|\^/| 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(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( sqrt(c(0.1) * c(x) + c(0.2))));
> end;
exact_soln_y := proc(x)
return
c(20.0)*sqrt(c(0.1)*c(x) + c(0.2))*cosh(sqrt(c(0.1)*c(x) + c(0.2)))
- c(20.0)*sinh(sqrt(c(0.1)*c(x) + c(0.2)))
end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> array_tmp4[1] := sinh(array_tmp3[1]);
> array_tmp4_g[1] := cosh(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2;
> #emit pre sinh FULL $eq_no = 1
> array_tmp4[2] := att(1,array_tmp4_g,array_tmp3,1);
> array_tmp4_g[2] := att(1,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[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_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0;
> array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre sinh FULL $eq_no = 1
> array_tmp4[3] := att(2,array_tmp4_g,array_tmp3,1);
> array_tmp4_g[3] := att(2,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[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_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0;
> array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre sinh FULL $eq_no = 1
> array_tmp4[4] := att(3,array_tmp4_g,array_tmp3,1);
> array_tmp4_g[4] := att(3,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[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_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0;
> array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre sinh FULL $eq_no = 1
> array_tmp4[5] := att(4,array_tmp4_g,array_tmp3,1);
> array_tmp4_g[5] := att(4,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[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_tmp5[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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0;
> array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2;
> #emit sinh FULL $eq_no = 1
> array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_tmp3,1);
> array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[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_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
array_tmp1[1] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4[1] := sinh(array_tmp3[1]);
array_tmp4_g[1] := cosh(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4[2] := att(1, array_tmp4_g, array_tmp3, 1);
array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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] := 0;
array_tmp3[3] :=
neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[3] := att(2, array_tmp4_g, array_tmp3, 1);
array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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] := 0;
array_tmp3[4] :=
neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[4] := att(3, array_tmp4_g, array_tmp3, 1);
array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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] := 0;
array_tmp3[5] :=
neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[5] := att(4, array_tmp4_g, array_tmp3, 1);
array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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] := 0;
array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/(
array_tmp3[1]*glob__2);
array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, array_tmp3, 1);
array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1);
array_tmp5[kkk] := array_tmp4[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_tmp5[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> 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 := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #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..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> 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..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4_g:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 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..(40) ,(0..40+ 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 <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <=40) do # do number 1
> term := 1;
> while (term <= 40) 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_g);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> 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/sinh_sqrtpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> 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,"glob_max_h := c(0.01);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-2.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( sqrt(c(0.1) * c(x) + c(0.2))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 2.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.01);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-2.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(0.5);
> array_given_ord_poles[1,2] := c(0.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 10
> omniout_str(INFO," ");
> fi;# end if 10;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> atomall();
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10
> display_alot(current_iter);
> fi;# end if 10;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (true) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:25:59-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sinh_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"sinh_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"sinh_sqrt maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
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 := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
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 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4_g := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
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 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 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 <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do
term := 1;
while term <= 40 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_g);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
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/sinh_sqrtpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh ( sqrt ( 0.1\
* x + 0.2 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
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, "glob_max_h := c(0.01);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-2.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * \
cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( sqrt(c(0.1\
) * c(x) + c(0.2))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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_max_h := c(0.01);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-2.0);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(0.5);
array_given_ord_poles[1, 2] := c(0.);
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius
;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] :=
array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
atomall();
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = sinh ( sqrt ( 0\
.1 * x + 0.2 ) ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:25:59-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sinh_sqrt");
logitem_str(html_log_file, "diff ( y , x , 1 ) = si\
nh ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file, "sinh_sqrt diffeq.mxt");
logitem_str(html_log_file, "sinh_sqrt maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.8MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sinh_sqrtpostcpx.cpx#################
diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 2.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.01);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-2.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(0.5);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( sqrt(c(0.1) * c(x) + c(0.2))));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 2.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 1.82253049093 0.0684985158039
y[1] (closed_form) = 1.82253049093 0.0684985158039
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30.8MB, alloc=40.3MB, time=0.40
x[1] = 2.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 1.82255167006 0.0719245109156
y[1] (closed_form) = 1.82255048799 0.0719245674309
absolute error = 1.183e-06
relative error = 6.488e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 1.82259036001 0.0739805736261
y[1] (closed_form) = 1.8225887528 0.0739806618945
absolute error = 1.610e-06
relative error = 8.824e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.102
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 1.82326517352 0.0746758296601
y[1] (closed_form) = 1.82326356709 0.074676012539
absolute error = 1.617e-06
relative error = 8.860e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=76.4MB, alloc=44.3MB, time=0.98
x[1] = 2.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 1.82391935845 0.0767415352815
y[1] (closed_form) = 1.82391737596 0.076742005256
absolute error = 2.037e-06
relative error = 0.0001116 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 1.82394548871 0.0794835040891
y[1] (closed_form) = 1.82394275009 0.0794840185134
absolute error = 2.787e-06
relative error = 0.0001526 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 1.82593535004 0.0836278740214
y[1] (closed_form) = 1.82593134979 0.0836301028177
absolute error = 4.579e-06
relative error = 0.0002505 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=121.8MB, alloc=44.3MB, time=1.54
x[1] = 2.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 1.82594619604 0.0870566738543
y[1] (closed_form) = 1.82594101405 0.0870589610522
absolute error = 5.664e-06
relative error = 0.0003099 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1055 0.13
h = 0.001 0.001
y[1] (numeric) = 1.82597870752 0.0891145047844
y[1] (closed_form) = 1.82597310064 0.0891168244385
absolute error = 6.068e-06
relative error = 0.0003319 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.108
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 1.82665196501 0.0898123581445
y[1] (closed_form) = 1.82664635907 0.0898147723619
absolute error = 6.104e-06
relative error = 0.0003337 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.109
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=167.3MB, alloc=44.3MB, time=2.12
x[1] = 2.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 1.8273004413 0.0918817025265
y[1] (closed_form) = 1.82729445997 0.0918844043341
absolute error = 6.563e-06
relative error = 0.0003587 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 1.82731831903 0.0946259637301
y[1] (closed_form) = 1.827311582 0.0946287112418
absolute error = 7.276e-06
relative error = 0.0003976 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 1.82929729009 0.0987796924952
y[1] (closed_form) = 1.82928929495 0.0987841556612
absolute error = 9.157e-06
relative error = 0.0004998 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=212.3MB, alloc=44.3MB, time=2.67
x[1] = 2.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 1.8292978124 0.102211313026
y[1] (closed_form) = 1.8292886362 0.102215836556
absolute error = 1.023e-05
relative error = 0.0005584 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 1.82932415142 0.104270921725
y[1] (closed_form) = 1.82931455061 0.10427547841
absolute error = 1.063e-05
relative error = 0.00058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.114
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 1.82999585804 0.104971373752
y[1] (closed_form) = 1.82998625832 0.104976024952
absolute error = 1.067e-05
relative error = 0.000582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=257.8MB, alloc=44.3MB, time=3.24
x[1] = 2.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 1.83063863464 0.107044364715
y[1] (closed_form) = 1.8306286602 0.107049303992
absolute error = 1.113e-05
relative error = 0.000607 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.116
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 1.83064826778 0.109790931072
y[1] (closed_form) = 1.83063753811 0.1097959173
absolute error = 1.183e-05
relative error = 0.0006452 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.116
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 1.83261636975 0.113954032335
y[1] (closed_form) = 1.83260438548 0.113960735462
absolute error = 1.373e-05
relative error = 0.0007478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.119
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=303.2MB, alloc=44.3MB, time=3.81
x[1] = 2.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 1.83260657828 0.117388489492
y[1] (closed_form) = 1.83259341365 0.117395254933
absolute error = 1.480e-05
relative error = 0.000806 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 1.83262675094 0.119449885425
y[1] (closed_form) = 1.83261316196 0.119456684716
absolute error = 1.520e-05
relative error = 0.0008274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 1.83329691183 0.120152937406
y[1] (closed_form) = 1.8332833241 0.120159831162
absolute error = 1.524e-05
relative error = 0.0008293 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.121
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=348.8MB, alloc=52.3MB, time=4.39
x[1] = 2.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 1.83393399775 0.122229582664
y[1] (closed_form) = 1.83392003598 0.122236764976
absolute error = 1.570e-05
relative error = 0.0008542 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.122
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 1.83393539435 0.124978466823
y[1] (closed_form) = 1.83392067782 0.124985697324
absolute error = 1.640e-05
relative error = 0.000892 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.122
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 1.83589264848 0.129150954007
y[1] (closed_form) = 1.83587668087 0.129159902616
absolute error = 1.830e-05
relative error = 0.0009946 %
Correct digits = 5
memory used=394.3MB, alloc=52.3MB, time=4.94
Radius of convergence (given) for eq 1 = 4.125
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 1.83587255327 0.13258826358
y[1] (closed_form) = 1.83585540601 0.132597276442
absolute error = 1.937e-05
relative error = 0.001052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 1.83588656574 0.134651456128
y[1] (closed_form) = 1.83586899441 0.13466050353
absolute error = 1.976e-05
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=439.9MB, alloc=52.3MB, time=5.50
x[1] = 2.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 1.83655518604 0.135357109299
y[1] (closed_form) = 1.83653761612 0.135366251114
absolute error = 1.981e-05
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.127
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 1.83654947158 0.138107900548
y[1] (closed_form) = 1.83653114733 0.138117091676
absolute error = 2.050e-05
relative error = 0.001113 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.127
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 1.83849729331 0.142288348513
y[1] (closed_form) = 1.83847772098 0.142299258801
absolute error = 2.241e-05
relative error = 0.001215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.131
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=485.4MB, alloc=52.3MB, time=6.06
x[1] = 2.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 1.83846830287 0.145728003315
y[1] (closed_form) = 1.83844755151 0.145738979524
absolute error = 2.348e-05
relative error = 0.001273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.131
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 1.83847699631 0.147792676499
y[1] (closed_form) = 1.83845582111 0.147803687841
absolute error = 2.387e-05
relative error = 0.001294 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.131
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 1.83914426364 0.148500551368
y[1] (closed_form) = 1.83912308999 0.148511657079
absolute error = 2.391e-05
relative error = 0.001296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=530.8MB, alloc=52.3MB, time=6.62
x[1] = 2.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 1.83977074091 0.150583949045
y[1] (closed_form) = 1.83974919448 0.150595344191
absolute error = 2.437e-05
relative error = 0.00132 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.134
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 1.83975680505 0.153337081488
y[1] (closed_form) = 1.83973450473 0.153348527114
absolute error = 2.507e-05
relative error = 0.001358 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.134
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 1.84169381851 0.157526939969
y[1] (closed_form) = 1.84167027364 0.157540105893
absolute error = 2.698e-05
relative error = 0.001459 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.137
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=576.4MB, alloc=52.3MB, time=7.18
x[1] = 2.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 1.84165454316 0.16096947632
y[1] (closed_form) = 1.84162982001 0.160982710081
absolute error = 2.804e-05
relative error = 0.001517 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.138
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.131 0.237
h = 0.001 0.001
y[1] (numeric) = 1.84165708797 0.163035963426
y[1] (closed_form) = 1.84163194127 0.163049233002
absolute error = 2.843e-05
relative error = 0.001538 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.138
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.132 0.238
h = 0.001 0.003
y[1] (numeric) = 1.84232282427 0.163746441702
y[1] (closed_form) = 1.84229767927 0.163759805594
absolute error = 2.848e-05
relative error = 0.00154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.139
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=621.9MB, alloc=52.3MB, time=7.73
x[1] = 2.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 1.8429436368 0.165833515255
y[1] (closed_form) = 1.8429181197 0.165847169039
absolute error = 2.894e-05
relative error = 0.001564 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 1.84292148783 0.168589001161
y[1] (closed_form) = 1.84289521734 0.168602706641
absolute error = 2.963e-05
relative error = 0.001601 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 1.84484771447 0.172788282894
y[1] (closed_form) = 1.84482020295 0.172803709775
absolute error = 3.154e-05
relative error = 0.001702 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=667.4MB, alloc=52.3MB, time=8.29
x[1] = 2.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 1.8447981646 0.176233716185
y[1] (closed_form) = 1.84476947556 0.176249212806
absolute error = 3.261e-05
relative error = 0.00176 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 1.84479456716 0.178302026351
y[1] (closed_form) = 1.84476545488 0.178317559464
absolute error = 3.300e-05
relative error = 0.00178 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 1.84545877757 0.179015109119
y[1] (closed_form) = 1.84542966713 0.179030736492
absolute error = 3.304e-05
relative error = 0.001782 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.145
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=713.0MB, alloc=52.3MB, time=8.85
x[1] = 2.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 1.84607393454 0.181105865846
y[1] (closed_form) = 1.84604445269 0.18112178356
absolute error = 3.350e-05
relative error = 0.001806 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 1.8460435809 0.183863717429
y[1] (closed_form) = 1.84601334617 0.183879688048
absolute error = 3.419e-05
relative error = 0.001843 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 1.84795904223 0.18807243491
y[1] (closed_form) = 1.84792756999 0.188090127994
absolute error = 3.610e-05
relative error = 0.001944 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.15
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=758.5MB, alloc=52.3MB, time=9.41
x[1] = 2.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 1.84789922834 0.191520780387
y[1] (closed_form) = 1.84786657936 0.191538545104
absolute error = 3.717e-05
relative error = 0.002001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 1.84788949511 0.193590922666
y[1] (closed_form) = 1.84785642319 0.193608724546
absolute error = 3.756e-05
relative error = 0.002021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 1.84855218475 0.194306610958
y[1] (closed_form) = 1.84851911483 0.194324507041
absolute error = 3.760e-05
relative error = 0.002023 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.152
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=804.1MB, alloc=52.3MB, time=9.97
x[1] = 2.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 1.8491616954 0.196401058048
y[1] (closed_form) = 1.84912825475 0.196419244914
absolute error = 3.807e-05
relative error = 0.002047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.153
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 1.84912314562 0.199161287407
y[1] (closed_form) = 1.8490889526 0.199179528378
absolute error = 3.875e-05
relative error = 0.002084 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.154
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 1.8510278632 0.203379452891
y[1] (closed_form) = 1.85099243621 0.203399417356
absolute error = 4.067e-05
relative error = 0.002184 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.157
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=849.7MB, alloc=52.3MB, time=10.54
x[1] = 2.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 1.85095779592 0.206830725661
y[1] (closed_form) = 1.85092119298 0.206850763635
absolute error = 4.173e-05
relative error = 0.002241 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.158
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 1.85094193342 0.208902709016
y[1] (closed_form) = 1.85090490783 0.208922784822
absolute error = 4.212e-05
relative error = 0.002261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.158
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 1.85160310742 0.209621003812
y[1] (closed_form) = 1.851566084 0.209641173764
absolute error = 4.216e-05
relative error = 0.002263 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=895.2MB, alloc=52.3MB, time=11.12
x[1] = 2.148 0.308
h = 0.003 0.006
y[1] (numeric) = 1.851557481 0.212383191933
y[1] (closed_form) = 1.85151970569 0.212403417077
absolute error = 4.285e-05
relative error = 0.002299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 1.85345285531 0.216609371943
y[1] (closed_form) = 1.85341384904 0.216631321481
absolute error = 4.476e-05
relative error = 0.002399 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 1.85337393573 0.220063054451
y[1] (closed_form) = 1.85333375419 0.220085079114
absolute error = 4.582e-05
relative error = 0.002455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=940.7MB, alloc=52.3MB, time=11.68
x[1] = 2.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 1.85335278055 0.222136556751
y[1] (closed_form) = 1.85331217662 0.222158619819
absolute error = 4.621e-05
relative error = 0.002476 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.164
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 1.85401262298 0.222857077913
y[1] (closed_form) = 1.85397202135 0.222879235078
absolute error = 4.625e-05
relative error = 0.002477 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.165
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 1.8546116077 0.224958343677
y[1] (closed_form) = 1.85457063661 0.224980792433
absolute error = 4.672e-05
relative error = 0.002501 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.166
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=986.3MB, alloc=52.3MB, time=12.24
x[1] = 2.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 1.85455780113 0.227722931937
y[1] (closed_form) = 1.85451607865 0.227745437015
absolute error = 4.741e-05
relative error = 0.002537 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.166
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 1.85644247184 0.231958582374
y[1] (closed_form) = 1.85639952192 0.231982812806
absolute error = 4.931e-05
relative error = 0.002636 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 1.85635331877 0.235415220026
y[1] (closed_form) = 1.85630919441 0.235439527438
absolute error = 5.038e-05
relative error = 0.002692 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1032.0MB, alloc=52.3MB, time=12.80
x[1] = 2.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 1.8563260465 0.23749057993
y[1] (closed_form) = 1.85628150007 0.237514926406
absolute error = 5.077e-05
relative error = 0.002713 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.171
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 1.85698438282 0.238213709344
y[1] (closed_form) = 1.85693983883 0.238238149856
absolute error = 5.081e-05
relative error = 0.002714 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.172
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 1.85757774777 0.240318685553
y[1] (closed_form) = 1.85753283502 0.240343418075
absolute error = 5.127e-05
relative error = 0.002737 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.173
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1077.5MB, alloc=52.3MB, time=13.36
x[1] = 2.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 1.85751576978 0.243085685665
y[1] (closed_form) = 1.85747010619 0.243110475684
absolute error = 5.196e-05
relative error = 0.002774 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.173
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 1.85938975862 0.247330818098
y[1] (closed_form) = 1.85934287111 0.247357334396
absolute error = 5.387e-05
relative error = 0.002872 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.177
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 1.859290383 0.250790425585
y[1] (closed_form) = 1.85924232189 0.250817020704
absolute error = 5.493e-05
relative error = 0.002928 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1123.1MB, alloc=52.3MB, time=13.91
x[1] = 2.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 1.85925700035 0.252867651807
y[1] (closed_form) = 1.8592085175 0.252894286643
absolute error = 5.532e-05
relative error = 0.002948 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 1.85991383567 0.253593390306
y[1] (closed_form) = 1.8598653554 0.253620119117
absolute error = 5.536e-05
relative error = 0.002949 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.179
