310e-07
relative error = 0.02864 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.883
Order of pole (three term test) = 6.471e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.000463599695315 -0.00105556076062
y[1] (closed_form) = 0.000463929629703 -0.0010555690674
absolute error = 3.300e-07
relative error = 0.02862 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.322
Order of pole (three term test) = 1.163e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 0.000466770361611 -0.00105241564442
y[1] (closed_form) = 0.000467106694968 -0.00105242659332
absolute error = 3.365e-07
relative error = 0.02923 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.823
Order of pole (three term test) = 1.401e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1881.3MB, alloc=44.3MB, time=23.27
x[1] = 2.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 0.00046887115926 -0.00105234798555
y[1] (closed_form) = 0.000469210185615 -0.00105236128563
absolute error = 3.393e-07
relative error = 0.02945 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.653
Order of pole (three term test) = 2.755e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.000473011716678 -0.00105010361748
y[1] (closed_form) = 0.000473345040623 -0.00105011235915
absolute error = 3.334e-07
relative error = 0.02895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.897
Order of pole (three term test) = 7.897e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 0.000477160391926 -0.00104583379518
y[1] (closed_form) = 0.000477487915165 -0.00104584473591
absolute error = 3.277e-07
relative error = 0.0285 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.491
Order of pole (three term test) = 6.351e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.000486445620983 -0.00104226070466
y[1] (closed_form) = 0.000486778448877 -0.0010422449962
absolute error = 3.332e-07
relative error = 0.02897 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 0 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) = 3.327e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.000491496310573 -0.00103680772077
y[1] (closed_form) = 0.000491828929037 -0.00103680965948
absolute error = 3.326e-07
relative error = 0.02899 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.873
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.325
Order of pole (three term test) = 4.306e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.437 1.521
h = 0.001 0.001
y[1] (numeric) = 0.000494538822408 -0.00103357339587
y[1] (closed_form) = 0.000494877897939 -0.00103357770049
absolute error = 3.391e-07
relative error = 0.02959 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.874
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.825
Order of pole (three term test) = 3.075e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.438 1.522
h = 0.001 0.003
y[1] (numeric) = 0.000496624014879 -0.00103343393723
y[1] (closed_form) = 0.000496965857467 -0.00103344046752
absolute error = 3.419e-07
relative error = 0.02982 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.874
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.662
Order of pole (three term test) = 1.488e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.000500661181811 -0.00103106137128
y[1] (closed_form) = 0.000500997182079 -0.0010310636059
absolute error = 3.360e-07
relative error = 0.02931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.874
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.902
Order of pole (three term test) = 1.864e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 0.000504636667346 -0.00102667609197
y[1] (closed_form) = 0.00050496699875 -0.00102668074146
absolute error = 3.304e-07
relative error = 0.02887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.497
Order of pole (three term test) = 9.300e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.000513739773531 -0.00102280687283
y[1] (closed_form) = 0.000514074302367 -0.00102278486298
absolute error = 3.353e-07
relative error = 0.02929 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.889
Order of pole (three term test) = 1.084e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1927.5MB, alloc=44.3MB, time=23.84
x[1] = 2.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.000518570478328 -0.00101721567365
y[1] (closed_form) = 0.000518905505666 -0.00101721118416
absolute error = 3.351e-07
relative error = 0.02934 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.877
Order of pole (given) = 0 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) = 1.289e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 0.000521482235238 -0.00101389794703
y[1] (closed_form) = 0.000521823764605 -0.00101389554701
absolute error = 3.415e-07
relative error = 0.02995 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.827
Order of pole (three term test) = 1.062e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 0.000523549067217 -0.00101368785864
y[1] (closed_form) = 0.000523893431312 -0.00101368755648
absolute error = 3.444e-07
relative error = 0.03018 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.877
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.67
Order of pole (three term test) = 1.534e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.000527478497098 -0.00101119220931
y[1] (closed_form) = 0.000527816892205 -0.0010111878783
absolute error = 3.384e-07
relative error = 0.02967 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.906
Order of pole (three term test) = 1.366e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 0.000531277496068 -0.00100669928721
y[1] (closed_form) = 0.000531610362844 -0.00100669757894
absolute error = 3.329e-07
relative error = 0.02924 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.504
Order of pole (three term test) = 4.821e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.000540188035406 -0.00100254349774
y[1] (closed_form) = 0.00054052400181 -0.00100251517063
absolute error = 3.372e-07
relative error = 0.0296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.892
Order of pole (three term test) = 1.590e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.000544794937357 -0.000996823953737
y[1] (closed_form) = 0.00054513209803 -0.000996812988987
absolute error = 3.373e-07
relative error = 0.02969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.881
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.329
Order of pole (three term test) = 1.163e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 0.000547573627185 -0.000993428699343
y[1] (closed_form) = 0.000547917321835 -0.000993419548078
absolute error = 3.438e-07
relative error = 0.03031 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.882
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.829
Order of pole (three term test) = 1.106e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 0.000549619421375 -0.000993149266504
y[1] (closed_form) = 0.000549966011984 -0.000993142083379
absolute error = 3.467e-07
relative error = 0.03054 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.881
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.679
Order of pole (three term test) = 4.598e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1973.7MB, alloc=44.3MB, time=24.41
x[1] = 2.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.000553437040026 -0.000990535801022
y[1] (closed_form) = 0.000553777548298 -0.000990524859233
absolute error = 3.407e-07
relative error = 0.03002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.882
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.911
Order of pole (three term test) = 3.932e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 0.000557056641852 -0.000985943130594
y[1] (closed_form) = 0.000557391770519 -0.00098593501109
absolute error = 3.352e-07
relative error = 0.0296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.51
Order of pole (three term test) = 1.804e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.00056576470058 -0.000981510719065
y[1] (closed_form) = 0.000566101842987 -0.000981476070861
absolute error = 3.389e-07
relative error = 0.02991 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.895
Order of pole (three term test) = 1.477e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.000570144466565 -0.000975672784683
y[1] (closed_form) = 0.000570483485373 -0.00097565531063
absolute error = 3.395e-07
relative error = 0.03004 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.885
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.332
Order of pole (three term test) = 1.254e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 0.000572788065917 -0.000972205927973
y[1] (closed_form) = 0.000573133637796 -0.00097218999253
absolute error = 3.459e-07
relative error = 0.03065 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.886
Order of pole (given) = 0 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) = 1.167e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.00057481022814 -0.000971858546136
y[1] (closed_form) = 0.000575158750737 -0.000971844447527
absolute error = 3.488e-07
relative error = 0.03089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.885
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.99
Order of pole (three term test) = 1.406e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.454 1.592
h = 0.003 0.006
y[1] (numeric) = 0.000578281086442 -0.000967190490746
y[1] (closed_form) = 0.000578615595465 -0.000967177446984
absolute error = 3.348e-07
relative error = 0.0297 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.517
Order of pole (three term test) = 5.183e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.000586804206233 -0.000962530775712
y[1] (closed_form) = 0.000587139807547 -0.000962491332422
absolute error = 3.379e-07
relative error = 0.02997 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 0 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) = 8.554e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.000590984913914 -0.000956601701914
y[1] (closed_form) = 0.000591322964082 -0.000956579239468
absolute error = 3.388e-07
relative error = 0.03013 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.889
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.334
Order of pole (three term test) = 3.735e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 0.000593510075575 -0.00095307962192
y[1] (closed_form) = 0.000593854681861 -0.000953058462837
absolute error = 3.453e-07
relative error = 0.03075 %
Correct digits = 4
memory used=2019.8MB, alloc=44.3MB, time=24.98
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.833
Order of pole (three term test) = 2.372e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 0.00059550910097 -0.000952675271287
y[1] (closed_form) = 0.000595856698333 -0.000952655834469
absolute error = 3.481e-07
relative error = 0.03098 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.889
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.697
Order of pole (three term test) = 1.650e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.000599107525357 -0.000949858488085
y[1] (closed_form) = 0.000599448868271 -0.000949835802791
absolute error = 3.421e-07
relative error = 0.03046 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.922
Order of pole (three term test) = 4.235e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 0.000602385923093 -0.000945103610574
y[1] (closed_form) = 0.000602722185318 -0.000945084093711
absolute error = 3.368e-07
relative error = 0.03005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.891
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.524
Order of pole (three term test) = 5.390e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.000610689702237 -0.000940186818161
y[1] (closed_form) = 0.000611025999946 -0.000940141080951
absolute error = 3.394e-07
relative error = 0.03027 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.891
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.901
Order of pole (three term test) = 5.629e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.000614638478333 -0.0009341580388
y[1] (closed_form) = 0.00061497787766 -0.000934129040952
absolute error = 3.406e-07
relative error = 0.03046 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.893
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.337
Order of pole (three term test) = 1.296e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 0.00061702562225 -0.000930575483205
y[1] (closed_form) = 0.000617371573444 -0.000930547517758
absolute error = 3.471e-07
relative error = 0.03108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.835
Order of pole (three term test) = 1.330e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 0.000618996445194 -0.000930106082911
y[1] (closed_form) = 0.000619345430159 -0.000930079706487
absolute error = 3.500e-07
relative error = 0.03132 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.706
Order of pole (three term test) = 6.193e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.000622473015704 -0.000927187293041
y[1] (closed_form) = 0.000622815671019 -0.000927157943821
absolute error = 3.439e-07
relative error = 0.03079 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.927
Order of pole (three term test) = 8.991e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 0.000625565914402 -0.000922355530223
y[1] (closed_form) = 0.000625903658214 -0.000922329523447
absolute error = 3.387e-07
relative error = 0.03039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.896
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.531
Order of pole (three term test) = 6.735e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2065.9MB, alloc=44.3MB, time=25.55
x[1] = 2.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.000633642032341 -0.000917192543757
y[1] (closed_form) = 0.000633978773378 -0.000917140541857
absolute error = 3.407e-07
relative error = 0.03056 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.904
Order of pole (three term test) = 9.270e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.000637356921553 -0.000911074107216
y[1] (closed_form) = 0.000637697399549 -0.000911038576083
absolute error = 3.423e-07
relative error = 0.03078 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 0 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) = 1.350e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 0.00063960484516 -0.000907437061654
y[1] (closed_form) = 0.000639951858572 -0.000907402294857
absolute error = 3.488e-07
relative error = 0.03141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.837
Order of pole (three term test) = 1.819e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 0.000641545135304 -0.000906904290422
y[1] (closed_form) = 0.000641895218733 -0.000906870978811
absolute error = 3.517e-07
relative error = 0.03165 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.898
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.716
Order of pole (three term test) = 8.004e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.000644896869004 -0.000903889200824
y[1] (closed_form) = 0.00064524056079 -0.00090385319273
absolute error = 3.456e-07
relative error = 0.03112 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.898
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.933
Order of pole (three term test) = 5.137e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 0.000647802839839 -0.000898988561308
y[1] (closed_form) = 0.000648141795466 -0.000898956060281
absolute error = 3.405e-07
relative error = 0.03073 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.539
Order of pole (three term test) = 7.020e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.000655643550819 -0.000893590531468
y[1] (closed_form) = 0.000655980486082 -0.000893532305114
absolute error = 3.419e-07
relative error = 0.03085 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.907
Order of pole (three term test) = 8.755e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.000659123071484 -0.000887392473204
y[1] (closed_form) = 0.00065946436045 -0.000887350423101
absolute error = 3.439e-07
relative error = 0.0311 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.902
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.342
Order of pole (three term test) = 1.408e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 0.000661230854494 -0.000883706917068
y[1] (closed_form) = 0.000661578650512 -0.000883665366722
absolute error = 3.503e-07
relative error = 0.03173 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.903
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.839
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2112.2MB, alloc=44.3MB, time=26.12
x[1] = 2.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 0.000663138380828 -0.000883112541757
y[1] (closed_form) = 0.000663489276707 -0.000883072312497
absolute error = 3.532e-07
relative error = 0.03198 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.903
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.727
Order of pole (three term test) = 1.867e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.000666362582571 -0.000880006936123
y[1] (closed_form) = 0.000666707037904 -0.00087996428665
absolute error = 3.471e-07
relative error = 0.03144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.903
