|\^/| Maple 18 (X86 64 WINDOWS) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #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_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > 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 6 # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) 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 0 > 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 1 > 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 2 > 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 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > 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 3 > 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 4 > 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 5 > 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 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > 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 6 > 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 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > 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 6 > 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 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > 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_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > 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 19 # Begin Function number 20 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 21 # Begin Function number 22 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > 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 22 # Begin Function number 23 > 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 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > 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 23 # Begin Function number 24 > 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 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > 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 24 # Begin Function number 25 > 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 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > 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 25 # Begin Function number 26 > 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 12 > 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 12; > 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 26 # Begin Function number 27 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 27 # Begin Function number 28 > 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 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > 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 28 # Begin Function number 29 > 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 29 # Begin Function number 30 > 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 12 > 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 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > 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 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > 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 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > 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 := 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 30 # Begin Function number 31 > 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 31 # Begin Function number 32 > 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 32 # Begin Function number 33 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > 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 33 # Begin Function number 34 > 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 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > 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 34 # Begin Function number 35 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 35 # Begin Function number 36 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 36 # Begin Function number 37 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 37 # Begin Function number 38 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 38 # Begin Function number 39 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 39 # Begin Function number 40 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 40 # Begin Function number 41 > 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 41 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0)); > end; exact_soln_y := proc(x) return c(10.0)*(c(0.1)*c(x) + c(0.2))*ln(c(0.1)*c(x) + c(0.2)) - c(x) - c(2.0) end proc #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 := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if (rad_given < glob_least_given_sing) 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 (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_float(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 (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_float(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 (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_float(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 := sqrt((array_x[1] - array_given_rad_poles[1, 1])* (array_x[1] - array_given_rad_poles[1, 1]) + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if rad_given < glob_least_given_sing 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 array_rad_test_poles[1, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_float(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 array_rad_test_poles[1, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_float(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 array_rad_test_poles[1, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_float(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_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 3 > if (iter >= 0) then # if number 4 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5 > relerr := abserr*glob__100/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 6 > glob_good_digits := -int_trunc(log10(c(relerr))) + 3; > else > glob_good_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 5; > if (glob_good_digits < glob_min_good_digits) then # if number 5 > glob_min_good_digits := glob_good_digits; > fi;# end if 5; > if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5 > glob_min_apfp_est_good_digits := glob_apfp_est_good_digits; > fi;# end if 5; > if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5 > est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*21*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 6 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 5; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > array_est_rel_error[1] := est_rel_err; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," "); > omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," "); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > 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_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_float(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if c(glob_prec) < c(float_abs(closed_form_val_y)) then relerr := abserr*glob__100/float_abs(closed_form_val_y); if c(glob_prec) < c(relerr) then glob_good_digits := -int_trunc(log10(c(relerr))) + 3 else glob_good_digits := Digits 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; if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits end if; if glob_prec < evalf(float_abs(numeric_val)) then est_rel_err := evalf(array_max_est_error[1]*100.0* sqrt(glob_iter)*21*ATS_MAX_TERMS/float_abs(numeric_val)) ; if glob_prec < evalf(est_rel_err) then glob_est_digits := -int_trunc(log10(est_rel_err)) + 3 else glob_est_digits := Digits end if else relerr := glob__m1; glob_est_digits := -16 end if; array_est_digits[1] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; array_est_rel_error[1] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if 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_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr((glob_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; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr((left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #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_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(glob_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; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") 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_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > #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 > ; > if (reached_interval()) 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_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; 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 reached_interval() then display_poles() end if 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_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre ln 1 LINEAR $eq_no = 1 > array_tmp3[1] := ln(array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre ln 2 LINEAR $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre ln ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := neg(array_tmp2[2]) * array_tmp3[2] * c(1) / array_tmp2[1] / c(2); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre ln ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := neg(array_tmp2[2]) * array_tmp3[3] * c(2) / array_tmp2[1] / c(3); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre ln ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := neg(array_tmp2[2]) * array_tmp3[4] * c(3) / array_tmp2[1] / c(4); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit ln LINEAR $eq_no = 1 > array_tmp3[kkk] := neg(array_tmp2[2]) * array_tmp3[kkk - 1] * c(kkk - 2)/ array_tmp2[1] / c(kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := ln(array_tmp2[1]); array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/array_tmp2[1]; array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := neg(array_tmp2[2])*array_tmp3[2]*c(1)/(array_tmp2[1]*c(2)); array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := neg(array_tmp2[2])*array_tmp3[3]*c(2)/(array_tmp2[1]*c(3)); array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := neg(array_tmp2[2])*array_tmp3[4]*c(3)/(array_tmp2[1]*c(4)); array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := neg(array_tmp2[2])*array_tmp3[kkk - 1]* c(kkk - 2)/(array_tmp2[1]*c(kkk - 1)); array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(30) ,(0..30+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=30) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_0D1); > array_const_0D1[1] := c(0.1); > zero_ats_ar(array_const_0D2); > array_const_0D2[1] := c(0.2); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_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_h := 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 := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/lin_lnpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(20.0);"); > omniout_str(ALWAYS,"x_end := c(30.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_min_h := c(0.001);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-2.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=100000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#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 := c(20.0); > x_end := c(30.0) ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_min_h := c(0.001); > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(-2.0); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(1.0); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=100000; > 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 > glob_check_sign := c(my_check_sign(x_start,x_end)); > glob__pi := arccos(glob__m1); > glob_prec = expt(10.0,c(-Digits)); > if (glob_optimize) then # if number 9 > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > found_h := false; > glob_min_pole_est := glob_larger_float; > last_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; > glob_min_h := float_abs(glob_min_h) * glob_check_sign; > glob_max_h := float_abs(glob_max_h) * glob_check_sign; > glob_h := float_abs(glob_min_h) * glob_check_sign; > glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign)); > display_max := c(x_end) - c(x_start)/glob__10; > if ((glob_display_interval) > (display_max)) then # if number 10 > glob_display_interval := c(display_max); > fi;# end if 10; > chk_data(); > min_value := glob_larger_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := glob_small_float; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > 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 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > 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 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > glob_h := glob_check_sign * float_abs(glob_min_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 10; > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if ( not found_h) then # if number 10 > est_answer := est_size_answer(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (estimated_step_error < est_needed_step_err) then # if number 11 > omniout_str(ALWAYS,"Double H and LOOP"); > glob_h := glob_h*glob__2; > else > omniout_str(ALWAYS,"Found H for OPTIMAL"); > found_h := true; > glob_h_reason := 3; > glob_h := glob_h/glob__2; > fi;# end if 11; > fi;# end if 10; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 10 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 10; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MAX H"); > glob_h := glob_check_sign * float_abs(glob_max_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 9; > #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 > 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; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > atomall(); > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (reached_interval()) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2015-05-01T22:07:56-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"lin_ln") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > 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 > 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 > 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," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"lin_ln diffeq.mxt") > ; > logitem_str(html_log_file,"lin_ln maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > fi;# end if 14 > #END OUTFILEMAIN > end; 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; 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_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_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 30 do term := 1; while term <= 30 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_0D1); array_const_0D1[1] := c(0.1); zero_ats_ar(array_const_0D2); array_const_0D2[1] := c(0.2); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_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_h := 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 := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/lin_lnpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(20.0);"); omniout_str(ALWAYS, "x_end := c(30.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_min_h := c(0.001);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-2.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=100000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(\ c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#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 := c(20.0); x_end := c(30.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_min_h := c(0.001); glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(-2.0); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(1.0); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 100000; 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; glob_check_sign := c(my_check_sign(x_start, x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0, c(-Digits)); if glob_optimize then omniout_str(ALWAYS, "START of Optimize"); found_h := false; glob_min_pole_est := glob_larger_float; last_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; glob_min_h := float_abs(glob_min_h)*glob_check_sign; glob_max_h := float_abs(glob_max_h)*glob_check_sign; glob_h := float_abs(glob_min_h)*glob_check_sign; glob_display_interval := c(float_abs(c(glob_display_interval))*glob_check_sign); display_max := c(x_end) - c(x_start)/glob__10; if display_max < glob_display_interval then glob_display_interval := c(display_max) end if; chk_data(); min_value := glob_larger_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := glob_small_float; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); 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; atomall(); if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); glob_h := float_abs(glob_min_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if; if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"); glob_h_reason := 2; glob_h := glob_display_interval; found_h := true end if; if glob_look_poles then check_for_pole() end if; if not found_h then est_answer := est_size_answer(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if estimated_step_error < est_needed_step_err then omniout_str(ALWAYS, "Double H and LOOP"); glob_h := glob_h*glob__2 else omniout_str(ALWAYS, "Found H for OPTIMAL"); found_h := true; glob_h_reason := 3; glob_h := glob_h/glob__2 end if end if; opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR MAX H"); glob_h := float_abs(glob_max_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if else found_h := true; glob_h := glob_check_sign*glob_h end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; 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; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec - glob_orig_start_sec < glob_max_sec do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); track_estimated_error(); atomall(); track_estimated_error(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = ln ( 0.1 * \ x + 0.2 ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2015-05-01T22:07:56-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "lin_ln"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ln\ ( 0.1 * x + 0.2 ) ; "); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); 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 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 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, " 308.maple.seems.ok "); logitem_str(html_log_file, "lin_ln diffeq.mxt"); logitem_str(html_log_file, "lin_ln maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/lin_lnpostode.ode################# diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(20.0); x_end := c(30.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_min_h := c(0.001); glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(-2.0); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(1.0); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=100000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 20 y[1] (closed_form) = -4.653938071986056271853946615743 y[1] (numeric) = -4.653938071986056271853946615743 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4.1MB, alloc=40.3MB, time=0.14 TOP MAIN SOLVE Loop x[1] = 20.01 y[1] (closed_form) = -4.646051225999415219345774709019 y[1] (numeric) = -4.6460512259994152193457747090191 absolute error = 1e-31 relative error = 2.1523654203465854471529329129402e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.02 y[1] (closed_form) = -4.638159836623249387277872764637 y[1] (numeric) = -4.6381598366232493872778727646372 absolute error = 2e-31 relative error = 4.3120549322338003199372180464529e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.03 y[1] (closed_form) = -4.630263905920860245762876704971 y[1] (numeric) = -4.630263905920860245762876704971 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.04 y[1] (closed_form) = -4.622363435953676090439722877789 y[1] (numeric) = -4.6223634359536760904397228777887 absolute error = 3e-31 relative error = 6.4901863333925547270051188783109e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.05 y[1] (closed_form) = -4.614458428781254592167020495606 y[1] (numeric) = -4.6144584287812545921670204956053 absolute error = 7e-31 relative error = 1.5169710829638574815761474036165e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.06 y[1] (closed_form) = -4.606548886461285342091129181895 y[1] (numeric) = -4.6065488864612853420911291818944 absolute error = 6e-31 relative error = 1.3024935038970470698882706141638e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.07 y[1] (closed_form) = -4.598634811049592392099425068955 y[1] (numeric) = -4.5986348110495923920994250689541 absolute error = 9e-31 relative error = 1.9571025684350525832714088476749e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.08 y[1] (closed_form) = -4.590716204600136790669210391691 y[1] (numeric) = -4.5907162046001367906692103916906 absolute error = 4e-31 relative error = 8.7132373723990858327058086717977e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.09 y[1] (closed_form) = -4.582793069165019114122693111398 y[1] (numeric) = -4.5827930691650191141226931113976 absolute error = 4e-31 relative error = 8.7283015829662946112357407191838e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.1 y[1] (closed_form) = -4.574865406794481993298434783459 y[1] (numeric) = -4.5748654067944819932984347834587 absolute error = 3e-31 relative error = 6.5575699681666500901856272679924e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.11 y[1] (closed_form) = -4.566933219536912635649636652446 y[1] (numeric) = -4.5669332195369126356496366524453 absolute error = 7e-31 relative error = 1.5327572494501683374377851896081e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.12 y[1] (closed_form) = -4.558996509438845342779605817013 y[1] (numeric) = -4.5589965094388453427796058170121 absolute error = 9e-31 relative error = 1.9741186424176020854418770797290e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.13 y[1] (closed_form) = -4.551055278544964023424715254968 y[1] (numeric) = -4.5510552785449640234247152549671 absolute error = 9e-31 relative error = 1.9775633230448094625178821471294e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=45.2MB, alloc=44.3MB, time=0.58 TOP MAIN SOLVE Loop x[1] = 20.14 y[1] (closed_form) = -4.543109528898104701895143535609 y[1] (numeric) = -4.5431095288981047018951435356083 absolute error = 7e-31 relative error = 1.5407949017020055551091620773864e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.15 y[1] (closed_form) = -4.535159262539258021983652171543 y[1] (numeric) = -4.5351592625392580219836521715423 absolute error = 7e-31 relative error = 1.5434959600692535550548205096450e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.16 y[1] (closed_form) = -4.527204481507571746352630775412 y[1] (numeric) = -4.5272044815075717463526307754106 absolute error = 1.4e-30 relative error = 3.0924160941230471808805809313725e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.17 y[1] (closed_form) = -4.519245187840353251409612487949 y[1] (numeric) = -4.5192451878403532514096124879482 absolute error = 8e-31 relative error = 1.7702071181101422042910065460712e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.18 y[1] (closed_form) = -4.511281383573072017681434532236 y[1] (numeric) = -4.5112813835730720176814345322344 absolute error = 1.6e-30 relative error = 3.5466641602673681003766261126580e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.19 y[1] (closed_form) = -4.503313070739362115697191224598 y[1] (numeric) = -4.5033130707393621156971912245968 absolute error = 1.2e-30 relative error = 2.6647048098811878104796660899568e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.2 y[1] (closed_form) = -4.495340251371024687390099335036 y[1] (numeric) = -4.4953402513710246873900993350352 absolute error = 8e-31 relative error = 1.7796205743403063335177114735505e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.21 y[1] (closed_form) = -4.487362927498030423028368338973 y[1] (numeric) = -4.4873629274980304230283683389719 absolute error = 1.1e-30 relative error = 2.4513283587100339523151312834675e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.22 y[1] (closed_form) = -4.479381101148522033685140837267 y[1] (numeric) = -4.4793811011485220336851408372665 absolute error = 5e-31 relative error = 1.1162256318664179449337990718095e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.23 y[1] (closed_form) = -4.471394774348816719257541242461 y[1] (numeric) = -4.47139477434881671925754124246 absolute error = 1.0e-30 relative error = 2.2364386292544100948404973179788e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.24 y[1] (closed_form) = -4.463403949123408632044843735829 y[1] (numeric) = -4.4634039491234086320448437358286 absolute error = 4e-31 relative error = 8.9617700875709020915221840073503e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.25 y[1] (closed_form) = -4.455408627494971335895743491712 y[1] (numeric) = -4.4554086274949713358957434917112 absolute error = 8e-31 relative error = 1.7955704333449557025136918447754e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.26 y[1] (closed_form) = -4.447408811484360260934688242435 y[1] (numeric) = -4.4474088114843602609346882424348 absolute error = 2e-31 relative error = 4.4970005789336984848106489286224e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=86.1MB, alloc=44.3MB, time=1.02 TOP MAIN SOLVE Loop x[1] = 20.27 y[1] (closed_form) = -4.439404503110615153877200418682 y[1] (numeric) = -4.4394045031106151538772004186818 absolute error = 2e-31 relative error = 4.5051087338372388690107778353706e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.28 y[1] (closed_form) = -4.431395704390962523944093346025 y[1] (numeric) = -4.431395704390962523944093346024 absolute error = 1.0e-30 relative error = 2.2566253765357136897186709403831e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.29 y[1] (closed_form) = -4.423382417340818084384458308287 y[1] (numeric) = -4.4233824173408180843844583082862 absolute error = 8e-31 relative error = 1.8085707373248814869155696967209e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.3 y[1] (closed_form) = -4.415364643973789189617272702097 y[1] (numeric) = -4.4153646439737891896172727020956 absolute error = 1.4e-30 relative error = 3.1707460490511432884190711168601e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.31 y[1] (closed_form) = -4.407342386301677268001453004124 y[1] (numeric) = -4.4073423863016772680014530041227 absolute error = 1.3e-30 relative error = 2.9496233468052975739703458303252e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.32 y[1] (closed_form) = -4.399315646334480250244149852818 y[1] (numeric) = -4.3993156463344802502441498528178 absolute error = 2e-31 relative error = 4.5461616323584431248965205895450e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.33 y[1] (closed_form) = -4.391284426080394993457056209616 y[1] (numeric) = -4.3912844260803949934570562096158 absolute error = 2e-31 relative error = 4.5544761075409882646335155459940e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.34 y[1] (closed_form) = -4.383248727545819700870473310299 y[1] (numeric) = -4.3832487275458197008704733102977 absolute error = 1.3e-30 relative error = 2.9658367133727996385901170904301e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.35 y[1] (closed_form) = -4.375208552735356337214852945186 y[1] (numeric) = -4.3752085527353563372148529451851 absolute error = 9e-31 relative error = 2.0570447994697874394662765398617e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.36 y[1] (closed_form) = -4.367163903651813039779508516804 y[1] (numeric) = -4.3671639036518130397795085168031 absolute error = 9e-31 relative