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 1.86050159024 0.255702083731
y[1] (closed_form) = 1.86045274191 0.255729104964
absolute error = 5.582e-05
relative error = 0.002973 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1168.7MB, alloc=52.3MB, time=14.47
x[1] = 2.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 1.86043144971 0.258471507345
y[1] (closed_form) = 1.86038185109 0.258498587242
absolute error = 5.651e-05
relative error = 0.003009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.181
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 1.86229477844 0.262726133103
y[1] (closed_form) = 1.86224395942 0.262754940168
absolute error = 5.842e-05
relative error = 0.003106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.184
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 1.86218519131 0.266188724971
y[1] (closed_form) = 1.86213319955 0.266217612684
absolute error = 5.948e-05
relative error = 0.003162 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.185
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1214.3MB, alloc=52.3MB, time=15.03
x[1] = 2.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 1.86214570506 0.268267826135
y[1] (closed_form) = 1.86209329187 0.268296754214
absolute error = 5.987e-05
relative error = 0.003182 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.185
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 1.86280104447 0.268996174502
y[1] (closed_form) = 1.86274863402 0.269025196493
absolute error = 5.991e-05
relative error = 0.003183 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.186
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 1.8633831981 0.271108591806
y[1] (closed_form) = 1.86333042028 0.271137906623
absolute error = 6.037e-05
relative error = 0.003206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.187
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1259.9MB, alloc=52.3MB, time=15.59
x[1] = 2.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 1.86330490397 0.273880450454
y[1] (closed_form) = 1.86325137643 0.273909825092
absolute error = 6.106e-05
relative error = 0.003242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.188
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 1.86515759439 0.278144580628
y[1] (closed_form) = 1.86510284997 0.278175683289
absolute error = 6.296e-05
relative error = 0.003339 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 1.86503780693 0.281610171275
y[1] (closed_form) = 1.86498189063 0.281641356397
absolute error = 6.402e-05
relative error = 0.003394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1305.6MB, alloc=52.3MB, time=16.15
x[1] = 2.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 1.86499222389 0.283691155916
y[1] (closed_form) = 1.86493588651 0.283722382048
absolute error = 6.441e-05
relative error = 0.003415 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 1.8656460725 0.284422114883
y[1] (closed_form) = 1.865589738 0.284453434863
absolute error = 6.446e-05
relative error = 0.003415 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 1.86556073802 0.287195981636
y[1] (closed_form) = 1.86550365431 0.28722736249
absolute error = 6.514e-05
relative error = 0.003451 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1351.3MB, alloc=52.3MB, time=16.71
x[1] = 2.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 1.86740417546 0.291468175226
y[1] (closed_form) = 1.86734587788 0.29150128485
absolute error = 6.704e-05
relative error = 0.003547 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 1.86727558093 0.294936237214
y[1] (closed_form) = 1.86721611222 0.29496943086
absolute error = 6.811e-05
relative error = 0.003603 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 1.86722473293 0.297018777343
y[1] (closed_form) = 1.86716484342 0.297052012553
absolute error = 6.849e-05
relative error = 0.003623 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.199
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1397.0MB, alloc=52.3MB, time=17.27
x[1] = 2.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 1.86787727127 0.2977519663
y[1] (closed_form) = 1.86781738477 0.297785295303
absolute error = 6.854e-05
relative error = 0.003624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 1.8684489835 0.299871263785
y[1] (closed_form) = 1.86838873092 0.299904886352
absolute error = 6.900e-05
relative error = 0.003646 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.201
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 1.86835551219 0.302647586876
y[1] (closed_form) = 1.86829451095 0.302681271405
absolute error = 6.968e-05
relative error = 0.003682 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.202
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1442.6MB, alloc=52.3MB, time=17.83
x[1] = 2.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 1.87018835189 0.306929305147
y[1] (closed_form) = 1.87012614029 0.306964719234
absolute error = 7.159e-05
relative error = 0.003777 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 1.87004957788 0.310400392446
y[1] (closed_form) = 1.86998619605 0.310435892343
absolute error = 7.265e-05
relative error = 0.003832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.206
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.182 0.451
h = 0.001 0.001
y[1] (numeric) = 1.86999264586 0.312484831777
y[1] (closed_form) = 1.86992884356 0.312520373873
absolute error = 7.303e-05
relative error = 0.003852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.206
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1488.2MB, alloc=52.3MB, time=18.38
x[1] = 2.183 0.452
h = 0.001 0.003
y[1] (numeric) = 1.87064370285 0.313220632625
y[1] (closed_form) = 1.87057990371 0.313256268447
absolute error = 7.308e-05
relative error = 0.003853 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.207
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 1.87120984119 0.315343672564
y[1] (closed_form) = 1.87114567668 0.315379602332
absolute error = 7.354e-05
relative error = 0.003876 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.209
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 1.8711082422 0.318122463131
y[1] (closed_form) = 1.87104332962 0.318158455994
absolute error = 7.422e-05
relative error = 0.003911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.209
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1533.9MB, alloc=52.3MB, time=18.94
x[1] = 2.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 1.87293050607 0.322413716495
y[1] (closed_form) = 1.87286438664 0.322451439667
absolute error = 7.612e-05
relative error = 0.004006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 1.87278156402 0.325887843077
y[1] (closed_form) = 1.87271427527 0.325925653836
absolute error = 7.718e-05
relative error = 0.00406 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 1.87271855499 0.32797418989
y[1] (closed_form) = 1.87265084611 0.328012043476
absolute error = 7.757e-05
relative error = 0.00408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.214
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1579.4MB, alloc=52.3MB, time=19.50
x[1] = 2.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 1.87336813569 0.328712603218
y[1] (closed_form) = 1.87330043012 0.328750550463
absolute error = 7.761e-05
relative error = 0.004081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.215
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 1.87392870971 0.330839391855
y[1] (closed_form) = 1.87386063947 0.33087763342
absolute error = 7.808e-05
relative error = 0.004103 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.216
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 1.87381899229 0.33362066097
y[1] (closed_form) = 1.87375017458 0.333658966754
absolute error = 7.876e-05
relative error = 0.004138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.217
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1625.2MB, alloc=52.3MB, time=20.06
x[1] = 2.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 1.87563070228 0.337921459602
y[1] (closed_form) = 1.87556068122 0.337961496412
absolute error = 8.066e-05
relative error = 0.004232 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 1.87547160373 0.341398639292
y[1] (closed_form) = 1.87540041427 0.341438765448
absolute error = 8.172e-05
relative error = 0.004287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 1.87540252472 0.343486901773
y[1] (closed_form) = 1.87533091549 0.343527071381
absolute error = 8.211e-05
relative error = 0.004307 %
Correct digits = 4
memory used=1670.8MB, alloc=52.3MB, time=20.62
Radius of convergence (given) for eq 1 = 4.222
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 1.87605063421 0.344227928121
y[1] (closed_form) = 1.87597902842 0.34426819132
absolute error = 8.215e-05
relative error = 0.004307 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.223
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 1.87660565348 0.346358471594
y[1] (closed_form) = 1.87653368373 0.346399029477
absolute error = 8.261e-05
relative error = 0.004329 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.224
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 1.87648782695 0.349142230207
y[1] (closed_form) = 1.87641511034 0.349182853425
absolute error = 8.329e-05
relative error = 0.004364 %
Correct digits = 4
memory used=1716.5MB, alloc=52.3MB, time=21.18
Radius of convergence (given) for eq 1 = 4.225
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 1.87828900503 0.353452584046
y[1] (closed_form) = 1.87821508858 0.353494938972
absolute error = 8.519e-05
relative error = 0.004458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.228
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 1.87811976161 0.356932830517
y[1] (closed_form) = 1.87804467769 0.356975276537
absolute error = 8.625e-05
relative error = 0.004512 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.229
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1762.1MB, alloc=52.3MB, time=21.74
x[1] = 2.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 1.87804461974 0.359023016763
y[1] (closed_form) = 1.8779691164 0.359065506853
absolute error = 8.664e-05
relative error = 0.004531 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 1.87869126306 0.359766656624
y[1] (closed_form) = 1.87861576331 0.359809240235
absolute error = 8.668e-05
relative error = 0.004532 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.231
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.199 0.522
h = 0.003 0.006
y[1] (numeric) = 1.87856643415 0.362552470297
y[1] (closed_form) = 1.87849018809 0.362595120255
absolute error = 8.736e-05
relative error = 0.004566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.231
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1807.8MB, alloc=52.3MB, time=22.30
x[1] = 2.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 1.88035845034 0.36687093162
y[1] (closed_form) = 1.88028100745 0.366915313887
absolute error = 8.926e-05
relative error = 0.004659 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.235
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 1.88018044718 0.370353708053
y[1] (closed_form) = 1.88010183763 0.370398182917
absolute error = 9.032e-05
relative error = 0.004713 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 1.88010006928 0.37244548452
y[1] (closed_form) = 1.88002104061 0.372490003987
absolute error = 9.071e-05
relative error = 0.004733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1853.5MB, alloc=52.3MB, time=22.86
x[1] = 2.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 1.88074542347 0.373191356979
y[1] (closed_form) = 1.88066639851 0.373235969908
absolute error = 9.075e-05
relative error = 0.004733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.237
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 1.88129008734 0.375328837387
y[1] (closed_form) = 1.88121069972 0.37537374567
absolute error = 9.121e-05
relative error = 0.004755 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 1.8811571668 0.37811716078
y[1] (closed_form) = 1.88107703346 0.378162136457
absolute error = 9.189e-05
relative error = 0.004789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1899.1MB, alloc=52.3MB, time=23.42
x[1] = 2.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 1.88293869192 0.382445195441
y[1] (closed_form) = 1.88285736523 0.382491904044
absolute error = 9.379e-05
relative error = 0.004881 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.243
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 1.8827505656 0.385931063838
y[1] (closed_form) = 1.88266807321 0.385977866759
absolute error = 9.484e-05
relative error = 0.004935 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.244
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 1.8826641381 0.388024778978
y[1] (closed_form) = 1.88258122696 0.38807162711
absolute error = 9.523e-05
relative error = 0.004954 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.244
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1944.7MB, alloc=52.3MB, time=23.98
x[1] = 2.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 1.88330803549 0.388773265797
y[1] (closed_form) = 1.88322512819 0.38882020732
absolute error = 9.527e-05
relative error = 0.004955 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.245
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 1.88384717209 0.390914518112
y[1] (closed_form) = 1.88376390285 0.390961755333
absolute error = 9.573e-05
relative error = 0.004976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 1.8837061694 0.393705361779
y[1] (closed_form) = 1.88362215507 0.393752667482
absolute error = 9.642e-05
relative error = 0.00501 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1990.4MB, alloc=52.3MB, time=24.54
x[1] = 2.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 1.88547722548 0.398042979047
y[1] (closed_form) = 1.88539202129 0.39809201826
absolute error = 9.831e-05
relative error = 0.005102 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.251
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 1.8852789879 0.40153195265
y[1] (closed_form) = 1.88519261898 0.401581087887
absolute error = 9.937e-05
relative error = 0.005155 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.252
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 1.88518651805 0.403627614297
y[1] (closed_form) = 1.88509973075 0.40367679535
absolute error = 9.975e-05
relative error = 0.005174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.253
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2036.0MB, alloc=52.3MB, time=25.10
x[1] = 2.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 1.88582896364 0.404378715832
y[1] (closed_form) = 1.88574218033 0.404427990201
absolute error = 9.980e-05
relative error = 0.005174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.254
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 1.88636258266 0.406523745773
y[1] (closed_form) = 1.8862754381 0.406573316177
absolute error = 0.0001003
relative error = 0.005196 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.255
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 1.88621350743 0.409317120197
y[1] (closed_form) = 1.88612561842 0.409366760163
absolute error = 0.0001009
relative error = 0.00523 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.256
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2081.6MB, alloc=52.3MB, time=25.66
x[1] = 2.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 1.88797411651 0.413664329109
y[1] (closed_form) = 1.88788504112 0.413715703135
absolute error = 0.0001028
relative error = 0.005321 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 1.88776577963 0.417156421009
y[1] (closed_form) = 1.8876755405 0.41720789275
absolute error = 0.0001039
relative error = 0.005374 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 1.88766727473 0.419254036906
y[1] (closed_form) = 1.8875766176 0.419305555061
absolute error = 0.0001043
relative error = 0.005393 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.261
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2127.3MB, alloc=52.3MB, time=26.22
x[1] = 2.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 1.88830827354 0.420007753462
y[1] (closed_form) = 1.88821762054 0.420059364861
absolute error = 0.0001043
relative error = 0.005393 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 1.88883638466 0.422156566643
y[1] (closed_form) = 1.88874537113 0.422208474406
absolute error = 0.0001048
relative error = 0.005414 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.263
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 1.88867924656 0.424952482186
y[1] (closed_form) = 1.88858748922 0.425004460581
absolute error = 0.0001055
relative error = 0.005448 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.264
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2172.9MB, alloc=52.3MB, time=26.78
x[1] = 2.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 1.8904294307 0.429309291546
y[1] (closed_form) = 1.89033649045 0.429363004517
absolute error = 0.0001073
relative error = 0.005538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.268
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 1.89021100657 0.432804514681
y[1] (closed_form) = 1.89011690358 0.432858327044
absolute error = 0.0001084
relative error = 0.005591 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 1.89010647398 0.43490409248
y[1] (closed_form) = 1.89001195336 0.434957951849
absolute error = 0.0001088
relative error = 0.005609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2218.7MB, alloc=52.3MB, time=27.34
x[1] = 2.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 1.890746031 0.435660424318
y[1] (closed_form) = 1.89065151464 0.435714376857
absolute error = 0.0001088
relative error = 0.005609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.27
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 1.89058192995 0.438458439438
y[1] (closed_form) = 1.89048667038 0.438512463581
absolute error = 0.0001095
relative error = 0.005643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.271
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 1.89232304382 0.442823395595
y[1] (closed_form) = 1.89222660433 0.442879154773
absolute error = 0.0001114
relative error = 0.005732 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.275
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2264.4MB, alloc=52.3MB, time=27.91
x[1] = 2.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 1.89209590912 0.446321204274
y[1] (closed_form) = 1.89199830774 0.446377064288
absolute error = 0.0001125
relative error = 0.005785 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.276
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 1.89198617053 0.448422405186
y[1] (closed_form) = 1.89188815183 0.448478312718
absolute error = 0.0001128
relative error = 0.005804 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.276
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 1.89262445932 0.449180971252
y[1] (closed_form) = 1.89252644501 0.449236971889
absolute error = 0.0001129
relative error = 0.005803 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.277
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2310.2MB, alloc=52.3MB, time=28.47
x[1] = 2.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 1.8931423022 0.451336773394
y[1] (closed_form) = 1.89304392867 0.451393070995
absolute error = 0.0001133
relative error = 0.005824 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.279
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 1.89297015635 0.454137348755
y[1] (closed_form) = 1.89287104023 0.454193718962
absolute error = 0.000114
relative error = 0.005858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.28
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 1.89470088625 0.458511921394
y[1] (closed_form) = 1.89460059367 0.458570027091
absolute error = 0.0001159
relative error = 0.005946 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.283
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2355.9MB, alloc=52.3MB, time=29.03
x[1] = 2.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 1.89446368678 0.462012885123
y[1] (closed_form) = 1.89436223334 0.462071093304
absolute error = 0.000117
relative error = 0.005999 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.284
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.233 0.665
h = 0.001 0.001
y[1] (numeric) = 1.8943479342 0.464116062016
y[1] (closed_form) = 1.89424606382 0.464174318299
absolute error = 0.0001174
relative error = 0.006017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.285
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.234 0.666
h = 0.001 0.003
y[1] (numeric) = 1.89498479044 0.464877243786
y[1] (closed_form) = 1.89488292458 0.464935593097
absolute error = 0.0001174
relative error = 0.006017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.286
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2401.7MB, alloc=52.3MB, time=29.59
x[1] = 2.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 1.89549715321 0.467036844749
y[1] (closed_form) = 1.89539492885 0.467095491331
absolute error = 0.0001179
relative error = 0.006037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 1.89531697236 0.469839990313
y[1] (closed_form) = 1.89521400608 0.469898710545
absolute error = 0.0001185
relative error = 0.006071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 1.89703734038 0.474224187582
y[1] (closed_form) = 1.89693320109 0.474284643725
absolute error = 0.0001204
relative error = 0.006158 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.292
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2447.4MB, alloc=52.3MB, time=30.15
x[1] = 2.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 1.89679008841 0.477728318862
y[1] (closed_form) = 1.89668478928 0.477788879125
absolute error = 0.0001215
relative error = 0.00621 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.293
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 1.89666832931 0.479833479125
y[1] (closed_form) = 1.89656261364 0.479894088066
absolute error = 0.0001219
relative error = 0.006229 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.294
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 1.89730375796 0.480597276726
y[1] (closed_form) = 1.89719804694 0.480657978618
absolute error = 0.0001219
relative error = 0.006228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.295
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2493.1MB, alloc=52.3MB, time=30.71
x[1] = 2.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 1.89781065039 0.482760681711
y[1] (closed_form) = 1.89770458158 0.482821681174
absolute error = 0.0001224
relative error = 0.006249 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.296
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 1.89762244444 0.485566407368
y[1] (closed_form) = 1.89751563439 0.485627481515
absolute error = 0.000123
relative error = 0.006282 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.297
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 1.89933247265 0.489960237187
y[1] (closed_form) = 1.89922449304 0.490023047633
absolute error = 0.0001249
relative error = 0.006369 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.301
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2538.8MB, alloc=52.3MB, time=31.27
x[1] = 2.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 1.89907518051 0.493467548369
y[1] (closed_form) = 1.89896604211 0.493530464556
absolute error = 0.000126
relative error = 0.006421 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.302
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 1.89894742242 0.495574699295
y[1] (closed_form) = 1.89883786788 0.495637664732
absolute error = 0.0001264
relative error = 0.006439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.302
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 1.89958142841 0.496341112812
y[1] (closed_form) = 1.89947187864 0.496404171121
absolute error = 0.0001264
relative error = 0.006438 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.304
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2584.4MB, alloc=52.3MB, time=31.83
x[1] = 2.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 1.90008286028 0.498508326914
y[1] (closed_form) = 1.89997295344 0.498571683087
absolute error = 0.0001269
relative error = 0.006458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.305
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 1.8998866392 0.50131664243
y[1] (closed_form) = 1.89977599179 0.501380074311
absolute error = 0.0001275
relative error = 0.006491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.306
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 1.90158634967 0.505720112495
y[1] (closed_form) = 1.90147453614 0.505785281031
absolute error = 0.0001294
relative error = 0.006578 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2630.1MB, alloc=52.3MB, time=32.39
x[1] = 2.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 1.90131902978 0.509230615775
y[1] (closed_form) = 1.90120605853 0.509295891655
absolute error = 0.0001305
relative error = 0.006629 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 1.90118528026 0.511339764567
y[1] (closed_form) = 1.90107189325 0.511405090265
absolute error = 0.0001309
relative error = 0.006647 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 1.9018178685 0.512108794037
y[1] (closed_form) = 1.90170448641 0.512174212528
absolute error = 0.0001309
relative error = 0.006647 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.312
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2675.7MB, alloc=52.3MB, time=32.95
x[1] = 2.25 0.736
h = 0.003 0.006
y[1] (numeric) = 1.90161472522 0.514919251183
y[1] (closed_form) = 1.90150060318 0.514984746313
absolute error = 0.0001316
relative error = 0.006679 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.313
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 1.90330545725 0.519330902692
y[1] (closed_form) = 1.90319017204 0.519398134798
absolute error = 0.0001335
relative error = 0.006765 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.317
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 1.90302947758 0.522844044024
y[1] (closed_form) = 1.90291303554 0.522911384859
absolute error = 0.0001345
relative error = 0.006816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.318
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2721.5MB, alloc=52.3MB, time=33.51