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.939
Order of pole (three term test) = 4.793e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 0.000669080572523 -0.000875045411421
y[1] (closed_form) = 0.000669420472646 -0.000875006424041
absolute error = 3.421e-07
relative error = 0.03105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.905
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.546
Order of pole (three term test) = 6.105e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.000676678712536 -0.00086942372402
y[1] (closed_form) = 0.000677015597395 -0.000869359324121
absolute error = 3.430e-07
relative error = 0.03113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.905
Order of pole (given) = 0 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) = 5.779e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.000679921850473 -0.000863156042698
y[1] (closed_form) = 0.000680263686088 -0.00086310749986
absolute error = 3.453e-07
relative error = 0.03142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.907
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.345
Order of pole (three term test) = 2.940e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 0.00068188885128 -0.000859427934924
y[1] (closed_form) = 0.000682237153986 -0.00085937963131
absolute error = 3.516e-07
relative error = 0.03205 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.908
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.841
Order of pole (three term test) = 1.401e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.000683761485432 -0.000858773804463
y[1] (closed_form) = 0.000684112911502 -0.000858726687901
absolute error = 3.546e-07
relative error = 0.03229 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.907
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.06
Order of pole (three term test) = 1.224e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 0.000686325141231 -0.000853768692372
y[1] (closed_form) = 0.0006866635435 -0.000853725162581
absolute error = 3.412e-07
relative error = 0.03114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.909
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.554
Order of pole (three term test) = 8.985e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.000693706719536 -0.000847966755932
y[1] (closed_form) = 0.000694041274181 -0.000847898127501
absolute error = 3.415e-07
relative error = 0.03117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.909
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.914
Order of pole (three term test) = 6.644e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.000696745258048 -0.000841649930514
y[1] (closed_form) = 0.000697085256653 -0.000841596858849
absolute error = 3.441e-07
relative error = 0.03149 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.911
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.347
Order of pole (three term test) = 1.532e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2158.3MB, alloc=44.3MB, time=26.69
x[1] = 2.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 0.000698590363095 -0.000837891623924
y[1] (closed_form) = 0.000698936782339 -0.000837838571531
absolute error = 3.505e-07
relative error = 0.03212 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.912
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.843
Order of pole (three term test) = 5.837e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 0.000700430658982 -0.000837188045087
y[1] (closed_form) = 0.000700780215216 -0.000837136064491
absolute error = 3.534e-07
relative error = 0.03237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.912
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.747
Order of pole (three term test) = 6.092e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 0.000703410454514 -0.000833931183858
y[1] (closed_form) = 0.00070375351674 -0.000833877294978
absolute error = 3.473e-07
relative error = 0.03183 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.912
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.95
Order of pole (three term test) = 1.475e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 0.000705776615166 -0.000828879750875
y[1] (closed_form) = 0.000706115473488 -0.000828829784172
absolute error = 3.425e-07
relative error = 0.03146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.914
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.562
Order of pole (three term test) = 6.644e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 0.000712903996938 -0.000822875927669
y[1] (closed_form) = 0.000713238060391 -0.000822801250362
absolute error = 3.423e-07
relative error = 0.03144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.914
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.918
Order of pole (three term test) = 4.914e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 0.000715705600513 -0.000816507906839
y[1] (closed_form) = 0.000716045665461 -0.000816448424923
absolute error = 3.452e-07
relative error = 0.03179 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.916
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.35
Order of pole (three term test) = 1.609e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.488 1.735
h = 0.001 0.001
y[1] (numeric) = 0.000717409525523 -0.000812718035313
y[1] (closed_form) = 0.000717755950567 -0.000812658321199
absolute error = 3.515e-07
relative error = 0.03242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 0 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) = 3.060e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.489 1.736
h = 0.001 0.003
y[1] (numeric) = 0.000719211275767 -0.000811958361375
y[1] (closed_form) = 0.00071956084974 -0.00081189958606
absolute error = 3.545e-07
relative error = 0.03267 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.758
Order of pole (three term test) = 3.005e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 0.000722057490133 -0.000808627836716
y[1] (closed_form) = 0.000722400557629 -0.000808567425525
absolute error = 3.483e-07
relative error = 0.03213 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.956
Order of pole (three term test) = 1.726e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2204.4MB, alloc=44.3MB, time=27.26
x[1] = 2.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 0.000724234774411 -0.000803538117901
y[1] (closed_form) = 0.000724573831824 -0.000803481755595
absolute error = 3.437e-07
relative error = 0.03177 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.919
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.57
Order of pole (three term test) = 1.555e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 0.000731102482886 -0.000797344282192
y[1] (closed_form) = 0.000731435825971 -0.000797263635345
absolute error = 3.430e-07
relative error = 0.0317 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.919
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.922
Order of pole (three term test) = 1.029e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 0.000733667428366 -0.000790934828579
y[1] (closed_form) = 0.000734007308152 -0.000790868994875
absolute error = 3.462e-07
relative error = 0.03208 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.921
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.353
Order of pole (three term test) = 1.751e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 0.000735230301731 -0.000787119214531
y[1] (closed_form) = 0.000735576470525 -0.000787052902661
absolute error = 3.525e-07
relative error = 0.03272 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.922
Order of pole (given) = 0 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) = 7.997e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 0.000736991687122 -0.000786305493614
y[1] (closed_form) = 0.000737341010723 -0.000786239988499
absolute error = 3.554e-07
relative error = 0.03297 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.922
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.769
Order of pole (three term test) = 4.978e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 0.000739702733597 -0.000782907238798
y[1] (closed_form) = 0.00074004555054 -0.000782840367723
absolute error = 3.493e-07
relative error = 0.03242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.922
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.963
Order of pole (three term test) = 8.088e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 0.000741691480143 -0.000777786984031
y[1] (closed_form) = 0.000742030484296 -0.000777724278487
absolute error = 3.448e-07
relative error = 0.03207 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.924
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.579
Order of pole (three term test) = 7.288e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 0.000748294629206 -0.000771415122151
y[1] (closed_form) = 0.000748627028915 -0.000771328594283
absolute error = 3.435e-07
relative error = 0.03195 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.924
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.925
Order of pole (three term test) = 1.079e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 0.000750623625646 -0.000764973876395
y[1] (closed_form) = 0.000750963074167 -0.000764901759933
absolute error = 3.470e-07
relative error = 0.03237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.926
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.357
Order of pole (three term test) = 1.759e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2250.5MB, alloc=44.3MB, time=27.83
x[1] = 2.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 0.000752045833662 -0.000761138270961
y[1] (closed_form) = 0.000752391489974 -0.000761065436326
absolute error = 3.532e-07
relative error = 0.03301 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.927
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.85
Order of pole (three term test) = 6.709e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 0.00075376514671 -0.000760272609098
y[1] (closed_form) = 0.000754113957765 -0.000760200450416
absolute error = 3.562e-07
relative error = 0.03326 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.927
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.781
Order of pole (three term test) = 6.603e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = 0.000756339720759 -0.00075681256109
y[1] (closed_form) = 0.000756682036982 -0.000756739303293
absolute error = 3.501e-07
relative error = 0.03271 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.927
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.969
Order of pole (three term test) = 6.117e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5007 1.787
h = 0.003 0.006
y[1] (numeric) = 0.000758140609394 -0.000751669417354
y[1] (closed_form) = 0.000758479313044 -0.00075160043163
absolute error = 3.457e-07
relative error = 0.03237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.929
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.587
Order of pole (three term test) = 7.797e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = 0.000764474901632 -0.000745131596719
y[1] (closed_form) = 0.000764806141494 -0.000745039285105
absolute error = 3.439e-07
relative error = 0.03221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.929
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.929
Order of pole (three term test) = 5.661e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = 0.000766569078621 -0.000738668057424
y[1] (closed_form) = 0.000766907855641 -0.000738589737397
absolute error = 3.477e-07
relative error = 0.03266 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.931
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.36
Order of pole (three term test) = 1.305e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5039 1.801
h = 0.001 0.001
y[1] (numeric) = 0.000767851258594 -0.000734818128497
y[1] (closed_form) = 0.000768196152484 -0.000734738856679
absolute error = 3.539e-07
relative error = 0.03329 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.933
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.853
Order of pole (three term test) = 3.937e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = 0.000769526904972 -0.000733902683298
y[1] (closed_form) = 0.000769874947743 -0.000733823958155
absolute error = 3.568e-07
relative error = 0.03355 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.932
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.13
Order of pole (three term test) = 1.531e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.505 1.806
h = 0.003 0.006
y[1] (numeric) = 0.000771174878259 -0.000728746708477
y[1] (closed_form) = 0.000771511344262 -0.00072867371953
absolute error = 3.443e-07
relative error = 0.03244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.934
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.596
Order of pole (three term test) = 4.796e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.508 1.812
h = 0.0001 0.005
y[1] (numeric) = 0.000777272972721 -0.000722079000171
y[1] (closed_form) = 0.000777601267303 -0.00072198314825
absolute error = 3.420e-07
relative error = 0.03223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.934
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.933
Order of pole (three term test) = 1.221e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2296.7MB, alloc=44.3MB, time=28.40
x[1] = 2.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = 0.000779166126686 -0.000715606526275
y[1] (closed_form) = 0.000779502354033 -0.000715524285764
absolute error = 3.461e-07
relative error = 0.03271 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.936
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.363
Order of pole (three term test) = 1.661e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5082 1.82
h = 0.001 0.001
y[1] (numeric) = 0.000780328391168 -0.000711750388027
y[1] (closed_form) = 0.000780670647025 -0.000711667001285
absolute error = 3.523e-07
relative error = 0.03335 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.938
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.855
Order of pole (three term test) = 7.594e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5092 1.821
h = 0.001 0.003
y[1] (numeric) = 0.000781964704034 -0.000710794397342
y[1] (closed_form) = 0.000782310097687 -0.000710711447582
absolute error = 3.552e-07
relative error = 0.03361 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.937
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.804
Order of pole (three term test) = 2.564e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = 0.000784282244323 -0.000707236771532
y[1] (closed_form) = 0.000784621199089 -0.000707153208654
absolute error = 3.491e-07
relative error = 0.03305 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.938
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.982
Order of pole (three term test) = 2.636e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5103 1.828
h = 0.003 0.006
y[1] (numeric) = 0.000785736447319 -0.000702073175638
y[1] (closed_form) = 0.000786072168988 -0.000701994053721
absolute error = 3.449e-07
relative error = 0.03273 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.939
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.605
Order of pole (three term test) = 8.444e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = 0.000791559386301 -0.000695262110101
y[1] (closed_form) = 0.000791886138165 -0.000695160679601
absolute error = 3.421e-07
relative error = 0.03247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.94
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.937
Order of pole (three term test) = 3.735e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = 0.000793221006405 -0.000688784549919
y[1] (closed_form) = 0.000793556133498 -0.000688696281461
absolute error = 3.466e-07
relative error = 0.03298 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.942
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.366
Order of pole (three term test) = 7.321e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5135 1.842
h = 0.001 0.001
y[1] (numeric) = 0.000794245135526 -0.000684924360309
y[1] (closed_form) = 0.000794586183441 -0.000684834725027
absolute error = 3.526e-07
relative error = 0.03362 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.943
Order of pole (given) = 0 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) = 4.332e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5145 1.843
h = 0.001 0.003
y[1] (numeric) = 0.00079583514651 -0.00068392273253
y[1] (closed_form) = 0.000796179316011 -0.000683833408556
absolute error = 3.556e-07
relative error = 0.03388 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.943
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.816
Order of pole (three term test) = 2.697e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2343.0MB, alloc=44.3MB, time=28.97
x[1] = 2.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = 0.000798014076312 -0.000680320197895
y[1] (closed_form) = 0.000798351851238 -0.000680230515729
absolute error = 3.495e-07
relative error = 0.03332 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.943
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.989
Order of pole (three term test) = 6.933e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5156 1.85