error = 2.0608340329233394253302826850105e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.37 y[1] (closed_form) = -4.359114782296206525158161315281 y[1] (numeric) = -4.3591147822962065251581613152801 absolute error = 9e-31 relative error = 2.0646393704868587115730034806094e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.38 y[1] (closed_form) = -4.351061190667764491690962524773 y[1] (numeric) = -4.351061190667764491690962524772 absolute error = 1.0e-30 relative error = 2.2982899025755332141049887833192e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.39 y[1] (closed_form) = -4.343003130763928017612605628314 y[1] (numeric) = -4.3430031307639280176126056283134 absolute error = 6e-31 relative error = 1.3815325062739728237807531335984e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=127.1MB, alloc=44.3MB, time=1.44 TOP MAIN SOLVE Loop x[1] = 20.4 y[1] (closed_form) = -4.334940604580353954916118113417 y[1] (numeric) = -4.3349406045803539549161181134157 absolute error = 1.3e-30 relative error = 2.9988876863189389320858977924163e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.41 y[1] (closed_form) = -4.326873614110917318941895696169 y[1] (numeric) = -4.326873614110917318941895696168 absolute error = 1.0e-30 relative error = 2.3111375306613369505719635391605e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.42 y[1] (closed_form) = -4.318802161347713673701516677257 y[1] (numeric) = -4.318802161347713673701516677256 absolute error = 1.0e-30 relative error = 2.3154568388192681550056424774375e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.43 y[1] (closed_form) = -4.310726248281061512945848518924 y[1] (numeric) = -4.3107262482810615129458485189228 absolute error = 1.2e-30 relative error = 2.7837536667481729595451696848298e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.44 y[1] (closed_form) = -4.302645876899504636986933287157 y[1] (numeric) = -4.3026458768995046369869332871557 absolute error = 1.3e-30 relative error = 3.0213966875116913919611341317178e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.45 y[1] (closed_form) = -4.294561049189814525283113238018 y[1] (numeric) = -4.294561049189814525283113238017 absolute error = 1.0e-30 relative error = 2.3285266842082821239754468788305e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.46 y[1] (closed_form) = -4.286471767136992704796832540766 y[1] (numeric) = -4.2864717671369927047968325407649 absolute error = 1.1e-30 relative error = 2.5662130996250762256326549875356e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.47 y[1] (closed_form) = -4.278378032724273114134525922943 y[1] (numeric) = -4.2783780327242731141345259229417 absolute error = 1.3e-30 relative error = 3.0385346737866924026433895171963e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.48 y[1] (closed_form) = -4.270279847933124463477979893672 y[1] (numeric) = -4.2702798479331244634779798936707 absolute error = 1.3e-30 relative error = 3.0442969695047463767924911407836e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.49 y[1] (closed_form) = -4.262177214743252590316527150712 y[1] (numeric) = -4.2621772147432525903165271507112 absolute error = 8e-31 relative error = 1.8769749817833204442705349036795e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.5 y[1] (closed_form) = -4.254070135132602810989409804104 y[1] (numeric) = -4.2540701351326028109894098041033 absolute error = 7e-31 relative error = 1.6454829792743424836631174708133e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.51 y[1] (closed_form) = -4.245958611077362268047622154207 y[1] (numeric) = -4.2459586110773622680476221542067 absolute error = 3e-31 relative error = 7.0655422598167652336058660261989e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.52 y[1] (closed_form) = -4.237842644551962273444518944328 y[1] (numeric) = -4.2378426445519622734445189443271 absolute error = 9e-31 relative error = 2.1237220809909301417685959292728e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=168.2MB, alloc=44.3MB, time=1.87 TOP MAIN SOLVE Loop x[1] = 20.53 y[1] (closed_form) = -4.22972223752908064756445026766 y[1] (numeric) = -4.2297222375290806475644502676588 absolute error = 1.2e-30 relative error = 2.8370657282238373676281720943293e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.54 y[1] (closed_form) = -4.221597391979644054098659644669 y[1] (numeric) = -4.2215973919796440540986596446682 absolute error = 8e-31 relative error = 1.8950172783408273597872288812539e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.55 y[1] (closed_form) = -4.21346810987283033077765720004 y[1] (numeric) = -4.2134681098728303307776572000386 absolute error = 1.4e-30 relative error = 3.3226785239446238336006345218617e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.56 y[1] (closed_form) = -4.20533439317607081596925535762 y[1] (numeric) = -4.2053343931760708159692553576186 absolute error = 1.4e-30 relative error = 3.3291050582606646367454920679759e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.57 y[1] (closed_form) = -4.197196243855052671151430037182 y[1] (numeric) = -4.1971962438550526711514300371815 absolute error = 5e-31 relative error = 1.1912714368122053462648450710779e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.58 y[1] (closed_form) = -4.189053663873721199269145977963 y[1] (numeric) = -4.1890536638737211992691459779622 absolute error = 8e-31 relative error = 1.9097392017179848608646627362149e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.59 y[1] (closed_form) = -4.180906655194282158984260530603 y[1] (numeric) = -4.1809066551942821589842605306025 absolute error = 5e-31 relative error = 1.1959128515313995856832771756608e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.6 y[1] (closed_form) = -4.172755219777204074827596051056 y[1] (numeric) = -4.1727552197772040748275960510556 absolute error = 4e-31 relative error = 9.5859924422156064200811419830620e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.61 y[1] (closed_form) = -4.164599359581220543262246896894 y[1] (numeric) = -4.1645993595812205432622468968936 absolute error = 4e-31 relative error = 9.6047654399155164959304431608105e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.62 y[1] (closed_form) = -4.156439076563332534667162968076 y[1] (numeric) = -4.1564390765633325346671629680747 absolute error = 1.3e-30 relative error = 3.1276772642482195832166679424218e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.63 y[1] (closed_form) = -4.148274372678810691250027750294 y[1] (numeric) = -4.1482743726788106912500277502928 absolute error = 1.2e-30 relative error = 2.8927691184155736444864045445129e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.64 y[1] (closed_form) = -4.140105249881197620898424909281 y[1] (numeric) = -4.1401052498811976208984249092798 absolute error = 1.2e-30 relative error = 2.8984770375932703565537050104678e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.65 y[1] (closed_form) = -4.131931710122310186978263648611 y[1] (numeric) = -4.13193171012231018697826364861 absolute error = 1.0e-30 relative error = 2.4201755260141963669803695916737e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=209.2MB, alloc=44.3MB, time=2.30 TOP MAIN SOLVE Loop x[1] = 20.66 y[1] (closed_form) = -4.1237537553522417940884092814 y[1] (numeric) = -4.1237537553522417940884092813993 absolute error = 7e-31 relative error = 1.6974825402498058967123409024256e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.67 y[1] (closed_form) = -4.115571387519364669780441777537 y[1] (numeric) = -4.1155713875193646697804417775363 absolute error = 7e-31 relative error = 1.7008573879262016466089508076881e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.68 y[1] (closed_form) = -4.107384608570332142252441432478 y[1] (numeric) = -4.1073846085703321422524414324775 absolute error = 5e-31 relative error = 1.2173196514315134414101280227780e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.69 y[1] (closed_form) = -4.099193420450080914025677260917 y[1] (numeric) = -4.0991934204500809140256772609163 absolute error = 7e-31 relative error = 1.7076530141462361077253971760560e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.7 y[1] (closed_form) = -4.09099782510183333161305024855 y[1] (numeric) = -4.0909978251018333316130502485488 absolute error = 1.2e-30 relative error = 2.9332697090107339211337259818472e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.71 y[1] (closed_form) = -4.082797824467099651188120197447 y[1] (numeric) = -4.0827978244670996511881201974456 absolute error = 1.4e-30 relative error = 3.4290211276448219806243359723390e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.72 y[1] (closed_form) = -4.074593420485680300263521574941 y[1] (numeric) = -4.0745934204856803002635215749404 absolute error = 6e-31 relative error = 1.4725395593665923469382424112181e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.73 y[1] (closed_form) = -4.066384615095668135387550522224 y[1] (numeric) = -4.0663846150956681353875505222232 absolute error = 8e-31 relative error = 1.9673495641070310648778534311539e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.74 y[1] (closed_form) = -4.058171410233450695867681996707 y[1] (numeric) = -4.0581714102334506958676819967056 absolute error = 1.4e-30 relative error = 3.4498296362485671522664489271709e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.75 y[1] (closed_form) = -4.049953807833712453529752911473 y[1] (numeric) = -4.0499538078337124535297529114721 absolute error = 9e-31 relative error = 2.2222475680072082678265925106100e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.76 y[1] (closed_form) = -4.041731809829437058521524095489 y[1] (numeric) = -4.0417318098294370585215240954883 absolute error = 7e-31 relative error = 1.7319308478054122101285591438664e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.77 y[1] (closed_form) = -4.033505418151909581169310929453 y[1] (numeric) = -4.0335054181519095811693109294521 absolute error = 9e-31 relative error = 2.2313097583797624315340721134138e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.78 y[1] (closed_form) = -4.025274634730718749896349613997 y[1] (numeric) = -4.025274634730718749896349613996 absolute error = 1.0e-30 relative error = 2.4843025401840627685908041327081e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=250.2MB, alloc=44.3MB, time=2.72 TOP MAIN SOLVE Loop x[1] = 20.79 y[1] (closed_form) = -4.017039461493759185211543199146 y[1] (numeric) = -4.0170394614937591852115431991452 absolute error = 8e-31 relative error = 1.9915164082120204198177812568325e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.8 y[1] (closed_form) = -4.008799900367233629777208746238 y[1] (numeric) = -4.0087999003672336297772087462368 absolute error = 1.2e-30 relative error = 2.9934145625229928549880292001635e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.81 y[1] (closed_form) = -4.000555953275655174564424305684 y[1] (numeric) = -4.0005559532756551745644243056838 absolute error = 2e-31 relative error = 4.9993051549807721598945847671306e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.82 y[1] (closed_form) = -3.992307622141849481104551775767 y[1] (numeric) = -3.9923076221418494811045517757666 absolute error = 4e-31 relative error = 1.0019267998827263725650576074446e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.83 y[1] (closed_form) = -3.984054908886956999845489158821 y[1] (numeric) = -3.9840549088869569998454891588202 absolute error = 8e-31 relative error = 2.0080044534915798390032448011475e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.84 y[1] (closed_form) = -3.975797815430435184621183251502 y[1] (numeric) = -3.9757978154304351846211832515015 absolute error = 5e-31 relative error = 1.2576092226306233185742834112912e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.85 y[1] (closed_form) = -3.967536343690060703242911395038 y[1] (numeric) = -3.9675363436900607032429113950371 absolute error = 9e-31 relative error = 2.2684102224579570150259498461289e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.86 y[1] (closed_form) = -3.959270495581931644220818569227 y[1] (numeric) = -3.9592704955819316442208185692268 absolute error = 2e-31 relative error = 5.0514356173233397041581578681275e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.87 y[1] (closed_form) = -3.951000273020469719624173840255 y[1] (numeric) = -3.9510002730204697196241738402547 absolute error = 3e-31 relative error = 7.5930139020379088529419673447054e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.88 y[1] (closed_form) = -3.942725677918422464088787966826 y[1] (numeric) = -3.9427256779184224640887879668253 absolute error = 7e-31 relative error = 1.7754215159335349813991310751530e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.89 y[1] (closed_form) = -3.934446712186865429980011831536 y[1] (numeric) = -3.934446712186865429980011831535 absolute error = 1.0e-30 relative error = 2.5416534347828912310984988810008e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.9 y[1] (closed_form) = -3.926163377735204378719713294487 y[1] (numeric) = -3.9261633777352043787197132944866 absolute error = 4e-31 relative error = 1.0188063040584388661799155018202e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.91 y[1] (closed_form) = -3.917875676471177468285608063706 y[1] (numeric) = -3.9178756764711774682856080637051 memory used=291.3MB, alloc=44.3MB, time=3.14 absolute error = 9e-31 relative error = 2.2971632443697859794668713322010e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.92 y[1] (closed_form) = -3.909583610300857436891298241712 y[1] (numeric) = -3.909583610300857436891298241711 absolute error = 1.0e-30 relative error = 2.5578171480083685149308245169910e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.93 y[1] (closed_form) = -3.901287181128653782855350339367 y[1] (numeric) = -3.9012871811286537828553503393664 absolute error = 6e-31 relative error = 1.5379539422330305007798454800125e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.94 y[1] (closed_form) = -3.892986390857314940667722746664 y[1] (numeric) = -3.8929863908573149406677227466638 absolute error = 2e-31 relative error = 5.1374441089673556265725629104431e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.95 y[1] (closed_form) = -3.884681241387930453261830915173 y[1] (numeric) = -3.8846812413879304532618309151728 absolute error = 2e-31 relative error = 5.1484275690157632059793522485482e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.96 y[1] (closed_form) = -3.876371734619933140500516838226 y[1] (numeric) = -3.8763717346199331405005168382251 absolute error = 9e-31 relative error = 2.3217587517783362325811181053764e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.97 y[1] (closed_form) = -3.868057872451101263884167812333 y[1] (numeric) = -3.8680578724511012638841678123325 absolute error = 5e-31 relative error = 1.2926383639734977574984928324394e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.98 y[1] (closed_form) = -3.859739656777560687489207926588 y[1] (numeric) = -3.8597396567775606874892079265873 absolute error = 7e-31 relative error = 1.8135938230207464386934307545545e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.99 y[1] (closed_form) = -3.851417089493787035145164255642 y[1] (numeric) = -3.8514170894937870351451642556418 absolute error = 2e-31 relative error = 5.1928938194093930700451819537716e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 22.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21 y[1] (closed_form) = -3.843090172492607843858488326106 y[1] (numeric) = -3.8430901724926078438584883261054 absolute error = 6e-31 relative error = 1.5612436166462448407692644209547e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.01 y[1] (closed_form) = -3.834758907665204713491292085566 y[1] (numeric) = -3.8347589076652047134912920855657 absolute error = 3e-31 relative error = 7.8231776031691958943515251125129e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.02 y[1] (closed_form) = -3.826423296901115452703136327745 y[1] (numeric) = -3.8264232969011154527031363277444 absolute error = 6e-31 relative error = 1.5680439759132731724792648370431e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.03 y[1] (closed_form) = -3.818083342088236221163988316297 y[1] (numeric) = -3.8180833420882362211639883162963 absolute error = 7e-31 relative error = 1.8333806187089326826564145965008e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=332.3MB, alloc=44.3MB, time=3.58 TOP MAIN SOLVE Loop x[1] = 21.04 y[1] (closed_form) = -3.809739045112823668046444203222 y[1] (numeric) = -3.8097390451128236680464442032218 absolute error = 2e-31 relative error = 5.2497033952118652806038386890559e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.05 y[1] (closed_form) = -3.801390407859497066805290755582 y[1] (numeric) = -3.801390407859497066805290755582 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.06 y[1] (closed_form) = -3.793037432211240446252459885941 y[1] (numeric) = -3.793037432211240446252459885941 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.07 y[1] (closed_form) = -3.784680120049404717935408527503 y[1] (numeric) = -3.7846801200494047179354085275027 absolute error = 3e-31 relative error = 7.9266936830604283498675219551810e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.08 y[1] (closed_form) = -3.776318473253709799826935504028 y[1] (numeric) = -3.7763184732537097998269355040283 absolute error = 3e-31 relative error = 7.9442452252052066621704919045264e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.09 y[1] (closed_form) = -3.767952493702246736334426217108 y[1] (numeric) = -3.7679524937022467363344262171077 absolute error = 3e-31 relative error = 7.9618838215561315653876365048755e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.1 y[1] (closed_form) = -3.759582183271479814636495208975 y[1] (numeric) = -3.7595821832714798146364952089753 absolute error = 3e-31 relative error = 7.9796101102636002481539940601930e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.11 y[1] (closed_form) = -3.751207543836248677354975957611 y[1] (numeric) = -3.751207543836248677354975957611 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.12 y[1] (closed_form) = -3.742828577269770431570186622115 y[1] (numeric) = -3.7428285772697704315701866221152 absolute error = 2e-31 relative error = 5.3435522325174518961454249870661e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.13 y[1] (closed_form) = -3.734445285443641754187379880084 y[1] (numeric) = -3.7344452854436417541873798800843 absolute error = 3e-31 relative error = 8.0333216065411126007494095855744e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.14 y[1] (closed_form) = -3.726057670227840993662264484725 y[1] (numeric) = -3.7260576702278409936622644847246 absolute error = 4e-31 relative error = 1.0735206896986669504076828270986e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.15 y[1] (closed_form) = -3.717665733490730268093465717504 y[1] (numeric) = -3.7176657334907302680934657175038 absolute error = 2e-31 relative error = 5.3797198117703952956499397547967e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.16 y[1] (closed_form) = -3.70926947709905755968977152205 y[1] (numeric) = -3.7092694770990575596897715220495 absolute error = 5e-31 relative error = 1.3479743197063147626805364523088e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=373.4MB, alloc=44.3MB, time=4.00 TOP MAIN SOLVE Loop x[1] = 21.17 y[1] (closed_form) = -3.700868902917958805619990776541 y[1] (numeric) = -3.700868902917958805619990776541 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.18 y[1] (closed_form) = -3.692464012810959985253229894784 y[1] (numeric) = -3.692464012810959985253229894784 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.19 y[1] (closed_form) = -3.684054808639979203797373740321 y[1] (numeric) = -3.684054808639979203797373740321 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.2 y[1] (closed_form) = -3.675641292265328772343536693069 y[1] (numeric) = -3.675641292265328772343536693069 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.21 y[1] (closed_form) = -3.667223465545717284324229623908 y[1] (numeric) = -3.6672234655457172843242296239076 absolute error = 4e-31 relative error = 1.0907434568906922182368804779057e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.22 y[1] (closed_form) = -3.65880133033825168839296850914 y[1] (numeric) = -3.6588013303382516883929685091401 absolute error = 1e-31 relative error = 2.7331355537348928110131417270330e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.23 y[1] (closed_form) = -3.650374888498439357733030453614 y[1] (numeric) = -3.6503748884984393577330304536135 absolute error = 5e-31 relative error = 1.3697223306444344795857028975401e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.24 y[1] (closed_form) = -3.641944141880190155803042988307 y[1] (numeric) = -3.6419441418801901558030429883067 absolute error = 3e-31 relative error = 8.2373586280519391485552779773827e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.25 y[1] (closed_form) = -3.633509092335818498527072665158 y[1] (numeric) = -3.6335090923358184985270726651581 absolute error = 1e-31 relative error = 2.7521604448694120982533525149087e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.26 y[1] (closed_form) = -3.625069741716045412936859188623 y[1] (numeric) = -3.6250697417160454129368591886228 absolute error = 2e-31 relative error = 5.5171352346265055270541809817073e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.27 y[1] (closed_form) = -3.616626091870000592273821599692 y[1] (numeric) = -3.6166260918700005922738215996924 absolute error = 4e-31 relative error = 1.1060031914805363185539205587800e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.28 y[1] (closed_form) = -3.608178144645224447558443363692 y[1] (numeric) = -3.6081781446452244475584433636922 absolute error = 2e-31 relative error = 5.5429635672732306186458490051899e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.29 y[1] (closed_form) = -3.59972590188767015563462360788 y[1] (numeric) = -3.59972590188767015563462360788 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=414.6MB, alloc=44.3MB, time=4.42 TOP MAIN SOLVE Loop x[1] = 21.3 y[1] (closed_form) = -3.591269365441705703696562208506 y[1] (numeric) = -3.591269365441705703696562208506 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.31 y[1] (closed_form) = -3.582808537150115930305726939346 y[1] (numeric) = -3.5828085371501159303057269393457 absolute error = 3e-31 relative error = 8.3733193356357773405026649490221e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.32 y[1] (closed_form) = -3.574343418854104562905431464604 y[1] (numeric) = -3.5743434188541045629054314646042 absolute error = 2e-31 relative error = 5.5954332464259355990048455076474e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.33 y[1] (closed_form) = -3.565874012393296251840533588282 y[1] (numeric) = -3.5658740123932962518405335882823 absolute error = 3e-31 relative error = 8.4130846731359967441380741127965e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.34 y[1] (closed_form) = -3.557400319605738600889743859419 y[1] (numeric) = -3.5574003196057386008897438594186 absolute error = 4e-31 relative error = 1.1244166078118849623813835856624e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.35 y[1] (closed_form) = -3.548922342327904194318015377863 y[1] (numeric) = -3.548922342327904194318015377863 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.36 y[1] (closed_form) = -3.540440082394692620456466448201 y[1] (numeric) = -3.5404400823946926204564664482009 absolute error = 1e-31 relative error = 2.8245076225767313197382126468599e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.37 y[1] (closed_form) = -3.531953541639432491817268589938 y[1] (numeric) = -3.531953541639432491817268589938 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.38 y[1] (closed_form) = -3.523462721893883461750913329875 y[1] (numeric) = -3.5234627218938834617509133298746 absolute error = 4e-31 relative error = 1.1352468624529606892493881298772e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.39 y[1] (closed_form) = -3.514967624988238237653252177547 y[1] (numeric) = -3.5149676249882382376532521775471 absolute error = 1e-31 relative error = 2.8449764171109433579776317344987e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.4 y[1] (closed_form) = -3.506468252751124590729685216504 y[1] (numeric) = -3.5064682527511245907296852165042 absolute error = 2e-31 relative error = 5.7037447820348259166179137479030e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.41 y[1] (closed_form) = -3.497964607009607362323854832815 y[1] (numeric) = -3.4979646070096073623238548328146 absolute error = 4e-31 relative error = 1.1435221477039415248725115505375e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.42 y[1] (closed_form) = -3.489456689589190466818182247381 y[1] (numeric) = -3.4894566895891904668181822473808 absolute error = 2e-31 relative error = 5.7315512926898014919788391011209e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=455.6MB, alloc=44.3MB, time=4.86 TOP MAIN SOLVE Loop x[1] = 21.43 y[1] (closed_form) = -3.480944502313818891113565720166 y[1] (numeric) = -3.4809445023138188911135657201658 absolute error = 2e-31 relative error = 5.7455670398381239468377331988965e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.44 y[1] (closed_form) = -3.47242804700588069069554055214 y[1] (numeric) = -3.4724280470058806906955405521405 absolute error = 5e-31 relative error = 1.4399146454053313627501616290247e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.45 y[1] (closed_form) = -3.463907325486208982294182324419 y[1] (numeric) = -3.463907325486208982294182324419 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.46 y[1] (closed_form) = -3.455382339574083933145016183504 y[1] (numeric) = -3.4553823395740839331450161835035 absolute error = 5e-31 relative error = 1.4470178720124813049534843669588e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.47 y[1] (closed_form) = -3.446853091087234746858176406594 y[1] (numeric) = -3.4468530910872347468581764065938 absolute error = 2e-31 relative error = 5.8023940886008099439795733204763e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.48 y[1] (closed_form) = -3.438319581841841645903041961355 y[1] (numeric) = -3.4383195818418416459030419613548 absolute error = 2e-31 relative error = 5.8167949557749907601011534951305e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.49 y[1] (closed_form) = -3.429781813652537850715555310185 y[1] (numeric) = -3.4297818136525378507155553101855 absolute error = 5e-31 relative error = 1.4578186810884223821352379712820e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.5 y[1] (closed_form) = -3.421239788332411555435413299704 y[1] (numeric) = -3.421239788332411555435413299704 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.51 y[1] (closed_form) = -3.412693507693007900280300621674 y[1] (numeric) = -3.4126935076930079002803006216743 absolute error = 3e-31 relative error = 8.7907103091364624871051884220013e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.52 y[1] (closed_form) = -3.404142973544330940564318031758 y[1] (numeric) = -3.404142973544330940564318031759 absolute error = 1.0e-30 relative error = 2.9375969451683118515826407463348e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.53 y[1] (closed_form) = -3.395588187694845612367739267103 y[1] (numeric) = -3.3955881876948456123677392671032 absolute error = 2e-31 relative error = 5.8899957516866465335821093596532e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.54 y[1] (closed_form) = -3.387029151951479694865212412657 y[1] (numeric) = -3.3870291519514796948652124126579 absolute error = 9e-31 relative error = 2.6571959071608628292722630141577e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.55 