x[1] = 2.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 1.90289055301 0.524954846963
y[1] (closed_form) = 1.90277369555 0.525022238103
absolute error = 0.0001349
relative error = 0.006834 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.319
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 1.90352189366 0.525726111348
y[1] (closed_form) = 1.90340504123 0.525793595213
absolute error = 0.0001349
relative error = 0.006833 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.32
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 1.90401314529 0.527900361758
y[1] (closed_form) = 1.9038959371 0.527968144019
absolute error = 0.0001354
relative error = 0.006853 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.321
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2767.3MB, alloc=52.3MB, time=34.07
x[1] = 2.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 1.90380200546 0.530713426779
y[1] (closed_form) = 1.90368405799 0.530781286636
absolute error = 0.0001361
relative error = 0.006885 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.322
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 1.90358938719 0.533526647212
y[1] (closed_form) = 1.90347070054 0.5335945848
absolute error = 0.0001368
relative error = 0.006918 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.323
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 1.90526770966 0.537949241939
y[1] (closed_form) = 1.90514786385 0.538018916975
absolute error = 0.0001386
relative error = 0.007003 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.327
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2812.9MB, alloc=52.3MB, time=34.63
x[1] = 2.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 1.90497987749 0.541465783837
y[1] (closed_form) = 1.90485887605 0.541535569489
absolute error = 0.0001397
relative error = 0.007053 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.328
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 1.90483386819 0.543578724686
y[1] (closed_form) = 1.90471245179 0.54364856131
absolute error = 0.0001401
relative error = 0.007071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.329
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 1.90546346012 0.544353005134
y[1] (closed_form) = 1.9053420489 0.544422934393
absolute error = 0.0001401
relative error = 0.007071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.33
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2858.6MB, alloc=52.3MB, time=35.19
x[1] = 2.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 1.90594819902 0.546531538888
y[1] (closed_form) = 1.90582643287 0.546601766888
absolute error = 0.0001406
relative error = 0.00709 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.331
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 1.90572759571 0.549347378491
y[1] (closed_form) = 1.90560509106 0.549417685282
absolute error = 0.0001412
relative error = 0.007122 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.332
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 1.90739566704 0.553779636514
y[1] (closed_form) = 1.90727200663 0.553851681011
absolute error = 0.0001431
relative error = 0.007206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.336
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2904.3MB, alloc=52.3MB, time=35.75
x[1] = 2.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 1.9070978446 0.557299407192
y[1] (closed_form) = 1.90697302966 0.557371563866
absolute error = 0.0001442
relative error = 0.007257 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.337
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 1.9069458667 0.559414367568
y[1] (closed_form) = 1.90682063721 0.559486575764
absolute error = 0.0001446
relative error = 0.007274 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.338
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 1.90757405571 0.560191264055
y[1] (closed_form) = 1.90744883152 0.560263564805
absolute error = 0.0001446
relative error = 0.007273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.339
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2950.0MB, alloc=52.3MB, time=36.31
x[1] = 2.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 1.90805337341 0.562373626894
y[1] (closed_form) = 1.907927795 0.562446226646
absolute error = 0.0001451
relative error = 0.007292 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.341
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.266 0.806
h = 0.003 0.006
y[1] (numeric) = 1.9078247952 0.565192095005
y[1] (closed_form) = 1.90769847901 0.565264774533
absolute error = 0.0001457
relative error = 0.007324 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.341
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 1.90948263743 0.569634023117
y[1] (closed_form) = 1.90935516889 0.569708440579
absolute error = 0.0001476
relative error = 0.007408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.346
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2995.8MB, alloc=52.3MB, time=36.87
x[1] = 2.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 1.90917483742 0.573157034157
y[1] (closed_form) = 1.90904621544 0.573231565341
absolute error = 0.0001487
relative error = 0.007458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.347
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 1.90901689863 0.575274020891
y[1] (closed_form) = 1.90888786251 0.575348604142
absolute error = 0.000149
relative error = 0.007476 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.347
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 1.90964368957 0.576053533279
y[1] (closed_form) = 1.90951465888 0.576128209
absolute error = 0.0001491
relative error = 0.007475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.348
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3041.6MB, alloc=52.3MB, time=37.44
x[1] = 2.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 1.9101175959 0.578239729771
y[1] (closed_form) = 1.9099882117 0.578314704751
absolute error = 0.0001495
relative error = 0.007493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.35
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 1.90988105302 0.581060835541
y[1] (closed_form) = 1.90975093176 0.581135891272
absolute error = 0.0001502
relative error = 0.007525 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.351
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 1.91152868819 0.585512440316
y[1] (closed_form) = 1.91139741797 0.585589234178
absolute error = 0.0001521
relative error = 0.007608 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.355
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3087.2MB, alloc=52.3MB, time=38.00
x[1] = 2.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 1.91121092333 0.589038703147
y[1] (closed_form) = 1.91107850078 0.58911561226
absolute error = 0.0001531
relative error = 0.007658 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 1.9110470314 0.591157722978
y[1] (closed_form) = 1.91091419512 0.591234684697
absolute error = 0.0001535
relative error = 0.007675 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.357
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 1.91167242911 0.591939851086
y[1] (closed_form) = 1.91153959839 0.592016905191
absolute error = 0.0001536
relative error = 0.007674 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.358
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3132.9MB, alloc=52.3MB, time=38.57
x[1] = 2.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 1.91214093391 0.594129885696
y[1] (closed_form) = 1.9120077504 0.594207239308
absolute error = 0.000154
relative error = 0.007692 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.359
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 1.91189643663 0.596953638152
y[1] (closed_form) = 1.91176251677 0.597031073482
absolute error = 0.0001547
relative error = 0.007724 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.36
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 1.91353388675 0.601414925946
y[1] (closed_form) = 1.91339882131 0.601494099573
absolute error = 0.0001566
relative error = 0.007806 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.364
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3178.8MB, alloc=52.3MB, time=39.13
x[1] = 2.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 1.91320616984 0.604944451843
y[1] (closed_form) = 1.9130699532 0.605023742236
absolute error = 0.0001576
relative error = 0.007855 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.365
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 1.91303633255 0.607065511418
y[1] (closed_form) = 1.9128997026 0.60714485495
absolute error = 0.000158
relative error = 0.007873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.366
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 1.91366034184 0.607850255022
y[1] (closed_form) = 1.91352371757 0.607929690855
absolute error = 0.000158
relative error = 0.007871 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.367
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3224.5MB, alloc=52.3MB, time=39.69
x[1] = 2.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 1.91340897421 0.610676198162
y[1] (closed_form) = 1.91327161425 0.610755716592
absolute error = 0.0001587
relative error = 0.007903 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.368
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 1.91503755954 0.615145704732
y[1] (closed_form) = 1.91489905692 0.615226961616
absolute error = 0.0001606
relative error = 0.007984 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.372
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 1.91470124748 0.61867792994
y[1] (closed_form) = 1.9145615946 0.618759304896
absolute error = 0.0001616
relative error = 0.008033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.373
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3270.3MB, alloc=52.3MB, time=40.26
x[1] = 2.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 1.91452627448 0.620800679815
y[1] (closed_form) = 1.91438620865 0.62088210837
absolute error = 0.000162
relative error = 0.00805 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.374
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 1.91514906134 0.62158765808
y[1] (closed_form) = 1.9150090013 0.621669178864
absolute error = 0.0001621
relative error = 0.008049 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 1.91560749556 0.623784782
y[1] (closed_form) = 1.91546708404 0.623866602743
absolute error = 0.0001625
relative error = 0.008067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.377
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3316.0MB, alloc=52.3MB, time=40.82
x[1] = 2.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 1.91534819267 0.626613388471
y[1] (closed_form) = 1.91520704616 0.626695292711
absolute error = 0.0001632
relative error = 0.008098 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.378
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 1.91696663379 0.63109258957
y[1] (closed_form) = 1.91682434797 0.631176232374
absolute error = 0.000165
relative error = 0.008179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.382
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 1.9166203935 0.634628098573
y[1] (closed_form) = 1.91647695857 0.634711860935
absolute error = 0.0001661
relative error = 0.008228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.383
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3361.9MB, alloc=52.3MB, time=41.40
x[1] = 2.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 1.91643948962 0.636752900407
y[1] (closed_form) = 1.91629564216 0.636836716892
absolute error = 0.0001665
relative error = 0.008245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.384
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 1.91706089698 0.637542493699
y[1] (closed_form) = 1.91691705543 0.637626402327
absolute error = 0.0001665
relative error = 0.008243 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.385
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 1.91751395781 0.639743468064
y[1] (closed_form) = 1.9173697655 0.639827676877
absolute error = 0.000167
relative error = 0.008261 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.387
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3407.7MB, alloc=52.3MB, time=41.96
x[1] = 2.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 1.91724673002 0.642574746496
y[1] (closed_form) = 1.91710180345 0.642659039745
absolute error = 0.0001677
relative error = 0.008292 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.388
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 1.91885504887 0.647063647862
y[1] (closed_form) = 1.91870898635 0.647149679755
absolute error = 0.0001695
relative error = 0.008372 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.392
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 1.9184988933 0.650602451501
y[1] (closed_form) = 1.91835168281 0.650688604422
absolute error = 0.0001706
relative error = 0.00842 %
Correct digits = 4
memory used=3453.6MB, alloc=52.3MB, time=42.52
Radius of convergence (given) for eq 1 = 4.393
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 1.91831206642 0.652729311679
y[1] (closed_form) = 1.91816444382 0.65281551924
absolute error = 0.000171
relative error = 0.008437 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.394
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 1.91893209903 0.653521519656
y[1] (closed_form) = 1.91878448246 0.653607819273
absolute error = 0.000171
relative error = 0.008436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.395
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 1.91937979633 0.655726348536
memory used=3499.4MB, alloc=52.3MB, time=43.14
y[1] (closed_form) = 1.91923182971 0.65581294856
absolute error = 0.0001714
relative error = 0.008453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.396
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 1.91910465406 0.658560307487
y[1] (closed_form) = 1.91895595393 0.658646992875
absolute error = 0.0001721
relative error = 0.008484 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.397
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 1.92070287256 0.663058914646
y[1] (closed_form) = 1.92055303982 0.663147338727
absolute error = 0.000174
relative error = 0.008563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3545.1MB, alloc=52.3MB, time=43.71
x[1] = 2.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 1.92033681471 0.666601023606
y[1] (closed_form) = 1.92018583515 0.666689570173
absolute error = 0.000175
relative error = 0.008611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3 0.949
h = 0.001 0.001
y[1] (numeric) = 1.92014407271 0.66872994842
y[1] (closed_form) = 1.91999268148 0.668818550138
absolute error = 0.0001754
relative error = 0.008628 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.301 0.95
h = 0.001 0.003
y[1] (numeric) = 1.92076273531 0.6695247707
y[1] (closed_form) = 1.92061135023 0.669613464386
absolute error = 0.0001755
relative error = 0.008626 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.405
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3590.8MB, alloc=52.3MB, time=44.28
x[1] = 2.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 1.92120507895 0.671733458066
y[1] (closed_form) = 1.92105334452 0.671822452373
absolute error = 0.0001759
relative error = 0.008643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.406
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 1.92092203266 0.67457010597
y[1] (closed_form) = 1.92076956548 0.674659186559
absolute error = 0.0001766
relative error = 0.008674 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.407
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 1.9225101727 0.679078424236
y[1] (closed_form) = 1.92235657624 0.679169243539
absolute error = 0.0001784
relative error = 0.008752 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.411
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3636.7MB, alloc=52.3MB, time=44.85
x[1] = 2.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 1.9221342256 0.682623849055
y[1] (closed_form) = 1.92197948349 0.682714792283
absolute error = 0.0001795
relative error = 0.0088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.413
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 1.92193557641 0.684754844704
y[1] (closed_form) = 1.92178042306 0.68484584359
absolute error = 0.0001799
relative error = 0.008816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.413
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 1.92255287373 0.685552280865
y[1] (closed_form) = 1.92239772664 0.685643371632
absolute error = 0.0001799
relative error = 0.008815 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.415
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3682.5MB, alloc=52.3MB, time=45.42
x[1] = 2.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 1.92226300012 0.688391155966
y[1] (closed_form) = 1.92210712096 0.68848233385
absolute error = 0.0001806
relative error = 0.008845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.416
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 1.92384236671 0.692907717623
y[1] (closed_form) = 1.92368536112 0.693000634255
absolute error = 0.0001824
relative error = 0.008923 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.42
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 1.92345787808 0.696455887356
y[1] (closed_form) = 1.92329972784 0.696548929155
absolute error = 0.0001835
relative error = 0.00897 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3728.3MB, alloc=52.3MB, time=46.00
x[1] = 2.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 1.92325412577 0.698588600169
y[1] (closed_form) = 1.92309556465 0.698681698062
absolute error = 0.0001839
relative error = 0.008987 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.422
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 1.92387022053 0.699388269717
y[1] (closed_form) = 1.92371166578 0.699481459415
absolute error = 0.0001839
relative error = 0.008985 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.423
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 1.9243025824 0.701604083555
y[1] (closed_form) = 1.92414367963 0.701697574262
absolute error = 0.0001844
relative error = 0.009002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.425
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3774.0MB, alloc=52.3MB, time=47.04
x[1] = 2.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 1.92400482429 0.70444566315
y[1] (closed_form) = 1.92384519016 0.70453924183
absolute error = 0.000185
relative error = 0.009032 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.426
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 1.925574153 0.708971945505
y[1] (closed_form) = 1.92541339576 0.7090672629
absolute error = 0.0001869
relative error = 0.009109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.43
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 1.9251797994 0.712523450455
y[1] (closed_form) = 1.92501789867 0.712618894428
absolute error = 0.0001879
relative error = 0.009156 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.431
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3819.9MB, alloc=52.3MB, time=47.71
x[1] = 2.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 1.92497015463 0.714658245493
y[1] (closed_form) = 1.92480784346 0.714753746057
absolute error = 0.0001883
relative error = 0.009172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 1.92558489283 0.715460528089
y[1] (closed_form) = 1.92542258815 0.715556120367
absolute error = 0.0001884
relative error = 0.00917 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.433
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 1.92601192919 0.717680211337
y[1] (closed_form) = 1.92584927719 0.717776104819
absolute error = 0.0001888
relative error = 0.009187 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3865.7MB, alloc=52.3MB, time=48.31
x[1] = 2.317 1.02
h = 0.003 0.006
y[1] (numeric) = 1.92570629708 0.72052450347
y[1] (closed_form) = 1.9255429145 0.720620485816
absolute error = 0.0001895
relative error = 0.009217 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.436
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 1.92726560971 0.725060511241
y[1] (closed_form) = 1.9271011073 0.72515823224
absolute error = 0.0001913
relative error = 0.009293 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.44
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 1.92686140429 0.728615361512
y[1] (closed_form) = 1.92669575959 0.728713210486
absolute error = 0.0001924
relative error = 0.00934 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.441
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3911.4MB, alloc=52.3MB, time=48.89
x[1] = 2.3202 1.034
h = 0.001 0.001
y[1] (numeric) = 1.92664587506 0.730752244715
y[1] (closed_form) = 1.92647982036 0.73085015077
absolute error = 0.0001928
relative error = 0.009356 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.442
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3212 1.035
h = 0.001 0.003
y[1] (numeric) = 1.92725926136 0.731557139825
y[1] (closed_form) = 1.92709321326 0.731655137504
absolute error = 0.0001928
relative error = 0.009354 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.443
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = 1.92768098205 0.733780696071
y[1] (closed_form) = 1.92751458734 0.733878995141
absolute error = 0.0001933
relative error = 0.00937 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.445
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3957.2MB, alloc=52.3MB, time=49.48
x[1] = 2.3223 1.042
h = 0.003 0.006
y[1] (numeric) = 1.92736748655 0.736627708709
y[1] (closed_form) = 1.92720036202 0.736726097523
absolute error = 0.0001939
relative error = 0.0094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.446
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = 1.92891680485 0.741173446409
y[1] (closed_form) = 1.92874856378 0.741273573786
absolute error = 0.0001958
relative error = 0.009475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.45
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = 1.92850276081 0.744731651955
y[1] (closed_form) = 1.92833337864 0.744831908688
absolute error = 0.0001968
relative error = 0.009522 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.452
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4002.9MB, alloc=52.3MB, time=50.06
x[1] = 2.3255 1.056
h = 0.001 0.001
y[1] (numeric) = 1.92828135512 0.746870629172
y[1] (closed_form) = 1.9281115634 0.746970943472
absolute error = 0.0001972
relative error = 0.009537 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.453
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3265 1.057
h = 0.001 0.003
y[1] (numeric) = 1.92889339416 0.747678136224
y[1] (closed_form) = 1.92872360915 0.747778542056
absolute error = 0.0001973
relative error = 0.009535 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.454
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = 1.92930980903 0.749905568957
y[1] (closed_form) = 1.92913967811 0.75000627636
absolute error = 0.0001977
relative error = 0.009552 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.455
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4048.6MB, alloc=52.3MB, time=50.65
x[1] = 2.3276 1.064
h = 0.003 0.006
y[1] (numeric) = 1.92898846076 0.752755309948
y[1] (closed_form) = 1.9288176008 0.752856107965
absolute error = 0.0001984
relative error = 0.009581 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.456
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = 1.93052780643 0.757310781886
y[1] (closed_form) = 1.93035583321 0.757413318349
absolute error = 0.0002002
relative error = 0.009656 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = 1.93010393702 0.760872352509
y[1] (closed_form) = 1.92993082389 0.760975019695
absolute error = 0.0002013
relative error = 0.009702 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.462
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4094.4MB, alloc=52.3MB, time=51.24
x[1] = 2.3308 1.078
h = 0.001 0.001
y[1] (numeric) = 1.92987666291 0.763013429501
y[1] (closed_form) = 1.92970314068 0.763116154732
absolute error = 0.0002016
relative error = 0.009718 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.463
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = 1.93048735931 0.763823547885
y[1] (closed_form) = 1.9303138439 0.763926364557
absolute error = 0.0002017
relative error = 0.009715 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.464
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3319 1.083
h = 0.003 0.006
y[1] (numeric) = 1.93015922749 0.766675550131
y[1] (closed_form) = 1.92998498374 0.766778458211
absolute error = 0.0002024
relative error = 0.009744 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.465
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4140.1MB, alloc=52.3MB, time=51.83
x[1] = 2.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = 1.9316898904 0.771239285832
y[1] (closed_form) = 1.93151453619 0.771343932272
absolute error = 0.0002042
relative error = 0.009818 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.335 1.094
h = 0.0001 0.003
y[1] (numeric) = 1.93125753402 0.774803643914
y[1] (closed_form) = 1.93108104093 0.774908422255
absolute error = 0.0002053
relative error = 0.009864 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.471
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3351 1.097
h = 0.001 0.001
y[1] (numeric) = 1.93102518991 0.776946463091
y[1] (closed_form) = 1.9308482881 0.77705129989
absolute error = 0.0002056
relative error = 0.00988 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.472
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4186.0MB, alloc=52.3MB, time=52.44
x[1] = 2.3361 1.098
h = 0.001 0.003
y[1] (numeric) = 1.93163470318 0.777758812787
y[1] (closed_form) = 1.9314578083 0.77786374095
absolute error = 0.0002057
relative error = 0.009878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.473
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = 1.93204122505 0.779993404785
y[1] (closed_form) = 1.93186398557 0.780098634846
absolute error = 0.0002061
relative error = 0.009894 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.475
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3372 1.105
h = 0.003 0.006
y[1] (numeric) = 1.93170526025 0.782848149835
y[1] (closed_form) = 1.93152729317 0.782953472113