h = 0.003 0.006
y[1] (numeric) = 0.000799284247286 -0.000675154862895
y[1] (closed_form) = 0.000799618994614 -0.000675069699339
absolute error = 3.454e-07
relative error = 0.03301 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.945
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.614
Order of pole (three term test) = 1.803e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = 0.000804829391697 -0.000668212566936
y[1] (closed_form) = 0.000805154404951 -0.000668105677612
absolute error = 3.421e-07
relative error = 0.0327 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.945
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.941
Order of pole (three term test) = 6.552e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = 0.000806261735577 -0.000661738906148
y[1] (closed_form) = 0.000806595541335 -0.000661644715521
absolute error = 3.468e-07
relative error = 0.03325 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.948
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.369
Order of pole (three term test) = 8.551e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5188 1.864
h = 0.001 0.001
y[1] (numeric) = 0.000807149040378 -0.000657880031268
y[1] (closed_form) = 0.000807488650893 -0.00065778426066
absolute error = 3.529e-07
relative error = 0.03388 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.949
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.86
Order of pole (three term test) = 5.769e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5198 1.865
h = 0.001 0.003
y[1] (numeric) = 0.000808691483943 -0.000656835035435
y[1] (closed_form) = 0.000809034194506 -0.000656739452715
absolute error = 3.558e-07
relative error = 0.03414 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.948
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.829
Order of pole (three term test) = 6.350e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = 0.000810731548554 -0.000653193411063
y[1] (closed_form) = 0.000811067919517 -0.000653097719996
absolute error = 3.497e-07
relative error = 0.03358 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.949
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.997
Order of pole (three term test) = 7.302e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5209 1.872
h = 0.003 0.006
y[1] (numeric) = 0.000811819586441 -0.000648033442805
y[1] (closed_form) = 0.000812153136182 -0.000647942338011
absolute error = 3.458e-07
relative error = 0.03328 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.951
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.624
Order of pole (three term test) = 9.312e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = 0.000817084862761 -0.000640972010817
y[1] (closed_form) = 0.000817407949205 -0.000640859789415
absolute error = 3.420e-07
relative error = 0.03293 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.951
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.945
Order of pole (three term test) = 6.904e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.524 1.883
h = 0.0001 0.003
y[1] (numeric) = 0.000818290555154 -0.000634511025024
y[1] (closed_form) = 0.000818622825852 -0.00063441102643
absolute error = 3.470e-07
relative error = 0.0335 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.953
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.373
Order of pole (three term test) = 4.595e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2389.2MB, alloc=44.3MB, time=29.54
x[1] = 2.5241 1.886
h = 0.001 0.001
y[1] (numeric) = 0.000819042566075 -0.000630658707066
y[1] (closed_form) = 0.000819380517566 -0.000630556923083
absolute error = 3.529e-07
relative error = 0.03414 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.955
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.863
Order of pole (three term test) = 6.081e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5251 1.887
h = 0.001 0.003
y[1] (numeric) = 0.000820536291939 -0.000629572639675
y[1] (closed_form) = 0.000820877316801 -0.000629470922645
absolute error = 3.559e-07
relative error = 0.0344 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.954
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.842
Order of pole (three term test) = 9.545e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = 0.00082243749528 -0.000625897683733
y[1] (closed_form) = 0.000822772245781 -0.000625796102667
absolute error = 3.498e-07
relative error = 0.03384 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.955
Order of pole (given) = 0 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) = 1.540e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5262 1.894
h = 0.003 0.006
y[1] (numeric) = 0.000823345587196 -0.00062075001641
y[1] (closed_form) = 0.000823677723225 -0.000620653079391
absolute error = 3.460e-07
relative error = 0.03355 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.957
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.633
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = 0.000828329477948 -0.000613581482931
y[1] (closed_form) = 0.000828650457302 -0.000613464062706
absolute error = 3.418e-07
relative error = 0.03315 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.957
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.95
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = 0.00082931149515 -0.000607141722524
y[1] (closed_form) = 0.00082964202473 -0.000607036038114
absolute error = 3.470e-07
relative error = 0.03376 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.959
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.376
Order of pole (three term test) = 3.361e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5294 1.908
h = 0.001 0.001
y[1] (numeric) = 0.000829929952818 -0.000603301070734
y[1] (closed_form) = 0.000830266031826 -0.000603193403552
absolute error = 3.529e-07
relative error = 0.03439 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 0 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) = 9.253e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = 0.000831373925673 -0.000602176249675
y[1] (closed_form) = 0.00083171304643 -0.000602068531215
absolute error = 3.558e-07
relative error = 0.03465 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.2
Order of pole (three term test) = 3.946e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5305 1.913
h = 0.003 0.006
y[1] (numeric) = 0.000832136706402 -0.00059704393985
y[1] (closed_form) = 0.000832466028473 -0.000596943651534
absolute error = 3.443e-07
relative error = 0.03361 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.962
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.642
Order of pole (three term test) = 1.031e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2435.3MB, alloc=44.3MB, time=30.11
x[1] = 2.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = 0.00083687650889 -0.000589796154971
y[1] (closed_form) = 0.000837194114571 -0.000589675954131
absolute error = 3.396e-07
relative error = 0.03316 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.962
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.954
Order of pole (three term test) = 7.648e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = 0.000837669020791 -0.000583383939202
y[1] (closed_form) = 0.000837996464984 -0.000583275043249
absolute error = 3.451e-07
relative error = 0.0338 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.965
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.38
Order of pole (three term test) = 9.987e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5337 1.927
h = 0.001 0.001
y[1] (numeric) = 0.000838174286711 -0.000579558871831
y[1] (closed_form) = 0.000838507159495 -0.000579447831494
absolute error = 3.509e-07
relative error = 0.03443 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.869
Order of pole (three term test) = 2.383e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5347 1.928
h = 0.001 0.003
y[1] (numeric) = 0.000839574268351 -0.000578403168265
y[1] (closed_form) = 0.0008399101505 -0.000578291977652
absolute error = 3.538e-07
relative error = 0.0347 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.867
Order of pole (three term test) = 6.637e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = 0.000841217712631 -0.000574682900336
y[1] (closed_form) = 0.000841547470416 -0.00057457228308
absolute error = 3.478e-07
relative error = 0.03413 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.018
Order of pole (three term test) = 8.536e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5358 1.935
h = 0.003 0.006
y[1] (numeric) = 0.000841798055416 -0.000569578011022
y[1] (closed_form) = 0.000842125583182 -0.000569472116987
absolute error = 3.442e-07
relative error = 0.03386 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.968
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.652
Order of pole (three term test) = 1.089e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = 0.000846255230857 -0.000562245271827
y[1] (closed_form) = 0.000846570417482 -0.000562120137724
absolute error = 3.391e-07
relative error = 0.03337 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.968
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.958
Order of pole (three term test) = 1.807e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = 0.000846830580744 -0.000555869500484
y[1] (closed_form) = 0.000847155923398 -0.000555755167705
absolute error = 3.448e-07
relative error = 0.03404 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.971
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.383
Order of pole (three term test) = 7.464e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.539 1.949
h = 0.001 0.001
y[1] (numeric) = 0.000847206115541 -0.000552065198064
y[1] (closed_form) = 0.000847536743085 -0.000551948539155
absolute error = 3.506e-07
relative error = 0.03466 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.871
Order of pole (three term test) = 1.284e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2481.5MB, alloc=44.3MB, time=30.69
x[1] = 2.54 1.95
h = 0.001 0.003
y[1] (numeric) = 0.00084855474933 -0.000550875099677
y[1] (closed_form) = 0.000848888346005 -0.000550758177871
absolute error = 3.535e-07
relative error = 0.03493 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.881
Order of pole (three term test) = 7.016e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.541 1.953
h = 0.0001 0.004
y[1] (numeric) = 0.000850060775047 -0.000547137522861
y[1] (closed_form) = 0.000850388339504 -0.000547021400536
absolute error = 3.475e-07
relative error = 0.03437 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.026
Order of pole (three term test) = 1.342e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5411 1.957
h = 0.003 0.006
y[1] (numeric) = 0.000850468980829 -0.000542063685795
y[1] (closed_form) = 0.000850794520316 -0.000541952316957
absolute error = 3.441e-07
relative error = 0.03411 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.974
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.663
Order of pole (three term test) = 6.910e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = 0.000854643536384 -0.000534657706743
y[1] (closed_form) = 0.000854956147391 -0.000534527788502
absolute error = 3.385e-07
relative error = 0.03357 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.974
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.963
Order of pole (three term test) = 8.549e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = 0.000855005612399 -0.000528326208702
y[1] (closed_form) = 0.000855328670915 -0.000528206581151
absolute error = 3.445e-07
relative error = 0.03427 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.977
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.387
Order of pole (three term test) = 1.396e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5443 1.971
h = 0.001 0.001
y[1] (numeric) = 0.000855253702363 -0.000524547353893
y[1] (closed_form) = 0.000855581896111 -0.000524425227106
absolute error = 3.502e-07
relative error = 0.0349 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.978
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.874
Order of pole (three term test) = 8.428e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5453 1.972
h = 0.001 0.003
y[1] (numeric) = 0.000856550277505 -0.000523325206046
y[1] (closed_form) = 0.00085688139581 -0.000523202706984
absolute error = 3.531e-07
relative error = 0.03517 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.978
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.895
Order of pole (three term test) = 8.301e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = 0.000857919818552 -0.000519575734295
y[1] (closed_form) = 0.000858245005345 -0.000519454253833
absolute error = 3.471e-07
relative error = 0.0346 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.979
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.034
Order of pole (three term test) = 3.820e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5464 1.979
h = 0.003 0.006
y[1] (numeric) = 0.000858159063059 -0.000514539115911
y[1] (closed_form) = 0.000858482428496 -0.000514422409928
absolute error = 3.438e-07
relative error = 0.03435 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.98
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.673
Order of pole (three term test) = 1.225e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = 0.000862051512956 -0.000507071455362
y[1] (closed_form) = 0.000862361400308 -0.000506936906749
absolute error = 3.378e-07
relative error = 0.03377 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.981
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.968
Order of pole (three term test) = 1.346e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2527.6MB, alloc=44.3MB, time=31.26
x[1] = 2.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = 0.000862204489928 -0.000500791786434
y[1] (closed_form) = 0.00086252509028 -0.000500667012184
absolute error = 3.440e-07
relative error = 0.0345 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.983
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.391
Order of pole (three term test) = 2.957e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5496 1.993
h = 0.001 0.001
y[1] (numeric) = 0.000862327593069 -0.000497042900274
y[1] (closed_form) = 0.000862653173552 -0.000496915462479
absolute error = 3.496e-07
relative error = 0.03512 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.985
Order of pole (given) = 0 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) = 7.984e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5506 1.994
h = 0.001 0.003
y[1] (numeric) = 0.000863571509642 -0.000495791047546
y[1] (closed_form) = 0.000863899965993 -0.000495663131501
absolute error = 3.525e-07
relative error = 0.03539 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.984
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.909
Order of pole (three term test) = 3.932e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = 0.000864805721329 -0.000492034981684
y[1] (closed_form) = 0.000865128354962 -0.000491908296045
absolute error = 3.466e-07
relative error = 0.03483 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.985
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.042
Order of pole (three term test) = 7.083e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5517 2.001
h = 0.003 0.006
y[1] (numeric) = 0.000864879403807 -0.000487041528139
y[1] (closed_form) = 0.000865200417834 -0.000486919628906
absolute error = 3.434e-07
relative error = 0.03459 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.987
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.684
Order of pole (three term test) = 1.391e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = 0.000868490754056 -0.000479523566105
y[1] (closed_form) = 0.000868797778329 -0.000479384545055
absolute error = 3.370e-07
relative error = 0.03397 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.987
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.973
Order of pole (three term test) = 9.663e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = 0.000868439075863 -0.000473302999311
y[1] (closed_form) = 0.000868757052766 -0.000473173231946
absolute error = 3.434e-07
relative error = 0.03472 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.99
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.395
Order of pole (three term test) = 9.403e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5549 2.015
h = 0.001 0.001
y[1] (numeric) = 0.000868439811452 -0.000469588435371
y[1] (closed_form) = 0.000868762608447 -0.000469455849078
absolute error = 3.490e-07
relative error = 0.03534 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.991
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.88
Order of pole (three term test) = 8.465e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = 0.00086963057867 -0.000468309216196
y[1] (closed_form) = 0.000869956198958 -0.000468176049227
absolute error = 3.518e-07
relative error = 0.03561 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.991
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.29
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2573.8MB, alloc=44.3MB, time=31.84
x[1] = 2.556 2.02
h = 0.003 0.006
y[1] (numeric) = 0.000869571613308 -0.000463355571301