y[1] (closed_form) = -3.378465868119625769319503329146 y[1] (numeric) = -3.3784658681196257693195033291471 absolute error = 1.1e-30 relative error = 3.2559156816707282424262467136747e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=496.7MB, alloc=44.3MB, time=5.28 TOP MAIN SOLVE Loop x[1] = 21.56 y[1] (closed_form) = -3.369898338003143174747860672486 y[1] (numeric) = -3.3698983380031431747478606724866 absolute error = 6e-31 relative error = 1.7804691412606060860806432097188e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.57 y[1] (closed_form) = -3.361326563404359960268064005098 y[1] (numeric) = -3.3613265634043599602680640050993 absolute error = 1.3e-30 relative error = 3.8675206811305972745624346668689e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.58 y[1] (closed_form) = -3.352750546124074834131198523744 y[1] (numeric) = -3.3527505461240748341311985237451 absolute error = 1.1e-30 relative error = 3.2808882881896708607201803815505e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.59 y[1] (closed_form) = -3.344170287961559109448182006031 y[1] (numeric) = -3.3441702879615591094481820060321 absolute error = 1.1e-30 relative error = 3.2893061814459981407837877405558e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.6 y[1] (closed_form) = -3.335585790714558646617051708491 y[1] (numeric) = -3.3355857907145586466170517084921 absolute error = 1.1e-30 relative error = 3.2977715730236243775124288604926e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.61 y[1] (closed_form) = -3.326997056179295792458001132836 y[1] (numeric) = -3.3269970561792957924580011328365 absolute error = 5e-31 relative error = 1.5028567550768954173512884283506e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.62 y[1] (closed_form) = -3.318404086150471316063138813554 y[1] (numeric) = -3.3184040861504713160631388135543 absolute error = 3e-31 relative error = 9.0404903143672375301375825961299e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.63 y[1] (closed_form) = -3.309806882421266341367923569203 y[1] (numeric) = -3.3098068824212663413679235692043 absolute error = 1.3e-30 relative error = 3.9277216048599004301692429003967e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.64 y[1] (closed_form) = -3.301205446783344276451213001415 y[1] (numeric) = -3.3012054467833442764512130014155 absolute error = 5e-31 relative error = 1.5145982522450825158310380537106e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.65 y[1] (closed_form) = -3.292599781026852739570844419552 y[1] (numeric) = -3.2925997810268527395708444195525 absolute error = 5e-31 relative error = 1.5185568646428888856171087938837e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.66 y[1] (closed_form) = -3.283989886940425481941649815059 y[1] (numeric) = -3.2839898869404254819416498150599 absolute error = 9e-31 relative error = 2.7405687318924645827961642251250e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.67 y[1] (closed_form) = -3.27537576631118430726278900749 y[1] (numeric) = -3.275375766311184307262789007491 absolute error = 1.0e-30 relative error = 3.0530848102543871353496620205826e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.68 y[1] (closed_form) = -3.266757420924740988001267633975 y[1] (numeric) = -3.2667574209247409880012676339755 absolute error = 5e-31 relative error = 1.5305697227388923914618705853317e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=537.9MB, alloc=44.3MB, time=5.70 TOP MAIN SOLVE Loop x[1] = 21.69 y[1] (closed_form) = -3.258134852565199178438489255218 y[1] (numeric) = -3.2581348525651991784384892552188 absolute error = 8e-31 relative error = 2.4553925365309631314206577911040e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.7 y[1] (closed_form) = -3.249508063015156324486673503866 y[1] (numeric) = -3.2495080630151563244866735038662 absolute error = 2e-31 relative error = 6.1547777731754211655656345862067e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.71 y[1] (closed_form) = -3.240877054055705570281954905049 y[1] (numeric) = -3.24087705405570557028195490505 absolute error = 1.0e-30 relative error = 3.0855844986423590988373135230693e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.72 y[1] (closed_form) = -3.232241827466437661560959753982 y[1] (numeric) = -3.2322418274664376615609597539826 absolute error = 6e-31 relative error = 1.8562967501423133104886988377089e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.73 y[1] (closed_form) = -3.223602385025442845827641241394 y[1] (numeric) = -3.2236023850254428458276412413941 absolute error = 1e-31 relative error = 3.1021195561998795488522060995975e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.74 y[1] (closed_form) = -3.214958728509312769317135874271 y[1] (numeric) = -3.2149587285093127693171358742714 absolute error = 4e-31 relative error = 1.2441839344714353778772563255363e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.75 y[1] (closed_form) = -3.206310859693142370763387146559 y[1] (numeric) = -3.2063108596931423707633871465594 absolute error = 4e-31 relative error = 1.2475396725515307852270391021220e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.76 y[1] (closed_form) = -3.197658780350531771977265372074 y[1] (numeric) = -3.1976587803505317719772653720744 absolute error = 4e-31 relative error = 1.2509152085206272307028188073597e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.77 y[1] (closed_form) = -3.189002492253588165241895599666 y[1] (numeric) = -3.1890024922535881652418955996671 absolute error = 1.1e-30 relative error = 3.4493544695308706358962401327352e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.78 y[1] (closed_form) = -3.180341997172927697531888588511 y[1] (numeric) = -3.180341997172927697531888588512 absolute error = 1.0e-30 relative error = 3.1443159285665530536841015429072e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.79 y[1] (closed_form) = -3.171677296877677351563152929102 y[1] (numeric) = -3.1716772968776773515631529291027 absolute error = 7e-31 relative error = 2.2070341162674628364918148605282e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.8 y[1] (closed_form) = -3.163008393135476823679949552943 y[1] (numeric) = -3.1630083931354768236799495529438 absolute error = 8e-31 relative error = 2.5292376768148989585098020643786e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.81 y[1] (closed_form) = -3.154335287712480398585833080878 y[1] (numeric) = -3.1543352877124803985858330808787 absolute error = 7e-31 relative error = 2.2191680216329793997000675179895e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=579.1MB, alloc=44.3MB, time=6.14 TOP MAIN SOLVE Loop x[1] = 21.82 y[1] (closed_form) = -3.145657982373358820925107716304 y[1] (numeric) = -3.1456579823733588209251077163043 absolute error = 3e-31 relative error = 9.5369554376554893889864889481119e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.83 y[1] (closed_form) = -3.136976478881301163721408695055 y[1] (numeric) = -3.1369764788813011637214086950553 absolute error = 3e-31 relative error = 9.5633487219191732945786487537870e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.84 y[1] (closed_form) = -3.128290778998016693680003658292 y[1] (numeric) = -3.1282907789980166936800036582926 absolute error = 6e-31 relative error = 1.9179802722564633888196473656415e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.85 y[1] (closed_form) = -3.119600884483736733360391718174 y[1] (numeric) = -3.1196008844837367333603917181749 absolute error = 9e-31 relative error = 2.8849844365553869527833890830229e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.86 y[1] (closed_form) = -3.110906797097216520225761438238 y[1] (numeric) = -3.110906797097216520225761438239 absolute error = 1.0e-30 relative error = 3.2144968178831292080939250932055e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.87 y[1] (closed_form) = -3.102208518595737062575852451105 y[1] (numeric) = -3.1022085185957370625758524511057 absolute error = 7e-31 relative error = 2.2564569589824538543243572386552e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.88 y[1] (closed_form) = -3.093506050735106992369748985215 y[1] (numeric) = -3.0935060507351069923697489852155 absolute error = 5e-31 relative error = 1.6162890642518234632764743039939e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.89 y[1] (closed_form) = -3.084799395269664414945117169599 y[1] (numeric) = -3.0847993952696644149451171695994 absolute error = 4e-31 relative error = 1.2966807521207813721088839203919e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.9 y[1] (closed_form) = -3.076088553952278755640381631053 y[1] (numeric) = -3.0760885539522787556403816310536 absolute error = 6e-31 relative error = 1.9505290224141842673717626732890e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.91 y[1] (closed_form) = -3.067373528534352603326320591356 y[1] (numeric) = -3.0673735285343526033263205913562 absolute error = 2e-31 relative error = 6.5202362261880662609127865841171e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.92 y[1] (closed_form) = -3.058654320765823550853542413169 y[1] (numeric) = -3.0586543207658235508535424131695 absolute error = 5e-31 relative error = 1.6347058136167881139360208060425e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.93 y[1] (closed_form) = -3.049930932395166032422290331855 y[1] (numeric) = -3.0499309323951660324222903318555 absolute error = 5e-31 relative error = 1.6393813862772982171774130858218e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.94 y[1] (closed_form) = -3.041203365169393157881005946447 y[1] (numeric) = -3.0412033651693931578810059464476 absolute error = 6e-31 relative error = 1.9729032489959130662933768362028e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=620.2MB, alloc=44.3MB, time=6.56 TOP MAIN SOLVE Loop x[1] = 21.95 y[1] (closed_form) = -3.032471620834058543960065926284 y[1] (numeric) = -3.0324716208340585439600659262843 absolute error = 3e-31 relative error = 9.8929202812287903010038093080128e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.96 y[1] (closed_form) = -3.023735701133258142447090320197 y[1] (numeric) = -3.0237357011332581424470903201974 absolute error = 4e-31 relative error = 1.3228669418761865551756821291672e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.97 y[1] (closed_form) = -3.014995607809632065310204832462 y[1] (numeric) = -3.0149956078096320653102048324626 absolute error = 6e-31 relative error = 1.9900526503118017852063852369627e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.98 y[1] (closed_form) = -3.006251342604366406775623453846 y[1] (numeric) = -3.0062513426043664067756234538463 absolute error = 3e-31 relative error = 9.9792055224532531504877309877529e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.99 y[1] (closed_form) = -2.997502907257195062365901906825 y[1] (numeric) = -2.9975029072571950623659019068258 absolute error = 8e-31 relative error = 2.6688881537466929785531322263794e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 23.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22 y[1] (closed_form) = -2.988750303506401544905196481295 y[1] (numeric) = -2.9887503035064015449051964812961 absolute error = 1.1e-30 relative error = 3.6804680495037678943087929070717e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.01 y[1] (closed_form) = -2.979993533088820797497847000632 y[1] (numeric) = -2.9799935330888207974978470006324 absolute error = 4e-31 relative error = 1.3422847920927945162413499222090e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.02 y[1] (closed_form) = -2.9712325977398410034865868677 y[1] (numeric) = -2.9712325977398410034865868677006 absolute error = 6e-31 relative error = 2.0193639517027659169719273667850e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.03 y[1] (closed_form) = -2.962467499193405393396667396155 y[1] (numeric) = -2.9624674991934053933966673961548 absolute error = 2e-31 relative error = 6.7511289171764497578718825821457e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.04 y[1] (closed_form) = -2.953698239182014048872167933964 y[1] (numeric) = -2.9536982391820140488721679339649 absolute error = 9e-31 relative error = 3.0470275807498960197614637911663e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.05 y[1] (closed_form) = -2.944924819436725703610747633435 y[1] (numeric) = -2.9449248194367257036107476334353 absolute error = 3e-31 relative error = 1.0187017271883390553285933455277e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.06 y[1] (closed_form) = -2.936147241687159541303079114852 y[1] (numeric) = -2.9361472416871595413030791148529 absolute error = 9e-31 relative error = 3.0652413721692134119771762820834e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.07 y[1] (closed_form) = -2.927365507661496990583188709183 y[1] (numeric) = -2.927365507661496990583188709184 absolute error = 1.0e-30 relative error = 3.4160407963501700484800318802152e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=661.2MB, alloc=44.3MB, time=7.00 TOP MAIN SOLVE Loop x[1] = 22.08 y[1] (closed_form) = -2.91857961908648351699591244878 y[1] (numeric) = -2.9185796190864835169959124487805 absolute error = 5e-31 relative error = 1.7131621036828187746244224758783e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.09 y[1] (closed_form) = -2.909789577687430411987661503701 y[1] (numeric) = -2.9097895776874304119876615037013 absolute error = 3e-31 relative error = 1.0310023869094564443161348120132e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.1 y[1] (closed_form) = -2.900995385188216578926675334856 y[1] (numeric) = -2.9009953851882165789266753348559 absolute error = 1e-31 relative error = 3.4470926948238492305416476930328e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.11 y[1] (closed_form) = -2.892197043311290316158925453588 y[1] (numeric) = -2.8921970433112903161589254535884 absolute error = 4e-31 relative error = 1.3830316330800133681212423726759e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.12 y[1] (closed_form) = -2.883394553777671097105817340383 y[1] (numeric) = -2.8833945537776710971058173403829 absolute error = 1e-31 relative error = 3.4681344552373273742828983770191e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.13 y[1] (closed_form) = -2.874587918306951347409822782953 y[1] (numeric) = -2.8745879183069513474098227829534 absolute error = 4e-31 relative error = 1.3915037959096007147831006128357e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.14 y[1] (closed_form) = -2.865777138617298219134159645919 y[1] (numeric) = -2.8657771386172982191341596459197 absolute error = 7e-31 relative error = 2.4426184107873136382724119848127e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.15 y[1] (closed_form) = -2.856962216425455362022620880422 y[1] (numeric) = -2.8569622164254553620226208804221 absolute error = 1e-31 relative error = 3.5002212988702725217034721630311e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.16 y[1] (closed_form) = -2.84814315344674469182563942226 y[1] (numeric) = -2.84814315344674469182563942226 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.17 y[1] (closed_form) = -2.83931995139506815569866051128 y[1] (numeric) = -2.8393199513950681556986605112808 absolute error = 8e-31 relative error = 2.8175760875660699400849683101672e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.18 y[1] (closed_form) = -2.830492611982909494678877892675 y[1] (numeric) = -2.8304926119829094946788778926752 absolute error = 2e-31 relative error = 7.0659078618788353636275093615920e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.19 y[1] (closed_form) = -2.82166113692133600324637533239 y[1] (numeric) = -2.8216611369213360032463753323902 absolute error = 2e-31 relative error = 7.0880233413930215126030410055453e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.2 y[1] (closed_form) = -2.812825527920000285975699893923 y[1] (numeric) = -2.8128255279200002859756998939234 absolute error = 4e-31 relative error = 1.4220576286357438816649327110110e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=702.3MB, alloc=44.3MB, time=7.42 TOP MAIN SOLVE Loop x[1] = 22.21 y[1] (closed_form) = -2.803985786687142011283878482147 y[1] (numeric) = -2.8039857866871420112838784821473 absolute error = 3e-31 relative error = 1.0699055659424169911018626363441e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.22 y[1] (closed_form) = -2.795141914929589662280874261414 y[1] (numeric) = -2.7951419149295896622808742614146 absolute error = 6e-31 relative error = 2.1465815270245917121025456540346e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.23 y[1] (closed_form) = -2.786293914352762284728464699841 y[1] (numeric) = -2.7862939143527622847284646998409 absolute error = 1e-31 relative error = 3.5889968206469467533945836318412e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.24 y[1] (closed_form) = -2.777441786660671232113508179236 y[1] (numeric) = -2.7774417866606712321135081792358 absolute error = 2e-31 relative error = 7.2008709943282288069841642060729e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.25 y[1] (closed_form) = -2.768585533555921907841551340496 y[1] (numeric) = -2.7685855335559219078415513404968 absolute error = 8e-31 relative error = 2.8895621619914132124011845504600e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.26 y[1] (closed_form) = -2.759725156739715504556714607256 y[1] (numeric) = -2.7597251567397155045567146072568 absolute error = 8e-31 relative error = 2.8988393936485476437416595938398e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.27 y[1] (closed_form) = -2.750860657911850740593778646055 y[1] (numeric) = -2.7508606579118507405937786460558 absolute error = 8e-31 relative error = 2.9081807459025261827604864780307e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.28 y[1] (closed_form) = -2.741992038770725593568379879122 y[1] (numeric) = -2.7419920387707255935683798791227 absolute error = 7e-31 relative error = 2.5528885208354581952528587751328e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.29 y[1] (closed_form) = -2.733119301013339031111208565902 y[1] (numeric) = -2.7331193010133390311112085659026 absolute error = 6e-31 relative error = 2.1952938526230534665568980874177e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.3 y[1] (closed_form) = -2.724242446335292738752088411573 y[1] (numeric) = -2.7242424463352927387520884115736 absolute error = 6e-31 relative error = 2.2024471456537666268257787847163e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.31 y[1] (closed_form) = -2.71536147643079284495980214485 y[1] (numeric) = -2.7153614764307928449598021448502 absolute error = 2e-31 relative error = 7.3655018580763699764600224177911e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.32 y[1] (closed_form) = -2.706476392992651643343513033219 y[1] (numeric) = -2.7064763929926516433435130332191 absolute error = 1e-31 relative error = 3.6948410212965604129004888321221e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.33 y[1] (closed_form) = -2.697587197712289312021617871263 y[1] (numeric) = -2.6975871977122893120216178712629 absolute error = 1e-31 relative error = 3.7070164065430696934504270581462e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=743.5MB, alloc=44.3MB, time=7.84 TOP MAIN SOLVE Loop x[1] = 22.34 y[1] (closed_form) = -2.688693892279735630163852586762 y[1] (numeric) = -2.6886938922797356301638525867621 absolute error = 1e-31 relative error = 3.7192779842710281387865036047916e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.35 y[1] (closed_form) = -2.679796478383631691712457259684 y[1] (numeric) = -2.6797964783836316917124572596846 absolute error = 6e-31 relative error = 2.2389760000054219973545055329102e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.36 y[1] (closed_form) = -2.670894957711231616288193040846 y[1] (numeric) = -2.6708949577112316162881930408464 absolute error = 4e-31 relative error = 1.4976253515517201602255662047556e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.37 y[1] (closed_form) = -2.661989331948404257286989189816 y[1] (numeric) = -2.6619893319484042572869891898163 absolute error = 3e-31 relative error = 1.1269767177482239439615044881596e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.38 y[1] (closed_form) = -2.653079602779634907172984225403 y[1] (numeric) = -2.6530796027796349071729842254032 absolute error = 2e-31 relative error = 7.5384093183807882409825390804252e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.39 y[1] (closed_form) = -2.644165771888026999973710996683 y[1] (numeric) = -2.6441657718880269999737109966833 absolute error = 3e-31 relative error = 1.1345733432809301114412210876139e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.4 y[1] (closed_form) = -2.635247840955303810983161337853 y[1] (numeric) = -2.6352478409553038109831613378531 absolute error = 1e-31 relative error = 3.7947094935764749774777962687478e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.41 y[1] (closed_form) = -2.626325811661810153678451866098 y[1] (numeric) = -2.6263258116618101536784518660981 absolute error = 1e-31 relative error = 3.8076007004144282064143892711997e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.42 y[1] (closed_form) = -2.617399685686514073855798418023 y[1] (numeric) = -2.6173996856865140738557984180237 absolute error = 7e-31 relative error = 2.6744100407286401380378134679435e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.43 y[1] (closed_form) = -2.608469464707008540991492596858 y[1] (numeric) = -2.6084694647070085409914925968588 absolute error = 8e-31 relative error = 3.0669325856565413361862927350382e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.44 y[1] (closed_form) = -2.599535150399513136833559919494 y[1] (numeric) = -2.599535150399513136833559919494 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.45 y[1] (closed_form) = -2.59059674443887574122976510931 y[1] (numeric) = -2.5905967444388757412297651093101 absolute error = 1e-31 relative error = 3.8601144780508877985425541616863e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.46 y[1] (closed_form) = -2.581654248498574215197616177573 y[1] (numeric) = -2.5816542484985742151976161775731 absolute error = 1e-31 relative error = 3.8734853847356790064732062762416e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=784.6MB, alloc=44.3MB, time=8.28 TOP MAIN SOLVE Loop x[1] = 22.47 y[1] (closed_form) = -2.572707664250718081242005072777 y[1] (numeric) = -2.5727076642507180812420050727768 absolute error = 2e-31 relative error = 7.7739108402838496734767801647551e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.48 y[1] (closed_form) = -2.563756993366050200926108853574 y[1] (numeric) = -2.5637569933660502009261088535743 absolute error = 3e-31 relative error = 1.1701577051814066127066480759439e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.49 y[1] (closed_form) = -2.554802237513948449701161556738 y[1] (numeric) = -2.5548022375139484497011615567383 absolute error = 3e-31 relative error = 1.1742591876384408031054491269600e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.5 y[1] (closed_form) = -2.545843398362427389000693186776 y[1] (numeric) = -2.5458433983624273890006931867766 absolute error = 6e-31 relative error = 2.3567828264139903525130745503845e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.51 y[1] (closed_form) = -2.536880477578139935604818548292 y[1] (numeric) = -2.5368804775781399356048185482924 absolute error = 4e-31 relative error = 1.5767396356877809062653373437058e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.52 y[1] (closed_form) = -2.527913476826379028280144975788 y[1] (numeric) = -2.5279134768263790282801449757882 absolute error = 2e-31 relative error = 7.9116631891644567749669622733494e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.53 y[1] (closed_form) = -2.518942397771079291700854388229 y[1] (numeric) = -2.5189423977710792917008543882293 absolute error = 3e-31 relative error = 1.1909760233717893357073780188415e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.54 y[1] (closed_form) = -2.50996724207481869765650150719 y[1] (numeric) = -2.50996724207481869765650150719 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.55 y[1] (closed_form) = -2.50098801139882022355205652768 y[1] (numeric) = -2.5009880113988202235520565276803 absolute error = 3e-31 relative error = 1.1995259418784973918467642366252e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.56 y[1] (closed_form) = -2.492004707402953508205707019647 y[1] (numeric) = -2.4920047074029535082057070196477 absolute error = 7e-31 relative error = 2.8089834578583363250301379127497e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.57 y[1] (closed_form) = -2.483017331745736504949920365566 y[1] (numeric) = -2.4830173317457365049499203655664 absolute error = 4e-31 relative error = 1.6109432458885486587602048245799e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.58 y[1] (closed_form) = -2.474025886084337132041254605322 y[1] (numeric) = -2.4740258860843371320412546053222 absolute error = 2e-31 relative error = 8.0839897886655416691841195635073e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.59 y[1] (closed_form) = -2.465030372074574920384392163651 y[1] (numeric) = -2.4650303720745749203843921636509 absolute error = 1e-31 relative error = 4.0567451473565326738360030720945e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=825.7MB, alloc=44.3MB, time=8.70 TOP MAIN SOLVE Loop x[1] = 22.6 y[1] (closed_form) = -2.456030791370922658575857577585 y[1] (numeric) = -2.4560307913709226585758575775851 absolute error = 1e-31 relative error = 4.0716101911809246218862309445649e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.61 y[1] (closed_form) = -2.447027145626508035272867021555 y[1] (numeric) = -2.4470271456265080352728670215547 absolute error = 3e-31 relative error = 1.2259774091030425827719752879286e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.62 y[1] (closed_form) = -2.438019436493115278892744145878 y[1] (numeric) = -2.4380194364931152788927441458777 absolute error = 3e-31 relative error = 1.2305070070791749807956316613641e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.63 y[1] (closed_form) = -2.429007665621186794648323500223 y[1] (numeric) = -2.4290076656211867946483235002233 absolute error = 3e-31 relative error = 1.2350722652959555063247449916114e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.64 y[1] (closed_form) = -2.41999183465982479892474960712 y[1] (numeric) = -2.4199918346598247989247496071201 absolute error = 1e-31 relative error = 4.1322453475987398907945775344243e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.65 y[1] (closed_form) = -2.41097194525679295100306658159 y[1] (numeric) = -2.4109719452567929510030665815896 absolute error = 4e-31 relative error = 1.6590819349305864502597092705528e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.66 y[1] (closed_form) = -2.401947999058517982135980061388 y[1] (numeric) = -2.4019479990585179821359800613883 absolute error = 3e-31 relative error = 1.2489862399918308329372259393299e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.67 y[1] (closed_form) = -2.392919997710091321981160118026 y[1] (numeric) = -2.3929199977100913219811601180256 absolute error = 4e-31 relative error = 1.6715978820135259416030146740635e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.68 y[1] (closed_form) = -2.383887942855270722397440761555 y[1] (numeric) = -2.3838879428552707223974407615552 absolute error = 2e-31 relative error = 8.3896560909844028123355811705220e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.69 y[1] (closed_form) = -2.374851836136481878609258632007 y[1] (numeric) = -2.3748518361364818786092586320073 absolute error = 3e-31 relative error = 1.2632367014864126798742198000933e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.7 y[1] (closed_form) = -2.365811679194820047744660487114 y[1] (numeric) = -2.3658116791948200477446604871141 