absolute error = 0.0002068
relative error = 0.009922 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.476
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4231.7MB, alloc=52.3MB, time=53.04
x[1] = 2.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = 1.93322599078 0.787421627516
y[1] (closed_form) = 1.93304691648 0.787528687985
absolute error = 0.0002086
relative error = 0.009996 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.48
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = 1.93278383364 0.790989368679
y[1] (closed_form) = 1.93260362168 0.791096562386
absolute error = 0.0002097
relative error = 0.01004 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3404 1.119
h = 0.001 0.001
y[1] (numeric) = 1.93254563604 0.793134298203
y[1] (closed_form) = 1.9323650158 0.793241550838
absolute error = 0.0002101
relative error = 0.01006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.482
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4277.4MB, alloc=52.3MB, time=53.63
x[1] = 2.3414 1.12
h = 0.001 0.003
y[1] (numeric) = 1.9331538152 0.793949258054
y[1] (closed_form) = 1.932973202 0.79405660196
absolute error = 0.0002101
relative error = 0.01005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.484
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = 1.93355505934 0.796187736102
y[1] (closed_form) = 1.93337410224 0.796295382068
absolute error = 0.0002106
relative error = 0.01007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3425 1.127
h = 0.003 0.006
y[1] (numeric) = 1.93321127221 0.79904523142
y[1] (closed_form) = 1.9330295883 0.799152970444
absolute error = 0.0002112
relative error = 0.0101 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.486
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4323.1MB, alloc=52.3MB, time=54.24
x[1] = 2.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = 1.93472209193 0.803628454817
y[1] (closed_form) = 1.93453930404 0.803737931837
absolute error = 0.0002131
relative error = 0.01017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.491
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = 1.93427014736 0.807199588438
y[1] (closed_form) = 1.93408622303 0.807309200019
absolute error = 0.0002141
relative error = 0.01022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.492
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3457 1.141
h = 0.001 0.001
y[1] (numeric) = 1.93402610436 0.809346633813
y[1] (closed_form) = 1.9338417722 0.809456304785
absolute error = 0.0002145
relative error = 0.01023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.493
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4368.8MB, alloc=52.3MB, time=54.84
x[1] = 2.3467 1.142
h = 0.001 0.003
y[1] (numeric) = 1.93463295397 0.810164203103
y[1] (closed_form) = 1.93444862896 0.810273965252
absolute error = 0.0002145
relative error = 0.01023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.494
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = 1.93502893017 0.81240657032
y[1] (closed_form) = 1.93484426196 0.812516634684
absolute error = 0.000215
relative error = 0.01024 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.496
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3478 1.149
h = 0.003 0.006
y[1] (numeric) = 1.93467733145 0.81526682329
y[1] (closed_form) = 1.93449193722 0.815376981546
absolute error = 0.0002157
relative error = 0.01027 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.497
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4414.3MB, alloc=52.3MB, time=55.43
x[1] = 2.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = 1.93617826189 0.819859795943
y[1] (closed_form) = 1.9359917669 0.819971691973
absolute error = 0.0002175
relative error = 0.01034 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.501
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = 1.93571654327 0.823434331253
y[1] (closed_form) = 1.93552891306 0.823546363149
absolute error = 0.0002185
relative error = 0.01039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.503
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.351 1.163
h = 0.001 0.001
y[1] (numeric) = 1.93546666296 0.825583497892
y[1] (closed_form) = 1.93527862538 0.825695589637
absolute error = 0.0002189
relative error = 0.0104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4460.1MB, alloc=52.3MB, time=56.03
x[1] = 2.352 1.164
h = 0.001 0.003
y[1] (numeric) = 1.93607218754 0.826403675872
y[1] (closed_form) = 1.93588415722 0.8265158587
absolute error = 0.000219
relative error = 0.0104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.505
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.353 1.167
h = 0.0001 0.004
y[1] (numeric) = 1.93646290562 0.82864993528
y[1] (closed_form) = 1.9362745328 0.828762420471
absolute error = 0.0002194
relative error = 0.01042 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.507
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3531 1.171
h = 0.003 0.006
y[1] (numeric) = 1.93610350603 0.831512953171
y[1] (closed_form) = 1.93591440799 0.831625533076
absolute error = 0.0002201
relative error = 0.01044 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.508
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4505.8MB, alloc=52.3MB, time=56.75
x[1] = 2.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = 1.93759456869 0.836115678425
y[1] (closed_form) = 1.93740437309 0.836229995856
absolute error = 0.0002219
relative error = 0.01052 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.512
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = 1.9371230894 0.839693624504
y[1] (closed_form) = 1.93693175981 0.839808079094
absolute error = 0.000223
relative error = 0.01056 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 1.9368673799 0.841844917733
y[1] (closed_form) = 1.93667564341 0.841959432624
absolute error = 0.0002233
relative error = 0.01058 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4551.5MB, alloc=52.3MB, time=57.54
x[1] = 2.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 1.93747158397 0.842667703617
y[1] (closed_form) = 1.93727985483 0.842782309496
absolute error = 0.0002234
relative error = 0.01057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 1.93710544518 0.8455330144
y[1] (closed_form) = 1.93691299155 0.845647715744
absolute error = 0.000224
relative error = 0.0106 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.517
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 1.93858791491 0.850144019701
y[1] (closed_form) = 1.93839436647 0.850260458374
absolute error = 0.0002259
relative error = 0.01067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.521
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4597.3MB, alloc=52.3MB, time=58.15
x[1] = 2.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 1.93810800393 0.853724792767
y[1] (closed_form) = 1.93791332256 0.853841369713
absolute error = 0.0002269
relative error = 0.01072 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.523
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 1.93784725796 0.855877851385
y[1] (closed_form) = 1.93765217007 0.855994489021
absolute error = 0.0002273
relative error = 0.01073 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.524
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 1.9384502979 0.856702865751
y[1] (closed_form) = 1.93825521745 0.856819594297
absolute error = 0.0002273
relative error = 0.01073 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.525
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4643.1MB, alloc=52.3MB, time=58.74
x[1] = 2.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 1.93883121144 0.858956312982
y[1] (closed_form) = 1.93863578979 0.859073344158
absolute error = 0.0002278
relative error = 0.01074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.527
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 1.9384572918 0.861824402066
y[1] (closed_form) = 1.93826114642 0.86194152947
absolute error = 0.0002285
relative error = 0.01077 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.528
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 1.93992993354 0.866445165934
y[1] (closed_form) = 1.93973269653 0.86656403037
absolute error = 0.0002303
relative error = 0.01084 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.532
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4688.8MB, alloc=52.3MB, time=59.32
x[1] = 2.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 1.93944028676 0.870029366438
y[1] (closed_form) = 1.93924191807 0.870148370411
absolute error = 0.0002313
relative error = 0.01088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.534
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 1.93917372669 0.872184561417
y[1] (closed_form) = 1.93897495193 0.872303626522
absolute error = 0.0002317
relative error = 0.0109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.535
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 1.93977545443 0.873012182186
y[1] (closed_form) = 1.93957668723 0.873131338105
absolute error = 0.0002317
relative error = 0.0109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.536
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4734.6MB, alloc=52.3MB, time=59.90
x[1] = 2.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 1.94015113779 0.875269529855
y[1] (closed_form) = 1.93995203009 0.875388988535
absolute error = 0.0002322
relative error = 0.01091 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.538
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.368 1.234
h = 0.003 0.006
y[1] (numeric) = 1.93976944806 0.878140404131
y[1] (closed_form) = 1.93956961742 0.878259959833
absolute error = 0.0002329
relative error = 0.01094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.539
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 1.94123228313 0.882770929361
y[1] (closed_form) = 1.94103136403 0.882892221774
absolute error = 0.0002347
relative error = 0.01101 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.543
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4780.4MB, alloc=52.3MB, time=60.49
x[1] = 2.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 1.94073291403 0.886358565969
y[1] (closed_form) = 1.94053086449 0.886479999166
absolute error = 0.0002357
relative error = 0.01105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.545
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 1.940460548 0.888515902381
y[1] (closed_form) = 1.94025809286 0.888637397148
absolute error = 0.0002361
relative error = 0.01106 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 1.94106096799 0.889346128669
y[1] (closed_form) = 1.94085852051 0.889467714153
absolute error = 0.0002362
relative error = 0.01106 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.547
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4826.3MB, alloc=52.3MB, time=61.07
x[1] = 2.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 1.94143143092 0.89160737944
y[1] (closed_form) = 1.94122864363 0.891729267809
absolute error = 0.0002366
relative error = 0.01108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.549
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 1.94104198191 0.894481045724
y[1] (closed_form) = 1.9408384725 0.8946030319
absolute error = 0.0002373
relative error = 0.0111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.55
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 1.94249503158 0.899121334925
y[1] (closed_form) = 1.94229043685 0.899245057464
absolute error = 0.0002391
relative error = 0.01117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.555
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4872.0MB, alloc=52.3MB, time=61.65
x[1] = 2.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 1.94198595363 0.902712416153
y[1] (closed_form) = 1.94178022973 0.90283628071
absolute error = 0.0002401
relative error = 0.01121 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.556
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 1.94170778982 0.904871898987
y[1] (closed_form) = 1.94150166078 0.904995825544
absolute error = 0.0002405
relative error = 0.01123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.557
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 1.94230690646 0.905704729876
y[1] (closed_form) = 1.94210078518 0.905828747053
absolute error = 0.0002406
relative error = 0.01123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.558
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4917.7MB, alloc=52.3MB, time=62.23
x[1] = 2.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 1.9426721587 0.907969886321
y[1] (closed_form) = 1.9424656983 0.908094206501
absolute error = 0.000241
relative error = 0.01124 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.56
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 1.94227496125 0.910846351312
y[1] (closed_form) = 1.94206777954 0.910970770075
absolute error = 0.0002417
relative error = 0.01127 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.561
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 1.94371824672 0.915496406906
y[1] (closed_form) = 1.94350998283 0.91562256166
absolute error = 0.0002435
relative error = 0.01133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.566
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4963.5MB, alloc=52.3MB, time=62.82
x[1] = 2.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 1.94319947342 0.91909094113
y[1] (closed_form) = 1.94299008162 0.91921723912
absolute error = 0.0002445
relative error = 0.01138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.567
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 1.94291552 0.921252575284
y[1] (closed_form) = 1.94270572353 0.921378935699
absolute error = 0.0002449
relative error = 0.01139 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.568
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 1.94351333769 0.922088009823
y[1] (closed_form) = 1.94330354908 0.922214460762
absolute error = 0.000245
relative error = 0.01139 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.57
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5009.2MB, alloc=52.3MB, time=63.40
x[1] = 2.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 1.94310944582 0.924966796963
y[1] (closed_form) = 1.94289893665 0.925093347192
absolute error = 0.0002456
relative error = 0.01141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.571
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 1.94454422717 0.929625144972
y[1] (closed_form) = 1.9443326385 0.929753430891
absolute error = 0.0002474
relative error = 0.01148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.575
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 1.944017078 0.933222542744
y[1] (closed_form) = 1.94380436249 0.93335097295
absolute error = 0.0002485
relative error = 0.01152 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.577
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5055.0MB, alloc=52.3MB, time=63.96
x[1] = 2.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 1.94372812192 0.935385963707
y[1] (closed_form) = 1.94351500214 0.935514456705
absolute error = 0.0002489
relative error = 0.01154 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.578
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 1.944324794 0.936223623194
y[1] (closed_form) = 1.94411168217 0.936352206633
absolute error = 0.0002489
relative error = 0.01153 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.579
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 1.94468032963 0.93849599193
y[1] (closed_form) = 1.94446687997 0.938624878583
absolute error = 0.0002493
relative error = 0.01155 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.581
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5100.8MB, alloc=52.3MB, time=64.53
x[1] = 2.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 1.94426870948 0.941377590106
y[1] (closed_form) = 1.94405454003 0.941506576767
absolute error = 0.00025
relative error = 0.01157 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.582
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 1.94569376591 0.946045708775
y[1] (closed_form) = 1.94547852006 0.946176430709
absolute error = 0.0002518
relative error = 0.01164 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.587
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 1.94515694646 0.949646574905
y[1] (closed_form) = 1.94494057505 0.949777442315
absolute error = 0.0002529
relative error = 0.01168 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.588
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5146.7MB, alloc=52.3MB, time=65.09
x[1] = 2.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 1.94486221596 0.951812156173
y[1] (closed_form) = 1.94464544074 0.951943086792
absolute error = 0.0002532
relative error = 0.0117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.589
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 1.94545759719 0.952652417507
y[1] (closed_form) = 1.94524083002 0.952783438469
absolute error = 0.0002533
relative error = 0.01169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.591
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 1.94580794987 0.954928698897
y[1] (closed_form) = 1.94559084556 0.955060023172
absolute error = 0.0002537
relative error = 0.01171 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.592
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5192.4MB, alloc=52.3MB, time=65.66
x[1] = 2.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 1.94538861226 0.957813114441
y[1] (closed_form) = 1.94517078897 0.957944539473
absolute error = 0.0002544
relative error = 0.01173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.594
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 1.94680396479 0.962491005668
y[1] (closed_form) = 1.9465850682 0.962624165531
absolute error = 0.0002562
relative error = 0.0118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.598
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 1.94625748861 0.966095348121
y[1] (closed_form) = 1.94603746774 0.966228654635
absolute error = 0.0002573
relative error = 0.01184 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.6
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5238.1MB, alloc=52.3MB, time=66.22
x[1] = 2.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 1.94595699187 0.968263094349
y[1] (closed_form) = 1.94573656767 0.968396464481
absolute error = 0.0002576
relative error = 0.01185 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.601
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 1.94655108657 0.969105956488
y[1] (closed_form) = 1.94633067052 0.969239416865
absolute error = 0.0002577
relative error = 0.01185 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 1.94689626597 0.971386152758
y[1] (closed_form) = 1.94667551345 0.971519916543
absolute error = 0.0002581
relative error = 0.01186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5283.9MB, alloc=52.3MB, time=66.79
x[1] = 2.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 1.94646922178 0.974273391929
y[1] (closed_form) = 1.94624775111 0.974407257208
absolute error = 0.0002588
relative error = 0.01189 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.605
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 1.94787489137 0.978961057433
y[1] (closed_form) = 1.94765235049 0.97909665708
absolute error = 0.0002606
relative error = 0.01195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.61
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 1.94731877203 0.982568884033
y[1] (closed_form) = 1.94709510813 0.98270463149
absolute error = 0.0002616
relative error = 0.012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.611
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5329.6MB, alloc=52.3MB, time=67.36
x[1] = 2.402 1.377
h = 0.001 0.001
y[1] (numeric) = 1.94701251726 0.98473879979
y[1] (closed_form) = 1.94678845051 0.984874611269
absolute error = 0.000262
relative error = 0.01201 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.612
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.403 1.378
h = 0.001 0.003
y[1] (numeric) = 1.94760532972 0.98558426166
y[1] (closed_form) = 1.94738127121 0.985720163285
absolute error = 0.0002621
relative error = 0.01201 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.614
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 1.94794534549 0.987868374951
y[1] (closed_form) = 1.9477209512 0.988004580073
absolute error = 0.0002625
relative error = 0.01202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.615
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5375.4MB, alloc=52.3MB, time=67.93
x[1] = 2.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 1.9475106056 0.990758443893
y[1] (closed_form) = 1.94728549399 0.990894751237
absolute error = 0.0002632
relative error = 0.01204 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.617
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 1.94890661316 0.995455885216
y[1] (closed_form) = 1.94868043439 0.995593926441
absolute error = 0.000265
relative error = 0.01211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.621
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 1.94834086421 0.999067203645
y[1] (closed_form) = 1.94811356371 0.999205393825
absolute error = 0.000266
relative error = 0.01215 %
Correct digits = 4
memory used=5421.2MB, alloc=52.3MB, time=68.50
Radius of convergence (given) for eq 1 = 4.623
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 1.94802885962 1.00123929341
y[1] (closed_form) = 1.94780115674 1.00137754802
absolute error = 0.0002664
relative error = 0.01216 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.624
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 1.94862039411 1.00208735391
y[1] (closed_form) = 1.94839269957 1.00222569856
absolute error = 0.0002664
relative error = 0.01216 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 1.95001001355 1.00679176335
y[1] (closed_form) = 1.94978125405 1.00693184157
absolute error = 0.0002682
relative error = 0.01222 %
Correct digits = 4
memory used=5467.0MB, alloc=52.3MB, time=69.08
Radius of convergence (given) for eq 1 = 4.63
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 1.94943773658 1.01040573031
y[1] (closed_form) = 1.94920785628 1.01054595824
absolute error = 0.0002693
relative error = 0.01226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 1.94912183644 1.01257946272
y[1] (closed_form) = 1.94889155408 1.01271975532
absolute error = 0.0002697
relative error = 0.01228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.633
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5512.7MB, alloc=52.3MB, time=69.65
x[1] = 2.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 1.94971255971 1.01342934218
y[1] (closed_form) = 1.94948228576 1.01356972477
absolute error = 0.0002697
relative error = 0.01227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.634
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 1.95004398048 1.01572020112
y[1] (closed_form) = 1.9498133719 1.01586088732
absolute error = 0.0002701
relative error = 0.01229 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.636
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 1.94959634744 1.01861525328
y[1] (closed_form) = 1.94936502296 1.01875604289
absolute error = 0.0002708
relative error = 0.01231 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.637
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5558.5MB, alloc=52.3MB, time=70.22
x[1] = 2.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 1.9509763401 1.02332944034
y[1] (closed_form) = 1.95074395357 1.02347196288
absolute error = 0.0002726
relative error = 0.01237 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.642
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 1.95039445664 1.02694691145
y[1] (closed_form) = 1.9501609506 1.02708958481
absolute error = 0.0002736
relative error = 0.01242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.643
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 1.95007282065 1.02912282503
y[1] (closed_form) = 1.94983891304 1.02926556346
absolute error = 0.000274
relative error = 0.01243 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.644
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5604.3MB, alloc=52.3MB, time=70.79
x[1] = 2.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 1.95066227307 1.02997530109
y[1] (closed_form) = 1.95042837394 1.0301181294
absolute error = 0.0002741
relative error = 0.01242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.646
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 1.9509885561 1.03227008213
y[1] (closed_form) = 1.95075432302 1.03241321413
absolute error = 0.0002745
relative error = 0.01244 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.648
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 1.95053325679 1.03516797975
y[1] (closed_form) = 1.95029830866 1.03531121586
absolute error = 0.0002752
relative error = 0.01246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.649
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5650.1MB, alloc=52.3MB, time=71.37
x[1] = 2.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 1.95190364326 1.03989194539
y[1] (closed_form) = 1.95166763609 1.04003691388
absolute error = 0.000277
relative error = 0.01252 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.654
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 1.95131216688 1.04351292794
y[1] (closed_form) = 1.9510750415 1.04365804836
absolute error = 0.000278
relative error = 0.01256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 1.95098480327 1.04569102697
y[1] (closed_form) = 1.95074727679 1.04583621284
absolute error = 0.0002784
relative error = 0.01258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.656
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5695.8MB, alloc=52.3MB, time=71.94
x[1] = 2.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 1.95157298902 1.04654609844
y[1] (closed_form) = 1.95133547112 1.04669137408
absolute error = 0.0002784
relative error = 0.01257 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.658
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 1.95189414387 1.04884480341
y[1] (closed_form) = 1.9516562927 1.04899038281
absolute error = 0.0002789
relative error = 0.01259 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.659
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 1.95143118922 1.05174555222
y[1] (closed_form) = 1.95119262382 1.05189123642