y[1] (closed_form) = 0.000869889412012 -0.000463231038785
absolute error = 3.413e-07
relative error = 0.03463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.993
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.694
Order of pole (three term test) = 1.368e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.559 2.026
h = 0.0001 0.005
y[1] (numeric) = 0.000872941753024 -0.000455806595827
y[1] (closed_form) = 0.00087324516077 -0.000455665577096
absolute error = 3.346e-07
relative error = 0.03397 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.993
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.977
Order of pole (three term test) = 1.180e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = 0.000872718481771 -0.000449644865077
y[1] (closed_form) = 0.0008730330216 -0.000449512646932
absolute error = 3.412e-07
relative error = 0.03475 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.996
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.398
Order of pole (three term test) = 4.675e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5592 2.034
h = 0.001 0.001
y[1] (numeric) = 0.0008726165764 -0.000445964611469
y[1] (closed_form) = 0.000872935793295 -0.000445829449847
absolute error = 3.467e-07
relative error = 0.03537 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.997
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.883
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5602 2.035
h = 0.001 0.003
y[1] (numeric) = 0.000873760994978 -0.00044466433929
y[1] (closed_form) = 0.000874082985818 -0.000444528512456
absolute error = 3.495e-07
relative error = 0.03564 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.997
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.937
Order of pole (three term test) = 8.796e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = 0.000874747251008 -0.00044091125704
y[1] (closed_form) = 0.000875063643751 -0.000440777032833
absolute error = 3.437e-07
relative error = 0.03508 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.997
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.058
Order of pole (three term test) = 1.219e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5613 2.042
h = 0.003 0.006
y[1] (numeric) = 0.000874523285754 -0.000436015031428
y[1] (closed_form) = 0.000874838427859 -0.000435885590174
absolute error = 3.407e-07
relative error = 0.03486 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 3.999
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.705
Order of pole (three term test) = 2.891e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = 0.000877615580081 -0.000428436359159
y[1] (closed_form) = 0.000877915890407 -0.000428291172736
absolute error = 3.336e-07
relative error = 0.03415 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.982
Order of pole (three term test) = 1.074e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = 0.000877196655818 -0.00042234642292
y[1] (closed_form) = 0.000877508290287 -0.000422209512089
absolute error = 3.404e-07
relative error = 0.03495 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.002
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.402
Order of pole (three term test) = 8.099e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5645 2.056
h = 0.001 0.001
y[1] (numeric) = 0.000876977696503 -0.000418708094293
y[1] (closed_form) = 0.000877293840271 -0.000418568101492
absolute error = 3.458e-07
relative error = 0.03557 %
Correct digits = 3
memory used=2620.0MB, alloc=44.3MB, time=32.41
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 0 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) = 7.497e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5655 2.057
h = 0.001 0.003
y[1] (numeric) = 0.000878068363387 -0.000417384775899
y[1] (closed_form) = 0.000878387221959 -0.000417244022444
absolute error = 3.485e-07
relative error = 0.03584 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.003
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.952
Order of pole (three term test) = 1.402e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = 0.000878923794922 -0.000413639539597
y[1] (closed_form) = 0.000879237184563 -0.000413500578143
absolute error = 3.428e-07
relative error = 0.03528 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.066
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5666 2.064
h = 0.003 0.006
y[1] (numeric) = 0.000878545161012 -0.000408802161935
y[1] (closed_form) = 0.000878857494148 -0.000408667970807
absolute error = 3.399e-07
relative error = 0.03507 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.006
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.716
Order of pole (three term test) = 1.543e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = 0.000881361927537 -0.000401204545578
y[1] (closed_form) = 0.000881659025941 -0.000401055358586
absolute error = 3.325e-07
relative error = 0.03432 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.007
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.987
Order of pole (three term test) = 1.331e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = 0.000880752461127 -0.000395192821591
y[1] (closed_form) = 0.000881061050619 -0.000395051384516
absolute error = 3.395e-07
relative error = 0.03516 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.009
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.406
Order of pole (three term test) = 5.277e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5698 2.078
h = 0.001 0.001
y[1] (numeric) = 0.000880419467489 -0.00039160026457
y[1] (closed_form) = 0.00088073239502 -0.000391455616157
absolute error = 3.447e-07
relative error = 0.03577 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.011
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.89
Order of pole (three term test) = 7.348e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5708 2.079
h = 0.001 0.003
y[1] (numeric) = 0.000881456191996 -0.000390256191727
y[1] (closed_form) = 0.000881771771975 -0.000390110691103
absolute error = 3.475e-07
relative error = 0.03604 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.01
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.967
Order of pole (three term test) = 5.065e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = 0.000882182721322 -0.000386523584613
y[1] (closed_form) = 0.000882492967742 -0.00038638005715
absolute error = 3.418e-07
relative error = 0.03548 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.011
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.075
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5719 2.086
h = 0.003 0.006
y[1] (numeric) = 0.000881653544488 -0.000381750086858
y[1] (closed_form) = 0.000881962925208 -0.00038161130902
absolute error = 3.391e-07
relative error = 0.03528 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.728
Order of pole (three term test) = 6.928e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2666.2MB, alloc=44.3MB, time=32.98
x[1] = 2.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = 0.000884197525405 -0.000374144026675
y[1] (closed_form) = 0.00088449130609 -0.000373991008593
absolute error = 3.312e-07
relative error = 0.03449 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.992
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.575 2.097
h = 0.0001 0.003
y[1] (numeric) = 0.00088340282719 -0.000368216622907
y[1] (closed_form) = 0.000883708241171 -0.000368070829597
absolute error = 3.384e-07
relative error = 0.03535 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.016
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.41
Order of pole (three term test) = 1.256e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5751 2.1
h = 0.001 0.001
y[1] (numeric) = 0.000882958938798 -0.000364673500378
y[1] (closed_form) = 0.000883268516555 -0.000364524375503
absolute error = 3.436e-07
relative error = 0.03596 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.017
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.893
Order of pole (three term test) = 3.960e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5761 2.101
h = 0.001 0.003
y[1] (numeric) = 0.000883941630342 -0.000363310939895
y[1] (closed_form) = 0.000884253795215 -0.000363160875225
absolute error = 3.464e-07
relative error = 0.03623 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.017
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.983
Order of pole (three term test) = 5.285e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = 0.000884541355217 -0.000359595594484
y[1] (closed_form) = 0.000884848327616 -0.00035944767576
absolute error = 3.408e-07
relative error = 0.03568 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.018
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.084
Order of pole (three term test) = 1.521e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5772 2.108
h = 0.003 0.006
y[1] (numeric) = 0.000883865915133 -0.000354890760587
y[1] (closed_form) = 0.00088417220898 -0.000354747563003
absolute error = 3.381e-07
relative error = 0.03549 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.739
Order of pole (three term test) = 1.872e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = 0.00088614025827 -0.000347286488251
y[1] (closed_form) = 0.000886430624107 -0.000347129810464
absolute error = 3.299e-07
relative error = 0.03466 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.997
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = 0.000885165820025 -0.000341449198469
y[1] (closed_form) = 0.000885467937063 -0.000341299222006
absolute error = 3.373e-07
relative error = 0.03554 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.023
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.415
Order of pole (three term test) = 9.454e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5804 2.122
h = 0.001 0.001
y[1] (numeric) = 0.00088461428567 -0.000337958986881
y[1] (closed_form) = 0.000884920389703 -0.00033780556776
absolute error = 3.424e-07
relative error = 0.03615 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.024
Order of pole (given) = 0 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2712.4MB, alloc=44.3MB, time=33.55
x[1] = 2.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = 0.000885542950927 -0.000336580176255
y[1] (closed_form) = 0.000885851574006 -0.000336425733806
absolute error = 3.451e-07
relative error = 0.03642 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.024
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.39
Order of pole (three term test) = 4.972e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5815 2.127
h = 0.003 0.006
y[1] (numeric) = 0.000884751288186 -0.000331935092893
y[1] (closed_form) = 0.000885054139094 -0.00033179000135
absolute error = 3.358e-07
relative error = 0.03553 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.026
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.75
Order of pole (three term test) = 1.840e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = 0.000886796534017 -0.000324343490399
y[1] (closed_form) = 0.000887083213279 -0.000324185578308
absolute error = 3.273e-07
relative error = 0.03465 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.027
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.002
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = 0.000885673065935 -0.000318590213811
y[1] (closed_form) = 0.00088597157261 -0.000318438553678
absolute error = 3.348e-07
relative error = 0.03556 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.029
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.418
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5847 2.141
h = 0.001 0.001
y[1] (numeric) = 0.000885032233708 -0.000315149413941
y[1] (closed_form) = 0.00088533457238 -0.00031499422495
absolute error = 3.398e-07
relative error = 0.03616 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.899
Order of pole (three term test) = 9.565e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5857 2.142
h = 0.001 0.003
y[1] (numeric) = 0.0008859143144 -0.000313759023732
y[1] (closed_form) = 0.000886219110585 -0.00031360274365
absolute error = 3.425e-07
relative error = 0.03644 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.013
Order of pole (three term test) = 8.430e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = 0.000886284556536 -0.000310089031662
y[1] (closed_form) = 0.000886584438111 -0.000309935194495
absolute error = 3.370e-07
relative error = 0.03589 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.101
Order of pole (three term test) = 1.535e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5868 2.149
h = 0.003 0.006
y[1] (numeric) = 0.000885349753473 -0.000305525451241
y[1] (closed_form) = 0.000885649293408 -0.000305376260427
absolute error = 3.346e-07
relative error = 0.03572 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.033
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.762
Order of pole (three term test) = 7.846e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = 0.000887132345135 -0.000297953862624
y[1] (closed_form) = 0.000887415453751 -0.000297792614227
absolute error = 3.258e-07
relative error = 0.03481 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.034
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.007
Order of pole (three term test) = 1.460e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = 0.000885839837517 -0.000292300564047
y[1] (closed_form) = 0.000886134847613 -0.00029214505055
absolute error = 3.335e-07
relative error = 0.03574 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.037
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.423
Order of pole (three term test) = 6.754e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2758.5MB, alloc=44.3MB, time=34.12
x[1] = 2.59 2.163
h = 0.001 0.001
y[1] (numeric) = 0.000885097694883 -0.000288918599827
y[1] (closed_form) = 0.000885396356873 -0.00028875946328
absolute error = 3.384e-07
relative error = 0.03634 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.903
Order of pole (three term test) = 1.020e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.591 2.164
h = 0.001 0.003
y[1] (numeric) = 0.000885926035785 -0.00028751602829
y[1] (closed_form) = 0.000886227082803 -0.000287355724835
absolute error = 3.411e-07
relative error = 0.03661 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.029
Order of pole (three term test) = 8.995e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.592 2.167
h = 0.0001 0.004
y[1] (numeric) = 0.000886176401808 -0.000283875637064
y[1] (closed_form) = 0.000886472688829 -0.000283717924665
absolute error = 3.356e-07
relative error = 0.03606 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.039
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.11
Order of pole (three term test) = 3.604e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5921 2.171
h = 0.003 0.006
y[1] (numeric) = 0.00088510834767 -0.000279392955259
y[1] (closed_form) = 0.000885404468019 -0.000279239840225
absolute error = 3.334e-07
relative error = 0.03591 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.041
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.774
Order of pole (three term test) = 9.362e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = 0.000886632480742 -0.000271850762269
y[1] (closed_form) = 0.000886911945995 -0.000271686351916
absolute error = 3.242e-07
relative error = 0.03496 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.041
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.013
Order of pole (three term test) = 1.567e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = 0.000885176842043 -0.000266302319849
y[1] (closed_form) = 0.000885468260077 -0.00026614313212
absolute error = 3.321e-07
relative error = 0.03591 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.044
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.427
Order of pole (three term test) = 5.099e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5953 2.185
h = 0.001 0.001
y[1] (numeric) = 0.000884336889406 -0.000262982124065
y[1] (closed_form) = 0.000884631778042 -0.000262819228062
absolute error = 3.369e-07
relative error = 0.03651 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.046
Order of pole (given) = 0 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) = 4.873e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5963 2.186
h = 0.001 0.003
y[1] (numeric) = 0.000885111757766 -0.000261569501838
y[1] (closed_form) = 0.000885408956884 -0.000261405367296
absolute error = 3.395e-07
relative error = 0.03678 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.045
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.045
Order of pole (three term test) = 1.358e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = 0.000885244925453 -0.00025796271106
y[1] (closed_form) = 0.000885537523013 -0.000257801306987
absolute error = 3.342e-07
relative error = 0.03623 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.046
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.119
Order of pole (three term test) = 1.758e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2804.7MB, alloc=44.3MB, time=34.70
x[1] = 2.5974 2.193
h = 0.003 0.006
y[1] (numeric) = 0.000884048357641 -0.000253564730103
y[1] (closed_form) = 0.00088434095877 -0.000253407867851
absolute error = 3.320e-07