absolute error = 1e-31 relative error = 4.2268791248014289674555608932923e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.71 y[1] (closed_form) = -2.356767473670051664752196149556 y[1] (numeric) = -2.356767473670051664752196149556 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.72 y[1] (closed_form) = -2.347719221200615955702000667208 y[1] (numeric) = -2.3477192212006159557020006672082 absolute error = 2e-31 relative error = 8.5189062726896554537211400482120e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=866.9MB, alloc=44.3MB, time=9.14 TOP MAIN SOLVE Loop x[1] = 22.73 y[1] (closed_form) = -2.338666923423626548476356566678 y[1] (numeric) = -2.3386669234236265484763565666783 absolute error = 3e-31 relative error = 1.2827820712528970328742206834153e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.74 y[1] (closed_form) = -2.329610581974873080855014243676 y[1] (numeric) = -2.3296105819748730808550142436755 absolute error = 5e-31 relative error = 2.1462814595224608404941572732403e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.75 y[1] (closed_form) = -2.320550198488822806000535733316 y[1] (numeric) = -2.3205501984888228060005357333154 absolute error = 6e-31 relative error = 2.5855937113135023967528905074083e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.76 y[1] (closed_form) = -2.311485774598622195348914339239 y[1] (numeric) = -2.3114857745986221953489143392381 absolute error = 9e-31 relative error = 3.8935995621962261240672136528536e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.77 y[1] (closed_form) = -2.302417311936098538910709872281 y[1] (numeric) = -2.302417311936098538910709872281 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.78 y[1] (closed_form) = -2.293344812131761542987926557266 y[1] (numeric) = -2.2933448121317615429879265572656 absolute error = 4e-31 relative error = 1.7441773163983264569579323810645e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.79 y[1] (closed_form) = -2.28426827681480492531184801015 y[1] (numeric) = -2.2842682768148049253118480101498 absolute error = 2e-31 relative error = 8.7555390069541655243710696546783e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.8 y[1] (closed_form) = -2.275187707613108007607031067206 y[1] (numeric) = -2.2751877076131080076070310672057 absolute error = 3e-31 relative error = 1.3185725247906205509575786639906e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.81 y[1] (closed_form) = -2.266103106153237305586647662934 y[1] (numeric) = -2.2661031061532373055866476629338 absolute error = 2e-31 relative error = 8.8257237482677762469663008082693e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.82 y[1] (closed_form) = -2.25701447406044811638435140397 y[1] (numeric) = -2.2570144740604481163843514039705 absolute error = 5e-31 relative error = 2.2153158774408853560645583219784e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.83 y[1] (closed_form) = -2.247921812958686103427832972187 y[1] (numeric) = -2.2479218129586861034278329721868 absolute error = 2e-31 relative error = 8.8971066007301447641115575422928e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.84 y[1] (closed_form) = -2.238825124470588878759216011405 y[1] (numeric) = -2.2388251244705888787592160114049 absolute error = 1e-31 relative error = 4.4666284519942944525139214372327e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.85 y[1] (closed_form) = -2.229724410217487582807432708537 y[1] (numeric) = -2.229724410217487582807432708537 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=908.0MB, alloc=44.3MB, time=9.56 TOP MAIN SOLVE Loop x[1] = 22.86 y[1] (closed_form) = -2.220619671819408461617705871402 y[1] (numeric) = -2.2206196718194084616177058714026 absolute error = 6e-31 relative error = 2.7019485038984870512075540242558e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.87 y[1] (closed_form) = -2.211510910895074441543251931852 y[1] (numeric) = -2.2115109108950744415432519318527 absolute error = 7e-31 relative error = 3.1652568230680171126767928962887e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.88 y[1] (closed_form) = -2.202398129061906701404306964037 y[1] (numeric) = -2.2023981290619067014043069640381 absolute error = 1.1e-30 relative error = 4.9945556413478062554528643504267e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.89 y[1] (closed_form) = -2.193281327936026242119565503583 y[1] (numeric) = -2.1932813279360262421195655035838 absolute error = 8e-31 relative error = 3.6475028981021555786806800552112e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.9 y[1] (closed_form) = -2.184160509132255453815109683955 y[1] (numeric) = -2.1841605091322554538151096839558 absolute error = 8e-31 relative error = 3.6627344769539477968586452599703e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.91 y[1] (closed_form) = -2.175035674264119680415893971324 y[1] (numeric) = -2.1750356742641196804158939713243 absolute error = 3e-31 relative error = 1.3792877218048346216299073948257e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.92 y[1] (closed_form) = -2.165906824943848781724838578631 y[1] (numeric) = -2.1659068249438487817248385786314 absolute error = 4e-31 relative error = 1.8468015123890198530738062029569e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.93 y[1] (closed_form) = -2.156773962782378692994572473238 y[1] (numeric) = -2.1567739627823786929945724732385 absolute error = 5e-31 relative error = 2.3182772447557159813527850527795e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.94 y[1] (closed_form) = -2.147637089389352981996854760366 y[1] (numeric) = -2.1476370893893529819968547603663 absolute error = 3e-31 relative error = 1.3968840521621849438952408032025e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.95 y[1] (closed_form) = -2.138496206373124403594691126421 y[1] (numeric) = -2.1384962063731244035946911264213 absolute error = 3e-31 relative error = 1.4028549552996310443180501424262e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.96 y[1] (closed_form) = -2.129351315340756451822149962132 y[1] (numeric) = -2.1293513153407564518221499621328 absolute error = 8e-31 relative error = 3.7570127307619849815223654616409e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.97 y[1] (closed_form) = -2.120202417898024909476870755084 y[1] (numeric) = -2.1202024178980249094768707550848 absolute error = 8e-31 relative error = 3.7732246376415437726321836359405e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.98 y[1] (closed_form) = -2.111049515649419395230245344614 y[1] (numeric) = -2.1110495156494193952302453446149 absolute error = 9e-31 relative error = 4.2632822836613293732472401031966e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=949.1MB, alloc=44.3MB, time=9.98 TOP MAIN SOLVE Loop x[1] = 22.99 y[1] (closed_form) = -2.101892610198144908260240669053 y[1] (numeric) = -2.1018926101981449082602406690544 absolute error = 1.4e-30 relative error = 6.6606637903732976083417392378551e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 24.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23 y[1] (closed_form) = -2.0927317031461233704118197058 y[1] (numeric) = -2.0927317031461233704118197058009 absolute error = 9e-31 relative error = 4.3005990622064858020839555361678e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.01 y[1] (closed_form) = -2.083566796093995165889905408628 y[1] (numeric) = -2.0835667960939951658899054086288 absolute error = 8e-31 relative error = 3.8395697296565571715489521777264e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.02 y[1] (closed_form) = -2.074397890641120678489820583855 y[1] (numeric) = -2.0743978906411206784898205838566 absolute error = 1.6e-30 relative error = 7.7130815029198588095366482730486e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.03 y[1] (closed_form) = -2.06522498838558182637012481739 y[1] (numeric) = -2.0652249883855818263701248173909 absolute error = 9e-31 relative error = 4.3578787060074450200474589257230e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.04 y[1] (closed_form) = -2.056048090924183594372757768151 y[1] (numeric) = -2.0560480909241835943727577681519 absolute error = 9e-31 relative error = 4.3773295185690641466342691322671e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.05 y[1] (closed_form) = -2.046867199852455563895386379848 y[1] (numeric) = -2.0468671998524555638953863798491 absolute error = 1.1e-30 relative error = 5.3740662807987316319247614191672e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.06 y[1] (closed_form) = -2.037682316764653440320841832406 y[1] (numeric) = -2.0376823167646534403208418324072 absolute error = 1.2e-30 relative error = 5.8890435968709278200622222348711e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.07 y[1] (closed_form) = -2.028493443253760578008520356445 y[1] (numeric) = -2.0284934432537605780085203564458 absolute error = 8e-31 relative error = 3.9438135856962765567765543085375e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.08 y[1] (closed_form) = -2.01930058091148950285261036898 y[1] (numeric) = -2.0193005809114895028526103689807 absolute error = 7e-31 relative error = 3.4665468163438446423639663521500e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.09 y[1] (closed_form) = -2.010103731328283432411996755837 y[1] (numeric) = -2.0101037313282834324119967558383 absolute error = 1.3e-30 relative error = 6.4673279281012803558787804249223e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.1 y[1] (closed_form) = -2.000902896093317793616681526048 y[1] (numeric) = -2.0009028960933177936166815260489 absolute error = 9e-31 relative error = 4.4979694005002126898765668145309e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.11 y[1] (closed_form) = -1.991698076794501738055548495616 y[1] (numeric) = -1.991698076794501738055548495617 absolute error = 1.0e-30 relative error = 5.0208413195308689172683676973907e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=990.2MB, alloc=44.3MB, time=10.42 TOP MAIN SOLVE Loop x[1] = 23.12 y[1] (closed_form) = -1.982489275018479654850288122441 y[1] (numeric) = -1.9824892750184796548502881224417 absolute error = 7e-31 relative error = 3.5309144358093689661551097397099e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.13 y[1] (closed_form) = -1.973276492350632681120287110681 y[1] (numeric) = -1.9732764923506326811202871106825 absolute error = 1.5e-30 relative error = 7.6015703111789977281434784488974e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.14 y[1] (closed_form) = -1.964059730375080210043275931431 y[1] (numeric) = -1.9640597303750802100432759314317 absolute error = 7e-31 relative error = 3.5640463941812995319987024865550e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.15 y[1] (closed_form) = -1.954838990674681396516515967061 y[1] (numeric) = -1.954838990674681396516515967062 absolute error = 1.0e-30 relative error = 5.1155108158287041424733133526441e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.16 y[1] (closed_form) = -1.945614274831036660423296578961 y[1] (numeric) = -1.9456142748310366604232965789623 absolute error = 1.3e-30 relative error = 6.6816943975850307736084617046465e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.17 y[1] (closed_form) = -1.936385584424489187509501022458 y[1] (numeric) = -1.9363855844244891875095010224587 absolute error = 7e-31 relative error = 3.6149824995110472873265773909085e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.18 y[1] (closed_form) = -1.927152921034126427874988788444 y[1] (numeric) = -1.9271529210341264278749887884446 absolute error = 6e-31 relative error = 3.1134010874343846335294316844094e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.19 y[1] (closed_form) = -1.917916286237781592084530638494 y[1] (numeric) = -1.9179162862377815920845306384942 absolute error = 2e-31 relative error = 1.0427983819477518845769325111293e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.2 y[1] (closed_form) = -1.908675681612035144903021318936 y[1] (numeric) = -1.9086756816120351449030213189372 absolute error = 1.2e-30 relative error = 6.2870817266687252481429658187077e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.21 y[1] (closed_form) = -1.8994311087322162966596836894 y[1] (numeric) = -1.8994311087322162966596836894002 absolute error = 2e-31 relative error = 1.0529468485618880145067780839197e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.22 y[1] (closed_form) = -1.890182569172404492245966782593 y[1] (numeric) = -1.8901825691724044922459667825931 absolute error = 1e-31 relative error = 5.2904942427748602449122414385585e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.23 y[1] (closed_form) = -1.880930064505430897751829124522 y[1] (numeric) = -1.8809300645054308977518291245226 absolute error = 6e-31 relative error = 3.1899112642327993998027477907576e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.24 y[1] (closed_form) = -1.871673596302879884745087487772 y[1] (numeric) = -1.8716735963028798847450874877721 absolute error = 1e-31 relative error = 5.3428119196386685264566613269414e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1031.3MB, alloc=44.3MB, time=10.84 TOP MAIN SOLVE Loop x[1] = 23.25 y[1] (closed_form) = -1.862413166135090512198500124865 y[1] (numeric) = -1.8624131661350905121985001248654 absolute error = 4e-31 relative error = 2.1477511396146665763393461427563e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.26 y[1] (closed_form) = -1.853148775571158006069242433974 y[1] (numeric) = -1.8531487755711580060692424339741 absolute error = 1e-31 relative error = 5.3962208171429222015762390554393e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.27 y[1] (closed_form) = -1.8438804261789352365354219452 y[1] (numeric) = -1.8438804261789352365354219452007 absolute error = 7e-31 relative error = 3.7963416177187081407112006316314e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.28 y[1] (closed_form) = -1.834608119525034192894268482299 y[1] (numeric) = -1.8346081195250341928942684822989 absolute error = 1e-31 relative error = 5.4507553376515756445488504353188e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.29 y[1] (closed_form) = -1.825331857174827456126624351871 y[1] (numeric) = -1.8253318571748274561266243518713 absolute error = 3e-31 relative error = 1.6435367564576859570023378033487e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.3 y[1] (closed_form) = -1.816051640692449669132348439713 y[1] (numeric) = -1.8160516406924496691323484397134 absolute error = 4e-31 relative error = 2.2025805381144469191114528269590e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.31 y[1] (closed_form) = -1.806767471640799004641237151967 y[1] (numeric) = -1.8067674716407990046412371519674 absolute error = 4e-31 relative error = 2.2138986132883150475029957583253e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.32 y[1] (closed_form) = -1.797479351581538630804054227001 y[1] (numeric) = -1.7974793515815386308040542270019 absolute error = 9e-31 relative error = 5.0070116199561445299244020035015e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.33 y[1] (closed_form) = -1.788187282075098174468250562351 y[1] (numeric) = -1.7881872820750981744682505623516 absolute error = 6e-31 relative error = 3.3553532452357633402442876392651e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.34 y[1] (closed_form) = -1.778891264680675182142944349545 y[1] (numeric) = -1.778891264680675182142944349545 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.35 y[1] (closed_form) = -1.769591300956236578657720988114 y[1] (numeric) = -1.7695913009562365786577209881147 absolute error = 7e-31 relative error = 3.9557156481371715618643139725501e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.36 y[1] (closed_form) = -1.760287392458520123519801458436 y[1] (numeric) = -1.760287392458520123519801458436 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.37 y[1] (closed_form) = -1.750979540743035864974117071174 y[1] (numeric) = -1.7509795407430358649741170711746 absolute error = 6e-31 relative error = 3.4266534019317402335433048810653e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1072.4MB, alloc=44.3MB, time=11.28 TOP MAIN SOLVE Loop x[1] = 23.38 y[1] (closed_form) = -1.74166774736406759177081777896 y[1] (numeric) = -1.7416677473640675917708177789607 absolute error = 7e-31 relative error = 4.0191362621224234796892768375763e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.39 y[1] (closed_form) = -1.732352013874674282644730533332 y[1] (numeric) = -1.7323520138746742826447305333325 absolute error = 5e-31 relative error = 2.8862494227236897358258728598735e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.4 y[1] (closed_form) = -1.723032341826691553511273496934 y[1] (numeric) = -1.7230323418266915535112734969351 absolute error = 1.1e-30 relative error = 6.3840937473862097532223201800855e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.41 y[1] (closed_form) = -1.713708732770733102383321277309 y[1] (numeric) = -1.7137087327707331023833212773095 absolute error = 5e-31 relative error = 2.9176486671197469227379972496773e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.42 y[1] (closed_form) = -1.704381188256192152013505734285 y[1] (numeric) = -1.7043811882561921520135057342861 absolute error = 1.1e-30 relative error = 6.4539552981422294970612966057485e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.43 y[1] (closed_form) = -1.695049709831242890266426327889 y[1] (numeric) = -1.6950497098312428902664263278904 absolute error = 1.4e-30 relative error = 8.2593447960849615177836468969470e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.44 y[1] (closed_form) = -1.685714299042841908225233417718 y[1] (numeric) = -1.6857142990428419082252334177193 absolute error = 1.3e-30 relative error = 7.7118643458037185549504716754069e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.45 y[1] (closed_form) = -1.676374957436729636037037397824 y[1] (numeric) = -1.676374957436729636037037397825 absolute error = 1.0e-30 relative error = 5.9652525562005263374150590807279e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.46 y[1] (closed_form) = -1.667031686557431776501586053181 y[1] (numeric) = -1.6670316865574317765015860531824 absolute error = 1.4e-30 relative error = 8.3981607025786301462153408265581e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.47 y[1] (closed_form) = -1.657684487948260736407642054727 y[1] (numeric) = -1.6576844879482607364076420547275 absolute error = 5e-31 relative error = 3.0162555277262501836302006688482e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.48 y[1] (closed_form) = -1.648333363151317055621482069615 y[1] (numeric) = -1.6483333631513170556214820696164 absolute error = 1.4e-30 relative error = 8.4934275511080579583172301235466e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.49 y[1] (closed_form) = -1.638978313707490833931928551723 y[1] (numeric) = -1.6389783137074908339319285517241 absolute error = 1.1e-30 relative error = 6.7114981986047038942952272047480e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.5 y[1] (closed_form) = -1.629619341156463155656314894346 y[1] (numeric) = -1.6296193411564631556563148943466 absolute error = 6e-31 relative error = 3.6818414266868519399552380383181e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1113.5MB, alloc=44.3MB, time=11.70 TOP MAIN SOLVE Loop x[1] = 23.51 y[1] (closed_form) = -1.620256447036707512011774272521 y[1] (numeric) = -1.620256447036707512011774272522 absolute error = 1.0e-30 relative error = 6.1718624963900213280735948489177e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.52 y[1] (closed_form) = -1.610889632885491221256232176251 y[1] (numeric) = -1.6108896328854912212562321762518 absolute error = 8e-31 relative error = 4.9661999411282284229933740597468e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.53 y[1] (closed_form) = -1.601518900238876846603472338096 y[1] (numeric) = -1.6015189002388768466034723380972 absolute error = 1.2e-30 relative error = 7.4928869076787809394801707596371e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.54 y[1] (closed_form) = -1.592144250631723611916635489042 y[1] (numeric) = -1.5921442506317236119166354890431 absolute error = 1.1e-30 relative error = 6.9089217234151183314168269319753e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.55 y[1] (closed_form) = -1.582765685597688815184500135099 y[1] (numeric) = -1.5827656855976888151845001351004 absolute error = 1.4e-30 relative error = 8.8452764217675575999705563479064e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.56 y[1] (closed_form) = -1.573383206669229239784884333742 y[1] (numeric) = -1.5733832066692292397848843337434 absolute error = 1.4e-30 relative error = 8.8980230249420768353044293437546e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.57 y[1] (closed_form) = -1.563996815377602563539497263882 y[1] (numeric) = -1.5639968153776025635394972638827 absolute error = 7e-31 relative error = 4.4757124382698691810594790099927e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.58 y[1] (closed_form) = -1.554606513252868765564559225556 y[1] (numeric) = -1.5546065132528687655645592255568 absolute error = 8e-31 relative error = 5.1459967083636797839382210318789e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.59 y[1] (closed_form) = -1.545212301823891530921498575809 y[1] (numeric) = -1.5452123018238915309214985758098 absolute error = 8e-31 relative error = 5.1772821058680409248074577017226e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.6 y[1] (closed_form) = -1.535814182618339653072024005205 y[1] (numeric) = -1.5358141826183396530720240052058 absolute error = 8e-31 relative error = 5.2089634869507223528256557660552e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.61 y[1] (closed_form) = -1.526412157162688434141860485052 y[1] (numeric) = -1.5264121571626884341418604850527 absolute error = 7e-31 relative error = 4.5859173534176223720082059121928e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.62 y[1] (closed_form) = -1.517006226982221082997427168548 y[1] (numeric) = -1.517006226982221082997427168549 absolute error = 1.0e-30 relative error = 6.5919307529099532099301616732017e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.63 y[1] (closed_form) = -1.507596393601030111139725509671 y[1] (numeric) = -1.5075963936010301111397255096718 memory used=1154.5MB, alloc=44.3MB, time=12.13 absolute error = 8e-31 relative error = 5.3064600273361477457525624725938e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.64 y[1] (closed_form) = -1.498182658542018726419695871585 y[1] (numeric) = -1.4981826585420187264196958715858 absolute error = 8e-31 relative error = 5.3398028300403186690265765601556e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.65 y[1] (closed_form) = -1.488765023326902224579290931598 y[1] (numeric) = -1.4887650233269022245792909315991 absolute error = 1.1e-30 relative error = 7.3886743896082423648832801815214e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.66 y[1] (closed_form) = -1.479343489476209378622504252126 y[1] (numeric) = -1.479343489476209378622504252127 absolute error = 1.0e-30 relative error = 6.7597553043889059404626088239595e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.67 y[1] (closed_form) = -1.469918058509283826020582476673 y[1] (numeric) = -1.4699180585092838260205824766741 absolute error = 1.1e-30 relative error = 7.4834103413598720138114333031415e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.68 y[1] (closed_form) = -1.460488731944285453755639726417 y[1] (numeric) = -1.4604887319442854537556397264183 absolute error = 1.3e-30 relative error = 8.9011299544185202357812583930212e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.69 y[1] (closed_form) = -1.451055511298191781206882916489 y[1] (numeric) = -1.4510555112981917812068829164897 absolute error = 7e-31 relative error = 4.8240745757117355447566193197996e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.7 y[1] (closed_form) = -1.441618398086799340883646881412 y[1] (numeric) = -1.4416183980867993408836468814131 absolute error = 1.1e-30 relative error = 7.6303132747184139620134762270486e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.71 y[1] (closed_form) = -1.43217739382472505700942839632 y[1] (numeric) = -1.4321773938247250570094283963213 absolute error = 1.3e-30 relative error = 9.0770878356644317016195650495533e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.72 y[1] (closed_form) = -1.422732500025407621961098404382 y[1] (numeric) = -1.4227325000254076219610984043826 absolute error = 6e-31 relative error = 4.2172369014504483724716719415542e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.73 y[1] (closed_form) = -1.413283718201108870567462011324 y[1] (numeric) = -1.4132837182011088705674620113253 absolute error = 1.3e-30 relative error = 9.1984361190738015005604976993395e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.74 y[1] (closed_form) = -1.403831049862915152271326084908 y[1] (numeric) = -1.4038310498629151522713260849087 absolute error = 7e-31 relative error = 4.9863550180654244101329770233430e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.75 y[1] (closed_form) = -1.394374496520738701159224600592 y[1] (numeric) = -1.3943744965207387011592246005934 absolute error = 1.4e-30 relative error = 1.0040344279770593394847068982690e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1195.6MB, alloc=44.3MB, time=12.56 TOP MAIN SOLVE Loop x[1] = 23.76 y[1] (closed_form) = -1.38491405968331900386294220443 y[1] (numeric) = -1.384914059683319003862942204431 absolute error = 1.0e-30 relative error = 7.2206646543011104064433570033127e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.77 y[1] (closed_form) = -1.375449740858224165336966820242 y[1] (numeric) = -1.3754497408582241653369668202427 absolute error = 7e-31 relative error = 5.0892444791419913349160966365690e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.78 y[1] (closed_form) = -1.365981541551852272515992510383 y[1] (numeric) = -1.3659815415518522725159925103842 absolute error = 1.2e-30 relative error = 8.7848917682790543022924846363727e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.79 y[1] (closed_form) = -1.356509463269432755856584207765 y[1] (numeric) = -1.3565094632694327558565842077653 absolute error = 3e-31 relative error = 2.2115584750654509111412890242433e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.8 y[1] (closed_form) = -1.347033507515027748767106371168 y[1] (numeric) = -1.3470335075150277487671063711688 absolute error = 8e-31 relative error = 5.9389762432548475837246780116323e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.81 y[1] (closed_form) = -1.337553675791533444930008076261 y[1] (numeric) = -1.3375536757915334449300080762613 absolute error = 3e-31 relative error = 2.2429006433888861522530401630279e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.82 y[1] (closed_form) = -1.328069969600681453520547540903 y[1] (numeric) = -1.3280699696006814535205475409044 absolute error = 1.4e-30 relative error = 1.0541613258682041943923660336272e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.83 y[1] (closed_form) = -1.31858239044304015232602959538 y[1] (numeric) = -1.318582390443040152326029595381 absolute error = 1.0e-30 relative error = 7.5839022820864661917096348820888e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.84 y[1] (closed_form) = -1.30909093981801603876962014587 y[1] (numeric) = -1.3090909398180160387696201458712 absolute error = 1.2e-30 relative error = 9.1666664515057955195401889826373e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.85 y[1] (closed_form) = -1.299595619223855078842792242866 y[1] (numeric) = -1.299595619223855078842792242867 absolute error = 1.0e-30 relative error = 7.6947012225019681688886118497324e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.86 y[1] (closed_form) = -1.290096430157644053950448955122 y[1] (numeric) = -1.290096430157644053950448955123 absolute error = 1.0e-30 relative error = 7.7513585544749119365046866741850e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.87 y[1] (closed_form) = -1.28059337411531190567275886412 y[1] (numeric) = -1.2805933741153119056727588641204 absolute error = 4e-31 relative error = 3.1235520039789127207784746011982e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.88 y[1] (closed_form) = -1.271086452591631078447730633802 y[1] (numeric) = -1.2710864525916310784477306338024 absolute error = 4e-31 relative error = 3.1469141944234865948919429994489e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1236.7MB, alloc=44.3MB, time=12.98 TOP MAIN SOLVE Loop x[1] = 23.89 y[1] (closed_form) = -1.261575667080218860178543775431 y[1] (numeric) = -1.2615756670802188601785437754317 absolute error = 7e-31 relative error = 5.5486168468996765145869307697780e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.9 y[1] (closed_form) = -1.252061019073538720769643417757 y[1] (numeric) = -1.252061019073538720769643417758 absolute error = 1.0e-30 relative error = 7.9868311908627982381271324182692e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.91 y[1] (closed_form) = -1.242542510062901648595597608177 y[1] (numeric) = -1.2425425100629016485955976081776 absolute error = 6e-31 relative error = 4.8288086334336037937280484273958e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.92 y[1] (closed_form) = -1.233020141538467484906706411149 y[1] (numeric) = -1.2330201415384674849067064111496 absolute error = 6e-31 relative error = 4.8661005590011388716573597515160e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.93 y[1] (closed_form) = -1.223493914989246256175342835712 y[1] (numeric) = -1.2234939149892462561753428357128 absolute error = 8e-31 relative error = 6.5386512364226306596345162831432e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.94 y[1] (closed_form) = -1.213963831903099504386996414471 y[1] (numeric) = -1.2139638319030995043869964144711 absolute error = 1e-31 relative error = 8.2374777050179989812227877428899e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.95 y[1] (closed_form) = -1.204429893766741615279981071775 y[1] (numeric) = -1.2044298937667416152799810717753 absolute error = 3e-31 relative error = 2.4908049987183406381422719436498e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.96 y[1] (closed_form) = -1.194892102065741144537759758972 y[1] (numeric) = -1.1948921020657411445377597589719 absolute error = 1e-31 relative error = 8.3689564795950213941950740398542e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.97 y[1] (closed_form) = -1.185350458284522141937829199436 y[1] (numeric) = -1.1853504582845221419378291994358 absolute error = 2e-31 relative error = 1.6872647123235310970231166293605e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.98 y[1] (closed_form) = -1.175804963906365473461098975562 y[1] (numeric) = -1.1758049639063654734610989755624 absolute error = 4e-31 relative error = 3.4019247432931722277192466333222e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.99 y[1] (closed_form) = -1.166255620413410141365690103912 y[1] (numeric) = -1.1662556204134101413656901039128 absolute error = 8e-31 relative error = 6.8595596539669309149799825174271e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 25.