absolute error = 0.0002795
relative error = 0.01261 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.661
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5741.6MB, alloc=52.3MB, time=72.51
x[1] = 2.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 1.9527919901 1.05647929734
y[1] (closed_form) = 1.95255236867 1.05662671335
absolute error = 0.0002813
relative error = 0.01267 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 1.95219093441 1.06010379851
y[1] (closed_form) = 1.95195019606 1.06025136754
absolute error = 0.0002824
relative error = 0.01271 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.667
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 1.95185785139 1.06228408716
y[1] (closed_form) = 1.95161671242 1.06243172203
absolute error = 0.0002827
relative error = 0.01272 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5787.4MB, alloc=52.3MB, time=73.08
x[1] = 2.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 1.95244477464 1.06314175282
y[1] (closed_form) = 1.95220364435 1.06328947736
absolute error = 0.0002828
relative error = 0.01272 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.669
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 1.95197520514 1.06604486929
y[1] (closed_form) = 1.95173336139 1.06619269928
absolute error = 0.0002834
relative error = 0.01275 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.671
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 1.95332765504 1.07078691902
y[1] (closed_form) = 1.95308475783 1.07093648034
absolute error = 0.0002853
relative error = 0.01281 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.676
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5833.1MB, alloc=52.3MB, time=73.66
x[1] = 2.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 1.95271832265 1.07441434064
y[1] (closed_form) = 1.95247430963 1.07456405592
absolute error = 0.0002863
relative error = 0.01285 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.677
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 1.95238029698 1.07659644933
y[1] (closed_form) = 1.95213588375 1.07674623078
absolute error = 0.0002867
relative error = 0.01286 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.678
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 1.95296610596 1.07745633202
y[1] (closed_form) = 1.95272170147 1.07760620305
absolute error = 0.0002867
relative error = 0.01285 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.68
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5878.8MB, alloc=52.3MB, time=74.23
x[1] = 2.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 1.95327769708 1.07976228226
y[1] (closed_form) = 1.95303296058 1.07991245716
absolute error = 0.0002871
relative error = 0.01287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.682
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 1.95280049251 1.08266826047
y[1] (closed_form) = 1.95255504334 1.08281854145
absolute error = 0.0002878
relative error = 0.01289 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.683
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 1.95414339501 1.08742009116
y[1] (closed_form) = 1.95389689535 1.08757210287
absolute error = 0.0002896
relative error = 0.01295 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.688
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5924.5MB, alloc=52.3MB, time=74.80
x[1] = 2.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 1.95352450851 1.09105104454
y[1] (closed_form) = 1.95327689435 1.09120321128
absolute error = 0.0002906
relative error = 0.01299 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.689
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.437 1.521
h = 0.001 0.001
y[1] (numeric) = 1.95318077868 1.0932353505
y[1] (closed_form) = 1.95293276479 1.09338758377
absolute error = 0.000291
relative error = 0.013 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.69
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.438 1.522
h = 0.001 0.003
y[1] (numeric) = 1.95376533286 1.0940978251
y[1] (closed_form) = 1.95351732781 1.09425014786
absolute error = 0.000291
relative error = 0.013 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.692
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5970.3MB, alloc=52.3MB, time=75.37
x[1] = 2.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 1.95407182305 1.09640770414
y[1] (closed_form) = 1.95382348664 1.09656033082
absolute error = 0.0002915
relative error = 0.01301 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.694
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 1.95358699426 1.09931654947
y[1] (closed_form) = 1.95333794603 1.0994692829
absolute error = 0.0002922
relative error = 0.01303 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 1.95492036977 1.10407816155
y[1] (closed_form) = 1.95467027401 1.10423262508
absolute error = 0.000294
relative error = 0.01309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.7
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6016.0MB, alloc=52.3MB, time=75.94
x[1] = 2.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 1.95429194277 1.10771265348
y[1] (closed_form) = 1.95404073381 1.10786727307
absolute error = 0.000295
relative error = 0.01313 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.702
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 1.95394251699 1.10989916066
y[1] (closed_form) = 1.95369090878 1.11005384714
absolute error = 0.0002954
relative error = 0.01314 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.703
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 1.95452582047 1.11076422587
y[1] (closed_form) = 1.95427422119 1.11091900175
absolute error = 0.0002954
relative error = 0.01314 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.704
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6061.8MB, alloc=52.3MB, time=76.51
x[1] = 2.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 1.95482721919 1.11307803522
y[1] (closed_form) = 1.95457528923 1.11323311506
absolute error = 0.0002958
relative error = 0.01315 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.706
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 1.9543347771 1.11598975298
y[1] (closed_form) = 1.95408213616 1.11614494023
absolute error = 0.0002965
relative error = 0.01318 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.707
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 1.95565864596 1.12076114672
y[1] (closed_form) = 1.95540496041 1.12091806342
absolute error = 0.0002983
relative error = 0.01323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.712
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6107.5MB, alloc=52.3MB, time=77.09
x[1] = 2.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 1.95502069205 1.12439918383
y[1] (closed_form) = 1.95476589462 1.12455625763
absolute error = 0.0002993
relative error = 0.01327 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.714
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 1.95466557855 1.12658789609
y[1] (closed_form) = 1.95441038235 1.12674503714
absolute error = 0.0002997
relative error = 0.01328 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 1.95524763539 1.1274555506
y[1] (closed_form) = 1.95499244821 1.12761278094
absolute error = 0.0002997
relative error = 0.01328 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.716
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6153.3MB, alloc=52.3MB, time=77.67
x[1] = 2.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 1.9555439521 1.12977329168
y[1] (closed_form) = 1.9552884349 1.12993082603
absolute error = 0.0003002
relative error = 0.01329 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.718
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 1.95504390761 1.13268788708
y[1] (closed_form) = 1.95478768028 1.13284552948
absolute error = 0.0003008
relative error = 0.01332 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.72
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 1.95635829008 1.13746906258
y[1] (closed_form) = 1.95610102106 1.13762843375
absolute error = 0.0003026
relative error = 0.01337 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.724
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6199.0MB, alloc=52.3MB, time=78.24
x[1] = 2.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 1.95571082285 1.14111065139
y[1] (closed_form) = 1.95545244327 1.14127018068
absolute error = 0.0003037
relative error = 0.01341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.726
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 1.95535002983 1.14330157251
y[1] (closed_form) = 1.95509125197 1.14346116941
absolute error = 0.000304
relative error = 0.01342 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 1.95593084409 1.14417181498
y[1] (closed_form) = 1.95567207532 1.14433150106
absolute error = 0.0003041
relative error = 0.01342 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.729
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6244.9MB, alloc=52.3MB, time=78.81
x[1] = 2.454 1.592
h = 0.003 0.006
y[1] (numeric) = 1.95542423003 1.14708880102
y[1] (closed_form) = 1.95516475191 1.14724859575
absolute error = 0.0003047
relative error = 0.01344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.73
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 1.95673034656 1.15187828363
y[1] (closed_form) = 1.95646982926 1.15203980657
absolute error = 0.0003065
relative error = 0.0135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.735
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 1.95607465906 1.15552282162
y[1] (closed_form) = 1.95581303232 1.15568450357
absolute error = 0.0003076
relative error = 0.01354 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.737
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6290.8MB, alloc=52.3MB, time=79.37
x[1] = 2.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 1.95570895752 1.15771557951
y[1] (closed_form) = 1.9554469329 1.15787732937
absolute error = 0.0003079
relative error = 0.01355 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.738
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 1.9562886746 1.15858803377
y[1] (closed_form) = 1.95602665916 1.15874987273
absolute error = 0.000308
relative error = 0.01355 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.739
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 1.95657551306 1.16091303412
y[1] (closed_form) = 1.95631316883 1.16107517716
absolute error = 0.0003084
relative error = 0.01356 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.741
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6336.5MB, alloc=52.3MB, time=79.94
x[1] = 2.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 1.95606131688 1.16383290737
y[1] (closed_form) = 1.9557982641 1.16399515965
absolute error = 0.0003091
relative error = 0.01358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 1.95735798449 1.16863217175
y[1] (closed_form) = 1.95709389541 1.16879615153
absolute error = 0.0003109
relative error = 0.01364 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.747
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 1.95669280889 1.17228027337
y[1] (closed_form) = 1.95642761169 1.17244441315
absolute error = 0.0003119
relative error = 0.01367 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.749
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6382.3MB, alloc=52.3MB, time=80.50
x[1] = 2.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 1.95632144307 1.17447524704
y[1] (closed_form) = 1.95605584847 1.17463945508
absolute error = 0.0003123
relative error = 0.01369 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.75
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 1.95689992502 1.17535028672
y[1] (closed_form) = 1.95663433969 1.17551458376
absolute error = 0.0003123
relative error = 0.01368 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.751
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 1.95718170834 1.17767922256
y[1] (closed_form) = 1.95691579488 1.17784382369
absolute error = 0.0003127
relative error = 0.01369 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.753
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6428.2MB, alloc=52.3MB, time=81.08
x[1] = 2.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 1.9566599409 1.18060198788
y[1] (closed_form) = 1.95639331973 1.18076669887
absolute error = 0.0003134
relative error = 0.01371 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 1.95794717961 1.18541103368
y[1] (closed_form) = 1.95767952501 1.18557747145
absolute error = 0.0003152
relative error = 0.01377 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.76
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 1.95727252949 1.18906270507
y[1] (closed_form) = 1.95700376809 1.18922930381
absolute error = 0.0003162
relative error = 0.01381 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.762
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6473.9MB, alloc=52.3MB, time=81.65
x[1] = 2.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 1.95689550759 1.19125989809
y[1] (closed_form) = 1.95662634929 1.19142656543
absolute error = 0.0003166
relative error = 0.01382 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.763
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 1.95747275838 1.19213752177
y[1] (closed_form) = 1.95720360943 1.192304278
absolute error = 0.0003166
relative error = 0.01382 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.764
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 1.95774949591 1.1944703942
y[1] (closed_form) = 1.95748001948 1.19463745455
absolute error = 0.0003171
relative error = 0.01383 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.766
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6519.6MB, alloc=52.3MB, time=82.22
x[1] = 2.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 1.95722016808 1.19739605639
y[1] (closed_form) = 1.95694998481 1.19756322722
absolute error = 0.0003177
relative error = 0.01385 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.767
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 1.95849799783 1.20221488312
y[1] (closed_form) = 1.95822678398 1.20238377998
absolute error = 0.0003195
relative error = 0.0139 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.772
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 1.95781388677 1.20587013027
y[1] (closed_form) = 1.95754156745 1.20603918907
absolute error = 0.0003205
relative error = 0.01394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.774
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6565.3MB, alloc=52.3MB, time=82.79
x[1] = 2.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 1.95743121699 1.20806954611
y[1] (closed_form) = 1.95715850125 1.20823867384
absolute error = 0.0003209
relative error = 0.01395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.775
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 1.95800724057 1.20894975235
y[1] (closed_form) = 1.95773453425 1.20911896887
absolute error = 0.0003209
relative error = 0.01395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 1.95827894162 1.21128656243
y[1] (closed_form) = 1.95800590847 1.21145608308
absolute error = 0.0003214
relative error = 0.01396 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.779
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6611.0MB, alloc=52.3MB, time=83.37
x[1] = 2.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 1.9577420643 1.21421512619
y[1] (closed_form) = 1.95746832516 1.21438475792
absolute error = 0.000322
relative error = 0.01398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.78
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 1.95901050495 1.21904373318
y[1] (closed_form) = 1.95873573807 1.21921509017
absolute error = 0.0003238
relative error = 0.01404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.785
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 1.95831694651 1.22270256198
y[1] (closed_form) = 1.95804107549 1.22287408186
absolute error = 0.0003248
relative error = 0.01407 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.787
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6656.9MB, alloc=52.3MB, time=83.94
x[1] = 2.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 1.95792863704 1.22490420405
y[1] (closed_form) = 1.9576523701 1.22507579318
absolute error = 0.0003252
relative error = 0.01408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.788
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 1.9585034373 1.22578699137
y[1] (closed_form) = 1.95822717985 1.2259586692
absolute error = 0.0003253
relative error = 0.01408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.789
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 1.95796003566 1.22871796661
y[1] (closed_form) = 1.95768307299 1.22888975606
absolute error = 0.0003259
relative error = 0.0141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.791
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6702.6MB, alloc=52.3MB, time=84.52
x[1] = 2.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 1.95922029383 1.23355487997
y[1] (closed_form) = 1.95894230586 1.23372839404
absolute error = 0.0003277
relative error = 0.01415 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.796
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 1.95851857151 1.23721668402
y[1] (closed_form) = 1.95823948052 1.2373903618
absolute error = 0.0003287
relative error = 0.01419 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.798
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 1.95812538757 1.23942017796
y[1] (closed_form) = 1.95784590107 1.23959392529
absolute error = 0.0003291
relative error = 0.0142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.799
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6748.2MB, alloc=52.3MB, time=85.09
x[1] = 2.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 1.95869910723 1.2403051713
y[1] (closed_form) = 1.9584196303 1.24047900722
absolute error = 0.0003291
relative error = 0.0142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.8
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 1.95896141434 1.24264925119
y[1] (closed_form) = 1.95868161179 1.24282339127
absolute error = 0.0003296
relative error = 0.01421 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.802
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 1.95841048342 1.24558313661
y[1] (closed_form) = 1.95812997648 1.24575738888
absolute error = 0.0003302
relative error = 0.01423 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6794.0MB, alloc=52.3MB, time=85.66
x[1] = 2.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 1.95966138922 1.25042982886
y[1] (closed_form) = 1.95937985977 1.25060580494
absolute error = 0.000332
relative error = 0.01428 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.809
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 1.95895024468 1.25409522531
y[1] (closed_form) = 1.95866761354 1.25427136603
absolute error = 0.000333
relative error = 0.01432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.488 1.735
h = 0.001 0.001
y[1] (numeric) = 1.95855143624 1.2563009517
y[1] (closed_form) = 1.95826841008 1.25647716228
absolute error = 0.0003334
relative error = 0.01433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.812
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6839.8MB, alloc=52.3MB, time=86.25
x[1] = 2.489 1.736
h = 0.001 0.003
y[1] (numeric) = 1.95912393981 1.25718852337
y[1] (closed_form) = 1.95884092329 1.25736482245
absolute error = 0.0003334
relative error = 0.01432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.813
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 1.95938123691 1.25953654358
y[1] (closed_form) = 1.95909789543 1.25971314681
absolute error = 0.0003339
relative error = 0.01433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.815
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 1.95882278755 1.26247334356
y[1] (closed_form) = 1.95853874252 1.26265005956
absolute error = 0.0003345
relative error = 0.01436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.817
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6885.6MB, alloc=52.3MB, time=86.82
x[1] = 2.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 1.96006436058 1.26732981362
y[1] (closed_form) = 1.95977929584 1.26750825261
absolute error = 0.0003363
relative error = 0.01441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.822
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 1.95934380735 1.27099880798
y[1] (closed_form) = 1.95905764225 1.27117741252
absolute error = 0.0003373
relative error = 0.01444 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.823
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 1.95893938258 1.27320677001
y[1] (closed_form) = 1.95865282295 1.27338544472
absolute error = 0.0003377
relative error = 0.01446 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.825
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6931.4MB, alloc=52.3MB, time=87.40
x[1] = 2.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 1.95951067389 1.27409691847
y[1] (closed_form) = 1.95922412398 1.27427568158
absolute error = 0.0003377
relative error = 0.01445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.826
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 1.9597629702 1.27644887975
y[1] (closed_form) = 1.95947609597 1.27662794701
absolute error = 0.0003382
relative error = 0.01446 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.828
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 1.95919701323 1.2793885986
y[1] (closed_form) = 1.95890943631 1.27956777919
absolute error = 0.0003388
relative error = 0.01448 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.829
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6977.2MB, alloc=52.3MB, time=87.97
x[1] = 2.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 1.96042927303 1.28425484525
y[1] (closed_form) = 1.96014067915 1.28443574799
absolute error = 0.0003406
relative error = 0.01453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.834
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 1.95969932464 1.28792744291
y[1] (closed_form) = 1.95940963175 1.2881085121
absolute error = 0.0003416
relative error = 0.01457 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.836
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 1.9592892917 1.29013764368
y[1] (closed_form) = 1.95899920476 1.29031878335
absolute error = 0.000342
relative error = 0.01458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.838
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7023.0MB, alloc=52.3MB, time=88.55
x[1] = 2.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 1.95985937456 1.29103036738
y[1] (closed_form) = 1.95956929742 1.29121159534
absolute error = 0.000342
relative error = 0.01457 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.839
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = 1.96010667923 1.29338627041
y[1] (closed_form) = 1.95981627841 1.29356780251
absolute error = 0.0003425
relative error = 0.01458 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5007 1.787
h = 0.003 0.006
y[1] (numeric) = 1.9595332255 1.29632891233
y[1] (closed_form) = 1.95924212285 1.29651055832
absolute error = 0.0003431
relative error = 0.01461 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.842
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7068.9MB, alloc=52.3MB, time=89.12
x[1] = 2.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = 1.96075619149 1.30120493418
y[1] (closed_form) = 1.96046407464 1.30138830148
absolute error = 0.0003449
relative error = 0.01466 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.847
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = 1.96001686145 1.30488114041
y[1] (closed_form) = 1.95972364691 1.30506467503
absolute error = 0.0003459
relative error = 0.01469 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.849
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5039 1.801
h = 0.001 0.001
y[1] (numeric) = 1.95960122849 1.30709358295
y[1] (closed_form) = 1.9593076204 1.30727718836
absolute error = 0.0003463
relative error = 0.0147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.851
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7114.7MB, alloc=52.3MB, time=89.70
x[1] = 2.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = 1.96017010667 1.3079888803
y[1] (closed_form) = 1.95987650846 1.3081725739
absolute error = 0.0003463
relative error = 0.0147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.852
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.505 1.806
h = 0.003 0.006
y[1] (numeric) = 1.95959017372 1.31093395244
y[1] (closed_form) = 1.95929587445 1.31111776044
absolute error = 0.000347
relative error = 0.01472 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.854
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.508 1.812
h = 0.0001 0.005
y[1] (numeric) = 1.96080503898 1.31581827688
y[1] (closed_form) = 1.96050972787 1.31600380546
absolute error = 0.0003488
relative error = 0.01477 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.859
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7160.4MB, alloc=52.3MB, time=90.27
x[1] = 2.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = 1.96005760126 1.31949748182
y[1] (closed_form) = 1.95976119362 1.3196831785
absolute error = 0.0003498
relative error = 0.0148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.86
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5082 1.82
h = 0.001 0.001
y[1] (numeric) = 1.95963712777 1.3217117898
y[1] (closed_form) = 1.95934032698 1.32189755753
absolute error = 0.0003501
relative error = 0.01481 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.862
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5092 1.821
h = 0.001 0.003
y[1] (numeric) = 1.96020494138 1.32260928689
y[1] (closed_form) = 1.95990815053 1.32279514272
absolute error = 0.0003502
relative error = 0.01481 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.863
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7206.2MB, alloc=52.3MB, time=90.84
x[1] = 2.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = 1.96044293512 1.32497246697
y[1] (closed_form) = 1.96014582177 1.32515862691
absolute error = 0.0003506
relative error = 0.01482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.865
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5103 1.828
h = 0.003 0.006
y[1] (numeric) = 1.95985552554 1.32792046988