relative error = 0.03609 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.048
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.787
Order of pole (three term test) = 1.140e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = 0.000885318555979 -0.000246060996009
y[1] (closed_form) = 0.000885594313481 -0.00024589359833
absolute error = 3.226e-07
relative error = 0.0351 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.049
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.018
Order of pole (three term test) = 1.166e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = 0.000883705807858 -0.000240621966254
y[1] (closed_form) = 0.000883993547292 -0.000240459284686
absolute error = 3.305e-07
relative error = 0.03608 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.051
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.432
Order of pole (three term test) = 1.111e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6006 2.207
h = 0.001 0.001
y[1] (numeric) = 0.000882771614271 -0.000237366280603
y[1] (closed_form) = 0.000883062642265 -0.000237199814404
absolute error = 3.353e-07
relative error = 0.03667 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.91
Order of pole (three term test) = 5.208e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6016 2.208
h = 0.001 0.003
y[1] (numeric) = 0.000883493362107 -0.000235945694441
y[1] (closed_form) = 0.000883786624207 -0.000235777922284
absolute error = 3.379e-07
relative error = 0.03694 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.062
Order of pole (three term test) = 8.861e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = 0.000883512134925 -0.000232376330491
y[1] (closed_form) = 0.000883800957259 -0.000232211419462
absolute error = 3.326e-07
relative error = 0.0364 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.129
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6027 2.215
h = 0.003 0.006
y[1] (numeric) = 0.000882191876356 -0.0002280665965
y[1] (closed_form) = 0.00088248086755 -0.000227906165526
absolute error = 3.305e-07
relative error = 0.03627 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.056
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.799
Order of pole (three term test) = 4.781e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = 0.000883212971474 -0.000220610056239
y[1] (closed_form) = 0.000883484965023 -0.000220439845751
absolute error = 3.209e-07
relative error = 0.03524 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.056
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.024
Order of pole (three term test) = 1.790e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = 0.000881449231753 -0.00021528467433
y[1] (closed_form) = 0.000881733214898 -0.00021511868014
absolute error = 3.289e-07
relative error = 0.03624 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.059
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.436
Order of pole (three term test) = 5.828e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6059 2.229
h = 0.001 0.001
y[1] (numeric) = 0.000880424424784 -0.000212096049551
y[1] (closed_form) = 0.000880711514126 -0.000211926203118
absolute error = 3.336e-07
relative error = 0.03682 %
Correct digits = 3
memory used=2850.8MB, alloc=44.3MB, time=35.27
Radius of convergence (given) for eq 1 = 4.061
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.913
Order of pole (three term test) = 5.571e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = 0.000881093485346 -0.000210669539131
y[1] (closed_form) = 0.000881382730815 -0.000210498323543
absolute error = 3.361e-07
relative error = 0.03709 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.06
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.49
Order of pole (three term test) = 9.701e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.607 2.234
h = 0.003 0.006
y[1] (numeric) = 0.000879675848368 -0.000206434612273
y[1] (closed_form) = 0.000879961330886 -0.000206273008216
absolute error = 3.280e-07
relative error = 0.0363 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.062
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.811
Order of pole (three term test) = 5.679e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.61 2.24
h = 0.0001 0.005
y[1] (numeric) = 0.000880487309777 -0.000199028316211
y[1] (closed_form) = 0.000880755698023 -0.000198857580235
absolute error = 3.181e-07
relative error = 0.03523 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.063
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.029
Order of pole (three term test) = 5.678e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = 0.000878599978081 -0.000193805603498
y[1] (closed_form) = 0.00087888034001 -0.000193638659879
absolute error = 3.263e-07
relative error = 0.03626 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.066
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.44
Order of pole (three term test) = 1.239e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6102 2.248
h = 0.001 0.001
y[1] (numeric) = 0.000877500952972 -0.0001906776194
y[1] (closed_form) = 0.000877784263516 -0.000190506774406
absolute error = 3.308e-07
relative error = 0.03683 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.067
Order of pole (given) = 0 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) = 6.038e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6112 2.249
h = 0.001 0.003
y[1] (numeric) = 0.000878125029926 -0.000189248223914
y[1] (closed_form) = 0.000878410427683 -0.0001890759597
absolute error = 3.334e-07
relative error = 0.0371 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.067
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.094
Order of pole (three term test) = 8.501e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = 0.000877939334959 -0.000185759360543
y[1] (closed_form) = 0.000878220602645 -0.000185590175292
absolute error = 3.282e-07
relative error = 0.03657 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.068
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.147
Order of pole (three term test) = 6.381e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6123 2.256
h = 0.003 0.006
y[1] (numeric) = 0.000876403129176 -0.000181623731728
y[1] (closed_form) = 0.000876684858537 -0.000181458894391
absolute error = 3.264e-07
relative error = 0.03646 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.07
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.824
Order of pole (three term test) = 9.805e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = 0.000876975319921 -0.000174279915569
y[1] (closed_form) = 0.000877239862963 -0.000174106690398
absolute error = 3.162e-07
relative error = 0.03536 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.071
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.035
Order of pole (three term test) = 4.055e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2896.9MB, alloc=44.3MB, time=35.84
x[1] = 2.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = 0.00087494862104 -0.00016917780607
y[1] (closed_form) = 0.000875225107417 -0.000169007888446
absolute error = 3.245e-07
relative error = 0.03641 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.074
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.445
Order of pole (three term test) = 8.497e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6155 2.27
h = 0.001 0.001
y[1] (numeric) = 0.000873765879558 -0.00016612107913
y[1] (closed_form) = 0.00087404513277 -0.000165947208399
absolute error = 3.290e-07
relative error = 0.03698 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.075
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.92
Order of pole (three term test) = 3.806e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6165 2.271
h = 0.001 0.003
y[1] (numeric) = 0.000874338301967 -0.000164689412255
y[1] (closed_form) = 0.00087461956208 -0.000164514066966
absolute error = 3.314e-07
relative error = 0.03724 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.075
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.112
Order of pole (three term test) = 7.959e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = 0.000874046872851 -0.000161247904961
y[1] (closed_form) = 0.000874324171623 -0.000161075744297
absolute error = 3.264e-07
relative error = 0.03671 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.076
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.157
Order of pole (three term test) = 1.228e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6176 2.278
h = 0.003 0.006
y[1] (numeric) = 0.000872401158606 -0.000157209200969
y[1] (closed_form) = 0.000872679069072 -0.000157041310615
absolute error = 3.247e-07
relative error = 0.03662 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.078
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.837
Order of pole (three term test) = 8.743e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = 0.000872739671577 -0.00014993561433
y[1] (closed_form) = 0.000873000335734 -0.000149760072055
absolute error = 3.143e-07
relative error = 0.03548 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.079
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.041
Order of pole (three term test) = 3.074e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = 0.000870579903935 -0.000144957432924
y[1] (closed_form) = 0.000870852461662 -0.000144784722454
absolute error = 3.227e-07
relative error = 0.03655 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.082
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.45
Order of pole (three term test) = 1.006e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6208 2.292
h = 0.001 0.001
y[1] (numeric) = 0.000869317184784 -0.000141973972573
y[1] (closed_form) = 0.000869592328384 -0.000141797265553
absolute error = 3.270e-07
relative error = 0.03711 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.083
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.924
Order of pole (three term test) = 2.040e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6218 2.293
h = 0.001 0.003
y[1] (numeric) = 0.000869838597313 -0.000140541923043
y[1] (closed_form) = 0.000870115666529 -0.000140363690314
absolute error = 3.294e-07
relative error = 0.03738 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.083
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.13
Order of pole (three term test) = 1.481e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2943.3MB, alloc=44.3MB, time=36.43
x[1] = 2.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = 0.000869444624613 -0.000137150906981
y[1] (closed_form) = 0.000869717902819 -0.000136975955913
absolute error = 3.245e-07
relative error = 0.03685 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.084
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.167
Order of pole (three term test) = 1.093e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6229 2.3
h = 0.003 0.006
y[1] (numeric) = 0.000867694428386 -0.000133211695482
y[1] (closed_form) = 0.000867968462695 -0.000133040932231
absolute error = 3.229e-07
relative error = 0.03677 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.086
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.85
Order of pole (three term test) = 4.421e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = 0.000867805084081 -0.000126015733498
y[1] (closed_form) = 0.000868061843188 -0.000125838044737
absolute error = 3.122e-07
relative error = 0.0356 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.087
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.047
Order of pole (three term test) = 6.595e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.626 2.311
h = 0.0001 0.003
y[1] (numeric) = 0.000865518580196 -0.000121164493011
y[1] (closed_form) = 0.000865787164466 -0.000120989170108
absolute error = 3.207e-07
relative error = 0.03669 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.09
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.455
Order of pole (three term test) = 7.634e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6261 2.314
h = 0.001 0.001
y[1] (numeric) = 0.000864179643641 -0.000118256123017
y[1] (closed_form) = 0.000864450633998 -0.000118076768223
absolute error = 3.250e-07
relative error = 0.03725 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.091
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.928
Order of pole (three term test) = 1.032e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6271 2.315
h = 0.001 0.003
y[1] (numeric) = 0.000864650757758 -0.0001168255225
y[1] (closed_form) = 0.000864923591688 -0.000116644595003
absolute error = 3.274e-07
relative error = 0.03751 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.091
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.148
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = 0.000864157508462 -0.000113487951274
y[1] (closed_form) = 0.00086442672289 -0.000113310393928
absolute error = 3.225e-07
relative error = 0.03699 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.092
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.177
Order of pole (three term test) = 3.711e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6282 2.322
h = 0.003 0.006
y[1] (numeric) = 0.000862307879841 -0.000109650552548
y[1] (closed_form) = 0.000862577989049 -0.000109477095986
absolute error = 3.210e-07
relative error = 0.03692 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.094
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.864
Order of pole (three term test) = 4.746e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = 0.0008621967059 -0.00010253925191
y[1] (closed_form) = 0.000862449541096 -0.000102359585501
absolute error = 3.102e-07
relative error = 0.03571 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.095
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.053
Order of pole (three term test) = 2.504e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = 0.000859789817428 -9.78176573086e-05
y[1] (closed_form) = 0.000860054391534 -9.76399012752e-05
absolute error = 3.187e-07
relative error = 0.03682 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.098
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.459
Order of pole (three term test) = 8.199e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2989.4MB, alloc=44.3MB, time=37.00
x[1] = 2.6314 2.336
h = 0.001 0.001
y[1] (numeric) = 0.000858378436372 -9.49860182145e-05
y[1] (closed_form) = 0.000858645238309 -9.48042028471e-05
absolute error = 3.229e-07
relative error = 0.03737 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.931
Order of pole (three term test) = 1.109e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = 0.000858800026502 -9.35586393091e-05
y[1] (closed_form) = 0.000859068589412 -9.33752083553e-05
absolute error = 3.252e-07
relative error = 0.03764 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.6
Order of pole (three term test) = 2.049e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6325 2.341
h = 0.003 0.006
y[1] (numeric) = 0.00085687300276 -8.98062014975e-05
y[1] (closed_form) = 0.000857139679475 -8.96322417090e-05
absolute error = 3.184e-07
relative error = 0.03695 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.876
Order of pole (three term test) = 2.504e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = 0.00085657697107 -8.27756747918e-05
y[1] (closed_form) = 0.000856826406415 -8.25961111852e-05
absolute error = 3.073e-07
relative error = 0.0357 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.102
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.058
Order of pole (three term test) = 8.010e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = 0.000854073132296 -7.81689406077e-05
y[1] (closed_form) = 0.000854334213391 -7.79909054694e-05
absolute error = 3.160e-07
relative error = 0.03684 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.105
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.464
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6357 2.355
h = 0.001 0.001
y[1] (numeric) = 0.000852603355223 -7.54053265431e-05
y[1] (closed_form) = 0.000852866511986 -7.52232166986e-05
absolute error = 3.200e-07
relative error = 0.03738 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 0 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) = 1.182e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6367 2.356
h = 0.001 0.003
y[1] (numeric) = 0.000852983048082 -7.39826700041e-05
y[1] (closed_form) = 0.000853247893978 -7.37989119046e-05
absolute error = 3.224e-07
relative error = 0.03764 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.106
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.182
Order of pole (three term test) = 1.166e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = 0.000852314696 -7.07528739661e-05
y[1] (closed_form) = 0.000852576244077 -7.05726262623e-05
absolute error = 3.176e-07
relative error = 0.03713 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.197
Order of pole (three term test) = 1.052e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6378 2.363
h = 0.003 0.006
y[1] (numeric) = 0.000850294783777 -6.71113104096e-05
y[1] (closed_form) = 0.000850557467944 -6.69349891545e-05
absolute error = 3.164e-07
relative error = 0.03708 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.89
Order of pole (three term test) = 7.692e-63 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3035.6MB, alloc=44.3MB, time=37.57