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24 y[1] (closed_form) = -1.156702429286654602229069183183 y[1] (numeric) = -1.156702429286654602229069183183 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.01 y[1] (closed_form) = -1.147145392005958082962425162551 y[1] (numeric) = -1.1471453920059580829624251625515 absolute error = 5e-31 relative error = 4.3586454122059802765003679230904e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=1277.9MB, alloc=44.3MB, time=13.42 x[1] = 24.02 y[1] (closed_form) = -1.137584510050041894801186765162 y[1] (numeric) = -1.1375845100500418948011867651626 absolute error = 6e-31 relative error = 5.2743334204999524490931735884671e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.03 y[1] (closed_form) = -1.128019784896490745275569612945 y[1] (numeric) = -1.1280197848964907452755696129457 absolute error = 7e-31 relative error = 6.2055649144862591212817656986316e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.04 y[1] (closed_form) = -1.118451218021754048165033134595 y[1] (numeric) = -1.1184512180217540481650331345953 absolute error = 3e-31 relative error = 2.6822805962929797969213787567847e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.05 y[1] (closed_form) = -1.108878810901147231440518398251 y[1] (numeric) = -1.1088788109011472314405183982518 absolute error = 8e-31 relative error = 7.2144944256791040330694231387176e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.06 y[1] (closed_form) = -1.099302565008853043198329094166 y[1] (numeric) = -1.0993025650088530431983290941665 absolute error = 5e-31 relative error = 4.5483383366432273941115394467893e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.07 y[1] (closed_form) = -1.089722481817922855589509000323 y[1] (numeric) = -1.0897224818179228555895090003231 absolute error = 1e-31 relative error = 9.1766483364806434491508252830833e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.08 y[1] (closed_form) = -1.080138562800277966748560395559 y[1] (numeric) = -1.080138562800277966748560395559 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.09 y[1] (closed_form) = -1.0705508094267109007253390401 y[1] (numeric) = -1.0705508094267109007253390400998 absolute error = 2e-31 relative error = 1.8681971769943521661214347325749e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.1 y[1] (closed_form) = -1.060959223166886705423952522522 y[1] (numeric) = -1.0609592231668867054239525225224 absolute error = 4e-31 relative error = 3.7701731722170138676582583268434e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.11 y[1] (closed_form) = -1.05136380548934424855247997492 y[1] (numeric) = -1.0513638054893442485524799749207 absolute error = 7e-31 relative error = 6.6580188165617293486352505139947e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.12 y[1] (closed_form) = -1.041764557861497511587322384394 y[1] (numeric) = -1.0417645578614975115873223843944 absolute error = 4e-31 relative error = 3.8396391678087781321394295467096e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.13 y[1] (closed_form) = -1.032161481749636881755983978836 y[1] (numeric) = -1.0321614817496368817559839788361 absolute error = 1e-31 relative error = 9.6884064914424113919929137958273e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.14 y[1] (closed_form) = -1.022554578618930442042076438293 y[1] (numeric) = -1.0225545786189304420420764382937 absolute error = 7e-31 relative error = 6.8456003682994117288134069933920e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=1319.0MB, alloc=44.3MB, time=13.84 x[1] = 24.15 y[1] (closed_form) = -1.012943849933425259216328979846 y[1] (numeric) = -1.0129438499334252592163289798465 absolute error = 5e-31 relative error = 4.9361077618750734255675667818377e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.16 y[1] (closed_form) = -1.003329297156048669897378683905 y[1] (numeric) = -1.0033292971560486698973786839055 absolute error = 5e-31 relative error = 4.9834087514164810566540263996085e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.17 y[1] (closed_form) = -0.993710921748609564646106773036 y[1] (numeric) = -0.99371092174860956464610677303641 absolute error = 4.1e-31 relative error = 4.1259484124269532459136203196282e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.18 y[1] (closed_form) = -0.984088725171799670097277920747 y[1] (numeric) = -0.98408872517179967009727792074721 absolute error = 2.1e-31 relative error = 2.1339539274097337303282457476722e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.19 y[1] (closed_form) = -0.974462708885194829132231057121 y[1] (numeric) = -0.97446270888519482913223105712118 absolute error = 1.8e-31 relative error = 1.8471717630521096419702146390136e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.2 y[1] (closed_form) = -0.964832874347256279096361550615 y[1] (numeric) = -0.96483287434725627909636155061516 absolute error = 1.6e-31 relative error = 1.6583182875919903221429366936383e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.21 y[1] (closed_form) = -0.955199223015331928065126080735 y[1] (numeric) = -0.95519922301533192806512608073565 absolute error = 6.5e-31 relative error = 6.8048631566942431731736627243057e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.22 y[1] (closed_form) = -0.945561756345657629162292974567 y[1] (numeric) = -0.9455617563456576291622929745675 absolute error = 5.0e-31 relative error = 5.2878619153588210340007537252901e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.23 y[1] (closed_form) = -0.935920475793358452934152261197 y[1] (numeric) = -0.93592047579335845293415226119747 absolute error = 4.7e-31 relative error = 5.0217941818357132714134623568822e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.24 y[1] (closed_form) = -0.926275382812449957783391201876 y[1] (numeric) = -0.92627538281244995778339120187654 absolute error = 5.4e-31 relative error = 5.8297997552347552673853732206363e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.25 y[1] (closed_form) = -0.916626478855839458466332580232 y[1] (numeric) = -0.91662647885583945846633258023192 absolute error = 8e-32 relative error = 8.7276553585772897171692073623559e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.26 y[1] (closed_form) = -0.906973765375327292657224585902 y[1] (numeric) = -0.90697376537532729265722458590243 absolute error = 4.3e-31 relative error = 4.7410412121684223550396738787246e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.27 y[1] (closed_form) = -0.897317243821608085583262696561 y[1] (numeric) = -0.89731724382160808558326269656151 absolute error = 5.1e-31 relative error = 5.6836085956394590564355039575632e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1360.0MB, alloc=44.3MB, time=14.28 TOP MAIN SOLVE Loop x[1] = 24.28 y[1] (closed_form) = -0.887656915644272012734015557341 y[1] (numeric) = -0.88765691564427201273401555734097 absolute error = 3e-32 relative error = 3.3796841404908833458484432367589e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.29 y[1] (closed_form) = -0.877992782291806060648918473107 y[1] (numeric) = -0.87799278229180606064891847310727 absolute error = 2.7e-31 relative error = 3.0751961228567812231357673672151e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.3 y[1] (closed_form) = -0.868324845211595285786489767804 y[1] (numeric) = -0.86832484521159528578648976780447 absolute error = 4.7e-31 relative error = 5.4127208566221478822946070509143e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.31 y[1] (closed_form) = -0.858653105849924071478916926092 y[1] (numeric) = -0.85865310584992407147891692609243 absolute error = 4.3e-31 relative error = 5.0078430634030184217700519035625e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.32 y[1] (closed_form) = -0.848977565651977382975651115712 y[1] (numeric) = -0.84897756565197738297565111571199 absolute error = 1e-32 relative error = 1.1778874265447097394163244540555e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.33 y[1] (closed_form) = -0.839298226061842020579640394329 y[1] (numeric) = -0.83929822606184202057964039432951 absolute error = 5.1e-31 relative error = 6.0765051582799564298725920609501e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.34 y[1] (closed_form) = -0.829615088522507870879823631987 y[1] (numeric) = -0.82961508852250787087982363198692 absolute error = 8e-32 relative error = 9.6430261583688108299595772067289e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.35 y[1] (closed_form) = -0.819928154475869156083498929641 y[1] (numeric) = -0.81992815447586915608349892964124 absolute error = 2.4e-31 relative error = 2.9270857292785316214720102695834e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.36 y[1] (closed_form) = -0.810237425362725681452172085554 y[1] (numeric) = -0.81023742536272568145217208555417 absolute error = 1.7e-31 relative error = 2.0981504270047103249711658317713e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.37 y[1] (closed_form) = -0.80054290262278408084448245442 y[1] (numeric) = -0.80054290262278408084448245442074 absolute error = 7.4e-31 relative error = 9.2437269454962377652456535065116e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.38 y[1] (closed_form) = -0.790844587694659060369795359039 y[1] (numeric) = -0.79084458769465906036979535903904 absolute error = 4e-32 relative error = 5.0578837640656383692166814181278e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.39 y[1] (closed_form) = -0.781142482015874640156042050956 y[1] (numeric) = -0.7811424820158746401560420509563 absolute error = 3.0e-31 relative error = 3.8405285451355505605915380655367e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.4 y[1] (closed_form) = -0.771436587022865394235380074813 y[1] (numeric) = -0.77143658702286539423538007481305 absolute error = 5e-32 relative error = 6.4814141357957137059954686313362e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=1401.2MB, alloc=44.3MB, time=14.72 x[1] = 24.41 y[1] (closed_form) = -0.761726904150977688551238770981 y[1] (numeric) = -0.76172690415097768855123877098115 absolute error = 1.5e-31 relative error = 1.9692096889657625548266643993527e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.42 y[1] (closed_form) = -0.752013434834470917090306552488 y[1] (numeric) = -0.7520134348344709170903065524881 absolute error = 1.0e-31 relative error = 1.3297634771912213627756104285300e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.43 y[1] (closed_form) = -0.742296180506518736143008515074 y[1] (numeric) = -0.74229618050651873614300851507465 absolute error = 6.5e-31 relative error = 8.7566124825869529766756504390870e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.44 y[1] (closed_form) = -0.732575142599210296696014883478 y[1] (numeric) = -0.73257514259921029669601488347869 absolute error = 6.9e-31 relative error = 9.4188290030132372121567401848231e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.45 y[1] (closed_form) = -0.722850322543551474960312762612 y[1] (numeric) = -0.72285032254355147496031276261259 absolute error = 5.9e-31 relative error = 8.1621323474536142265428886080614e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.46 y[1] (closed_form) = -0.713121721769466101038365649138 y[1] (numeric) = -0.71312172176946610103836564913865 absolute error = 6.5e-31 relative error = 9.1148534697156269050482304919702e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.47 y[1] (closed_form) = -0.703389341705797185733877166983 y[1] (numeric) = -0.70338934170579718573387716698298 absolute error = 2e-32 relative error = 2.8433754699065785180205003056418e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.48 y[1] (closed_form) = -0.693653183780308145507667519499 y[1] (numeric) = -0.69365318378030814550766751949933 absolute error = 3.3e-31 relative error = 4.7574206781773621490202152011191e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.49 y[1] (closed_form) = -0.683913249419684025583163201236 y[1] (numeric) = -0.68391324941968402558316320123591 absolute error = 9e-32 relative error = 1.3159563742385024790881944702843e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.5 y[1] (closed_form) = -0.674169540049532721204992583507 y[1] (numeric) = -0.67416954004953272120499258350762 absolute error = 6.2e-31 relative error = 9.1964997403241806835425042603645e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.51 y[1] (closed_form) = -0.664422057094386197054172080168 y[1] (numeric) = -0.6644220570943861970541720801685 absolute error = 5.0e-31 relative error = 7.5253371657553386181066107911513e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.52 y[1] (closed_form) = -0.654670801977701704823359713053 y[1] (numeric) = -0.6546708019777017048233597130537 absolute error = 7.0e-31 relative error = 1.0692396818146812999912598869333e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.53 y[1] (closed_form) = -0.64491577612186299895564503045 y[1] (numeric) = -0.64491577612186299895564503045056 absolute error = 5.6e-31 relative error = 8.6833044055381062414828597201711e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1442.4MB, alloc=44.3MB, time=15.14 TOP MAIN SOLVE Loop x[1] = 24.54 y[1] (closed_form) = -0.635156980948181550550336486605 y[1] (numeric) = -0.63515698094818155055033648660536 absolute error = 3.6e-31 relative error = 5.6678901562662684164825845810289e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.55 y[1] (closed_form) = -0.62539441787689775943919956561 y[1] (numeric) = -0.62539441787689775943919956561058 absolute error = 5.8e-31 relative error = 9.2741473767705875516329427347271e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.56 y[1] (closed_form) = -0.615628088327182164436591128986 y[1] (numeric) = -0.61562808832718216443659112898581 absolute error = 1.9e-31 relative error = 3.0862789337029479045082409680317e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.57 y[1] (closed_form) = -0.605857993717136651766927682802 y[1] (numeric) = -0.60585799371713665176692768280266 absolute error = 6.6e-31 relative error = 1.0893641857404314467520798826595e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.58 y[1] (closed_form) = -0.596084135463795661672917497245 y[1] (numeric) = -0.59608413546379566167291749724502 absolute error = 2e-32 relative error = 3.3552310504688375826044882612320e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.59 y[1] (closed_form) = -0.586306514983127393207978768984 y[1] (numeric) = -0.58630651498312739320797876898406 absolute error = 6e-32 relative error = 1.0233555054684437116517785639615e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.6 y[1] (closed_form) = -0.576525133690035007216258294615 y[1] (numeric) = -0.57652513369003500721625829461551 absolute error = 5.1e-31 relative error = 8.8461017603128155524605570272548e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.61 y[1] (closed_form) = -0.566739992998357827503657421598 y[1] (numeric) = -0.56673999299835782750365742159798 absolute error = 2e-32 relative error = 3.5289551199994371193756400370684e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.62 y[1] (closed_form) = -0.556951094320872540203264361581 y[1] (numeric) = -0.55695109432087254020326436158175 absolute error = 7.5e-31 relative error = 1.3466173379451292972804335101313e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.63 y[1] (closed_form) = -0.547158439069294391338584289667 y[1] (numeric) = -0.54715843906929439133858428966795 absolute error = 9.5e-31 relative error = 1.7362429822263750177318108076959e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.64 y[1] (closed_form) = -0.537362028654278382587951011927 y[1] (numeric) = -0.53736202865427838258795101192731 absolute error = 3.1e-31 relative error = 5.7689226902826833028978275935814e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.65 y[1] (closed_form) = -0.527561864485420465253496362374 y[1] (numeric) = -0.52756186448542046525349636237469 absolute error = 6.9e-31 relative error = 1.3079034828891970152513860746602e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.66 y[1] (closed_form) = -0.517757947971258732438045889481 y[1] (numeric) = -0.51775794797125873243804588948126 absolute error = 2.6e-31 relative error = 5.0216515462247015678703684868446e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=1483.5MB, alloc=44.3MB, time=15.56 x[1] = 24.67 y[1] (closed_form) = -0.507950280519274609433301811149 y[1] (numeric) = -0.50795028051927460943330181114942 absolute error = 4.2e-31 relative error = 8.2685258008054735085441013119821e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.68 y[1] (closed_form) = -0.498138863535894042322666655816 y[1] (numeric) = -0.4981388635358940423226666558167 absolute error = 7.0e-31 relative error = 1.4052306520138848622548904117689e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.69 y[1] (closed_form) = -0.488323698426488684802053465935 y[1] (numeric) = -0.48832369842648868480205346593486 absolute error = 1.4e-31 relative error = 2.8669507634202056266306235394350e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.7 y[1] (closed_form) = -0.478504786595377083222020918429 y[1] (numeric) = -0.47850478659537708322202091842895 absolute error = 5e-32 relative error = 1.0449216267146753464050143475803e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.71 y[1] (closed_form) = -0.468682129445825859854564214819 y[1] (numeric) = -0.46868212944582585985456421481933 absolute error = 3.3e-31 relative error = 7.0410194728396214127220228128347e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.72 y[1] (closed_form) = -0.458855728380050894387885111428 y[1] (numeric) = -0.45885572838005089438788511142854 absolute error = 5.4e-31 relative error = 1.1768404895072830373621936299201e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.73 y[1] (closed_form) = -0.449025584799218503652456997436 y[1] (numeric) = -0.44902558479921850365245699743602 absolute error = 2e-32 relative error = 4.4540891826783070522886915340063e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.74 y[1] (closed_form) = -0.439191700103446619581693485426 y[1] (numeric) = -0.43919170010344661958169348542644 absolute error = 4.4e-31 relative error = 1.0018404261655286166676029645394e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.75 y[1] (closed_form) = -0.429354075691805965410521555447 y[1] (numeric) = -0.42935407569180596541052155544683 absolute error = 1.7e-31 relative error = 3.9594360371701107758772798531500e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.76 y[1] (closed_form) = -0.419512712962321230115152889381 y[1] (numeric) = -0.41951271296232123011515288938144 absolute error = 4.4e-31 relative error = 1.0488359146329824027869670121585e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.77 y[1] (closed_form) = -0.409667613311972241097339647616 y[1] (numeric) = -0.40966761331197224109733964761669 absolute error = 6.9e-31 relative error = 1.6842922837411303040407133619169e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.78 y[1] (closed_form) = -0.399818778136695135116393574442 y[1] (numeric) = -0.39981877813669513511639357444177 absolute error = 2.3e-31 relative error = 5.7526062450564708395477018659313e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.79 y[1] (closed_form) = -0.389966208831383527472239972356 y[1] (numeric) = -0.38996620883138352747223997235606 absolute error = 6e-32 relative error = 1.5385948485075855277623102895841e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.8 y[1] (closed_form) = -0.380109906789889679442770758376 y[1] (numeric) = -0.3801099067898896794427707583762 absolute error = 2.0e-31 relative error = 5.2616360801812093875847257121696e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1524.6MB, alloc=44.3MB, time=16.00 Radius of convergence (given) for eq 1 = 26.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.81 y[1] (closed_form) = -0.370249873405025663978753507494 y[1] (numeric) = -0.37024987340502566397875350749435 absolute error = 3.5e-31 relative error = 9.4530754806532015388622769098285e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.82 y[1] (closed_form) = -0.360386110068564529659546099579 y[1] (numeric) = -0.36038611006856452965954609957917 absolute error = 1.7e-31 relative error = 4.7171629330458100678970926035473e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.83 y[1] (closed_form) = -0.350518618171241462912859316174 y[1] (numeric) = -0.35051861817124146291285931617463 absolute error = 6.3e-31 relative error = 1.7973367671220860018652271657119e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.84 y[1] (closed_form) = -0.340647399102754948501802482783 y[1] (numeric) = -0.34064739910275494850180248278282 absolute error = 1.8e-31 relative error = 5.2840561963516917317288884037538e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.85 y[1] (closed_form) = -0.330772454251767928282440020258 y[1] (numeric) = -0.33077245425176792828244002025823 absolute error = 2.3e-31 relative error = 6.9534206081421510964502093380416e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.86 y[1] (closed_form) = -0.320893785005908958235079555837 y[1] (numeric) = -0.32089378500590895823507955583686 absolute error = 1.4e-31 relative error = 4.3628143186824896356390888068224e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.87 y[1] (closed_form) = -0.311011392751773363772505050017 y[1] (numeric) = -0.31101139275177336377250505001726 absolute error = 2.6e-31 relative error = 8.3598223749801043063417912537860e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.88 y[1] (closed_form) = -0.301125278874924393328361219946 y[1] (numeric) = -0.30112527887492439332836121994675 absolute error = 7.5e-31 relative error = 2.4906577182831618899908634519737e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.89 y[1] (closed_form) = -0.291235444759894370228888383088 y[1] (numeric) = -0.29123544475989437022888838308836 absolute error = 3.6e-31 relative error = 1.2361132769975775333319606506994e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.9 y[1] (closed_form) = -0.281341891790185842851199706697 y[1] (numeric) = -0.2813418917901858428511997066972 absolute error = 2.0e-31 relative error = 7.1087884824899253318546772114532e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.91 y[1] (closed_form) = -0.271444621348272733071285728963 y[1] (numeric) = -0.27144462134827273307128572896357 absolute error = 5.7e-31 relative error = 2.0998758316477028476527278714626e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.92 y[1] (closed_form) = -0.261543634815601483004923916528 y[1] (numeric) = -0.26154363481560148300492391652869 absolute error = 6.9e-31 relative error = 2.6381831103879742786208487092056e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1565.7MB, alloc=44.3MB, time=16.42 TOP MAIN SOLVE Loop x[1] = 24.93 y[1] (closed_form) = -0.251638933572592200044663940392 y[1] (numeric) = -0.25163893357259220004466394039274 absolute error = 7.4e-31 relative error = 2.9407214118022263951409816924551e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.94 y[1] (closed_form) = -0.241730518998639800196052287959 y[1] (numeric) = -0.24173051899863980019605228795907 absolute error = 7e-32 relative error = 2.8957866094017646500745844593284e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.95 y[1] (closed_form) = -0.231818392472115149716252783038 y[1] (numeric) = -0.23181839247211514971625278303775 absolute error = 2.5e-31 relative error = 1.0784303925758257944887597237828e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.96 y[1] (closed_form) = -0.221902555370366205058212558012 y[1] (numeric) = -0.22190255537036620505821255801263 absolute error = 6.3e-31 relative error = 2.8390840247355386418029394979870e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.97 y[1] (closed_form) = -0.211983009069719151123516013003 y[1] (numeric) = -0.21198300906971915112351601300355 absolute error = 5.5e-31 relative error = 2.5945475649848443571233162030484e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.98 y[1] (closed_form) = -0.202059754945479537827062305675 y[1] (numeric) = -0.20205975494547953782706230567517 absolute error = 1.7e-31 relative error = 8.4133527750674540891165858761208e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.99 y[1] (closed_form) = -0.192132794371933414976694942303 y[1] (numeric) = -0.19213279437193341497669494230341 absolute error = 4.1e-31 relative error = 2.1339407535306863240712053590259e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 26.