y[1] (closed_form) = 1.95955771195 1.32810674475
absolute error = 0.0003513
relative error = 0.01484 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.867
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = 1.96106113293 1.33281456685
y[1] (closed_form) = 1.96076231023 1.33300256141
absolute error = 0.000353
relative error = 0.01489 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.872
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7252.0MB, alloc=52.3MB, time=91.42
x[1] = 2.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = 1.9603043386 1.33649738999
y[1] (closed_form) = 1.96000442069 1.3366855535
absolute error = 0.0003541
relative error = 0.01492 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.874
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5135 1.842
h = 0.001 0.001
y[1] (numeric) = 1.95987828019 1.33871394529
y[1] (closed_form) = 1.95957796963 1.33890218015
absolute error = 0.0003544
relative error = 0.01493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.875
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5145 1.843
h = 0.001 0.003
y[1] (numeric) = 1.96044489611 1.33961401307
y[1] (closed_form) = 1.96014459556 1.33980233592
absolute error = 0.0003545
relative error = 0.01493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.876
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7297.8MB, alloc=52.3MB, time=92.00
x[1] = 2.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = 1.96067792426 1.34198113656
y[1] (closed_form) = 1.96037730185 1.3421697635
absolute error = 0.0003549
relative error = 0.01494 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.878
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5156 1.85
h = 0.003 0.006
y[1] (numeric) = 1.9600830488 1.34493207415
y[1] (closed_form) = 1.95978172702 1.34512081655
absolute error = 0.0003556
relative error = 0.01496 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.88
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = 1.96127941751 1.34983594188
y[1] (closed_form) = 1.9609770893 1.35002640307
absolute error = 0.0003573
relative error = 0.01501 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.885
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7343.6MB, alloc=52.3MB, time=92.57
x[1] = 2.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = 1.96051328003 1.35352238812
y[1] (closed_form) = 1.96020985796 1.3537130191
absolute error = 0.0003583
relative error = 0.01504 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5188 1.864
h = 0.001 0.001
y[1] (numeric) = 1.96008164483 1.35574119357
y[1] (closed_form) = 1.9597778306 1.35593189619
absolute error = 0.0003587
relative error = 0.01505 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.888
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5198 1.865
h = 0.001 0.003
y[1] (numeric) = 1.96064706675 1.35664383039
y[1] (closed_form) = 1.9603432626 1.3568346209
absolute error = 0.0003587
relative error = 0.01505 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.889
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7389.4MB, alloc=52.3MB, time=93.15
x[1] = 2.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = 1.96087513836 1.3590148977
y[1] (closed_form) = 1.96057101297 1.35920599227
absolute error = 0.0003592
relative error = 0.01506 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.892
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5209 1.872
h = 0.003 0.006
y[1] (numeric) = 1.96027280781 1.36196877379
y[1] (closed_form) = 1.95996798391 1.36215998434
absolute error = 0.0003598
relative error = 0.01508 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.893
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = 1.96145995691 1.36688241037
y[1] (closed_form) = 1.96115412927 1.3670753388
absolute error = 0.0003616
relative error = 0.01513 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.898
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7435.1MB, alloc=52.3MB, time=93.72
x[1] = 2.524 1.883
h = 0.0001 0.003
y[1] (numeric) = 1.96068448973 1.37057248451
y[1] (closed_form) = 1.96037756957 1.37076558356
absolute error = 0.0003626
relative error = 0.01516 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.9
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5241 1.886
h = 0.001 0.001
y[1] (numeric) = 1.96024728585 1.37279354286
y[1] (closed_form) = 1.95993997401 1.37298671383
absolute error = 0.000363
relative error = 0.01517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.901
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5251 1.887
h = 0.001 0.003
y[1] (numeric) = 1.96081151745 1.37369874706
y[1] (closed_form) = 1.96050421576 1.37389200582
absolute error = 0.000363
relative error = 0.01516 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.903
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7480.9MB, alloc=52.3MB, time=94.30
x[1] = 2.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = 1.96103464151 1.37607375853
y[1] (closed_form) = 1.96072701923 1.37626732132
absolute error = 0.0003635
relative error = 0.01517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.905
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5262 1.894
h = 0.003 0.006
y[1] (numeric) = 1.96042486665 1.37903057684
y[1] (closed_form) = 1.96011654671 1.37922425613
absolute error = 0.0003641
relative error = 0.01519 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.906
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = 1.96160281514 1.38395398024
y[1] (closed_form) = 1.96129349412 1.38414937647
absolute error = 0.0003659
relative error = 0.01524 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.912
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7526.7MB, alloc=52.3MB, time=94.87
x[1] = 2.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = 1.96081803168 1.38764768695
y[1] (closed_form) = 1.96050761948 1.38784325461
absolute error = 0.0003669
relative error = 0.01527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.914
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5294 1.908
h = 0.001 0.001
y[1] (numeric) = 1.96037526722 1.38987100088
y[1] (closed_form) = 1.96006446383 1.39006664074
absolute error = 0.0003673
relative error = 0.01528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.915
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = 1.96093831213 1.39077877077
y[1] (closed_form) = 1.96062751897 1.39097449832
absolute error = 0.0003673
relative error = 0.01528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7572.6MB, alloc=52.3MB, time=95.45
x[1] = 2.5305 1.913
h = 0.003 0.006
y[1] (numeric) = 1.96032210291 1.39373803604
y[1] (closed_form) = 1.96001061288 1.39393388056
absolute error = 0.0003679
relative error = 0.0153 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.918
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = 1.96149203065 1.39866973537
y[1] (closed_form) = 1.96117954183 1.39886729604
absolute error = 0.0003697
relative error = 0.01535 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.923
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = 1.96069919545 1.40236646176
y[1] (closed_form) = 1.96038561659 1.40256419458
absolute error = 0.0003707
relative error = 0.01538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.925
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7618.5MB, alloc=52.3MB, time=96.02
x[1] = 2.5337 1.927
h = 0.001 0.001
y[1] (numeric) = 1.96025162417 1.4045916532
y[1] (closed_form) = 1.95993765455 1.40478945847
absolute error = 0.0003711
relative error = 0.01539 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.926
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5347 1.928
h = 0.001 0.003
y[1] (numeric) = 1.96081362 1.40550161612
y[1] (closed_form) = 1.96049966066 1.40569950898
absolute error = 0.0003711
relative error = 0.01538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.928
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = 1.96102751472 1.40788390873
y[1] (closed_form) = 1.96071323594 1.40808210555
absolute error = 0.0003716
relative error = 0.01539 %
Correct digits = 4
memory used=7664.2MB, alloc=52.3MB, time=96.60
Radius of convergence (given) for eq 1 = 4.93
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5358 1.935
h = 0.003 0.006
y[1] (numeric) = 1.96040388118 1.41084612306
y[1] (closed_form) = 1.96008890635 1.41104443733
absolute error = 0.0003722
relative error = 0.01541 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.931
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = 1.96156464343 1.41578758529
y[1] (closed_form) = 1.96124867244 1.41598761475
absolute error = 0.000374
relative error = 0.01546 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.936
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = 1.96076251682 1.41948795279
y[1] (closed_form) = 1.96044545713 1.41968815519
absolute error = 0.000375
relative error = 0.01549 %
Correct digits = 4
memory used=7710.1MB, alloc=52.3MB, time=97.18
Radius of convergence (given) for eq 1 = 4.938
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.539 1.949
h = 0.001 0.001
y[1] (numeric) = 1.96030939996 1.42171540471
y[1] (closed_form) = 1.95999195 1.42191567982
absolute error = 0.0003753
relative error = 0.0155 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.94
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.54 1.95
h = 0.001 0.003
y[1] (numeric) = 1.96087021585 1.42262793017
y[1] (closed_form) = 1.96055277622 1.42282829277
absolute error = 0.0003754
relative error = 0.0155 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.941
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7755.9MB, alloc=52.3MB, time=97.75
x[1] = 2.541 1.953
h = 0.0001 0.004
y[1] (numeric) = 1.9610791886 1.42501416763
y[1] (closed_form) = 1.96076143016 1.42521483415
absolute error = 0.0003758
relative error = 0.0155 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.943
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5411 1.957
h = 0.003 0.006
y[1] (numeric) = 1.96044814143 1.42797933446
y[1] (closed_form) = 1.9601296878 1.42818011893
absolute error = 0.0003765
relative error = 0.01552 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.945
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = 1.96159975691 1.43293055719
y[1] (closed_form) = 1.96128030973 1.43313305585
absolute error = 0.0003782
relative error = 0.01557 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7801.7MB, alloc=52.3MB, time=98.32
x[1] = 2.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = 1.96078835227 1.43663457013
y[1] (closed_form) = 1.96046781773 1.43683724251
absolute error = 0.0003792
relative error = 0.0156 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.952
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5443 1.971
h = 0.001 0.001
y[1] (numeric) = 1.96032969787 1.438864285
y[1] (closed_form) = 1.96000877356 1.43906703037
absolute error = 0.0003796
relative error = 0.01561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.953
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5453 1.972
h = 0.001 0.003
y[1] (numeric) = 1.96088933738 1.43977937127
y[1] (closed_form) = 1.96056842347 1.43998220402
absolute error = 0.0003796
relative error = 0.01561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.955
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7847.5MB, alloc=52.3MB, time=98.90
x[1] = 2.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = 1.96109339705 1.44216955366
y[1] (closed_form) = 1.96077216493 1.44237269028
absolute error = 0.0003801
relative error = 0.01561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.957
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5464 1.979
h = 0.003 0.006
y[1] (numeric) = 1.96045494694 1.44513767636
y[1] (closed_form) = 1.9601330205 1.44534093141
absolute error = 0.0003807
relative error = 0.01563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.958
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = 1.96159743428 1.45009865703
y[1] (closed_form) = 1.96127451689 1.45030362529
absolute error = 0.0003825
relative error = 0.01568 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.964
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7893.2MB, alloc=52.3MB, time=99.47
x[1] = 2.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = 1.96077676494 1.45380631964
y[1] (closed_form) = 1.96045276154 1.45401146238
absolute error = 0.0003835
relative error = 0.01571 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.966
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5496 1.993
h = 0.001 0.001
y[1] (numeric) = 1.96031258106 1.45603829988
y[1] (closed_form) = 1.95998818837 1.45624351587
absolute error = 0.0003839
relative error = 0.01572 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.967
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5506 1.994
h = 0.001 0.003
y[1] (numeric) = 1.96087104772 1.45695594518
y[1] (closed_form) = 1.9605466655 1.45716124845
absolute error = 0.0003839
relative error = 0.01572 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.968
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7939.0MB, alloc=52.3MB, time=100.04
x[1] = 2.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = 1.96107020314 1.45935007252
y[1] (closed_form) = 1.96074550333 1.45955567961
absolute error = 0.0003843
relative error = 0.01572 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5517 2.001
h = 0.003 0.006
y[1] (numeric) = 1.96042436078 1.46232115436
y[1] (closed_form) = 1.96009896751 1.46252688034
absolute error = 0.000385
relative error = 0.01574 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.972
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = 1.96155773853 1.46729189031
y[1] (closed_form) = 1.96123135688 1.4674993285
absolute error = 0.0003867
relative error = 0.01579 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7984.7MB, alloc=52.3MB, time=100.62
x[1] = 2.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = 1.96072781782 1.47100320669
y[1] (closed_form) = 1.96040035149 1.47121082012
absolute error = 0.0003877
relative error = 0.01582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.979
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5549 2.015
h = 0.001 0.001
y[1] (numeric) = 1.96025811247 1.47323745465
y[1] (closed_form) = 1.95993025735 1.47344514157
absolute error = 0.0003881
relative error = 0.01583 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.981
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = 1.9608154098 1.4741576572
y[1] (closed_form) = 1.96048756522 1.4743654313
absolute error = 0.0003881
relative error = 0.01582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.982
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8030.4MB, alloc=52.3MB, time=101.19
x[1] = 2.556 2.02
h = 0.003 0.006
y[1] (numeric) = 1.96016317764 1.4771312008
y[1] (closed_form) = 1.95983464037 1.47733909425
absolute error = 0.0003888
relative error = 0.01584 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.984
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.559 2.026
h = 0.0001 0.005
y[1] (numeric) = 1.96128861275 1.48211022334
y[1] (closed_form) = 1.96095908933 1.48231982813
absolute error = 0.0003905
relative error = 0.01589 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.989
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = 1.96045069583 1.48582457798
y[1] (closed_form) = 1.96012008887 1.48603435867
absolute error = 0.0003915
relative error = 0.01592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.991
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8076.2MB, alloc=52.3MB, time=101.76
x[1] = 2.5592 2.034
h = 0.001 0.001
y[1] (numeric) = 1.95997621715 1.48806071409
y[1] (closed_form) = 1.95964522182 1.48827056849
absolute error = 0.0003919
relative error = 0.01593 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.992
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5602 2.035
h = 0.001 0.003
y[1] (numeric) = 1.96053248032 1.48898310254
y[1] (closed_form) = 1.96020149559 1.48919304403
absolute error = 0.000392
relative error = 0.01592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.994
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = 1.96072248648 1.49138451215
y[1] (closed_form) = 1.96039118529 1.49159475736
absolute error = 0.0003924
relative error = 0.01593 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.996
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8122.0MB, alloc=52.3MB, time=102.34
x[1] = 2.5613 2.042
h = 0.003 0.006
y[1] (numeric) = 1.9600628819 1.49436102089
y[1] (closed_form) = 1.95973088885 1.49457138588
absolute error = 0.000393
relative error = 0.01595 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.998
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = 1.96117924169 1.49934979365
y[1] (closed_form) = 1.96084626502 1.49956186894
absolute error = 0.0003948
relative error = 0.01599 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.003
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = 1.96033209806 1.50306780956
y[1] (closed_form) = 1.9599980392 1.50328006147
absolute error = 0.0003958
relative error = 0.01602 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.005
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8167.8MB, alloc=52.3MB, time=102.91
x[1] = 2.5645 2.056
h = 0.001 0.001
y[1] (numeric) = 1.95985211279 1.50530621764
y[1] (closed_form) = 1.95951766603 1.50551854354
absolute error = 0.0003962
relative error = 0.01603 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.006
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5655 2.057
h = 0.001 0.003
y[1] (numeric) = 1.96040721311 1.50623116003
y[1] (closed_form) = 1.96007277702 1.5064435729
absolute error = 0.0003962
relative error = 0.01603 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.007
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = 1.9605923401 1.50863651438
y[1] (closed_form) = 1.96025758815 1.5088492309
absolute error = 0.0003966
relative error = 0.01603 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.01
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8213.5MB, alloc=52.3MB, time=103.48
x[1] = 2.5666 2.064
h = 0.003 0.006
y[1] (numeric) = 1.95992537369 1.51161599125
y[1] (closed_form) = 1.95958993074 1.511828828
absolute error = 0.0003973
relative error = 0.01605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.011
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = 1.9610326764 1.51661451122
y[1] (closed_form) = 1.96069625237 1.51682905722
absolute error = 0.000399
relative error = 0.0161 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.017
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = 1.96017631931 1.52033619218
y[1] (closed_form) = 1.95983881443 1.52055091552
absolute error = 0.0004
relative error = 0.01613 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.019
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8259.4MB, alloc=52.3MB, time=104.06
x[1] = 2.5698 2.078
h = 0.001 0.001
y[1] (numeric) = 1.95969083542 1.5225768744
y[1] (closed_form) = 1.95935294313 1.52279167196
absolute error = 0.0004004
relative error = 0.01613 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.02
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5708 2.079
h = 0.001 0.003
y[1] (numeric) = 1.96024477634 1.52350436889
y[1] (closed_form) = 1.95990689477 1.52371925333
absolute error = 0.0004004
relative error = 0.01613 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.021
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = 1.96042503285 1.52591366775
y[1] (closed_form) = 1.96008683604 1.52612885577
absolute error = 0.0004009
relative error = 0.01614 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.024
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8305.1MB, alloc=52.3MB, time=104.64
x[1] = 2.5719 2.086
h = 0.003 0.006
y[1] (numeric) = 1.95975071521 1.52889611567
y[1] (closed_form) = 1.95941182825 1.52911142437
absolute error = 0.0004015
relative error = 0.01615 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.025
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = 1.96084897902 1.53390437971
y[1] (closed_form) = 1.96050911349 1.5341213966
absolute error = 0.0004032
relative error = 0.0162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.031
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.575 2.097
h = 0.0001 0.003
y[1] (numeric) = 1.95998342169 1.5376297294
y[1] (closed_form) = 1.95964247665 1.53784692433
absolute error = 0.0004042
relative error = 0.01623 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.033
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8350.9MB, alloc=52.3MB, time=105.22
x[1] = 2.5751 2.1
h = 0.001 0.001
y[1] (numeric) = 1.95949244714 1.53987268783
y[1] (closed_form) = 1.95915111518 1.54008995722
absolute error = 0.0004046
relative error = 0.01624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.034
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5761 2.101
h = 0.001 0.003
y[1] (numeric) = 1.96004523205 1.54080273259
y[1] (closed_form) = 1.95970391088 1.54102008875
absolute error = 0.0004047
relative error = 0.01623 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.035
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = 1.96022062675 1.54321597566
y[1] (closed_form) = 1.95987899093 1.54343363533
absolute error = 0.0004051
relative error = 0.01624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.038
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8396.8MB, alloc=52.3MB, time=105.80
x[1] = 2.5772 2.108
h = 0.003 0.006
y[1] (numeric) = 1.95953896846 1.54620139748
y[1] (closed_form) = 1.95919664335 1.54641917826
absolute error = 0.0004057
relative error = 0.01626 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.039
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = 1.96062821143 1.55121940234
y[1] (closed_form) = 1.96028491024 1.55143889023
absolute error = 0.0004075
relative error = 0.0163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.045
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = 1.95975346705 1.55494842432
y[1] (closed_form) = 1.95940908769 1.55516809094
absolute error = 0.0004085
relative error = 0.01633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.047
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8442.5MB, alloc=52.3MB, time=106.38
x[1] = 2.5804 2.122
h = 0.001 0.001
y[1] (numeric) = 1.95925700979 1.55719366099
y[1] (closed_form) = 1.958912244 1.55741340231
absolute error = 0.0004088
relative error = 0.01634 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.048
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = 1.95980864208 1.55812625413
y[1] (closed_form) = 1.95946388713 1.55834608212
absolute error = 0.0004089
relative error = 0.01633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.049
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5815 2.127
h = 0.003 0.006
y[1] (numeric) = 1.95912063813 1.56111415068
y[1] (closed_form) = 1.95877519469 1.56133410019
absolute error = 0.0004095
relative error = 0.01635 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.051
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8488.2MB, alloc=52.3MB, time=106.95
x[1] = 2.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = 1.96020201469 1.56614043027
y[1] (closed_form) = 1.9598555973 1.56636208597
absolute error = 0.0004113
relative error = 0.01639 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.056
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = 1.95931932914 1.56987250678
y[1] (closed_form) = 1.95897183472 1.57009434182
absolute error = 0.0004123
relative error = 0.01642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5847 2.141
h = 0.001 0.001
y[1] (numeric) = 1.95881813171 1.57211964086
y[1] (closed_form) = 1.95847025129 1.57234155081
absolute error = 0.0004126
relative error = 0.01643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.06
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8533.9MB, alloc=52.3MB, time=107.52
x[1] = 2.5857 2.142
h = 0.001 0.003
y[1] (numeric) = 1.95936874422 1.5730544124
y[1] (closed_form) = 1.95902087469 1.57327640892
absolute error = 0.0004127
relative error = 0.01642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.061
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = 1.95953506816 1.57547493608
y[1] (closed_form) = 1.95918688509 1.57569723597
absolute error = 0.0004131
relative error = 0.01643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.063
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5868 2.149
h = 0.003 0.006
y[1] (numeric) = 1.95883974321 1.57846581173
y[1] (closed_form) = 1.95849087245 1.57868823353
absolute error = 0.0004137
relative error = 0.01645 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.065
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8579.7MB, alloc=52.3MB, time=108.09
x[1] = 2.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = 1.95991213232 1.58350182599
y[1] (closed_form) = 1.95956229008 1.58372595289
absolute error = 0.0004155
relative error = 0.01649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.071
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = 1.95902028415 1.58723758129
y[1] (closed_form) = 1.95866936622 1.5874618882
absolute error = 0.0004165
relative error = 0.01652 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.073
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.59 2.163
h = 0.001 0.001
y[1] (numeric) = 1.95851361872 1.58948699729
y[1] (closed_form) = 1.95816231526 1.58971137932
absolute error = 0.0004168
relative error = 0.01653 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.074
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8625.5MB, alloc=52.3MB, time=108.65
x[1] = 2.591 2.164
h = 0.001 0.003
y[1] (numeric) = 1.95906308484 1.59042431375
y[1] (closed_form) = 1.95871179234 1.59064878225
absolute error = 0.0004169
relative error = 0.01652 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.075
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.592 2.167
h = 0.0001 0.004
y[1] (numeric) = 1.95922457153 1.59284878058
y[1] (closed_form) = 1.95887296608 1.59307355236
absolute error = 0.0004173
relative error = 0.01653 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.078
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5921 2.171
h = 0.003 0.006
y[1] (numeric) = 1.95852193603 1.59584263788
y[1] (closed_form) = 1.95816964376 1.596067532
absolute error = 0.000418
relative error = 0.01654 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.079