x[1] = 2.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = 0.000849788694274 -6.01774991120e-05
y[1] (closed_form) = 0.000850034191254 -5.99962663052e-05
absolute error = 3.051e-07
relative error = 0.03581 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.111
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.064
Order of pole (three term test) = 8.537e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = 0.000847176315564 -5.57045663243e-05
y[1] (closed_form) = 0.000847433341144 -5.55244277730e-05
absolute error = 3.139e-07
relative error = 0.03696 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.469
Order of pole (three term test) = 4.702e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.641 2.377
h = 0.001 0.001
y[1] (numeric) = 0.000845641133431 -5.30202132825e-05
y[1] (closed_form) = 0.000845900060223 -5.28359866602e-05
absolute error = 3.178e-07
relative error = 0.03749 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.939
Order of pole (three term test) = 1.272e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.642 2.378
h = 0.001 0.003
y[1] (numeric) = 0.000845972916991 -5.16039028084e-05
y[1] (closed_form) = 0.000846233449848 -5.14179925576e-05
absolute error = 3.201e-07
relative error = 0.03775 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.201
Order of pole (three term test) = 5.017e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.643 2.381
h = 0.0001 0.004
y[1] (numeric) = 0.000845214998081 -4.84349581761e-05
y[1] (closed_form) = 0.000845472405666 -4.82526230198e-05
absolute error = 3.154e-07
relative error = 0.03725 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.116
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.208
Order of pole (three term test) = 6.470e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6431 2.385
h = 0.003 0.006
y[1] (numeric) = 0.000843110141365 -4.49004526047e-05
y[1] (closed_form) = 0.000843368806787 -4.47219458513e-05
absolute error = 3.143e-07
relative error = 0.03721 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.118
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.904
Order of pole (three term test) = 8.277e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = 0.000842400499107 -3.80693543752e-05
y[1] (closed_form) = 0.000842642058491 -3.78866144502e-05
absolute error = 3.029e-07
relative error = 0.03591 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.119
Order of pole (given) = 0 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) = 4.157e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = 0.000839685905602 -3.37320765321e-05
y[1] (closed_form) = 0.000839938860953 -3.35500087315e-05
absolute error = 3.117e-07
relative error = 0.03708 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.122
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.474
Order of pole (three term test) = 4.049e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6463 2.399
h = 0.001 0.001
y[1] (numeric) = 0.000838089079031 -3.11281180334e-05
y[1] (closed_form) = 0.000838343763563 -3.09419560362e-05
absolute error = 3.155e-07
relative error = 0.0376 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.123
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.943
Order of pole (three term test) = 9.682e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3081.8MB, alloc=44.3MB, time=38.14
x[1] = 2.6473 2.4
h = 0.001 0.003
y[1] (numeric) = 0.00083837388565 -2.97197476440e-05
y[1] (closed_form) = 0.00083863009317 -2.95318705839e-05
absolute error = 3.177e-07
relative error = 0.03786 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.123
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.22
Order of pole (three term test) = 2.701e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = 0.000837529870296 -2.66139096379e-05
y[1] (closed_form) = 0.000837783124755 -2.64296643374e-05
absolute error = 3.132e-07
relative error = 0.03736 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.124
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.218
Order of pole (three term test) = 4.926e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6484 2.407
h = 0.003 0.006
y[1] (numeric) = 0.000835345098657 -2.31878651123e-05
y[1] (closed_form) = 0.000835599726691 -2.30073469515e-05
absolute error = 3.121e-07
relative error = 0.03734 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.918
Order of pole (three term test) = 6.302e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = 0.000834438539394 -1.64651143168e-05
y[1] (closed_form) = 0.000834676168361 -1.62810265282e-05
absolute error = 3.006e-07
relative error = 0.03601 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.127
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.077
Order of pole (three term test) = 4.707e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = 0.000831628022824 -1.22650593494e-05
y[1] (closed_form) = 0.000831876900484 -1.20812341004e-05
absolute error = 3.094e-07
relative error = 0.03719 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.479
Order of pole (three term test) = 1.110e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6516 2.421
h = 0.001 0.001
y[1] (numeric) = 0.000829973293738 -9.74245873002e-06
y[1] (closed_form) = 0.000830223731253 -9.55454014930e-06
absolute error = 3.131e-07
relative error = 0.03771 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.947
Order of pole (three term test) = 4.172e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6526 2.422
h = 0.001 0.003
y[1] (numeric) = 0.000830212103767 -8.34355784714e-06
y[1] (closed_form) = 0.00083046398136 -8.15389663259e-06
absolute error = 3.153e-07
relative error = 0.03796 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.239
Order of pole (three term test) = 2.910e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = 0.000829285493493 -5.30290398524e-06
y[1] (closed_form) = 0.000829534589545 -5.11692333215e-06
absolute error = 3.109e-07
relative error = 0.03747 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.133
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.229
Order of pole (three term test) = 5.308e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6537 2.429
h = 0.003 0.006
y[1] (numeric) = 0.000827025806631 -1.98649801229e-06
y[1] (closed_form) = 0.000827276385956 -1.80414035086e-06
absolute error = 3.099e-07
relative error = 0.03746 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.135
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.932
Order of pole (three term test) = 1.074e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = 0.000825929077921 4.62263315833e-06
y[1] (closed_form) = 0.000826162789806 4.80791261236e-06
absolute error = 2.982e-07
relative error = 0.0361 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.136
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.083
Order of pole (three term test) = 5.074e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3127.8MB, alloc=44.3MB, time=38.71
x[1] = 2.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = 0.000823028884404 8.68417590156e-06
y[1] (closed_form) = 0.000823273683915 8.86958944135e-06
absolute error = 3.071e-07
relative error = 0.0373 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.139
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.484
Order of pole (three term test) = 2.351e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6569 2.443
h = 0.001 0.001
y[1] (numeric) = 0.000821319968747 1.11246213515e-05
y[1] (closed_form) = 0.000821566161752 1.13141206250e-05
absolute error = 3.107e-07
relative error = 0.03781 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.141
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.951
Order of pole (three term test) = 1.373e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = 0.000821513806693 1.25125888065e-05
y[1] (closed_form) = 0.000821761357205 1.27038545042e-05
absolute error = 3.128e-07
relative error = 0.03806 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.71
Order of pole (three term test) = 1.386e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.658 2.448
h = 0.003 0.006
y[1] (numeric) = 0.000819196712435 1.57385038941e-05
y[1] (closed_form) = 0.000819444052169 1.59207701892e-05
absolute error = 3.072e-07
relative error = 0.03749 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.143
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.945
Order of pole (three term test) = 5.136e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.661 2.454
h = 0.0001 0.005
y[1] (numeric) = 0.000817943199437 2.22437341032e-05
y[1] (closed_form) = 0.000818173811319 2.24283796900e-05
absolute error = 2.954e-07
relative error = 0.03609 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.089
Order of pole (three term test) = 1.535e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = 0.000814972439146 2.61842567999e-05
y[1] (closed_form) = 0.000815213985109 2.63693650929e-05
absolute error = 3.043e-07
relative error = 0.03731 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.147
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.489
Order of pole (three term test) = 1.258e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6612 2.462
h = 0.001 0.001
y[1] (numeric) = 0.000813220820719 2.85528850502e-05
y[1] (closed_form) = 0.000813463619733 2.87420654178e-05
absolute error = 3.078e-07
relative error = 0.03781 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.148
Order of pole (given) = 0 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) = 2.406e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6622 2.463
h = 0.001 0.003
y[1] (numeric) = 0.000813376952249 2.99298012817e-05
y[1] (closed_form) = 0.000813621037865 3.01207646171e-05
absolute error = 3.099e-07
relative error = 0.03806 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.148
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.276
Order of pole (three term test) = 5.035e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = 0.000812306869395 3.28433485926e-05
y[1] (closed_form) = 0.00081254849001 3.30305628536e-05
absolute error = 3.057e-07
relative error = 0.03759 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.149
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.25
Order of pole (three term test) = 1.225e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3173.9MB, alloc=44.3MB, time=39.28
x[1] = 2.6633 2.47
h = 0.003 0.006
y[1] (numeric) = 0.000809922276973 3.59526034665e-05
y[1] (closed_form) = 0.000810165567577 3.61363962311e-05
absolute error = 3.049e-07
relative error = 0.0376 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 0 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) = 5.542e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = 0.000808491437775 4.23354427323e-05
y[1] (closed_form) = 0.000808718174657 4.25209985029e-05
absolute error = 2.930e-07
relative error = 0.03618 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.153
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.096
Order of pole (three term test) = 8.286e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = 0.000805442470364 4.61358421248e-05
y[1] (closed_form) = 0.000805679957023 4.63222320474e-05
absolute error = 3.019e-07
relative error = 0.03741 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.156
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.494
Order of pole (three term test) = 2.716e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6665 2.484
h = 0.001 0.001
y[1] (numeric) = 0.000803643492323 4.84213015026e-05
y[1] (closed_form) = 0.000803882071892 4.86117441241e-05
absolute error = 3.053e-07
relative error = 0.0379 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.157
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.959
Order of pole (three term test) = 7.794e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6675 2.485
h = 0.001 0.003
y[1] (numeric) = 0.000803756678286 4.97847501147e-05
y[1] (closed_form) = 0.000803996462982 4.99769927104e-05
absolute error = 3.073e-07
relative error = 0.03815 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.157
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.295
Order of pole (three term test) = 3.625e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = 0.000802614131732 5.26281736318e-05
y[1] (closed_form) = 0.00080285161907 5.28166397645e-05
absolute error = 3.032e-07
relative error = 0.03768 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.158
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.261
Order of pole (three term test) = 1.871e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6686 2.492
h = 0.003 0.006
y[1] (numeric) = 0.000800168684289 5.56256718660e-05
y[1] (closed_form) = 0.00080040793401 5.58108270499e-05
absolute error = 3.025e-07
relative error = 0.03771 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.16
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.975
Order of pole (three term test) = 5.986e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = 0.000798567482174 6.18818705318e-05
y[1] (closed_form) = 0.000798790373528 6.20681902040e-05
absolute error = 2.905e-07
relative error = 0.03626 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.162
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.102
Order of pole (three term test) = 6.329e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = 0.000795446358437 6.55416105251e-05
y[1] (closed_form) = 0.000795679803901 6.57291219428e-05
absolute error = 2.994e-07
relative error = 0.0375 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.164
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.5
Order of pole (three term test) = 5.868e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6718 2.506
h = 0.001 0.001
y[1] (numeric) = 0.000793603623658 6.77435530118e-05
y[1] (closed_form) = 0.000793838005498 6.79350917945e-05
absolute error = 3.027e-07
relative error = 0.03799 %
Correct digits = 3
memory used=3220.2MB, alloc=44.3MB, time=39.86
Radius of convergence (given) for eq 1 = 4.166
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.963
Order of pole (three term test) = 1.637e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6728 2.507
h = 0.001 0.003
y[1] (numeric) = 0.000793674993321 6.90922609775e-05
y[1] (closed_form) = 0.00079391049959 6.92856132334e-05
absolute error = 3.047e-07
relative error = 0.03824 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.166
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.315
Order of pole (three term test) = 3.916e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = 0.000792463524902 7.18641466521e-05
y[1] (closed_form) = 0.000792696899553 7.20537021383e-05
absolute error = 3.007e-07
relative error = 0.03777 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.167
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.273
Order of pole (three term test) = 1.583e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6739 2.514
h = 0.003 0.006
y[1] (numeric) = 0.000789962019339 7.47495240406e-05
y[1] (closed_form) = 0.000790197242776 7.49358807881e-05
absolute error = 3.001e-07
relative error = 0.03781 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.169
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.99
Order of pole (three term test) = 7.544e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = 0.000788197461252 8.08751819346e-05
y[1] (closed_form) = 0.000788416541693 8.10621230020e-05
absolute error = 2.880e-07
relative error = 0.03634 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.171
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.109
Order of pole (three term test) = 6.842e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.677 2.525
h = 0.0001 0.003
y[1] (numeric) = 0.000785010145216 8.43939738760e-05
y[1] (closed_form) = 0.000785239573575 8.45824502076e-05
absolute error = 2.969e-07
relative error = 0.0376 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.173
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.505
Order of pole (three term test) = 7.093e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6771 2.528
h = 0.001 0.001
y[1] (numeric) = 0.000783127205993 8.65121991357e-05
y[1] (closed_form) = 0.000783357417991 8.67046718193e-05
absolute error = 3.001e-07
relative error = 0.03807 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.175
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.967
Order of pole (three term test) = 3.035e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6781 2.529
h = 0.001 0.003
y[1] (numeric) = 0.000783157918439 8.78449604662e-05
y[1] (closed_form) = 0.000783389175088 8.80392567195e-05
absolute error = 3.020e-07
relative error = 0.03831 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.175
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.336
Order of pole (three term test) = 2.117e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = 0.000781881062257 9.05440585400e-05
y[1] (closed_form) = 0.000782110350849 9.07345445721e-05
absolute error = 2.981e-07
relative error = 0.03786 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.176
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.284
Order of pole (three term test) = 5.465e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6792 2.536
h = 0.003 0.006
y[1] (numeric) = 0.000779328223974 9.33171455494e-05