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25 y[1] (closed_form) = -0.182202128722348465470905085753 y[1] (numeric) = -0.18220212872234846547090508575354 absolute error = 5.4e-31 relative error = 2.9637414435639627446560144646024e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.01 y[1] (closed_form) = -0.1722677593689751368177232591 y[1] (numeric) = -0.17226775936897513681772325909991 absolute error = 9e-32 relative error = 5.2244250653560603102540207029287e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.02 y[1] (closed_form) = -0.16232968768304777097790720467 y[1] (numeric) = -0.16232968768304777097790720466997 absolute error = 3e-32 relative error = 1.8480907853759719778436610615038e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.03 y[1] (closed_form) = -0.152387915034785732535526757273 y[1] (numeric) = -0.15238791503478573253552675727348 absolute error = 4.8e-31 relative error = 3.1498560754665483088564907892585e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.04 y[1] (closed_form) = -0.142442442793394535199039707227 y[1] (numeric) = -0.14244244279339453519903970722711 absolute error = 1.1e-31 relative error = 7.7224174089424571169534336807894e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.05 y[1] (closed_form) = -0.132493272327066966635945763453 y[1] (numeric) = -0.13249327232706696663594576345328 absolute error = 2.8e-31 relative error = 2.1133148504990089028867212676935e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1606.9MB, alloc=44.3MB, time=16.86 TOP MAIN SOLVE Loop x[1] = 25.06 y[1] (closed_form) = -0.122540405002984211644098879366 y[1] (numeric) = -0.12254040500298421164409887936652 absolute error = 5.2e-31 relative error = 4.2434982974581853468577283816185e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.07 y[1] (closed_form) = -0.112583842187316973662751374408 y[1] (numeric) = -0.11258384218731697366275137440866 absolute error = 6.6e-31 relative error = 5.8622977078885985668194165212377e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.08 y[1] (closed_form) = -0.102623585245226594626396471904 y[1] (numeric) = -0.10262358524522659462639647190371 absolute error = 2.9e-31 relative error = 2.8258611244873554120609448380046e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.09 y[1] (closed_form) = -0.092659635540866173164469079321 y[1] (numeric) = -0.092659635540866173164469079321375 absolute error = 3.75e-31 relative error = 4.0470696631934382078943900041351e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.1 y[1] (closed_form) = -0.082691994437381681149957860014 y[1] (numeric) = -0.082691994437381681149957860013953 absolute error = 4.7e-32 relative error = 5.6837424613806648200782942024260e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.11 y[1] (closed_form) = -0.072720663296913078599974885972 y[1] (numeric) = -0.072720663296913078599974885971889 absolute error = 1.11e-31 relative error = 1.5263887176990565485865433544339e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.12 y[1] (closed_form) = -0.062745643480595426931322419077 y[1] (numeric) = -0.062745643480595426931322419077497 absolute error = 4.97e-31 relative error = 7.9208686441107433119566944271995e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.13 y[1] (closed_form) = -0.052766936348560000574089643673 y[1] (numeric) = -0.052766936348560000574089643672864 absolute error = 1.36e-31 relative error = 2.5773715400422600721638929387668e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.14 y[1] (closed_form) = -0.042784543259935396946305465945 y[1] (numeric) = -0.042784543259935396946305465944981 absolute error = 1.9e-32 relative error = 4.4408561018324843714878629554184e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.15 y[1] (closed_form) = -0.032798465572848644792666805618 y[1] (numeric) = -0.032798465572848644792666805617979 absolute error = 2.1e-32 relative error = 6.4027385529231290853466755614753e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.16 y[1] (closed_form) = -0.022808704644426310890355132678 y[1] (numeric) = -0.022808704644426310890355132677758 absolute error = 2.42e-31 relative error = 1.0609984379763396795573368824773e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.17 y[1] (closed_form) = -0.012815261830795605124947346287 y[1] (numeric) = -0.012815261830795605124947346287553 absolute error = 5.53e-31 relative error = 4.3151673941699582665641639619629e-27 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.18 y[1] (closed_form) = -0.002818138487085483939420454633 y[1] (numeric) = -0.0028181384870854839394204546335316 absolute error = 5.316e-31 relative error = 1.8863515843388526972126401741304e-26 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1648.0MB, alloc=44.3MB, time=17.28 TOP MAIN SOLVE Loop x[1] = 25.19 y[1] (closed_form) = 0.007182664032572247840757106883 y[1] (numeric) = 0.007182664032572247840757106883305 absolute error = 3.050e-31 relative error = 4.2463353237304868250121431366868e-27 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.2 y[1] (closed_form) = 0.017187144375041836803461285969 y[1] (numeric) = 0.017187144375041836803461285968963 absolute error = 3.7e-32 relative error = 2.1527718155279611368631888225448e-28 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.21 y[1] (closed_form) = 0.027195301188182482363695706411 y[1] (numeric) = 0.027195301188182482363695706412078 absolute error = 1.078e-30 relative error = 3.9639200630307302959294336605691e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.22 y[1] (closed_form) = 0.037207133120847239792349368186 y[1] (numeric) = 0.037207133120847239792349368187087 absolute error = 1.087e-30 relative error = 2.9214828147857257836114811635101e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.23 y[1] (closed_form) = 0.047222638822881924856962232597 y[1] (numeric) = 0.047222638822881924856962232595857 absolute error = 1.143e-30 relative error = 2.4204492347135726453980434674836e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.24 y[1] (closed_form) = 0.05724181694512402007153870695 y[1] (numeric) = 0.057241816945124020071538706948999 absolute error = 1.001e-30 relative error = 1.7487215700361644665781989521523e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.25 y[1] (closed_form) = 0.067264666139401582552455563082 y[1] (numeric) = 0.06726466613940158255245556308092 absolute error = 1.080e-30 relative error = 1.6055978004287886552129039962907e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.26 y[1] (closed_form) = 0.077291185058532153477517327039 y[1] (numeric) = 0.077291185058532153477517327037477 absolute error = 1.523e-30 relative error = 1.9704704991217836590612964141394e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.27 y[1] (closed_form) = 0.087321372356321669145218663622 y[1] (numeric) = 0.087321372356321669145218663620929 absolute error = 1.071e-30 relative error = 1.2265038570737310269751539561203e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.28 y[1] (closed_form) = 0.097355226687563373631279749172 y[1] (numeric) = 0.097355226687563373631279749172759 absolute error = 7.59e-31 relative error = 7.7961915946825926497691028825886e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.29 y[1] (closed_form) = 0.10739274670803673303952707907 y[1] (numeric) = 0.10739274670803673303952707906966 absolute error = 3.4e-31 relative error = 3.1659493813333681128910711151259e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.3 y[1] (closed_form) = 0.117433931074506351344198592951 y[1] (numeric) = 0.11743393107450635134419859295039 absolute error = 6.1e-31 relative error = 5.1944101199591407237867520680610e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.31 y[1] (closed_form) = 0.127478778444720887820758420728 y[1] (numeric) = 0.12747877844472088782075842072921 absolute error = 1.21e-30 relative error = 9.4917759235094721750562149609207e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1689.1MB, alloc=44.3MB, time=17.70 TOP MAIN SOLVE Loop x[1] = 25.32 y[1] (closed_form) = 0.137527287477411976062312956035 y[1] (numeric) = 0.13752728747741197606231295603489 absolute error = 1.1e-31 relative error = 7.9984126799611919712912463691246e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.33 y[1] (closed_form) = 0.147579456832293144578726350889 y[1] (numeric) = 0.14757945683229314457872635088895 absolute error = 5e-32 relative error = 3.3880054225175238011658865680268e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.34 y[1] (closed_form) = 0.157635285170058738975539896254 y[1] (numeric) = 0.15763528517005873897553989625306 absolute error = 9.4e-31 relative error = 5.9631319154586316516147340994379e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.35 y[1] (closed_form) = 0.167694771152382845709806107581 y[1] (numeric) = 0.16769477115238284570980610757992 absolute error = 1.08e-30 relative error = 6.4402723625688541609060776089110e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.36 y[1] (closed_form) = 0.177757913441918217419954672742 y[1] (numeric) = 0.17775791344191821741995467274226 absolute error = 2.6e-31 relative error = 1.4626634334620163030329641336839e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.37 y[1] (closed_form) = 0.187824710702295199826813741739 y[1] (numeric) = 0.18782471070229519982681374173898 absolute error = 2e-32 relative error = 1.0648226170676913988917374089846e-29 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.38 y[1] (closed_form) = 0.197895161598120660202916343434 y[1] (numeric) = 0.197895161598120660202916343433 absolute error = 1.00e-30 relative error = 5.0531806433487691873154827905843e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.39 y[1] (closed_form) = 0.207969264794976917407228004308 y[1] (numeric) = 0.20796926479497691740722800430907 absolute error = 1.07e-30 relative error = 5.1449910209320685872675744163077e-28 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.4 y[1] (closed_form) = 0.218047018959420673482437917899 y[1] (numeric) = 0.21804701895942067348243791789895 absolute error = 5e-32 relative error = 2.2930834018558711875621258634582e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.41 y[1] (closed_form) = 0.228128422758981946811962271154 y[1] (numeric) = 0.2281284227589819468119622711535 absolute error = 5.0e-31 relative error = 2.1917479372057502054631196886858e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.42 y[1] (closed_form) = 0.238213474862163006833814575692 y[1] (numeric) = 0.23821347486216300683381457569133 absolute error = 6.7e-31 relative error = 2.8126032769039651457911966334189e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.43 y[1] (closed_form) = 0.248302173938437310308504077571 y[1] (numeric) = 0.24830217393843731030850407757102 absolute error = 2e-32 relative error = 8.0547019314291993092338718893281e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.44 y[1] (closed_form) = 0.258394518658248439138129529063 y[1] (numeric) = 0.25839451865824843913812952906254 absolute error = 4.6e-31 relative error = 1.7802235217241359799595418115073e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1730.2MB, alloc=44.3MB, time=18.14 TOP MAIN SOLVE Loop x[1] = 25.45 y[1] (closed_form) = 0.268490507693009039733841799882 y[1] (numeric) = 0.26849050769300903973384179988099 absolute error = 1.01e-30 relative error = 3.7617717239926780348249542370954e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.46 y[1] (closed_form) = 0.278590139715099763928854983539 y[1] (numeric) = 0.27859013971509976392885498353814 absolute error = 8.6e-31 relative error = 3.0869721407924885340767189181824e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.47 y[1] (closed_form) = 0.28869341339786821143419181691 y[1] (numeric) = 0.28869341339786821143419181691036 absolute error = 3.6e-31 relative error = 1.2469976220200745850206930616179e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.48 y[1] (closed_form) = 0.298800327415627873834355377862 y[1] (numeric) = 0.29880032741562787383435537786125 absolute error = 7.5e-31 relative error = 2.5100374102226417173381197629266e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.49 y[1] (closed_form) = 0.30891088044365708012012515684 y[1] (numeric) = 0.30891088044365708012012515683933 absolute error = 6.7e-31 relative error = 2.1689103311535921798481930072388e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.5 y[1] (closed_form) = 0.319025071158197943755681713842 y[1] (numeric) = 0.31902507115819794375568171384111 absolute error = 8.9e-31 relative error = 2.7897493973402089823439821819876e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.51 y[1] (closed_form) = 0.329142898236455311277270232033 y[1] (numeric) = 0.3291428982364553112772702320334 absolute error = 4.0e-31 relative error = 1.2152776260499509566937605186938e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.52 y[1] (closed_form) = 0.33926436035659571242061936371 y[1] (numeric) = 0.33926436035659571242061936371047 absolute error = 4.7e-31 relative error = 1.3853503489314056017279616344260e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.53 y[1] (closed_form) = 0.349389456197746311774337833167 y[1] (numeric) = 0.34938945619774631177433783316766 absolute error = 6.6e-31 relative error = 1.8890094943977225791729206460178e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.54 y[1] (closed_form) = 0.359518184439993861956517314547 y[1] (numeric) = 0.3595181844399938619565173145471 absolute error = 1.0e-31 relative error = 2.7815004727998872650594462260301e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.55 y[1] (closed_form) = 0.369650543764383658311776140801 y[1] (numeric) = 0.36965054376438365831177614079954 absolute error = 1.46e-30 relative error = 3.9496763216737164757570640896405e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.56 y[1] (closed_form) = 0.379786532852918495125984422651 y[1] (numeric) = 0.3797865328529184951259844226522 absolute error = 1.20e-30 relative error = 3.1596696991484133910971948473741e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.57 y[1] (closed_form) = 0.389926150388557623355917163922 y[1] (numeric) = 0.38992615038855762335591716392153 absolute error = 4.7e-31 relative error = 1.2053564489882239569836695883151e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1771.3MB, alloc=44.3MB, time=18.56 TOP MAIN SOLVE Loop x[1] = 25.58 y[1] (closed_form) = 0.400069395055215709871087951706 y[1] (numeric) = 0.40006939505521570987108795170572 absolute error = 2.8e-31 relative error = 6.9987857971829039158890366335276e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.59 y[1] (closed_form) = 0.41021626553776179820502177698 y[1] (numeric) = 0.41021626553776179820502177697969 absolute error = 3.1e-31 relative error = 7.5569894722144665629129308397962e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.6 y[1] (closed_form) = 0.420366760522018270813231502936 y[1] (numeric) = 0.42036676052201827081323150293732 absolute error = 1.32e-30 relative error = 3.1401150708509934528595849764543e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.61 y[1] (closed_form) = 0.430520878694759812835168445129 y[1] (numeric) = 0.43052087869475981283516844512895 absolute error = 5e-32 relative error = 1.1613838602111119141821095455943e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.62 y[1] (closed_form) = 0.440678618743712377357423459068 y[1] (numeric) = 0.44067861874371237735742345906723 absolute error = 7.7e-31 relative error = 1.7473051045569621141028002854083e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.63 y[1] (closed_form) = 0.450839979357552152175460847568 y[1] (numeric) = 0.45083997935755215217546084756681 absolute error = 1.19e-30 relative error = 2.6395174662543288984494548369325e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.64 y[1] (closed_form) = 0.461004959225904528051173301687 y[1] (numeric) = 0.46100495922590452805117330168672 absolute error = 2.8e-31 relative error = 6.0736873735623449559140819303881e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.65 y[1] (closed_form) = 0.471173557039343068463551975801 y[1] (numeric) = 0.47117355703934306846355197580071 absolute error = 2.9e-31 relative error = 6.1548445507476760404392014266877e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.66 y[1] (closed_form) = 0.481345771489388480849771669074 y[1] (numeric) = 0.48134577148938848084977166907478 absolute error = 7.8e-31 relative error = 1.6204567406638068030388225192719e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.67 y[1] (closed_form) = 0.491521601268507589333996942526 y[1] (numeric) = 0.49152160126850758933399694252499 absolute error = 1.01e-30 relative error = 2.0548435661696563109732224169575e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.68 y[1] (closed_form) = 0.501701045070112308941220842906 y[1] (numeric) = 0.50170104507011230894122084290602 absolute error = 2e-32 relative error = 3.9864377793363010492438159031450e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.69 y[1] (closed_form) = 0.511884101588558621293453731985 y[1] (numeric) = 0.51188410158855862129345373198385 absolute error = 1.15e-30 relative error = 2.2466023000736700897727993788806e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.7 y[1] (closed_form) = 0.522070769519145551785585532318 y[1] (numeric) = 0.52207076951914555178558553231762 absolute error = 3.8e-31 relative error = 7.2787066847278166647777739631090e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1812.5MB, alloc=44.3MB, time=19.00 TOP MAIN SOLVE Loop x[1] = 25.71 y[1] (closed_form) = 0.53226104755811414823825049856 y[1] (numeric) = 0.53226104755811414823825049855879 absolute error = 1.21e-30 relative error = 2.2733205925009718282913255426169e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.72 y[1] (closed_form) = 0.542454934402646461025029406512 y[1] (numeric) = 0.5424549344026464610250294065124 absolute error = 4.0e-31 relative error = 7.3738844396444028406047259707657e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.73 y[1] (closed_form) = 0.552652428750864524671329820838 y[1] (numeric) = 0.55265242875086452467132982083701 absolute error = 9.9e-31 relative error = 1.7913609865746045076651597479102e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.74 y[1] (closed_form) = 0.562853529301829340922290856332 y[1] (numeric) = 0.56285352930182934092229085633094 absolute error = 1.06e-30 relative error = 1.8832608215406190114686532324856e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.75 y[1] (closed_form) = 0.573058234755539863277064587304 y[1] (numeric) = 0.57305823475553986327706458730253 absolute error = 1.47e-30 relative error = 2.5651843230681176937222838720918e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.76 y[1] (closed_form) = 0.583266543812931982986831984595 y[1] (numeric) = 0.58326654381293198298683198459424 absolute error = 7.6e-31 relative error = 1.3030063322880230393202898163697e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.77 y[1] (closed_form) = 0.593478455175877516513916970467 y[1] (numeric) = 0.59347845517587751651391697046647 absolute error = 5.3e-31 relative error = 8.9304000065669501437404951871247e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.78 y[1] (closed_form) = 0.603693967547183194449367877787 y[1] (numeric) = 0.60369396754718319444936787778765 absolute error = 6.5e-31 relative error = 1.0767044809822414584742544790912e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.79 y[1] (closed_form) = 0.613913079630589651886381281864 y[1] (numeric) = 0.61391307963058965188638128186514 absolute error = 1.14e-30 relative error = 1.8569404005628500370087651756990e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.8 y[1] (closed_form) = 0.624135790130770420246948840827 y[1] (numeric) = 0.62413579013077042024694884082648 absolute error = 5.2e-31 relative error = 8.3315202912982823661032833759515e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.81 y[1] (closed_form) = 0.634362097753330920559113433765 y[1] (numeric) = 0.63436209775333092055911343376571 absolute error = 7.1e-31 relative error = 1.1192345862316644350718542462027e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.82 y[1] (closed_form) = 0.644592001204807458182226524945 y[1] (numeric) = 0.64459200120480745818222652494388 absolute error = 1.12e-30 relative error = 1.7375331960474331772079885416680e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.83 y[1] (closed_form) = 0.65482549919266621897760430722 y[1] (numeric) = 0.65482549919266621897760430721898 absolute error = 1.02e-30 relative error = 1.5576668918017962057551928911537e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1853.7MB, alloc=44.3MB, time=19.42 TOP MAIN SOLVE Loop x[1] = 25.84 y[1] (closed_form) = 0.665062590425302266921985788618 y[1] (numeric) = 0.66506259042530226692198578861849 absolute error = 4.9e-31 relative error = 7.3677275951824154651447886764366e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.85 y[1] (closed_form) = 0.675303273612038543161201582599 y[1] (numeric) = 0.67530327361203854316120158259755 absolute error = 1.45e-30 relative error = 2.1471834310002536904492899317837e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.86 y[1] (closed_form) = 0.68554754746312486650146774509 y[1] (numeric) = 0.68554754746312486650146774508975 absolute error = 2.5e-31 relative error = 3.6467200696016978886476717298646e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.87 y[1] (closed_form) = 0.695795410689736935335724569994 y[1] (numeric) = 0.69579541068973693533572456999425 absolute error = 2.5e-31 relative error = 3.5930101889027525543409127108959e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.88 y[1] (closed_form) = 0.706046862003975331002445809294 y[1] (numeric) = 0.70604686200397533100244580929308 absolute error = 9.2e-31 relative error = 1.3030296564009373443115777820738e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.89 y[1] (closed_form) = 0.716301900118864522574349324597 y[1] (numeric) = 0.71630190011886452257434932459761 absolute error = 6.1e-31 relative error = 8.5159623323458365852506740268702e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.9 y[1] (closed_form) = 0.726560523748351873074445703622 y[1] (numeric) = 0.72656052374835187307444570362084 absolute error = 1.16e-30 relative error = 1.5965634824412401049662287572129e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.91 y[1] (closed_form) = 0.736822731607306647116866887905 y[1] (numeric) = 0.73682273160730664711686688790466 absolute error = 3.4e-31 relative error = 4.6144070400532199814460024866099e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.92 y[1] (closed_form) = 0.747088522411519019969922357137 y[1] (numeric) = 0.74708852241151901996992235713621 absolute error = 7.9e-31 relative error = 1.0574382771267419318190515517972e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.93 y[1] (closed_form) = 0.757357894877699088038835900606 y[1] (numeric) = 0.75735789487769908803883590060669 absolute error = 6.9e-31 relative error = 9.1106200208215128424562219375352e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.94 y[1] (closed_form) = 0.767630847723475880765621477837 y[1] (numeric) = 0.76763084772347588076562147783662 absolute error = 3.8e-31 relative error = 4.9502961107796390589851714513662e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.95 y[1] (closed_form) = 0.777907379667396373943562128156 y[1] (numeric) = 0.77790737966739637394356212815473 absolute error = 1.27e-30 relative error = 1.6325851035672186646335481371080e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.96 y[1] (closed_form) = 0.788187489428924504443761333113 y[1] (numeric) = 0.78818748942892450444376133311232 absolute error = 6.8e-31 relative error = 8.6273889032759076058092261269405e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1894.8MB, alloc=44.3MB, time=19.86 TOP MAIN SOLVE Loop x[1] = 25.97 y[1] (closed_form) = 0.798471175728440186351241666078 y[1] (numeric) = 0.798471175728440186351241666079 absolute error = 1.00e-30 relative error = 1.2523933617111555044051125266279e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.98 y[1] (closed_form) = 0.808758437287238328508070980239 y[1] (numeric) = 0.80875843728723832850807098024008 absolute error = 1.08e-30 relative error = 1.3353801953801783025556447272939e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.99 y[1] (closed_form) = 0.819049272827527853461001789537 y[1] (numeric) = 0.81904927282752785346100178953735 absolute error = 3.5e-31 relative error = 4.2732471856269093041448874943964e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 27.