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8671.3MB, alloc=52.3MB, time=109.22
x[1] = 2.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = 1.9595853555 1.60088838326
y[1] (closed_form) = 1.95923209418 1.60111498135
absolute error = 0.0004197
relative error = 0.01659 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.085
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = 1.9586843578 1.6046278206
y[1] (closed_form) = 1.95833002213 1.60485459936
absolute error = 0.0004207
relative error = 0.01662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.087
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5953 2.185
h = 0.001 0.001
y[1] (numeric) = 1.95817223225 1.60687952035
y[1] (closed_form) = 1.95781751155 1.60710637446
absolute error = 0.0004211
relative error = 0.01662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.088
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8717.1MB, alloc=52.3MB, time=109.79
x[1] = 2.5963 2.186
h = 0.001 0.003
y[1] (numeric) = 1.9587205553 1.60781937981
y[1] (closed_form) = 1.95836584559 1.60804632029
absolute error = 0.0004211
relative error = 0.01662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.09
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = 1.95887721325 1.61024778927
y[1] (closed_form) = 1.95852219118 1.61047503294
absolute error = 0.0004215
relative error = 0.01662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.092
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5974 2.193
h = 0.003 0.006
y[1] (numeric) = 1.95816727769 1.61324463074
y[1] (closed_form) = 1.95781156967 1.61347199715
absolute error = 0.0004222
relative error = 0.01664 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.094
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8762.9MB, alloc=52.3MB, time=110.36
x[1] = 2.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = 1.9592217452 1.61830010354
y[1] (closed_form) = 1.95886507054 1.6185291728
absolute error = 0.0004239
relative error = 0.01668 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.099
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = 1.95831161105 1.62204322608
y[1] (closed_form) = 1.95795386339 1.62227247664
absolute error = 0.0004249
relative error = 0.01671 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6006 2.207
h = 0.001 0.001
y[1] (numeric) = 1.95779403326 1.62429721135
y[1] (closed_form) = 1.95743590104 1.62452653748
absolute error = 0.0004253
relative error = 0.01672 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8808.7MB, alloc=52.3MB, time=110.95
x[1] = 2.6016 2.208
h = 0.001 0.003
y[1] (numeric) = 1.95834121649 1.62523961189
y[1] (closed_form) = 1.95798309534 1.62546902429
absolute error = 0.0004253
relative error = 0.01671 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = 1.95849305417 1.6276719634
y[1] (closed_form) = 1.95813462125 1.62790167889
absolute error = 0.0004257
relative error = 0.01672 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.106
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6027 2.215
h = 0.003 0.006
y[1] (numeric) = 1.95777582902 1.63067179146
y[1] (closed_form) = 1.95741671099 1.63090163009
absolute error = 0.0004264
relative error = 0.01673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.108
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8854.4MB, alloc=52.3MB, time=111.51
x[1] = 2.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = 1.95882136216 1.63573698788
y[1] (closed_form) = 1.9584612799 1.63596852822
absolute error = 0.0004281
relative error = 0.01678 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = 1.9579021046 1.63948379867
y[1] (closed_form) = 1.95754095067 1.63971552095
absolute error = 0.0004291
relative error = 0.0168 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.116
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6059 2.229
h = 0.001 0.001
y[1] (numeric) = 1.95737908241 1.64174007116
y[1] (closed_form) = 1.95701754442 1.64197186923
absolute error = 0.0004295
relative error = 0.01681 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.117
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8900.1MB, alloc=52.3MB, time=112.07
x[1] = 2.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = 1.95792512909 1.64268501085
y[1] (closed_form) = 1.95756360221 1.64291689507
absolute error = 0.0004295
relative error = 0.01681 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.118
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.607 2.234
h = 0.003 0.006
y[1] (numeric) = 1.95720160199 1.64568732485
y[1] (closed_form) = 1.95683939079 1.64591933258
absolute error = 0.0004301
relative error = 0.01682 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.61 2.24
h = 0.0001 0.005
y[1] (numeric) = 1.95823934296 1.65076078178
y[1] (closed_form) = 1.95787616961 1.65099449026
absolute error = 0.0004319
relative error = 0.01686 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.125
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8946.0MB, alloc=52.3MB, time=112.63
x[1] = 2.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = 1.95731219872 1.65451066118
y[1] (closed_form) = 1.95694795483 1.65474455215
absolute error = 0.0004329
relative error = 0.01689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.128
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6102 2.248
h = 0.001 0.001
y[1] (numeric) = 1.95678446918 1.65676883904
y[1] (closed_form) = 1.95641984164 1.65700280598
absolute error = 0.0004332
relative error = 0.0169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.129
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6112 2.249
h = 0.001 0.003
y[1] (numeric) = 1.9573295099 1.65771594928
y[1] (closed_form) = 1.95696489353 1.65795000229
absolute error = 0.0004333
relative error = 0.01689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.13
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8991.7MB, alloc=52.3MB, time=113.19
x[1] = 2.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = 1.95747235367 1.6601555771
y[1] (closed_form) = 1.9571074266 1.66038993303
absolute error = 0.0004337
relative error = 0.0169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.133
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6123 2.256
h = 0.003 0.006
y[1] (numeric) = 1.95674155639 1.66316088212
y[1] (closed_form) = 1.95637594581 1.66339536193
absolute error = 0.0004343
relative error = 0.01691 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.134
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = 1.95777039551 1.66824405555
y[1] (closed_form) = 1.95740382514 1.66848023493
absolute error = 0.0004361
relative error = 0.01695 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.14
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9037.5MB, alloc=52.3MB, time=113.76
x[1] = 2.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = 1.95683415201 1.67199762873
y[1] (closed_form) = 1.95646651244 1.67223399122
absolute error = 0.0004371
relative error = 0.01698 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.142
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6155 2.27
h = 0.001 0.001
y[1] (numeric) = 1.9563009926 1.67425809693
y[1] (closed_form) = 1.95593296987 1.67449453559
absolute error = 0.0004374
relative error = 0.01699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6165 2.271
h = 0.001 0.003
y[1] (numeric) = 1.95684490276 1.6752077427
y[1] (closed_form) = 1.95647689125 1.67544426733
absolute error = 0.0004375
relative error = 0.01698 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.145
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9083.3MB, alloc=52.3MB, time=114.32
x[1] = 2.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = 1.95698295029 1.6776513107
y[1] (closed_form) = 1.95661462866 1.67788813815
absolute error = 0.0004379
relative error = 0.01699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6176 2.278
h = 0.003 0.006
y[1] (numeric) = 1.95624489316 1.68065960891
y[1] (closed_form) = 1.95587588888 1.68089656061
absolute error = 0.0004385
relative error = 0.017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.149
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = 1.95726484773 1.68575249473
y[1] (closed_form) = 1.95689488601 1.68599114483
absolute error = 0.0004403
relative error = 0.01704 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.154
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9129.1MB, alloc=52.3MB, time=114.88
x[1] = 2.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = 1.95631951792 1.68950976445
y[1] (closed_form) = 1.95594848833 1.68974859825
absolute error = 0.0004413
relative error = 0.01707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.157
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6208 2.292
h = 0.001 0.001
y[1] (numeric) = 1.95578093644 1.69177252452
y[1] (closed_form) = 1.95540952418 1.6920114347
absolute error = 0.0004416
relative error = 0.01708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.158
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6218 2.293
h = 0.001 0.003
y[1] (numeric) = 1.95632371921 1.69272470384
y[1] (closed_form) = 1.95595231821 1.69296369988
absolute error = 0.0004417
relative error = 0.01707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9174.9MB, alloc=52.3MB, time=115.44
x[1] = 2.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = 1.95645697882 1.69517221123
y[1] (closed_form) = 1.95608526828 1.69541150998
absolute error = 0.0004421
relative error = 0.01708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.162
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6229 2.3
h = 0.003 0.006
y[1] (numeric) = 1.9557116722 1.69818350472
y[1] (closed_form) = 1.95533927987 1.6984229281
absolute error = 0.0004427
relative error = 0.01709 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = 1.95672275943 1.70328609874
y[1] (closed_form) = 1.95634941199 1.70352721933
absolute error = 0.0004444
relative error = 0.01713 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.169
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9220.7MB, alloc=52.3MB, time=116.01
x[1] = 2.626 2.311
h = 0.0001 0.003
y[1] (numeric) = 1.95576835621 1.70704706765
y[1] (closed_form) = 1.95539394224 1.70728837253
absolute error = 0.0004454
relative error = 0.01716 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.171
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6261 2.314
h = 0.001 0.001
y[1] (numeric) = 1.95522436043 1.70931212107
y[1] (closed_form) = 1.95484956426 1.70955350253
absolute error = 0.0004458
relative error = 0.01717 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.173
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6271 2.315
h = 0.001 0.003
y[1] (numeric) = 1.95576601895 1.71026683194
y[1] (closed_form) = 1.9553912341 1.71050829915
absolute error = 0.0004458
relative error = 0.01716 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.174
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9266.5MB, alloc=52.3MB, time=116.57
x[1] = 2.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = 1.95589449893 1.71271827786
y[1] (closed_form) = 1.9555194051 1.71296004767
absolute error = 0.0004463
relative error = 0.01717 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.176
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6282 2.322
h = 0.003 0.006
y[1] (numeric) = 1.95514195315 1.71573256867
y[1] (closed_form) = 1.95476617839 1.71597446347
absolute error = 0.0004469
relative error = 0.01718 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = 1.95614419014 1.72084486658
y[1] (closed_form) = 1.95576746258 1.7210884574
absolute error = 0.0004486
relative error = 0.01722 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.183
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9312.2MB, alloc=52.3MB, time=117.13
x[1] = 2.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = 1.9551807264 1.72460953724
y[1] (closed_form) = 1.95480293364 1.72485331292
absolute error = 0.0004496
relative error = 0.01725 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.186
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6314 2.336
h = 0.001 0.001
y[1] (numeric) = 1.95463132406 1.72687688542
y[1] (closed_form) = 1.9542531496 1.72712073787
absolute error = 0.00045
relative error = 0.01725 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.187
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = 1.95517186145 1.72783412583
y[1] (closed_form) = 1.95479369835 1.72807806393
absolute error = 0.00045
relative error = 0.01725 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.189
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9357.8MB, alloc=52.3MB, time=117.69
x[1] = 2.6325 2.341
h = 0.003 0.006
y[1] (numeric) = 1.95441305692 1.73085091211
y[1] (closed_form) = 1.95403421366 1.73109497553
absolute error = 0.0004507
relative error = 0.01726 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.19
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = 1.95540757401 1.73597145413
y[1] (closed_form) = 1.95502777996 1.73621721257
absolute error = 0.0004524
relative error = 0.0173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.196
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = 1.95443627743 1.73973920537
y[1] (closed_form) = 1.9540554193 1.73998514918
absolute error = 0.0004534
relative error = 0.01733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9403.6MB, alloc=52.3MB, time=118.26
x[1] = 2.6357 2.355
h = 0.001 0.001
y[1] (numeric) = 1.95388220014 1.74200846562
y[1] (closed_form) = 1.95350096072 1.74225448636
absolute error = 0.0004537
relative error = 0.01733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6367 2.356
h = 0.001 0.003
y[1] (numeric) = 1.95442174487 1.74296786845
y[1] (closed_form) = 1.95404051686 1.74321397475
absolute error = 0.0004538
relative error = 0.01733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.201
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = 1.95454130607 1.74542658392
y[1] (closed_form) = 1.95415977014 1.74567299262
absolute error = 0.0004542
relative error = 0.01733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.203
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9449.4MB, alloc=52.3MB, time=118.82
x[1] = 2.6378 2.363
h = 0.003 0.006
y[1] (numeric) = 1.95377528155 1.74844637122
y[1] (closed_form) = 1.95339306626 1.74869290557
absolute error = 0.0004548
relative error = 0.01735 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = 1.95476098002 1.75357660908
y[1] (closed_form) = 1.95437781622 1.75382483722
absolute error = 0.0004565
relative error = 0.01739 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.21
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = 1.95378064675 1.75734806671
y[1] (closed_form) = 1.95339642021 1.75759648076
absolute error = 0.0004575
relative error = 0.01741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9495.2MB, alloc=52.3MB, time=119.38
x[1] = 2.641 2.377
h = 0.001 0.001
y[1] (numeric) = 1.95322117724 1.75961962428
y[1] (closed_form) = 1.95283656989 1.75986811547
absolute error = 0.0004579
relative error = 0.01742 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.214
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.642 2.378
h = 0.001 0.003
y[1] (numeric) = 1.9537596066 1.76058155292
y[1] (closed_form) = 1.9533750107 1.76083012956
absolute error = 0.0004579
relative error = 0.01741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.216
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.643 2.381
h = 0.0001 0.004
y[1] (numeric) = 1.95387441164 1.7630442043
y[1] (closed_form) = 1.95348950838 1.76329308322
absolute error = 0.0004584
relative error = 0.01742 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.218
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9540.9MB, alloc=52.3MB, time=119.94
x[1] = 2.6431 2.385
h = 0.003 0.006
y[1] (numeric) = 1.95310117732 1.7660669944
y[1] (closed_form) = 1.95271559556 1.76631599931
absolute error = 0.000459
relative error = 0.01743 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.22
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = 1.95407807399 1.7712069235
y[1] (closed_form) = 1.95369154599 1.77145762097
absolute error = 0.0004607
relative error = 0.01747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.225
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = 1.95308871681 1.77498208979
y[1] (closed_form) = 1.95270112739 1.77523297372
absolute error = 0.0004617
relative error = 0.0175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.228
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9586.7MB, alloc=52.3MB, time=120.50
x[1] = 2.6463 2.399
h = 0.001 0.001
y[1] (numeric) = 1.95252386277 1.77725594594
y[1] (closed_form) = 1.95213589301 1.77750690718
absolute error = 0.0004621
relative error = 0.0175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.229
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6473 2.4
h = 0.001 0.003
y[1] (numeric) = 1.95306117979 1.77822039834
y[1] (closed_form) = 1.95267322154 1.77847144493
absolute error = 0.0004621
relative error = 0.0175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.23
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = 1.9531712368 1.78068698459
y[1] (closed_form) = 1.95278297175 1.78093833333
absolute error = 0.0004625
relative error = 0.0175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.233
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9632.4MB, alloc=52.3MB, time=121.06
x[1] = 2.6484 2.407
h = 0.003 0.006
y[1] (numeric) = 1.95239080291 1.78371277921
y[1] (closed_form) = 1.9520018602 1.78396425429
absolute error = 0.0004632
relative error = 0.01751 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.235
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = 1.95335891449 1.78886239488
y[1] (closed_form) = 1.95296902779 1.78911556128
absolute error = 0.0004649
relative error = 0.01755 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.24
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = 1.95236054614 1.792641272
y[1] (closed_form) = 1.95196959934 1.79289462539
absolute error = 0.0004659
relative error = 0.01758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.242
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9678.1MB, alloc=52.3MB, time=121.62
x[1] = 2.6516 2.421
h = 0.001 0.001
y[1] (numeric) = 1.95179031522 1.79491742792
y[1] (closed_form) = 1.95139898857 1.7951708588
absolute error = 0.0004662
relative error = 0.01758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.244
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6526 2.422
h = 0.001 0.003
y[1] (numeric) = 1.95232652292 1.79588440202
y[1] (closed_form) = 1.95193520783 1.79613791815
absolute error = 0.0004663
relative error = 0.01758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.245
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = 1.95243183999 1.79835492203
y[1] (closed_form) = 1.95204021864 1.79860874018
absolute error = 0.0004667
relative error = 0.01758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.248
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9724.0MB, alloc=52.3MB, time=122.18
x[1] = 2.6537 2.429
h = 0.003 0.006
y[1] (numeric) = 1.9516442167 1.80138372283
y[1] (closed_form) = 1.95125191855 1.80163766764
absolute error = 0.0004673
relative error = 0.0176 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.249
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = 1.95260355982 1.80654302031
y[1] (closed_form) = 1.9522103199 1.80679865519
absolute error = 0.000469
relative error = 0.01763 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.255
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = 1.95159619299 1.81032561034
y[1] (closed_form) = 1.9512018943 1.81058143274
absolute error = 0.00047
relative error = 0.01766 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.257
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9769.8MB, alloc=52.3MB, time=122.74
x[1] = 2.6569 2.443
h = 0.001 0.001
y[1] (numeric) = 1.95102059283 1.81260406717
y[1] (closed_form) = 1.95062591477 1.81285996723
absolute error = 0.0004704
relative error = 0.01766 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.259
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = 1.9515556942 1.8135735609
y[1] (closed_form) = 1.95116102774 1.8138295461
absolute error = 0.0004704
relative error = 0.01766 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.26
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.658 2.448
h = 0.003 0.006
y[1] (numeric) = 1.95076185477 1.81660486508
y[1] (closed_form) = 1.95036651228 1.81686097725
absolute error = 0.0004711
relative error = 0.01767 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9815.6MB, alloc=52.3MB, time=123.30
x[1] = 2.661 2.454
h = 0.0001 0.005
y[1] (numeric) = 1.95171354827 1.82177238825
y[1] (closed_form) = 1.95131726593 1.82203018944
absolute error = 0.0004728
relative error = 0.01771 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.268
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = 1.95069840173 1.82555806885
y[1] (closed_form) = 1.95030106175 1.82581605801
absolute error = 0.0004737
relative error = 0.01773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.27
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6612 2.462
h = 0.001 0.001
y[1] (numeric) = 1.95011815858 1.82783844325
y[1] (closed_form) = 1.94972043964 1.82809651022
absolute error = 0.0004741
relative error = 0.01774 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.271
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9861.4MB, alloc=52.3MB, time=123.86
x[1] = 2.6622 2.463
h = 0.001 0.003
y[1] (numeric) = 1.95065228005 1.828810091
y[1] (closed_form) = 1.95025457275 1.82906824303
absolute error = 0.0004741
relative error = 0.01773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.273
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = 1.95074875173 1.83128787148
y[1] (closed_form) = 1.95035073921 1.8315463253
absolute error = 0.0004746
relative error = 0.01774 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.275
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6633 2.47
h = 0.003 0.006
y[1] (numeric) = 1.94994774181 1.83432218485
y[1] (closed_form) = 1.94954905405 1.83458076593
absolute error = 0.0004752
relative error = 0.01775 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.277
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9907.2MB, alloc=52.3MB, time=124.42
x[1] = 2.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = 1.95089069756 1.83949938091
y[1] (closed_form) = 1.95049107215 1.83975964974
absolute error = 0.0004769
relative error = 0.01779 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.283
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = 1.94986657604 1.84328877819
y[1] (closed_form) = 1.94946589431 1.84354923549
absolute error = 0.0004779
relative error = 0.01781 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.285
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6665 2.484
h = 0.001 0.001
y[1] (numeric) = 1.94928097778 1.84557145555
y[1] (closed_form) = 1.94887991757 1.84583199083
absolute error = 0.0004783
relative error = 0.01782 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.286
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9952.9MB, alloc=52.3MB, time=124.98
x[1] = 2.6675 2.485
h = 0.001 0.003
y[1] (numeric) = 1.94981399844 1.84654561909
y[1] (closed_form) = 1.94941294992 1.84680623932
absolute error = 0.0004783
relative error = 0.01781 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = 1.94990575309 1.84902733001
y[1] (closed_form) = 1.94950439988 1.84928825189
absolute error = 0.0004787
relative error = 0.01782 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.29
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6686 2.492
h = 0.003 0.006
y[1] (numeric) = 1.94909758272 1.85206465398
y[1] (closed_form) = 1.94869555513 1.85232570342
absolute error = 0.0004793
relative error = 0.01783 %
Correct digits = 4
memory used=9998.7MB, alloc=52.3MB, time=125.54
Radius of convergence (given) for eq 1 = 5.292
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = 1.95003181705 1.85725151788
y[1] (closed_form) = 1.94962885399 1.85751425381
absolute error = 0.0004811
relative error = 0.01786 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.298
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = 1.94899873315 1.86104463368
y[1] (closed_form) = 1.94859471508 1.86130755856
absolute error = 0.000482
relative error = 0.01789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.3
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10044.4MB, alloc=52.3MB, time=126.10
x[1] = 2.6718 2.506
h = 0.001 0.001
y[1] (numeric) = 1.94840778735 1.86332961497
y[1] (closed_form) = 1.94800339127 1.863592618
absolute error = 0.0004824
relative error = 0.01789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.301
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6728 2.507
h = 0.001 0.003
y[1] (numeric) = 1.94893971011 1.86430629219
y[1] (closed_form) = 1.94853532576 1.86456938007
absolute error = 0.0004824
relative error = 0.01789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.303
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = 1.94902675566 1.86679193226
y[1] (closed_form) = 1.94862206717 1.86705532165
absolute error = 0.0004829
relative error = 0.01789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.305
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10090.1MB, alloc=52.3MB, time=126.66
x[1] = 2.6739 2.514
h = 0.003 0.006
y[1] (numeric) = 1.9482114349 1.86983226819
y[1] (closed_form) = 1.94780607288 1.87009578544
absolute error = 0.0004835
relative error = 0.01791 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.307
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = 1.94913696404 1.87502879483
y[1] (closed_form) = 1.94873066871 1.87529399728
absolute error = 0.0004852
relative error = 0.01794 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.313
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.677 2.525
h = 0.0001 0.003
y[1] (numeric) = 1.9480949303 1.87882563086
y[1] (closed_form) = 1.94768758127 1.87909102275
absolute error = 0.0004862
relative error = 0.01796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.315
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10135.8MB, alloc=52.3MB, time=127.22
x[1] = 2.6771 2.528
h = 0.001 0.001
y[1] (numeric) = 1.9474986445 1.88111291701
y[1] (closed_form) = 1.94709091795 1.8813783872
absolute error = 0.0004865