y[1] (closed_form) = 0.000779559441811 9.35045464179e-05
absolute error = 2.976e-07
relative error = 0.03791 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.178
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.005
Order of pole (three term test) = 7.032e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3266.3MB, alloc=44.3MB, time=40.43
x[1] = 2.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = 0.000777407344241 9.93087068709e-05
y[1] (closed_form) = 0.000777622653254 9.94961307485e-05
absolute error = 2.855e-07
relative error = 0.03641 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.116
Order of pole (three term test) = 2.617e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = 0.000774159704022 0.000102686500725
y[1] (closed_form) = 0.000774385145073 0.000102875789135
absolute error = 2.944e-07
relative error = 0.03768 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.183
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.51
Order of pole (three term test) = 1.848e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6824 2.55
h = 0.001 0.001
y[1] (numeric) = 0.000772240056597 0.000104720950892
y[1] (closed_form) = 0.000772466132517 0.000104914199244
absolute error = 2.974e-07
relative error = 0.03815 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.184
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.971
Order of pole (three term test) = 8.211e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = 0.000772231297177 0.00010603662659
y[1] (closed_form) = 0.000772458339016 0.000106231705315
absolute error = 2.993e-07
relative error = 0.03839 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.184
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.84
Order of pole (three term test) = 8.587e-63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6835 2.555
h = 0.003 0.006
y[1] (numeric) = 0.000769640108466 0.000108717816291
y[1] (closed_form) = 0.00076986836865 0.000108904622152
absolute error = 2.950e-07
relative error = 0.03793 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.187
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.019
Order of pole (three term test) = 6.004e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = 0.000767591963201 0.000114589615171
y[1] (closed_form) = 0.000767804536634 0.000114775979392
absolute error = 2.827e-07
relative error = 0.03641 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.188
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.122
Order of pole (three term test) = 1.708e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = 0.000764298693564 0.000117845552602
y[1] (closed_form) = 0.00076452120239 0.00011803405055
absolute error = 2.916e-07
relative error = 0.0377 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.191
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.515
Order of pole (three term test) = 3.683e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6867 2.569
h = 0.001 0.001
y[1] (numeric) = 0.00076235119839 0.000119807568716
y[1] (closed_form) = 0.000762574217844 0.000119999989456
absolute error = 2.946e-07
relative error = 0.03816 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.193
Order of pole (given) = 0 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) = 1.495e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6877 2.57
h = 0.001 0.003
y[1] (numeric) = 0.00076230965034 0.000121107226033
y[1] (closed_form) = 0.000762533568845 0.000121301479533
absolute error = 2.964e-07
relative error = 0.03839 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.374
Order of pole (three term test) = 8.866e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3312.7MB, alloc=44.3MB, time=41.00
x[1] = 2.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = 0.000760921368045 0.000123667424
y[1] (closed_form) = 0.000761143616159 0.000123857861558
absolute error = 2.927e-07
relative error = 0.03795 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.193
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.306
Order of pole (three term test) = 6.348e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6888 2.577
h = 0.003 0.006
y[1] (numeric) = 0.000758286648026 0.000126231268322
y[1] (closed_form) = 0.000758510958127 0.000126418835501
absolute error = 2.924e-07
relative error = 0.03802 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.196
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.034
Order of pole (three term test) = 8.168e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = 0.000756095322986 0.000131963334209
y[1] (closed_form) = 0.000756304212044 0.000132149934832
absolute error = 2.801e-07
relative error = 0.03648 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.197
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.129
Order of pole (three term test) = 8.603e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = 0.000752752358753 0.000135078851141
y[1] (closed_form) = 0.000752970951643 0.00013526788783
absolute error = 2.890e-07
relative error = 0.03778 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.2
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.521
Order of pole (three term test) = 3.990e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.692 2.591
h = 0.001 0.001
y[1] (numeric) = 0.000750774491644 0.000136957385065
y[1] (closed_form) = 0.000750993454229 0.0001371502989
absolute error = 2.918e-07
relative error = 0.03823 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.202
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.98
Order of pole (three term test) = 1.222e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.693 2.592
h = 0.001 0.003
y[1] (numeric) = 0.000750695747181 0.000138238029474
y[1] (closed_form) = 0.000750915532393 0.000138432777065
absolute error = 2.937e-07
relative error = 0.03846 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.202
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.395
Order of pole (three term test) = 1.130e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.694 2.595
h = 0.0001 0.004
y[1] (numeric) = 0.000749252091498 0.000140722779145
y[1] (closed_form) = 0.000749470362221 0.000140913715597
absolute error = 2.900e-07
relative error = 0.03803 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.203
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.318
Order of pole (three term test) = 1.538e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6941 2.599
h = 0.003 0.006
y[1] (numeric) = 0.000746579095583 0.000143174911788
y[1] (closed_form) = 0.000746799492128 0.000143363093715
absolute error = 2.898e-07
relative error = 0.03811 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.205
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.05
Order of pole (three term test) = 8.808e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = 0.000744251615249 0.00014876463967
y[1] (closed_form) = 0.000744456871819 0.000148951350039
absolute error = 2.775e-07
relative error = 0.03655 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.207
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.136
Order of pole (three term test) = 6.725e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = 0.000740864502903 0.000151740316484
y[1] (closed_form) = 0.000741079224368 0.000151929750752
absolute error = 2.863e-07
relative error = 0.03785 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.21
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.527
Order of pole (three term test) = 1.181e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3358.5MB, alloc=44.3MB, time=41.57
x[1] = 2.6973 2.613
h = 0.001 0.001
y[1] (numeric) = 0.000738859571422 0.00015353568706
y[1] (closed_form) = 0.000739074526011 0.000153728948247
absolute error = 2.891e-07
relative error = 0.03829 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.211
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.984
Order of pole (three term test) = 1.055e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6983 2.614
h = 0.001 0.003
y[1] (numeric) = 0.000738744871421 0.000154796369635
y[1] (closed_form) = 0.000738960573585 0.000154991462613
absolute error = 2.908e-07
relative error = 0.03852 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.211
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.417
Order of pole (three term test) = 8.170e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = 0.0007372492816 0.000157205018463
y[1] (closed_form) = 0.000737463622109 0.000157396311014
absolute error = 2.873e-07
relative error = 0.0381 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.212
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.33
Order of pole (three term test) = 7.459e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6994 2.621
h = 0.003 0.006
y[1] (numeric) = 0.000734542395078 0.00015954595225
y[1] (closed_form) = 0.000734758919607 0.000159734606439
absolute error = 2.872e-07
relative error = 0.03819 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.215
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.066
Order of pole (three term test) = 9.552e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = 0.000732085754492 0.000164991055659
y[1] (closed_form) = 0.000732287434291 0.000165177753453
absolute error = 2.748e-07
relative error = 0.03661 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.216
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.143
Order of pole (three term test) = 1.012e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = 0.00072865991537 0.00016782767526
y[1] (closed_form) = 0.000728870814534 0.000168017370263
absolute error = 2.837e-07
relative error = 0.03792 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.219
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.532
Order of pole (three term test) = 5.246e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7026 2.635
h = 0.001 0.001
y[1] (numeric) = 0.000726631153493 0.000169540322452
y[1] (closed_form) = 0.000726842153679 0.00016973378985
absolute error = 2.863e-07
relative error = 0.03835 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.989
Order of pole (three term test) = 1.384e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7036 2.636
h = 0.001 0.003
y[1] (numeric) = 0.000726481752231 0.000170780159509
y[1] (closed_form) = 0.000726693426413 0.000170975453896
absolute error = 2.880e-07
relative error = 0.03858 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.438
Order of pole (three term test) = 2.194e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = 0.000724937628716 0.000173112199114
y[1] (closed_form) = 0.000725148090816 0.00017330370944
absolute error = 2.846e-07
relative error = 0.03817 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.222
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.342
Order of pole (three term test) = 8.094e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3404.6MB, alloc=44.3MB, time=42.14
x[1] = 2.7047 2.643
h = 0.003 0.006
y[1] (numeric) = 0.000722201135663 0.000175342605568
y[1] (closed_form) = 0.00072241383445 0.000175531593752
absolute error = 2.845e-07
relative error = 0.03827 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.224
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.082
Order of pole (three term test) = 1.037e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = 0.000719622287308 0.000180641108643
y[1] (closed_form) = 0.000719820449623 0.000180827675944
absolute error = 2.722e-07
relative error = 0.03667 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.226
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.15
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = 0.000716163011515 0.000183339646815
y[1] (closed_form) = 0.000716370141833 0.000183529470138
absolute error = 2.810e-07
relative error = 0.03799 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.229
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.538
Order of pole (three term test) = 8.053e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7079 2.657
h = 0.001 0.001
y[1] (numeric) = 0.000714113575971 0.000184970125997
y[1] (closed_form) = 0.000714320679764 0.000185163663174
absolute error = 2.835e-07
relative error = 0.03841 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.231
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.993
Order of pole (three term test) = 6.095e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = 0.000713930738041 0.000186188298301
y[1] (closed_form) = 0.000714138443817 0.000186383654951
absolute error = 2.851e-07
relative error = 0.03863 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.97
Order of pole (three term test) = 6.011e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.709 2.662
h = 0.003 0.006
y[1] (numeric) = 0.000711173311147 0.000188328881325
y[1] (closed_form) = 0.000711383395482 0.000188516869494
absolute error = 2.819e-07
relative error = 0.03831 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.233
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.096
Order of pole (three term test) = 1.115e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.712 2.668
h = 0.0001 0.005
y[1] (numeric) = 0.000708496568812 0.000193498500417
y[1] (closed_form) = 0.000708692396757 0.000193683688141
absolute error = 2.695e-07
relative error = 0.03669 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.234
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.157
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = 0.000705014269361 0.000196078789095
y[1] (closed_form) = 0.000705218841995 0.000196267440979
absolute error = 2.783e-07
relative error = 0.03802 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.237
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.543
Order of pole (three term test) = 2.740e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7122 2.676
h = 0.001 0.001
y[1] (numeric) = 0.000702950472753 0.000197638872802
y[1] (closed_form) = 0.00070315491354 0.000197831183705
absolute error = 2.807e-07
relative error = 0.03842 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.997
Order of pole (three term test) = 9.458e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7132 2.677
h = 0.001 0.003
y[1] (numeric) = 0.000702740142156 0.000198837411653
y[1] (closed_form) = 0.000702945124385 0.000199031532648
absolute error = 2.823e-07
relative error = 0.03864 %
Correct digits = 3
memory used=3450.9MB, alloc=44.3MB, time=42.72
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.479
Order of pole (three term test) = 3.662e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = 0.000701115524556 0.000201025535733
y[1] (closed_form) = 0.000701319563424 0.000201215918961
absolute error = 2.791e-07
relative error = 0.03825 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.24
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.365
Order of pole (three term test) = 9.505e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7143 2.684
h = 0.003 0.006
y[1] (numeric) = 0.000698336267876 0.000203052338167
y[1] (closed_form) = 0.000698542625733 0.000203240415337
absolute error = 2.792e-07
relative error = 0.03838 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.243
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.113
Order of pole (three term test) = 6.057e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = 0.000695550114587 0.000208072559067
y[1] (closed_form) = 0.000695742545244 0.000208257409584
absolute error = 2.668e-07
relative error = 0.03674 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.244
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.164
Order of pole (three term test) = 9.078e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = 0.000692043837873 0.000210517121187
y[1] (closed_form) = 0.000692244753142 0.000210705667833
absolute error = 2.755e-07
relative error = 0.03808 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.549
Order of pole (three term test) = 9.418e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7175 2.698
h = 0.001 0.001
y[1] (numeric) = 0.000689965015279 0.000211996393045
y[1] (closed_form) = 0.000690165679862 0.000212188533496
absolute error = 2.778e-07
relative error = 0.03848 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.249
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.002
Order of pole (three term test) = 1.176e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7185 2.699
h = 0.001 0.003
y[1] (numeric) = 0.000689723626473 0.000213171926231
y[1] (closed_form) = 0.000689924763637 0.000213365864559
absolute error = 2.794e-07
relative error = 0.03869 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.249
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.501
Order of pole (three term test) = 5.629e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = 0.000688059942768 0.000215282778718
y[1] (closed_form) = 0.000688260275858 0.000215473010335
absolute error = 2.763e-07
relative error = 0.03831 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.25
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.378
Order of pole (three term test) = 2.056e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7196 2.706
h = 0.003 0.006
y[1] (numeric) = 0.000685262722738 0.00021720182889
y[1] (closed_form) = 0.000685465412329 0.000217389869499
absolute error = 2.765e-07
relative error = 0.03845 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.252