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26 y[1] (closed_form) = 0.829343681072430717811114886906 y[1] (numeric) = 0.82934368107243071781111488690437 absolute error = 1.63e-30 relative error = 1.9654095608375943901545262561700e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.01 y[1] (closed_form) = 0.839641660745980933962963620481 y[1] (numeric) = 0.83964166074598093396296362048144 absolute error = 4.4e-31 relative error = 5.2403307335784329532795434436996e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.02 y[1] (closed_form) = 0.849943210573123593270720611394 y[1] (numeric) = 0.84994321057312359327072061139351 absolute error = 4.9e-31 relative error = 5.7650910543727860351810817232306e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.03 y[1] (closed_form) = 0.860248329279713890578834046175 y[1] (numeric) = 0.8602483292797138905788340461756 absolute error = 6.0e-31 relative error = 6.9747301979927136604548714780415e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.04 y[1] (closed_form) = 0.870557015592516150154706013072 y[1] (numeric) = 0.87055701559251615015470601307062 absolute error = 1.38e-30 relative error = 1.5851919808615270881986007030993e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.05 y[1] (closed_form) = 0.880869268239202853010910674246 y[1] (numeric) = 0.88086926823920285301091067424491 absolute error = 1.09e-30 relative error = 1.2374140400866011723041830663718e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.06 y[1] (closed_form) = 0.891185085948353665614475375504 y[1] (numeric) = 0.89118508594835366561447537550317 absolute error = 8.3e-31 relative error = 9.3134413163653471468719858615661e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.07 y[1] (closed_form) = 0.901504467449454469980753091375 y[1] (numeric) = 0.90150446744945446998075309137565 absolute error = 6.5e-31 relative error = 7.2101694830086261752743565608690e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.08 y[1] (closed_form) = 0.911827411472896395149419886533 y[1] (numeric) = 0.91182741147289639514941988653331 absolute error = 3.1e-31 relative error = 3.3997661849104718642911490407473e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.09 y[1] (closed_form) = 0.9221539167499748500401363444 y[1] (numeric) = 0.92215391674997485004013634440073 absolute error = 7.3e-31 relative error = 7.9162489768823064464244052073152e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1935.9MB, alloc=44.3MB, time=20.28 TOP MAIN SOLVE Loop x[1] = 26.1 y[1] (closed_form) = 0.932483982012888557685417170616 y[1] (numeric) = 0.93248398201288855768541717061651 absolute error = 5.1e-31 relative error = 5.4692628488813109609806511080737e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.11 y[1] (closed_form) = 0.942817605994738590838258422678 y[1] (numeric) = 0.94281760599473859083825842267681 absolute error = 1.19e-30 relative error = 1.2621741389146702194466645674919e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.12 y[1] (closed_form) = 0.953154787429527408952077047727 y[1] (numeric) = 0.95315478742952740895207704772527 absolute error = 1.73e-30 relative error = 1.8150252433452835505124386814722e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.13 y[1] (closed_form) = 0.96349552505215789653052262806 y[1] (numeric) = 0.96349552505215789653052262805916 absolute error = 8.4e-31 relative error = 8.7182553334072559811769414137248e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.14 y[1] (closed_form) = 0.973839817598432402844726438545 y[1] (numeric) = 0.97383981759843240284472643854483 absolute error = 1.7e-31 relative error = 1.7456669662494774772807027490235e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.15 y[1] (closed_form) = 0.984187663805051783015558111811 y[1] (numeric) = 0.9841876638050517830155581118117 absolute error = 7.0e-31 relative error = 7.1124646827381513575490382942297e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.16 y[1] (closed_form) = 0.99453906240961444045846538586 y[1] (numeric) = 0.99453906240961444045846538586062 absolute error = 6.2e-31 relative error = 6.2340437237109201330882903687709e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.17 y[1] (closed_form) = 1.004894012150615370688477574616 y[1] (numeric) = 1.0048940121506153706884775746147 absolute error = 1.3e-30 relative error = 1.2936687693240564346801487891930e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.18 y[1] (closed_form) = 1.015252511767445206482958554998 y[1] (numeric) = 1.0152525117674452064829585549974 absolute error = 6e-31 relative error = 5.9098597939488439542973901117552e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.19 y[1] (closed_form) = 1.025614560000389264399700204379 y[1] (numeric) = 1.0256145600003892643997002043771 absolute error = 1.9e-30 relative error = 1.8525478031428091944126589641860e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.2 y[1] (closed_form) = 1.035980155590626592647952349712 y[1] (numeric) = 1.0359801555906265926479523497125 absolute error = 5e-31 relative error = 4.8263472741419751950149975697299e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.21 y[1] (closed_form) = 1.046349297280229020309990404493 y[1] (numeric) = 1.0463492972802290203099904044914 absolute error = 1.6e-30 relative error = 1.5291260807063881426521315192951e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.22 y[1] (closed_form) = 1.056721983812160207910826971634 y[1] (numeric) = 1.0567219838121602079108269716332 absolute error = 8e-31 relative error = 7.5705815934099620969939502443469e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1977.1MB, alloc=44.3MB, time=20.70 TOP MAIN SOLVE Loop x[1] = 26.23 y[1] (closed_form) = 1.067098213930274699333678779937 y[1] (numeric) = 1.0670982139302746993336787799382 absolute error = 1.2e-30 relative error = 1.1245450365625007416488277935960e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.24 y[1] (closed_form) = 1.077477986379316975078805398465 y[1] (numeric) = 1.0774779863793169750788053984654 absolute error = 4e-31 relative error = 3.7123728285543218219476699390473e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.25 y[1] (closed_form) = 1.087861299904920506863341237432 y[1] (numeric) = 1.0878612999049205068633412374322 absolute error = 2e-31 relative error = 1.8384696653652453340605554914682e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.26 y[1] (closed_form) = 1.098248153253606813559747395891 y[1] (numeric) = 1.0982481532536068135597473958908 absolute error = 2e-31 relative error = 1.8210820515153292351444998023045e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.27 y[1] (closed_form) = 1.108638545172784518470514955594 y[1] (numeric) = 1.1086385451727845184705149555937 absolute error = 3e-31 relative error = 2.7060217354543101669523675185648e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.28 y[1] (closed_form) = 1.119032474410748407936756347125 y[1] (numeric) = 1.119032474410748407936756347125 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.29 y[1] (closed_form) = 1.129429939716678491278326428614 y[1] (numeric) = 1.1294299397166784912783264286146 absolute error = 6e-31 relative error = 5.3124145101954011365976995234793e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.3 y[1] (closed_form) = 1.139830939840639062063119919167 y[1] (numeric) = 1.139830939840639062063119919167 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.31 y[1] (closed_form) = 1.1502354735335777607031968186 y[1] (numeric) = 1.1502354735335777607031968185994 absolute error = 6e-31 relative error = 5.2163232121225720025864054514925e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.32 y[1] (closed_form) = 1.160643539547324638375392422185 y[1] (numeric) = 1.1606435395473246383753924221861 absolute error = 1.1e-30 relative error = 9.4775007357471968291417420956522e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.33 y[1] (closed_form) = 1.171055136634591222264073503933 y[1] (numeric) = 1.1710551366345912222640735039315 absolute error = 1.5e-30 relative error = 1.2808961363772666594777830910216e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.34 y[1] (closed_form) = 1.18147026354896958212370719443 y[1] (numeric) = 1.1814702635489695821237071944297 absolute error = 3e-31 relative error = 2.5392090622648633367793257540136e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.35 y[1] (closed_form) = 1.191888919044931398158914019686 y[1] (numeric) = 1.1918889190449313981589140196855 absolute error = 5e-31 relative error = 4.1950218011981633375392096158193e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2018.2MB, alloc=44.3MB, time=21.14 TOP MAIN SOLVE Loop x[1] = 26.36 y[1] (closed_form) = 1.202311101877827030219681495388 y[1] (numeric) = 1.2023111018778270302196814953878 absolute error = 2e-31 relative error = 1.6634629729995042593651000075879e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.37 y[1] (closed_form) = 1.212736810803884588309419587072 y[1] (numeric) = 1.2127368108038845883094195870704 absolute error = 1.6e-30 relative error = 1.3193299533304435474525347603060e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.38 y[1] (closed_form) = 1.223166044580209004403544250423 y[1] (numeric) = 1.2231660445802090044035442504228 absolute error = 2e-31 relative error = 1.6351009814750054387866321798676e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.39 y[1] (closed_form) = 1.233598801964781105576280157735 y[1] (numeric) = 1.2335988019647811055762801577348 absolute error = 2e-31 relative error = 1.6212726510552329721941304464453e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.4 y[1] (closed_form) = 1.244035081716456688433378596124 y[1] (numeric) = 1.2440350817164566884333785961226 absolute error = 1.4e-30 relative error = 1.1253701929919458583719459477822e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.41 y[1] (closed_form) = 1.254474882594965594848451390824 y[1] (numeric) = 1.2544748825949655948484513908236 absolute error = 4e-31 relative error = 3.1885851645955088408230765955867e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.42 y[1] (closed_form) = 1.26491820336091078900062656249 y[1] (numeric) = 1.2649182033609107890006265624882 absolute error = 1.8e-30 relative error = 1.4230169154158483102294546663496e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.43 y[1] (closed_form) = 1.27536504277576743571123627108 y[1] (numeric) = 1.2753650427757674357112362710803 absolute error = 3e-31 relative error = 2.3522677032692160898420493241553e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.44 y[1] (closed_form) = 1.285815399601881980077252430755 y[1] (numeric) = 1.2858153996018819800772524307556 absolute error = 6e-31 relative error = 4.6662996895648768810637206956634e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.45 y[1] (closed_form) = 1.296269272602471228399190199952 y[1] (numeric) = 1.2962692726024712283991901999531 absolute error = 1.1e-30 relative error = 8.4858911898109814260973335264730e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.46 y[1] (closed_form) = 1.306726660541621430401204358941 y[1] (numeric) = 1.3067266605416214304012043589409 absolute error = 1e-31 relative error = 7.6527098604195680364814418084862e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.47 y[1] (closed_form) = 1.317187562184287362741108383233 y[1] (numeric) = 1.3171875621842873627411083832327 absolute error = 3e-31 relative error = 2.2775799636500597285984249196316e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.48 y[1] (closed_form) = 1.327651976296291413808050805688 y[1] (numeric) = 1.3276519762962914138080508056896 absolute error = 1.6e-30 relative error = 1.2051351020946537699957186555129e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2059.3MB, alloc=44.3MB, time=21.56 TOP MAIN SOLVE Loop x[1] = 26.49 y[1] (closed_form) = 1.338119901644322669805588232737 y[1] (numeric) = 1.3381199016443226698055882327361 absolute error = 9e-31 relative error = 6.7258546778510092252507596238694e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.5 y[1] (closed_form) = 1.348591336995936002117899141032 y[1] (numeric) = 1.3485913369959360021178991410336 absolute error = 1.6e-30 relative error = 1.1864231632720488261766232953603e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.51 y[1] (closed_form) = 1.359066281119551155956887330154 y[1] (numeric) = 1.3590662811195511559568873301548 absolute error = 8e-31 relative error = 5.8863942922709262315521954131487e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.52 y[1] (closed_form) = 1.369544732784451840287928644355 y[1] (numeric) = 1.3695447327844518402879286443553 absolute error = 3e-31 relative error = 2.1905089539504367352832067705292e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.53 y[1] (closed_form) = 1.380026690760784819032019302455 y[1] (numeric) = 1.3800266907607848190320193024544 absolute error = 6e-31 relative error = 4.3477419967089940063665273989776e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.54 y[1] (closed_form) = 1.390512153819559003542088889163 y[1] (numeric) = 1.3905121538195590035420888891643 absolute error = 1.3e-30 relative error = 9.3490732636105790526185562300577e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.55 y[1] (closed_form) = 1.401001120732644546351245763968 y[1] (numeric) = 1.4010011207326445463512457639687 absolute error = 7e-31 relative error = 4.9964271237266355051595101080513e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.56 y[1] (closed_form) = 1.411493590272771936190727334882 y[1] (numeric) = 1.4114935902727719361907273348817 absolute error = 3e-31 relative error = 2.1254081638587167086948508057090e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.57 y[1] (closed_form) = 1.421989561213531094275332324149 y[1] (numeric) = 1.4219895612135310942753323241503 absolute error = 1.3e-30 relative error = 9.1421205574151700775939294117025e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.58 y[1] (closed_form) = 1.432489032329370471854116821234 y[1] (numeric) = 1.4324890323293704718541168212347 absolute error = 7e-31 relative error = 4.8865993679667478671562793674812e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.59 y[1] (closed_form) = 1.44299200239559614902414057523 y[1] (numeric) = 1.4429920023955961490241405752305 absolute error = 5e-31 relative error = 3.4650226693558973556399926984809e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.6 y[1] (closed_form) = 1.453498470188370934805054624329 y[1] (numeric) = 1.4534984701883709348050546243293 absolute error = 3e-31 relative error = 2.0639856604810909031854356315277e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.61 y[1] (closed_form) = 1.464008434484713468472325993977 y[1] (numeric) = 1.4640084344847134684723259939777 absolute error = 7e-31 relative error = 4.7813932181775903000618118443184e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2100.4MB, alloc=44.3MB, time=21.98 TOP MAIN SOLVE Loop x[1] = 26.62 y[1] (closed_form) = 1.474521894062497322146899818113 y[1] (numeric) = 1.4745218940624973221468998181136 absolute error = 6e-31 relative error = 4.0691155717391410759615702680119e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.63 y[1] (closed_form) = 1.485038847700450104639103849285 y[1] (numeric) = 1.4850388477004501046391038492843 absolute error = 7e-31 relative error = 4.7136814035803477992294887639005e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.64 y[1] (closed_form) = 1.495559294178152566544604923581 y[1] (numeric) = 1.4955592941781525665446049235816 absolute error = 6e-31 relative error = 4.0118770438300481104029663904164e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.65 y[1] (closed_form) = 1.506083232276037706590231535238 y[1] (numeric) = 1.5060832322760377065902315352379 absolute error = 1e-31 relative error = 6.6397392824616359556629208043160e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.66 y[1] (closed_form) = 1.516610660775389879227481253408 y[1] (numeric) = 1.5166106607753898792274812534094 absolute error = 1.4e-30 relative error = 9.2311101076147589840368196773232e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.67 y[1] (closed_form) = 1.527141578458343903471536280179 y[1] (numeric) = 1.5271415784583439034715362801789 absolute error = 1e-31 relative error = 6.5481813481203515501841776728355e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.68 y[1] (closed_form) = 1.537675984107884172983615004168 y[1] (numeric) = 1.5376759841078841729836150041684 absolute error = 4e-31 relative error = 2.6013282650835482200407178741216e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.69 y[1] (closed_form) = 1.548213876507843767394491948388 y[1] (numeric) = 1.5482138765078437673944919483895 absolute error = 1.5e-30 relative error = 9.6885838756555060509414914212865e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.7 y[1] (closed_form) = 1.558755254442903564867023044112 y[1] (numeric) = 1.5587552544429035648670230441111 absolute error = 9e-31 relative error = 5.7738377941934087992416738420029e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.71 y[1] (closed_form) = 1.569300116698591355895517684616 y[1] (numeric) = 1.5693001166985913558955176846171 absolute error = 1.1e-30 relative error = 7.0094941579060126521310527196082e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.72 y[1] (closed_form) = 1.579848462061280958339803523798 y[1] (numeric) = 1.5798484620612809583398035237988 absolute error = 8e-31 relative error = 5.0637768065186032408706235433838e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.73 y[1] (closed_form) = 1.590400289318191333691834484594 y[1] (numeric) = 1.5904002893181913336918344845934 absolute error = 6e-31 relative error = 3.7726351285890518326619746410336e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.74 y[1] (closed_form) = 1.6009555972573857045726969314 y[1] (numeric) = 1.6009555972573857045726969314009 absolute error = 9e-31 relative error = 5.6216424836628804942968219033535e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2141.5MB, alloc=44.3MB, time=22.42 TOP MAIN SOLVE Loop x[1] = 26.75 y[1] (closed_form) = 1.611514384667770673457873438776 y[1] (numeric) = 1.6115143846677706734578734387759 absolute error = 1e-31 relative error = 6.2053433063593763872200672653613e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.76 y[1] (closed_form) = 1.62207665033909534262862805597 y[1] (numeric) = 1.6220766503390953426286280559691 absolute error = 9e-31 relative error = 5.5484431010819055841677911186451e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.77 y[1] (closed_form) = 1.632642393061950435347381423295 y[1] (numeric) = 1.6326423930619504353473814232949 absolute error = 1e-31 relative error = 6.1250400225400438343778259093462e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.78 y[1] (closed_form) = 1.643211611627767418254948541851 y[1] (numeric) = 1.6432116116277674182549485418507 absolute error = 3e-31 relative error = 1.8256930384201681464049358312335e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.79 y[1] (closed_form) = 1.653784304828817624987516432862 y[1] (numeric) = 1.653784304828817624987516432863 absolute error = 1.0e-30 relative error = 6.0467377582441713464767087251851e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.8 y[1] (closed_form) = 1.664360471458211381011243346895 y[1] (numeric) = 1.6643604714582113810112433468958 absolute error = 8e-31 relative error = 4.8066510453657234127280804543234e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.81 y[1] (closed_form) = 1.674940110309897129672365596364 y[1] (numeric) = 1.6749401103098971296723655963633 absolute error = 7e-31 relative error = 4.1792539069978216773669331421019e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.82 y[1] (closed_form) = 1.685523220178660559460702487274 y[1] (numeric) = 1.6855232201786605594607024872754 absolute error = 1.4e-30 relative error = 8.3060261836772801712746345474952e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.83 y[1] (closed_form) = 1.696109799860123732484454217937 y[1] (numeric) = 1.696109799860123732484454217938 absolute error = 1.0e-30 relative error = 5.8958447152564584867213957701394e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.84 y[1] (closed_form) = 1.70669984815074421415419199346 y[1] (numeric) = 1.7066998481507442141541919934589 absolute error = 1.1e-30 relative error = 6.4451871908928800243451996729463e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.85 y[1] (closed_form) = 1.717293363847814204073943975404 y[1] (numeric) = 1.7172933638478142040739439754029 absolute error = 1.1e-30 relative error = 6.4054285840557264549658102476868e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.86 y[1] (closed_form) = 1.727890345749459668137285045838 y[1] (numeric) = 1.7278903457494596681372850458371 absolute error = 9e-31 relative error = 5.2086638611875086964246796515855e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.87 y[1] (closed_form) = 1.738490792654639471826342714314 y[1] (numeric) = 1.7384907926546394718263427143149 absolute error = 9e-31 relative error = 5.1769040354002601335434116584950e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2182.7MB, alloc=44.3MB, time=22.84 TOP MAIN SOLVE Loop x[1] = 26.88 y[1] (closed_form) = 1.749094703363144514711635835124 y[1] (numeric) = 1.749094703363144514711635835125 absolute error = 1.0e-30 relative error = 5.7172433149400569941053379559110e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.89 y[1] (closed_form) = 1.759702076675596866150667130385 y[1] (numeric) = 1.7597020766755968661506671303834 absolute error = 1.6e-30 relative error = 9.0924482115898637393052948243177e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.9 y[1] (closed_form) = 1.77031291139344890218319483231 y[1] (numeric) = 1.7703129113934489021831948323099 absolute error = 1e-31 relative error = 5.6487188991514493622689268209321e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.91 y[1] (closed_form) = 1.780927206318982443621113065347 y[1] (numeric) = 1.7809272063189824436211130653455 absolute error = 1.5e-30 relative error = 8.4225789503231078074923774297440e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.92 y[1] (closed_form) = 1.791544960255307895330874885642 y[1] (numeric) = 1.791544960255307895330874885641 absolute error = 1.0e-30 relative error = 5.5817745140903016447860109763171e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.93 y[1] (closed_form) = 1.802166172006363386706396181928 y[1] (numeric) = 1.8021661720063633867063961819271 absolute error = 9e-31 relative error = 4.9939900880395735837071825134858e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.94 y[1] (closed_form) = 1.812790840376913913330382917888 y[1] (numeric) = 1.8127908403769139133303829178864 absolute error = 1.6e-30 relative error = 8.8261699273995083475515077183745e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.95 y[1] (closed_form) = 1.823418964172550479822028461908 y[1] (numeric) = 1.8234189641725504798220284619067 absolute error = 1.3e-30 relative error = 7.1294640756899617025513081503552e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.96 y[1] (closed_form) = 1.834050542199689243869032005549 y[1] (numeric) = 1.8340505421996892438690320055485 absolute error = 5e-31 relative error = 2.7262062222141345660118723291880e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.97 y[1] (closed_form) = 1.844685573265570661441893317222 y[1] (numeric) = 1.8446855732655706614418933172212 absolute error = 8e-31 relative error = 4.3367824392088297744223338063901e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.98 y[1] (closed_form) = 1.855324056178258633188443312471 y[1] (numeric) = 1.8553240561782586331884433124706 absolute error = 4e-31 relative error = 2.1559576003339882016558228294652e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.99 y[1] (closed_form) = 1.865965989746639652006574146954 y[1] (numeric) = 1.8659659897466396520065741469523 absolute error = 1.7e-30 relative error = 9.1105626219416010451031973519272e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 28.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27 y[1] (closed_form) = 1.876611372780421951793136752648 y[1] (numeric) = 1.8766113727804219517931367526477 absolute error = 3e-31 relative error = 1.5986261425854756387013462957707e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2223.9MB, alloc=44.3MB, time=23.28 TOP MAIN SOLVE Loop x[1] = 27.01 y[1] (closed_form) = 1.88726020409013465736697794218 y[1] (numeric) = 1.8872602040901346573669779421798 absolute error = 2e-31 relative error = 1.0597372824719833615192234829887e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.02 y[1] (closed_form) = 1.897912482487126935564093400241 y[1] (numeric) = 1.8979124824871269355640934002382 absolute error = 2.8e-30 relative error = 1.4753051185641230945715637246412e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.03 y[1] (closed_form) = 1.908568206783567147502877065176 y[1] (numeric) = 1.9085682067835671475028770651753 absolute error = 7e-31 relative error = 3.6676708619163352052343675641565e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.04 y[1] (closed_form) = 1.919227375792442002017451577779 y[1] (numeric) = 1.9192273757924420020174515777782 absolute error = 8e-31 relative error = 4.1683440434965810661564005877600e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.05 y[1] (closed_form) = 1.929889988327555710257068638116 y[1] (numeric) = 1.9298899883275557102570686381159 absolute error = 1e-31 relative error = 5.1816425083722043786632276511145e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.06 y[1] (closed_form) = 1.940556043203529141449572265222 y[1] (numeric) = 1.9405560432035291414495722652195 absolute error = 2.5e-30 relative error = 1.2882905437108240896606423454007e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.07 y[1] (closed_form) = 1.951225539235798979826922098203 y[1] (numeric) = 1.9512255392357989798269220982025 absolute error = 5e-31 relative error = 2.5624920848249347255923333148581e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.08 y[1] (closed_form) = 1.961898475240616882710778011305 y[1] (numeric) = 1.9618984752406168827107780113045 absolute error = 5e-31 relative error = 2.5485518558175011563870167598418e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.09 y[1] (closed_form) = 1.972574850035048639756151439261 y[1] (numeric) = 1.9725748500350486397561514392598 absolute error = 1.2e-30 relative error = 6.0834193439031144632762283254703e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.1 y[1] (closed_form) = 1.983254662436973333351132923402 y[1] (numeric) = 1.9832546624369733333511329233993 absolute error = 2.7e-30 relative error = 1.3613985390470773250466389819760e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.11 y[1] (closed_form) = 1.993937911265082500170709492986 y[1] (numeric) = 1.9939379112650825001707094929862 absolute error = 2e-31 relative error = 1.0030402595289796765553251726808e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.12 y[1] (closed_form) = 2.004624595338879293882689590532 y[1] (numeric) = 2.0046245953388792938826895905303 absolute error = 1.7e-30 relative error = 8.4803908120892685893390129307893e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.13 y[1] (closed_form) = 2.01531471347867764900375733421 y[1] (numeric) = 2.0153147134786776490037573342091 absolute error = 9e-31 relative error = 4.4658037475769272375662487936602e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2265.1MB, alloc=44.3MB, time=23.70 TOP MAIN SOLVE Loop x[1] = 27.14 y[1] (closed_form) = 2.026008264505601445903681985109 y[1] (numeric) = 2.026008264505601445903681985108 absolute error = 1.0e-30 relative error = 4.9358140216867571937621217976547e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.15 y[1] (closed_form) = 2.036705247241583676955712551777 y[1] (numeric) = 2.0367052472415836769557125517747 absolute error = 2.3e-30 relative error = 1.1292748438268179268527849357462e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.16 y[1] (closed_form) = 2.047405660509365613831191519617 y[1] (numeric) = 2.0474056605093656138311915196164 absolute error = 6e-31 relative error = 2.9305379562676820650432834281042e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.17 y[1] (closed_form) = 2.058109503132495975936425737958 y[1] (numeric) = 2.0581095031324959759364257379566 absolute error = 1.4e-30 relative error = 6.8023591449782615315080417771076e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.18 y[1] (closed_form) = 2.068816773935330099989856533163 y[1] (numeric) = 2.0688167739353300999898565331611 absolute error = 1.9e-30 relative error = 9.1839935944921567749477295488504e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.19 y[1] (closed_form) = 2.079527471743029110737575142144 y[1] (numeric) = 2.079527471743029110737575142141 absolute error = 3.0e-30 relative error = 1.4426354259631128875469927893873e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.2 y[1] (closed_form) = 2.090241595381559092805233576797 y[1] (numeric) = 2.0902415953815590928052335767949 absolute error = 2.1e-30 relative error = 1.0046685534533435491098797688240e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.21 y[1] (closed_form) = 2.100959143677690263684405036578 y[1] (numeric) = 2.1009591436776902636844050365767 absolute error = 1.3e-30 relative error = 6.1876500735962621192380421715060e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.22 y[1] (closed_form) = 2.111680115458996147851451983395 y[1] (numeric) = 2.1116801154589961478514519833925 absolute error = 2.5e-30 relative error = 1.1838914339810404438687300209888e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.23 y[1] (closed_form) = 2.12240450955385275201696398048 y[1] (numeric) = 2.1224045095538527520169639804777 absolute error = 2.3e-30 relative error = 1.0836765515935882133972783199488e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.24 y[1] (closed_form) = 2.133132324791437741503831374804 y[1] (numeric) = 2.133132324791437741503831374803 absolute error = 1.0e-30 relative error = 4.6879417107786445976333824715248e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.25 y[1] (closed_form) = 2.143863560001729617752024870934 y[1] (numeric) = 2.1438635600017296177520248709306 absolute error = 3.4e-30 relative error = 1.5859218205086040836786855583996e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.26 y[1] (closed_form) = 2.154598214015506896948155003117 y[1] (numeric) = 2.1545982140155068969481550031165 absolute error = 5e-31 relative error = 2.3206182793039363447123088884474e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2306.1MB, alloc=44.3MB, time=24.13 TOP MAIN SOLVE Loop x[1] = 27.27 y[1] (closed_form) = 2.165336285664347289777889461867 y[1] (numeric) = 2.1653362856643472897778894618653 absolute error = 1.7e-30 relative error = 7.8509745172372735431060968941094e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.28 y[1] (closed_form) = 2.176077773780626882299310171102 y[1] (numeric) = 2.1760777737806268822993101710987 absolute error = 3.3e-30 relative error = 1.5164899158299463982289044982318e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.29 y[1] (closed_form) = 2.186822677197519317935295942647 y[1] (numeric) = 