relative error = 0.01797 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.317
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6781 2.529
h = 0.001 0.003
y[1] (numeric) = 1.94802947225 1.8820921058
y[1] (closed_form) = 1.94762175747 1.88235766074
absolute error = 0.0004866
relative error = 0.01796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.318
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = 1.94811181658 1.88458167367
y[1] (closed_form) = 1.94770379819 1.88484752998
absolute error = 0.000487
relative error = 0.01797 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.32
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10181.6MB, alloc=52.3MB, time=127.79
x[1] = 2.6792 2.536
h = 0.003 0.006
y[1] (numeric) = 1.94728935547 1.88762502286
y[1] (closed_form) = 1.94688066439 1.88789100733
absolute error = 0.0004876
relative error = 0.01798 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.322
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = 1.94820619555 1.89283120704
y[1] (closed_form) = 1.9477965733 1.8930988754
absolute error = 0.0004893
relative error = 0.01801 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.328
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = 1.94715522448 1.89663176493
y[1] (closed_form) = 1.94674454985 1.89689962321
absolute error = 0.0004903
relative error = 0.01804 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.33
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10227.4MB, alloc=52.3MB, time=128.36
x[1] = 2.6824 2.55
h = 0.001 0.001
y[1] (numeric) = 1.9465536062 1.8989213568
y[1] (closed_form) = 1.94614255452 1.89918929354
absolute error = 0.0004907
relative error = 0.01804 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.332
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = 1.9470833418 1.89990305505
y[1] (closed_form) = 1.94667230193 1.90017107643
absolute error = 0.0004907
relative error = 0.01804 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.333
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6835 2.555
h = 0.003 0.006
y[1] (numeric) = 1.94625470657 1.902948914
y[1] (closed_form) = 1.94584299476 1.90321706382
absolute error = 0.0004913
relative error = 0.01805 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.335
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10273.0MB, alloc=52.3MB, time=128.92
x[1] = 2.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = 1.94716396528 1.90816330359
y[1] (closed_form) = 1.94675132416 1.90843313621
absolute error = 0.000493
relative error = 0.01809 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.341
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = 1.94610526688 1.91196696013
y[1] (closed_form) = 1.94569157449 1.91223698307
absolute error = 0.000494
relative error = 0.01811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.343
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6867 2.569
h = 0.001 0.001
y[1] (numeric) = 1.94549903708 1.91425847395
y[1] (closed_form) = 1.94508496806 1.91452857549
absolute error = 0.0004944
relative error = 0.01811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.345
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10318.7MB, alloc=52.3MB, time=129.48
x[1] = 2.6877 2.57
h = 0.001 0.003
y[1] (numeric) = 1.94602780502 1.91524231758
y[1] (closed_form) = 1.94561374784 1.91551250367
absolute error = 0.0004944
relative error = 0.01811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.346
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = 1.94610137558 1.91773913469
y[1] (closed_form) = 1.9456870158 1.91800962189
absolute error = 0.0004948
relative error = 0.01811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.348
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6888 2.577
h = 0.003 0.006
y[1] (numeric) = 1.9452656186 1.92078800925
y[1] (closed_form) = 1.94485058768 1.92105862515
absolute error = 0.0004955
relative error = 0.01812 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.35
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10364.4MB, alloc=52.3MB, time=130.04
x[1] = 2.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = 1.94616621805 1.92601204666
y[1] (closed_form) = 1.94575025994 1.92628434405
absolute error = 0.0004972
relative error = 0.01816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = 1.94509860547 1.92981942802
y[1] (closed_form) = 1.94468159739 1.93009191618
absolute error = 0.0004981
relative error = 0.01818 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.358
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.692 2.591
h = 0.001 0.001
y[1] (numeric) = 1.94448705711 1.93211324914
y[1] (closed_form) = 1.94406967286 1.93238581604
absolute error = 0.0004985
relative error = 0.01819 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.36
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10410.2MB, alloc=52.3MB, time=130.60
x[1] = 2.693 2.592
h = 0.001 0.003
y[1] (numeric) = 1.94501473818 1.93309959827
y[1] (closed_form) = 1.94459736582 1.93337224962
absolute error = 0.0004985
relative error = 0.01818 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.361
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.694 2.595
h = 0.0001 0.004
y[1] (numeric) = 1.94508362986 1.93560033921
y[1] (closed_form) = 1.94466595544 1.93587329151
absolute error = 0.000499
relative error = 0.01818 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.364
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6941 2.599
h = 0.003 0.006
y[1] (numeric) = 1.94424076103 1.93865223044
y[1] (closed_form) = 1.9438224163 1.93892531172
absolute error = 0.0004996
relative error = 0.0182 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.366
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10455.9MB, alloc=52.3MB, time=131.16
x[1] = 2.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = 1.94513271708 1.94388591023
y[1] (closed_form) = 1.94471344724 1.94416067168
absolute error = 0.0005013
relative error = 0.01823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.371
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = 1.9440562027 1.9476970178
y[1] (closed_form) = 1.94363588421 1.94797197046
absolute error = 0.0005023
relative error = 0.01825 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.374
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6973 2.613
h = 0.001 0.001
y[1] (numeric) = 1.94343934321 1.94999314692
y[1] (closed_form) = 1.94301864903 1.95026817847
absolute error = 0.0005026
relative error = 0.01826 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10501.7MB, alloc=52.3MB, time=131.72
x[1] = 2.6983 2.614
h = 0.001 0.003
y[1] (numeric) = 1.94396594021 1.95098199942
y[1] (closed_form) = 1.94354525795 1.95125711532
absolute error = 0.0005027
relative error = 0.01825 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.377
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = 1.94403016075 1.95348666266
y[1] (closed_form) = 1.94360917695 1.95376207936
absolute error = 0.0005031
relative error = 0.01825 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.379
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6994 2.621
h = 0.003 0.006
y[1] (numeric) = 1.94318018996 1.95654157159
y[1] (closed_form) = 1.9427585367 1.95681711753
absolute error = 0.0005037
relative error = 0.01827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.381
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10547.4MB, alloc=52.3MB, time=132.28
x[1] = 2.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = 1.94406351834 1.96178488824
y[1] (closed_form) = 1.94364094205 1.96206211302
absolute error = 0.0005054
relative error = 0.0183 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.386
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = 1.94297811452 1.96559972331
y[1] (closed_form) = 1.94255449088 1.96587713973
absolute error = 0.0005064
relative error = 0.01832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.389
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7026 2.635
h = 0.001 0.001
y[1] (numeric) = 1.94235595131 1.96789816111
y[1] (closed_form) = 1.94193195245 1.96817565657
absolute error = 0.0005067
relative error = 0.01833 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.391
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10593.1MB, alloc=52.3MB, time=132.84
x[1] = 2.7036 2.636
h = 0.001 0.003
y[1] (numeric) = 1.942881467 1.96888951481
y[1] (closed_form) = 1.9424574801 1.96916709451
absolute error = 0.0005068
relative error = 0.01832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.392
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = 1.94294102408 1.9713980988
y[1] (closed_form) = 1.94251673616 1.97167597915
absolute error = 0.0005072
relative error = 0.01832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.394
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7047 2.643
h = 0.003 0.006
y[1] (numeric) = 1.94208396122 1.97445602637
y[1] (closed_form) = 1.94165900467 1.97473403622
absolute error = 0.0005078
relative error = 0.01834 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.396
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10638.9MB, alloc=52.3MB, time=133.40
x[1] = 2.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = 1.94295867757 1.97970897428
y[1] (closed_form) = 1.94253280005 1.97998866164
absolute error = 0.0005095
relative error = 0.01837 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = 1.94186439661 1.98352753807
y[1] (closed_form) = 1.94143747304 1.98380741749
absolute error = 0.0005105
relative error = 0.01839 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.404
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7079 2.657
h = 0.001 0.001
y[1] (numeric) = 1.94123693708 1.98582828517
y[1] (closed_form) = 1.94080963876 1.98610824375
absolute error = 0.0005108
relative error = 0.0184 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.406
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10684.6MB, alloc=52.3MB, time=133.97
x[1] = 2.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = 1.9417613742 1.98682213789
y[1] (closed_form) = 1.94133408788 1.98710218062
absolute error = 0.0005109
relative error = 0.01839 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.407
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.709 2.662
h = 0.003 0.006
y[1] (numeric) = 1.94089817856 1.98988258018
y[1] (closed_form) = 1.94047022438 1.99016275266
absolute error = 0.0005115
relative error = 0.0184 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.409
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.712 2.668
h = 0.0001 0.005
y[1] (numeric) = 1.94176537978 1.99514371147
y[1] (closed_form) = 1.94133650641 1.99542556034
absolute error = 0.0005132
relative error = 0.01843 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.415
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10730.5MB, alloc=52.3MB, time=134.53
x[1] = 2.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = 1.94066342306 1.99896538018
y[1] (closed_form) = 1.94023350474 1.99924742147
absolute error = 0.0005142
relative error = 0.01846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.417
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7122 2.676
h = 0.001 0.001
y[1] (numeric) = 1.94003138301 2.00126805253
y[1] (closed_form) = 1.93960109036 2.0015501731
absolute error = 0.0005145
relative error = 0.01846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.419
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7132 2.677
h = 0.001 0.003
y[1] (numeric) = 1.94055486418 2.00226404179
y[1] (closed_form) = 1.94012458355 2.00254624642
absolute error = 0.0005146
relative error = 0.01845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.42
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10776.3MB, alloc=52.3MB, time=135.09
x[1] = 2.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = 1.9406057173 2.00477986177
y[1] (closed_form) = 1.94017513662 2.00506236675
absolute error = 0.000515
relative error = 0.01846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.423
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7143 2.684
h = 0.003 0.006
y[1] (numeric) = 1.93973544789 2.00784332442
y[1] (closed_form) = 1.93930420012 2.00812595939
absolute error = 0.0005156
relative error = 0.01847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.425
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = 1.94059406598 2.01311407653
y[1] (closed_form) = 1.94016190106 2.01339838654
absolute error = 0.0005173
relative error = 0.0185 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.43
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10822.0MB, alloc=52.3MB, time=135.65
x[1] = 2.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = 1.93948325489 2.01693947614
y[1] (closed_form) = 1.93905004632 2.01722397896
absolute error = 0.0005183
relative error = 0.01852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.433
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7175 2.698
h = 0.001 0.001
y[1] (numeric) = 1.93884593221 2.01924445889
y[1] (closed_form) = 1.93841234976 2.01952904113
absolute error = 0.0005186
relative error = 0.01853 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7185 2.699
h = 0.001 0.003
y[1] (numeric) = 1.93936833985 2.02024294315
y[1] (closed_form) = 1.93893476948 2.02052760935
absolute error = 0.0005187
relative error = 0.01852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.436
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10867.8MB, alloc=52.3MB, time=136.21
x[1] = 2.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = 1.93941455129 2.02276267929
y[1] (closed_form) = 1.93898068138 2.02304764567
absolute error = 0.0005191
relative error = 0.01852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.438
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7196 2.706
h = 0.003 0.006
y[1] (numeric) = 1.93853721782 2.02582916305
y[1] (closed_form) = 1.93810268166 2.02611425967
absolute error = 0.0005197
relative error = 0.01854 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.44
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = 1.93938726815 2.03110953016
y[1] (closed_form) = 1.93895181684 2.03139630045
absolute error = 0.0005214
relative error = 0.01857 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.446
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10913.5MB, alloc=52.3MB, time=136.77
x[1] = 2.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = 1.93826761488 2.03493866164
y[1] (closed_form) = 1.93783112121 2.03522562513
absolute error = 0.0005224
relative error = 0.01859 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.448
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7228 2.72
h = 0.001 0.001
y[1] (numeric) = 1.93762501686 2.03724595525
y[1] (closed_form) = 1.93718814979 2.0375329983
absolute error = 0.0005227
relative error = 0.01859 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.45
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7238 2.721
h = 0.001 0.003
y[1] (numeric) = 1.93814635366 2.03824693233
y[1] (closed_form) = 1.93770949869 2.03853405923
absolute error = 0.0005228
relative error = 0.01859 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.451
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10959.3MB, alloc=52.3MB, time=137.33
x[1] = 2.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = 1.93818793093 2.0407705829
y[1] (closed_form) = 1.93775077694 2.04105800983
absolute error = 0.0005232
relative error = 0.01859 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.454
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7249 2.728
h = 0.003 0.006
y[1] (numeric) = 1.93730354315 2.04384008847
y[1] (closed_form) = 1.93686572373 2.04412764586
absolute error = 0.0005238
relative error = 0.0186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.456
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = 1.93814504096 2.04913006468
y[1] (closed_form) = 1.93770630839 2.04941929438
absolute error = 0.0005255
relative error = 0.01863 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11005.1MB, alloc=52.3MB, time=137.90
x[1] = 2.728 2.739
h = 0.0001 0.003
y[1] (numeric) = 1.93701655764 2.05296292892
y[1] (closed_form) = 1.936576784 2.05325235221
absolute error = 0.0005265
relative error = 0.01865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.464
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7281 2.742
h = 0.001 0.001
y[1] (numeric) = 1.93636869159 2.05527253384
y[1] (closed_form) = 1.93592854501 2.0555620368
absolute error = 0.0005268
relative error = 0.01866 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.466
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7291 2.743
h = 0.001 0.003
y[1] (numeric) = 1.93688896019 2.05627600152
y[1] (closed_form) = 1.93644882575 2.05656558823
absolute error = 0.0005269
relative error = 0.01865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.467
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11050.9MB, alloc=52.3MB, time=138.46
x[1] = 2.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = 1.93692591078 2.05880356477
y[1] (closed_form) = 1.93648547782 2.05909345134
absolute error = 0.0005273
relative error = 0.01865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.469
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7302 2.75
h = 0.003 0.006
y[1] (numeric) = 1.93603447837 2.06187609277
y[1] (closed_form) = 1.93559338081 2.06216611004
absolute error = 0.0005279
relative error = 0.01867 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.471
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = 1.93686743883 2.06717567211
y[1] (closed_form) = 1.9364254301 2.06746736033
absolute error = 0.0005296
relative error = 0.0187 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.477
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11096.6MB, alloc=52.3MB, time=139.02
x[1] = 2.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = 1.93573013756 2.07101226993
y[1] (closed_form) = 1.93528708904 2.0713041521
absolute error = 0.0005306
relative error = 0.01872 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.48
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7334 2.764
h = 0.001 0.001
y[1] (numeric) = 1.93507701073 2.07332418653
y[1] (closed_form) = 1.93463358975 2.07361614849
absolute error = 0.0005309
relative error = 0.01872 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = 1.93559621374 2.07433014261
y[1] (closed_form) = 1.93515280492 2.07462218822
absolute error = 0.0005309
relative error = 0.01871 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.483
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11142.3MB, alloc=52.3MB, time=139.58
x[1] = 2.7345 2.769
h = 0.003 0.006
y[1] (numeric) = 1.93469868924 2.0774051889
y[1] (closed_form) = 1.93425461658 2.07769736543
absolute error = 0.0005316
relative error = 0.01873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = 1.93552419879 2.08271292802
y[1] (closed_form) = 1.93507921666 2.08300677433
absolute error = 0.0005332
relative error = 0.01876 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.49
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = 1.93437927248 2.08655263532
y[1] (closed_form) = 1.93393325167 2.08684667591
absolute error = 0.0005342
relative error = 0.01878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.493
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11188.1MB, alloc=52.3MB, time=140.14
x[1] = 2.7377 2.783
h = 0.001 0.001
y[1] (numeric) = 1.93372159561 2.08886647945
y[1] (closed_form) = 1.93327520273 2.08916059994
absolute error = 0.0005346
relative error = 0.01878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.495
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7387 2.784
h = 0.001 0.003
y[1] (numeric) = 1.93423985386 2.08987456304
y[1] (closed_form) = 1.93379347318 2.0901687671
absolute error = 0.0005346
relative error = 0.01877 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.496
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = 1.93426816849 2.09240934714
y[1] (closed_form) = 1.93382149023 2.09270385074
absolute error = 0.000535
relative error = 0.01878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.498
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11233.7MB, alloc=52.3MB, time=140.71
x[1] = 2.7398 2.791
h = 0.003 0.006
y[1] (numeric) = 1.93336361737 2.095487417
y[1] (closed_form) = 1.93291627604 2.09578205172
absolute error = 0.0005357
relative error = 0.01879 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.5
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = 1.93418061756 2.10080474814
y[1] (closed_form) = 1.93373236872 2.10110105125
absolute error = 0.0005373
relative error = 0.01882 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.506
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = 1.93302689568 2.10464819045
y[1] (closed_form) = 1.93257760944 2.1049446882
absolute error = 0.0005383
relative error = 0.01884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.509
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11279.6MB, alloc=52.3MB, time=141.27
x[1] = 2.743 2.805
h = 0.001 0.001
y[1] (numeric) = 1.93236397147 2.10696434693
y[1] (closed_form) = 1.93191431361 2.10726092469
absolute error = 0.0005387
relative error = 0.01884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.744 2.806
h = 0.001 0.003
y[1] (numeric) = 1.93288116897 2.10797491482
y[1] (closed_form) = 1.93243152334 2.10827157605
absolute error = 0.0005387
relative error = 0.01884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.512
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.745 2.809
h = 0.0001 0.004
y[1] (numeric) = 1.93290487811 2.11051360643
y[1] (closed_form) = 1.93245493541 2.11081056703
absolute error = 0.0005391
relative error = 0.01884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11325.4MB, alloc=52.3MB, time=141.83
x[1] = 2.7451 2.813
h = 0.003 0.006
y[1] (numeric) = 1.93199330991 2.11359470029
y[1] (closed_form) = 1.93154270496 2.11389179222
absolute error = 0.0005397
relative error = 0.01885 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = 1.93280181562 2.11892161728
y[1] (closed_form) = 1.93235030508 2.11922037622
absolute error = 0.0005414
relative error = 0.01888 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = 1.93163931014 2.1227687952
y[1] (closed_form) = 1.93118676348 2.12306774911
absolute error = 0.0005424
relative error = 0.0189 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.525
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11371.3MB, alloc=52.3MB, time=142.39
x[1] = 2.7483 2.827
h = 0.001 0.001
y[1] (numeric) = 1.93097114577 2.12508726427
y[1] (closed_form) = 1.93051822797 2.1253862983
absolute error = 0.0005427
relative error = 0.0189 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.526
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7493 2.828
h = 0.001 0.003
y[1] (numeric) = 1.93148728506 2.12610031423
y[1] (closed_form) = 1.93103437952 2.12639943163
absolute error = 0.0005428
relative error = 0.0189 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.528
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = 1.93150639604 2.12864291144
y[1] (closed_form) = 1.93105319391 2.12894232802
absolute error = 0.0005432
relative error = 0.0189 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.53
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11417.0MB, alloc=52.3MB, time=142.95
x[1] = 2.7504 2.835
h = 0.003 0.006
y[1] (numeric) = 1.93058782032 2.13172702969
y[1] (closed_form) = 1.93013395676 2.13202657781
absolute error = 0.0005438
relative error = 0.01891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.532
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = 1.93138784632 2.1370635263
y[1] (closed_form) = 1.93093307909 2.13736474003
absolute error = 0.0005455
relative error = 0.01894 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.538
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = 1.93021656916 2.14091444033
y[1] (closed_form) = 1.92976076708 2.14121584937
absolute error = 0.0005464
relative error = 0.01896 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.54
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11462.7MB, alloc=52.3MB, time=143.51
x[1] = 2.7536 2.849
h = 0.001 0.001
y[1] (numeric) = 1.92954317179 2.14323522218
y[1] (closed_form) = 1.92908699903 2.14353671146
absolute error = 0.0005468
relative error = 0.01896 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7546 2.85
h = 0.001 0.003
y[1] (numeric) = 1.93005825539 2.14425075198
y[1] (closed_form) = 1.92960209493 2.14455232452
absolute error = 0.0005468
relative error = 0.01896 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.543
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = 1.93007277549 2.14679725284
y[1] (closed_form) = 1.92961631893 2.14709912438
absolute error = 0.0005472
relative error = 0.01896 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11508.5MB, alloc=52.3MB, time=144.08
x[1] = 2.7557 2.857
h = 0.003 0.006
y[1] (numeric) = 1.92914720177 2.14988439579
y[1] (closed_form) = 1.9286900846 2.15018639909
absolute error = 0.0005479
relative error = 0.01897 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.548
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = 1.92993876273 2.15523046572
y[1] (closed_form) = 1.92948074379 2.15553413322
absolute error = 0.0005495
relative error = 0.019 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.554
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = 1.92875872577 2.15908511629
y[1] (closed_form) = 1.92829967325 2.15938897943
absolute error = 0.0005505
relative error = 0.01902 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.556
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11554.4MB, alloc=52.3MB, time=144.64
x[1] = 2.7589 2.871
h = 0.001 0.001
y[1] (numeric) = 1.92808010253 2.16140821109
y[1] (closed_form) = 1.92762067978 2.16171215456
absolute error = 0.0005509
relative error = 0.01902 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.558
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7599 2.872
h = 0.001 0.003
y[1] (numeric) = 1.92859413294 2.16242621849
y[1] (closed_form) = 1.92813472252 2.16273024512
absolute error = 0.0005509
relative error = 0.01901 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.559
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ;
Iterations = 754
Total Elapsed Time = 2 Minutes 25 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 2 Minutes 25 Seconds
> quit
memory used=11596.5MB, alloc=52.3MB, time=145.13