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.129
Order of pole (three term test) = 1.324e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = 0.000682373919606 0.000222071515762
y[1] (closed_form) = 0.00068256302098 0.000222255924056
absolute error = 2.641e-07
relative error = 0.0368 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.254
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.171
Order of pole (three term test) = 1.063e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3496.9MB, alloc=44.3MB, time=43.29
x[1] = 2.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = 0.000678848550098 0.000224381823447
y[1] (closed_form) = 0.000679045872245 0.000224570145604
absolute error = 2.728e-07
relative error = 0.03814 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.257
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.555
Order of pole (three term test) = 4.581e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7228 2.72
h = 0.001 0.001
y[1] (numeric) = 0.000676757619058 0.00022578113614
y[1] (closed_form) = 0.000676954576408 0.000225972983667
absolute error = 2.750e-07
relative error = 0.03853 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.259
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.007
Order of pole (three term test) = 3.101e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7238 2.721
h = 0.001 0.003
y[1] (numeric) = 0.000676486449388 0.000226933023304
y[1] (closed_form) = 0.000676683812236 0.000227126654136
absolute error = 2.765e-07
relative error = 0.03874 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.259
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.523
Order of pole (three term test) = 4.329e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = 0.000674786901368 0.000228966606372
y[1] (closed_form) = 0.000674983595594 0.000229156566192
absolute error = 2.734e-07
relative error = 0.03836 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.39
Order of pole (three term test) = 4.473e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7249 2.728
h = 0.003 0.006
y[1] (numeric) = 0.000671975570073 0.000230779114652
y[1] (closed_form) = 0.000672174653268 0.000230966997715
absolute error = 2.737e-07
relative error = 0.03851 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.262
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.146
Order of pole (three term test) = 5.731e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = 0.000668990791596 0.000235497407794
y[1] (closed_form) = 0.000669176634267 0.000235681273394
absolute error = 2.614e-07
relative error = 0.03685 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.264
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.179
Order of pole (three term test) = 1.080e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.728 2.739
h = 0.0001 0.003
y[1] (numeric) = 0.000665451064667 0.000237675088462
y[1] (closed_form) = 0.000665644861192 0.000237863071578
absolute error = 2.700e-07
relative error = 0.0382 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.267
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.561
Order of pole (three term test) = 4.985e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7281 2.742
h = 0.001 0.001
y[1] (numeric) = 0.000663350854688 0.000238995387812
y[1] (closed_form) = 0.000663544177068 0.000239186824907
absolute error = 2.721e-07
relative error = 0.03857 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.011
Order of pole (three term test) = 3.375e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7291 2.743
h = 0.001 0.003
y[1] (numeric) = 0.000663051180983 0.000240123048816
y[1] (closed_form) = 0.000663244843617 0.000240316252415
absolute error = 2.736e-07
relative error = 0.03878 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.545
Order of pole (three term test) = 4.712e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3543.1MB, alloc=44.3MB, time=43.86
x[1] = 2.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = 0.000661318908807 0.000242079484737
y[1] (closed_form) = 0.00066151203432 0.000242269057403
absolute error = 2.706e-07
relative error = 0.03841 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.27
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.403
Order of pole (three term test) = 3.652e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7302 2.75
h = 0.003 0.006
y[1] (numeric) = 0.000658497198807 0.000243786782607
y[1] (closed_form) = 0.00065869274086 0.000243974391776
absolute error = 2.710e-07
relative error = 0.03858 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.272
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.163
Order of pole (three term test) = 1.680e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = 0.000655423023114 0.000248353088817
y[1] (closed_form) = 0.000655605679996 0.000248536315811
absolute error = 2.587e-07
relative error = 0.0369 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.274
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.186
Order of pole (three term test) = 8.187e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = 0.000651873521745 0.000250399915536
y[1] (closed_form) = 0.000652063863142 0.000250587449791
absolute error = 2.672e-07
relative error = 0.03825 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.277
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.567
Order of pole (three term test) = 7.676e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7334 2.764
h = 0.001 0.001
y[1] (numeric) = 0.000649766772308 0.00025164223477
y[1] (closed_form) = 0.000649956534991 0.000251833148925
absolute error = 2.692e-07
relative error = 0.03862 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.279
Order of pole (given) = 0 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) = 1.039e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = 0.000649439868363 0.000252745148372
y[1] (closed_form) = 0.000649629907948 0.000252937810124
absolute error = 2.706e-07
relative error = 0.03882 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.279
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.11
Order of pole (three term test) = 6.607e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7345 2.769
h = 0.003 0.006
y[1] (numeric) = 0.000646612518737 0.000254367463794
y[1] (closed_form) = 0.000646805824851 0.000254553767332
absolute error = 2.685e-07
relative error = 0.03862 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.281
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.178
Order of pole (three term test) = 1.682e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = 0.000643468395515 0.000258801705678
y[1] (closed_form) = 0.000643649131701 0.000258983333713
absolute error = 2.562e-07
relative error = 0.03693 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.283
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.193
Order of pole (three term test) = 1.262e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = 0.000639915559622 0.000260737376615
y[1] (closed_form) = 0.000640103744993 0.000260923461024
absolute error = 2.647e-07
relative error = 0.03829 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.286
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.573
Order of pole (three term test) = 4.140e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7377 2.783
h = 0.001 0.001
y[1] (numeric) = 0.00063780621558 0.000261913427897
y[1] (closed_form) = 0.000637993736984 0.000262102825315
absolute error = 2.665e-07
relative error = 0.03864 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.02
Order of pole (three term test) = 1.254e-61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3589.3MB, alloc=44.3MB, time=44.44
x[1] = 2.7387 2.784
h = 0.001 0.003
y[1] (numeric) = 0.000637457190858 0.000262994362464
y[1] (closed_form) = 0.00063764493644 0.000263185488893
absolute error = 2.679e-07
relative error = 0.03884 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.588
Order of pole (three term test) = 1.238e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = 0.000635673068307 0.000264807655992
y[1] (closed_form) = 0.000635860510038 0.000264995238286
absolute error = 2.652e-07
relative error = 0.0385 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.289
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.427
Order of pole (three term test) = 1.438e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7398 2.791
h = 0.003 0.006
y[1] (numeric) = 0.000632842771591 0.000266323084233
y[1] (closed_form) = 0.000633032667327 0.000266508910712
absolute error = 2.657e-07
relative error = 0.03868 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.292
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.195
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = 0.000629621204491 0.000270604986027
y[1] (closed_form) = 0.000629798896971 0.000270785810008
absolute error = 2.535e-07
relative error = 0.03698 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.293
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.201
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = 0.00062606668257 0.000272413507417
y[1] (closed_form) = 0.000626251552219 0.000272598952193
absolute error = 2.619e-07
relative error = 0.03834 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.296
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.579
Order of pole (three term test) = 1.354e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.743 2.805
h = 0.001 0.001
y[1] (numeric) = 0.000623955636935 0.000273513744447
y[1] (closed_form) = 0.00062413974698 0.000273702423888
absolute error = 2.636e-07
relative error = 0.03868 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.298
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.025
Order of pole (three term test) = 4.322e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.744 2.806
h = 0.001 0.003
y[1] (numeric) = 0.000623581740643 0.000274569128512
y[1] (closed_form) = 0.000623766015173 0.000274759514498
absolute error = 2.650e-07
relative error = 0.03887 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.298
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.611
Order of pole (three term test) = 1.207e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.745 2.809
h = 0.0001 0.004
y[1] (numeric) = 0.000621773499262 0.000276306275788
y[1] (closed_form) = 0.000621957589614 0.000276493168764
absolute error = 2.623e-07
relative error = 0.03854 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.299
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.44
Order of pole (three term test) = 3.119e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7451 2.813
h = 0.003 0.006
y[1] (numeric) = 0.000618942801285 0.000277720942805
y[1] (closed_form) = 0.000619129360053 0.000277906189359
absolute error = 2.629e-07
relative error = 0.03874 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.302
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.212
Order of pole (three term test) = 9.993e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3635.4MB, alloc=44.3MB, time=45.01
x[1] = 2.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = 0.000615650042197 0.000281850617221
y[1] (closed_form) = 0.000615824769201 0.000282030554222
absolute error = 2.508e-07
relative error = 0.03703 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.304
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.208
Order of pole (three term test) = 4.499e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = 0.000612097966399 0.00028353412443
y[1] (closed_form) = 0.000612279597878 0.000283718833398
absolute error = 2.591e-07
relative error = 0.03839 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.307
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.585
Order of pole (three term test) = 1.014e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7483 2.827
h = 0.001 0.001
y[1] (numeric) = 0.000609987692007 0.000284559798229
y[1] (closed_form) = 0.000610168473014 0.000284747661551
absolute error = 2.607e-07
relative error = 0.03872 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.309
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.03
Order of pole (three term test) = 1.012e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7493 2.828
h = 0.001 0.003
y[1] (numeric) = 0.000609590175818 0.000285589270821
y[1] (closed_form) = 0.000609771063621 0.000285778816474
absolute error = 2.620e-07
relative error = 0.03891 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.309
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.634
Order of pole (three term test) = 1.984e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = 0.000607760684844 0.000287250807718
y[1] (closed_form) = 0.000607941503899 0.000287436914871
absolute error = 2.595e-07
relative error = 0.03859 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.31
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.453
Order of pole (three term test) = 2.406e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7504 2.835
h = 0.003 0.006
y[1] (numeric) = 0.000604932836073 0.000288566439945
y[1] (closed_form) = 0.000605116133656 0.000288751008433
absolute error = 2.601e-07
relative error = 0.0388 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.312
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.23
Order of pole (three term test) = 2.181e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = 0.00060157500933 0.000292544227207
y[1] (closed_form) = 0.000601746850534 0.000292723198787
absolute error = 2.481e-07
relative error = 0.03708 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.314
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.216
Order of pole (three term test) = 3.273e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = 0.000598029351611 0.000294104964959
y[1] (closed_form) = 0.00059820782448 0.000294288846694
absolute error = 2.563e-07
relative error = 0.03844 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.317
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.591
Order of pole (three term test) = 1.080e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7536 2.849
h = 0.001 0.001
y[1] (numeric) = 0.00059592222647 0.000295057392409
y[1] (closed_form) = 0.000596099762738 0.000295244346459
absolute error = 2.578e-07
relative error = 0.03876 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.319
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.035
Order of pole (three term test) = 5.677e-62 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3681.7MB, alloc=44.3MB, time=45.58
x[1] = 2.7546 2.85
h = 0.001 0.003
y[1] (numeric) = 0.000595502330481 0.000296060645564
y[1] (closed_form) = 0.000595679917889 0.000296249256104
absolute error = 2.591e-07
relative error = 0.03894 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.319
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.658
Order of pole (three term test) = 1.453e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = 0.000593654382631 0.000297647202462
y[1] (closed_form) = 0.000593832012433 0.000297832432145
absolute error = 2.566e-07
relative error = 0.03863 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.32
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.467
Order of pole (three term test) = 4.153e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7557 2.857
h = 0.003 0.006
y[1] (numeric) = 0.000590832505817 0.000298865611059
y[1] (closed_form) = 0.000591012620124 0.000299049408058
absolute error = 2.573e-07
relative error = 0.03885 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.323
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.248
Order of pole (three term test) = 1.065e-61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = 0.000587415601687 0.000302692068576
y[1] (closed_form) = 0.000587584637995 0.000302870000728
absolute error = 2.454e-07
relative error = 0.03713 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.325
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.224
Order of pole (three term test) = 7.991e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = 0.000583880172906 0.000304132381919
y[1] (closed_form) = 0.000584055568487 0.000304315349718
absolute error = 2.535e-07
relative error = 0.03849 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.328
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.598
Order of pole (three term test) = 5.866e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7589 2.871
h = 0.001 0.001
y[1] (numeric) = 0.000581778479615 0.000305012940395
y[1] (closed_form) = 0.000581952857173 0.000305198896976
absolute error = 2.549e-07
relative error = 0.03879 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.33
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.04
Order of pole (three term test) = 2.248e-62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7599 2.872
h = 0.001 0.003
y[1] (numeric) = 0.000581337430435 0.000305989717494
y[1] (closed_form) = 0.000581511805529 0.000306177303217
absolute error = 2.561e-07
relative error = 0.03897 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.33
Order of pole (given) = 0 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.682
Order of pole (three term test) = 9.151e-62 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
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=3716.6MB, alloc=44.3MB, time=46.00