2.1868226771975193179352959426448 absolute error = 2.2e-30 relative error = 1.0060257847789322486366115507216e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.3 y[1] (closed_form) = 2.197570994748994980583020455903 y[1] (numeric) = 2.1975709947489949805830204559004 absolute error = 2.6e-30 relative error = 1.1831244616044680633663591720913e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.31 y[1] (closed_form) = 2.208322725269820178838659222299 y[1] (numeric) = 2.2083227252698201788386592222982 absolute error = 8e-31 relative error = 3.6226589114245217599017249618117e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.32 y[1] (closed_form) = 2.219077867595556331335403096651 y[1] (numeric) = 2.2190778675955563313354030966479 absolute error = 3.1e-30 relative error = 1.3969766655187056138226604975636e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.33 y[1] (closed_form) = 2.229836420562559153192879790547 y[1] (numeric) = 2.2298364205625591531928797905447 absolute error = 2.3e-30 relative error = 1.0314657966792646946149950021512e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.34 y[1] (closed_form) = 2.240598383007977843576088726862 y[1] (numeric) = 2.2405983830079778435760887268596 absolute error = 2.4e-30 relative error = 1.0711424315044034347291352731177e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.35 y[1] (closed_form) = 2.251363753769754274361958448901 y[1] (numeric) = 2.2513637537697542743619584488983 absolute error = 2.7e-30 relative error = 1.1992731052363417885750189099449e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.36 y[1] (closed_form) = 2.26213253168662217991163966313 y[1] (numeric) = 2.262132531686622179911639663127 absolute error = 3.0e-30 relative error = 1.3261822452830522756774933799688e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.37 y[1] (closed_form) = 2.272904715598106347946650850484 y[1] (numeric) = 2.2729047155981063479466508504827 absolute error = 1.3e-30 relative error = 5.7195534466472778539421161395353e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.38 y[1] (closed_form) = 2.283680304344521811526997228188 y[1] (numeric) = 2.2836803043445218115269972281872 absolute error = 8e-31 relative error = 3.5031173079614648544385476728370e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.39 y[1] (closed_form) = 2.294459296766973042129387681746 y[1] (numeric) = 2.2944592967669730421293876817451 absolute error = 9e-31 relative error = 3.9224927688547471135181774452262e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2347.3MB, alloc=44.3MB, time=24.56 TOP MAIN SOLVE Loop x[1] = 27.4 y[1] (closed_form) = 2.30524169170735314382367811541 y[1] (numeric) = 2.3052416917073531438236781154091 absolute error = 9e-31 relative error = 3.9041459437314983441166056565873e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.41 y[1] (closed_form) = 2.316027488008343048545673488896 y[1] (numeric) = 2.3160274880083430485456734888948 absolute error = 1.2e-30 relative error = 5.1812856549122150497775377585547e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.42 y[1] (closed_form) = 2.326816684513410712464424618527 y[1] (numeric) = 2.3268166845134107124644246185247 absolute error = 2.3e-30 relative error = 9.8847494747141256657994092934892e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.43 y[1] (closed_form) = 2.337609280066810313442159622324 y[1] (numeric) = 2.3376092800668103134421596223219 absolute error = 2.1e-30 relative error = 8.9835372314229549352872698708695e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.44 y[1] (closed_form) = 2.348405273513581449584993680869 y[1] (numeric) = 2.3484052735135814495849936808681 absolute error = 9e-31 relative error = 3.8323879193707451094611619205825e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.45 y[1] (closed_form) = 2.359204663699548338882564569017 y[1] (numeric) = 2.3592046636995483388825645690153 absolute error = 1.7e-30 relative error = 7.2058182410260782954380434112691e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.46 y[1] (closed_form) = 2.370007449471319019934745187836 y[1] (numeric) = 2.3700074494713190199347451878337 absolute error = 2.3e-30 relative error = 9.7046108463206067868624971403252e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.47 y[1] (closed_form) = 2.380813629676284553763588091489 y[1] (numeric) = 2.3808136296762845537635880914862 absolute error = 2.8e-30 relative error = 1.1760685360242630797370300659862e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.48 y[1] (closed_form) = 2.391623203162618226708660760103 y[1] (numeric) = 2.3916232031626182267086607601015 absolute error = 1.5e-30 relative error = 6.2718909818922994494859118114823e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.49 y[1] (closed_form) = 2.402436168779274754403934117167 y[1] (numeric) = 2.4024361687792747544039341171666 absolute error = 4e-31 relative error = 1.6649765983303851801850626424784e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.5 y[1] (closed_form) = 2.413252525375989486834390528527 y[1] (numeric) = 2.4132525253759894868343905285241 absolute error = 2.9e-30 relative error = 1.2016976961613970754636243319479e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.51 y[1] (closed_form) = 2.424072271803277614470521249742 y[1] (numeric) = 2.4240722718032776144705212497403 absolute error = 1.7e-30 relative error = 7.0129922270649249687914849222210e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.52 y[1] (closed_form) = 2.434895406912433375478887009459 y[1] (numeric) = 2.4348954069124333754788870094571 absolute error = 1.9e-30 relative error = 7.8032099227181715051639937816873e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2388.4MB, alloc=44.3MB, time=24.98 TOP MAIN SOLVE Loop x[1] = 27.53 y[1] (closed_form) = 2.445721929555529264006919128357 y[1] (numeric) = 2.4457219295555292640069191283553 absolute error = 1.7e-30 relative error = 6.9509128550396885685623538686744e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.54 y[1] (closed_form) = 2.456551838585415239540142276576 y[1] (numeric) = 2.4565518385854152395401422765752 absolute error = 8e-31 relative error = 3.2565972654608147258460111686342e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.55 y[1] (closed_form) = 2.467385132855717937330003666889 y[1] (numeric) = 2.4673851328557179373300036668853 absolute error = 3.7e-30 relative error = 1.4995632221053672348561679632974e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.56 y[1] (closed_form) = 2.478221811220839879890497166579 y[1] (numeric) = 2.4782218112208398798904971665767 absolute error = 2.3e-30 relative error = 9.2808480241199921539514620074947e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.57 y[1] (closed_form) = 2.489061872535958689561774488033 y[1] (numeric) = 2.489061872535958689561774488031 absolute error = 2.0e-30 relative error = 8.0351558234360710236481185992304e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.58 y[1] (closed_form) = 2.499905315657026302138939286162 y[1] (numeric) = 2.4999053156570263021389392861612 absolute error = 8e-31 relative error = 3.2001212005493240855830792424287e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.59 y[1] (closed_form) = 2.510752139440768181564223650512 y[1] (numeric) = 2.5107521394407681815642236505092 absolute error = 2.8e-30 relative error = 1.1152036698547461463954466120906e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.6 y[1] (closed_form) = 2.521602342744682535680750130701 y[1] (numeric) = 2.5216023427446825356807501307006 absolute error = 4e-31 relative error = 1.5862929424653569540793279077003e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.61 y[1] (closed_form) = 2.532455924427039533046086076246 y[1] (numeric) = 2.5324559244270395330460860762447 absolute error = 1.3e-30 relative error = 5.1333568630384793548924670404130e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.62 y[1] (closed_form) = 2.54331288334688052080380070535 y[1] (numeric) = 2.5433128833468805208038007053468 absolute error = 3.2e-30 relative error = 1.2582014666590883698084069105004e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.63 y[1] (closed_form) = 2.554173218364017243611238942489 y[1] (numeric) = 2.554173218364017243611238942487 absolute error = 2.0e-30 relative error = 7.8303224919139480186603369238275e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.64 y[1] (closed_form) = 2.565036928339031063621729681044 y[1] (numeric) = 2.5650369283390310636217296810407 absolute error = 3.3e-30 relative error = 1.2865311853957940225930108922167e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.65 y[1] (closed_form) = 2.575904012133272181519449735208 y[1] (numeric) = 2.5759040121332721815194497352072 absolute error = 8e-31 relative error = 3.1057057880719259559373956181927e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2429.5MB, alloc=44.3MB, time=25.42 TOP MAIN SOLVE Loop x[1] = 27.66 y[1] (closed_form) = 2.586774468608858858605168344977 y[1] (numeric) = 2.586774468608858858605168344974 absolute error = 3.0e-30 relative error = 1.1597454808703789518942936203704e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.67 y[1] (closed_form) = 2.597648296628676639931100688817 y[1] (numeric) = 2.5976482966286766399311006888139 absolute error = 3.1e-30 relative error = 1.1933871124983677928882515974397e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.68 y[1] (closed_form) = 2.608525495056377578483102441317 y[1] (numeric) = 2.6085254950563775784831024413141 absolute error = 2.9e-30 relative error = 1.1117391819616172994376728584673e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.69 y[1] (closed_form) = 2.619406062756379460408440986987 y[1] (numeric) = 2.6194060627563794604084409869836 absolute error = 3.4e-30 relative error = 1.2980041729086508864036712715363e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.7 y[1] (closed_form) = 2.630289998593865031287382467111 y[1] (numeric) = 2.6302899985938650312873824671079 absolute error = 3.1e-30 relative error = 1.1785772677755071530321428461097e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.71 y[1] (closed_form) = 2.641177301434781223446837393743 y[1] (numeric) = 2.6411773014347812234468373937394 absolute error = 3.6e-30 relative error = 1.3630285244554965189534247405499e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.72 y[1] (closed_form) = 2.652067970145838384314311113755 y[1] (numeric) = 2.6520679701458383843143111137516 absolute error = 3.4e-30 relative error = 1.2820184242159647606434327524181e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.73 y[1] (closed_form) = 2.66296200359450950581040894636 y[1] (numeric) = 2.6629620035945095058104089463592 absolute error = 8e-31 relative error = 3.0041735440466178784452375799250e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.74 y[1] (closed_form) = 2.673859400649029454778149349657 y[1] (numeric) = 2.6738594006490294547781493496545 absolute error = 2.5e-30 relative error = 9.3497810669969096698921163321241e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.75 y[1] (closed_form) = 2.684760160178394204447341995539 y[1] (numeric) = 2.6847601601783942044473419955367 absolute error = 2.3e-30 relative error = 8.5668732504104647701163035318197e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.76 y[1] (closed_form) = 2.695664281052360066932291147952 y[1] (numeric) = 2.6956642810523600669322911479494 absolute error = 2.6e-30 relative error = 9.6451179706435339221261360017184e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.77 y[1] (closed_form) = 2.706571762141442926761088246612 y[1] (numeric) = 2.7065717621414429267610882466106 absolute error = 1.4e-30 relative error = 5.1725951610916027141588721623894e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.78 y[1] (closed_form) = 2.717482602316917475434761097443 y[1] (numeric) = 2.7174826023169174754347610974401 absolute error = 2.9e-30 relative error = 1.0671641457897352282816284891008e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2470.7MB, alloc=44.3MB, time=25.84 TOP MAIN SOLVE Loop x[1] = 27.79 y[1] (closed_form) = 2.728396800450816447014550561691 y[1] (numeric) = 2.7283968004508164470145505616886 absolute error = 2.4e-30 relative error = 8.7963744848382939417520768115689e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.8 y[1] (closed_form) = 2.739314355415929854735589118369 y[1] (numeric) = 2.7393143554159298547355891183664 absolute error = 2.6e-30 relative error = 9.4914261842913726073377666357694e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.81 y[1] (closed_form) = 2.750235266085804228645259148985 y[1] (numeric) = 2.7502352660858042286452591489825 absolute error = 2.5e-30 relative error = 9.0901314183133699534807673308050e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.82 y[1] (closed_form) = 2.761159531334741854264512259863 y[1] (numeric) = 2.7611595313347418542645122598615 absolute error = 1.5e-30 relative error = 5.4325003064017146693950147678138e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.83 y[1] (closed_form) = 2.772087150037800012270434415426 y[1] (numeric) = 2.7720871500378000122704344154244 absolute error = 1.6e-30 relative error = 5.7718243092688572111763677967962e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.84 y[1] (closed_form) = 2.783018121070790219198345105825 y[1] (numeric) = 2.7830181210707902191983451058233 absolute error = 1.7e-30 relative error = 6.1084762155479977306743090639875e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.85 y[1] (closed_form) = 2.793952443310277469161722214231 y[1] (numeric) = 2.793952443310277469161722214228 absolute error = 3.0e-30 relative error = 1.0737476964516966483766089028561e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.86 y[1] (closed_form) = 2.804890115633579476588247682909 y[1] (numeric) = 2.8048901156335794765882476829074 absolute error = 1.6e-30 relative error = 5.7043232855437040315053720631529e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.87 y[1] (closed_form) = 2.815831136918765919970272503032 y[1] (numeric) = 2.8158311369187659199702725030286 absolute error = 3.4e-30 relative error = 1.2074587696052196905310045627465e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.88 y[1] (closed_form) = 2.826775506044657686628002970871 y[1] (numeric) = 2.8267755060446576866280029708682 absolute error = 2.8e-30 relative error = 9.9052789795744229698894314598255e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.89 y[1] (closed_form) = 2.837723221890826118483713562879 y[1] (numeric) = 2.8377232218908261184837135628755 absolute error = 3.5e-30 relative error = 1.2333831477996951831132699257800e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.9 y[1] (closed_form) = 2.848674283337592258845295183803 y[1] (numeric) = 2.8486742833375922588452951838003 absolute error = 2.7e-30 relative error = 9.4780930757608377472083028203373e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.91 y[1] (closed_form) = 2.859628689266026100197450935905 y[1] (numeric) = 2.8596286892660261001974509359031 absolute error = 1.9e-30 relative error = 6.6442192552196990015150500265358e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2511.9MB, alloc=44.3MB, time=26.28 TOP MAIN SOLVE Loop x[1] = 27.92 y[1] (closed_form) = 2.870586438557945832998854943128 y[1] (numeric) = 2.8705864385579458329988549431243 absolute error = 3.7e-30 relative error = 1.2889352329897839354830609792538e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.93 y[1] (closed_form) = 2.881547530095917095483593142037 y[1] (numeric) = 2.881547530095917095483593142034 absolute error = 3.0e-30 relative error = 1.0411072413926623717078439962180e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.94 y[1] (closed_form) = 2.892511962763252224465208321421 y[1] (numeric) = 2.8925119627632522244652083214192 absolute error = 1.8e-30 relative error = 6.2229647557980637686878945205718e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.95 y[1] (closed_form) = 2.903479735444009507141675054535 y[1] (numeric) = 2.9034797354440095071416750545316 absolute error = 3.4e-30 relative error = 1.1710086895027221565626933987057e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.96 y[1] (closed_form) = 2.914450847022992433899633522318 y[1] (numeric) = 2.9144508470229924338996335223162 absolute error = 1.8e-30 relative error = 6.1761206295128833080881813381677e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.97 y[1] (closed_form) = 2.925425296385748952116214572415 y[1] (numeric) = 2.9254252963857489521162145724117 absolute error = 3.3e-30 relative error = 1.1280411104932413641381260297197e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.98 y[1] (closed_form) = 2.936403082418570720956791697364 y[1] (numeric) = 2.9364030824185707209567916973611 absolute error = 2.9e-30 relative error = 9.8760283196931284606369838778028e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.99 y[1] (closed_form) = 2.947384204008492367166998946328 y[1] (numeric) = 2.9473842040084923671669989463259 absolute error = 2.1e-30 relative error = 7.1249618463177093853863279007848e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 29.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28 y[1] (closed_form) = 2.958368660043290741857357107675 y[1] (numeric) = 2.9583686600432907418573571076734 absolute error = 1.6e-30 relative error = 5.4083861203984857494389884644243e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.01 y[1] (closed_form) = 2.96935644941148417827885381514 y[1] (numeric) = 2.9693564494114841782788538151378 absolute error = 2.2e-30 relative error = 7.4090128197173233505658934507842e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.02 y[1] (closed_form) = 2.980347571002331750587826537844 y[1] (numeric) = 2.9803475710023317505878265378438 absolute error = 2e-31 relative error = 6.7106267049496263240486487695246e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.03 y[1] (closed_form) = 2.991342023705832533598500714368 y[1] (numeric) = 2.9913420237058325335985007143649 absolute error = 3.1e-30 relative error = 1.0363241566604798420521517020826e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.04 y[1] (closed_form) = 3.002339806412724863521538583175 y[1] (numeric) = 3.0023398064127248635215385831729 absolute error = 2.1e-30 relative error = 6.9945447064805620109153327115798e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2553.0MB, alloc=44.3MB, time=26.70 TOP MAIN SOLVE Loop x[1] = 28.05 y[1] (closed_form) = 3.013340918014485599686957546354 y[1] (numeric) = 3.0133409180144855996869575463529 absolute error = 1.1e-30 relative error = 3.6504332895887491760675297771864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.06 y[1] (closed_form) = 3.024345357403329387249780180327 y[1] (numeric) = 3.0243453574033293872497801803251 absolute error = 1.9e-30 relative error = 6.2823513040564907607696332699225e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.07 y[1] (closed_form) = 3.03535312347220792087678127655 y[1] (numeric) = 3.0353531234722079208767812765483 absolute error = 1.7e-30 relative error = 5.6006663173849512608233796468688e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.08 y[1] (closed_form) = 3.0463642151148092094127005568 y[1] (numeric) = 3.0463642151148092094127005567998 absolute error = 2e-31 relative error = 6.5652031693282788297510461147332e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.09 y[1] (closed_form) = 3.057378631225556841524292961671 y[1] (numeric) = 3.0573786312255568415242929616674 absolute error = 3.6e-30 relative error = 1.1774792834726303455542225540131e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.1 y[1] (closed_form) = 3.068396370699609252320591657351 y[1] (numeric) = 3.068396370699609252320591657349 absolute error = 2.0e-30 relative error = 6.5180627219422447082751781712274e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.11 y[1] (closed_form) = 3.07941743243285899094776214477 y[1] (numeric) = 3.0794174324328589909477621447672 absolute error = 2.8e-30 relative error = 9.0926289190611342298307663158977e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.12 y[1] (closed_form) = 3.090441815321931989156929086395 y[1] (numeric) = 3.0904418153219319891569290863945 absolute error = 5e-31 relative error = 1.6178916474695540979436771483699e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.13 y[1] (closed_form) = 3.101469518264186830843360690058 y[1] (numeric) = 3.1014695182641868308433606900573 absolute error = 7e-31 relative error = 2.2569946145779697924292525118716e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.14 y[1] (closed_form) = 3.112500540157714022555398705372 y[1] (numeric) = 3.1125005401577140225553987053694 absolute error = 2.6e-30 relative error = 8.3534122049285009149259018519625e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.15 y[1] (closed_form) = 3.123534879901335264971525297364 y[1] (numeric) = 3.1235348799013352649715252973613 absolute error = 2.7e-30 relative error = 8.6440526640934655308459249928442e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.16 y[1] (closed_form) = 3.134572536394602725343961263341 y[1] (numeric) = 3.1345725363946027253439612633377 absolute error = 3.3e-30 relative error = 1.0527751269701586084856964231128e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.17 y[1] (closed_form) = 3.145613508537798310907193253025 y[1] (numeric) = 3.1456135085377983109071932530237 absolute error = 1.3e-30 relative error = 4.1327391190034970699203385244474e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2594.1MB, alloc=44.3MB, time=27.14 TOP MAIN SOLVE Loop x[1] = 28.18 y[1] (closed_form) = 3.156657795231932943249830838689 y[1] (numeric) = 3.1566577952319329432498308386879 absolute error = 1.1e-30 relative error = 3.4846982832967435010855693474949e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.19 y[1] (closed_form) = 3.167705395378745833648197461165 y[1] (numeric) = 3.1677053953787458336481974611618 absolute error = 3.2e-30 relative error = 1.0101949520521597844921446300632e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.2 y[1] (closed_form) = 3.178756307880703759360062449532 y[1] (numeric) = 3.1787563078807037593600624495304 absolute error = 1.6e-30 relative error = 5.0334151002180150448438539771308e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.21 y[1] (closed_form) = 3.189810531641000340876924476784 y[1] (numeric) = 3.1898105316410003408769244767833 absolute error = 7e-31 relative error = 2.1944877072052442326177830317844e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.22 y[1] (closed_form) = 3.200868065563555320133259970891 y[1] (numeric) = 3.200868065563555320133259970887 absolute error = 4.0e-30 relative error = 1.2496610038488877525534277346008e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.23 y[1] (closed_form) = 3.211928908553013839671153150604 y[1] (numeric) = 3.2119289085530138396711531506035 absolute error = 5e-31 relative error = 1.5566969700623040786746439022597e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.24 y[1] (closed_form) = 3.22299305951474572275872749795 y[1] (numeric) = 3.2229930595147457227587274979464 absolute error = 3.6e-30 relative error = 1.1169741707548127621245316501111e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.25 y[1] (closed_form) = 3.234060517354844754460801614467 y[1] (numeric) = 3.2340605173548447544608016144662 absolute error = 8e-31 relative error = 2.4736704700081625001493495099626e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.26 y[1] (closed_form) = 3.24513128098012796366019553659 y[1] (numeric) = 3.2451312809801279636601955365857 absolute error = 4.3e-30 relative error = 1.3250619551826789960075832600040e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.27 y[1] (closed_form) = 3.256205349298134906028116706024 y[1] (numeric) = 3.2562053492981349060281167060206 absolute error = 3.4e-30 relative error = 1.0441601911663401666896293765971e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.28 y[1] (closed_form) = 3.267282721217126947942057904898 y[1] (numeric) = 3.2672827212171269479420579048953 absolute error = 2.7e-30 relative error = 8.2637476777467148635428991204510e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.29 y[1] (closed_form) = 3.278363395646086551349642571566 y[1] (numeric) = 3.2783633956460865513496425715635 absolute error = 2.5e-30 relative error = 7.6257562029889311503179886416973e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.3 y[1] (closed_form) = 3.289447371494716559576856012344 y[1] (numeric) = 3.2894473714947165595768560123412 absolute error = 2.8e-30 relative error = 8.5120680885910847911627140362154e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2635.2MB, alloc=44.3MB, time=27.56 TOP MAIN SOLVE Loop x[1] = 28.31 y[1] (closed_form) = 3.30053464767343948407910411642 y[1] (numeric) = 3.3005346476734394840791041164188 absolute error = 1.2e-30 relative error = 3.6357745883561166679640492943955e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.32 y[1] (closed_form) = 3.311625223093396792133544266125 y[1] (numeric) = 3.3116252230933967921335442661214 absolute error = 3.6e-30 relative error = 1.0870795327006332137879505826706e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.33 y[1] (closed_form) = 3.322719096666448195471136212477 y[1] (numeric) = 3.3227190966664481954711362124745 absolute error = 2.5e-30 relative error = 7.5239583222913742068880794035533e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.34 y[1] (closed_form) = 3.333816267305170939846863756718 y[1] (numeric) = 3.3338162673051709398468637567169 absolute error = 1.1e-30 relative error = 3.2995219646257373610115009315348e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.35 y[1] (closed_form) = 3.344916733922859095546581142001 y[1] (numeric) = 3.3449167339228590955465811419981 absolute error = 2.9e-30 relative error = 8.6698720198004192737859625633881e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.36 y[1] (closed_form) = 3.356020495433522848828941116035 y[1] (numeric) = 3.3560204954335228488289411160329 absolute error = 2.1e-30 relative error = 6.2574111298111334390734566607435e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.37 y[1] (closed_form) = 3.367127550751887794300864674969 y[1] (numeric) = 3.3671275507518877943008646749671 absolute error = 1.9e-30 relative error = 5.6427918793148342895899914067220e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.38 y[1] (closed_form) = 3.378237898793394228225015541171 y[1] (numeric) = 3.3782378987933942282250155411685 absolute error = 2.5e-30 relative error = 7.4003077192785191377411379526959e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.39 y[1] (closed_form) = 3.389351538474196442757745463105 y[1] (numeric) = 3.3893515384741964427577454631008 absolute error = 4.2e-30 relative error = 1.2391750906696263679363602430512e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.4 y[1] (closed_form) = 3.400468468711162021115979453895 y[1] (numeric) = 3.4004684687111620211159794538932 absolute error = 1.8e-30 relative error = 5.2933882980018690999493532798276e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.41 y[1] (closed_form) = 3.411588688421871133671513106702 y[1] (numeric) = 3.4115886884218711336715131066989 absolute error = 3.1e-30 relative error = 9.0866756901870093858381991288288e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.42 y[1] (closed_form) = 3.422712196524615834971197139464 y[1] (numeric) = 3.4227121965246158349711971394607 absolute error = 3.3e-30 relative error = 9.6414767310870705280781919844642e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.43 y[1] (closed_form) = 3.433838991938399361681487329294 y[1] (numeric) = 3.4338389919383993616814873292927 absolute error = 1.3e-30 relative error = 3.7858501899827022490404514931343e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2676.4MB, alloc=44.3MB, time=27.98 TOP MAIN SOLVE Loop x[1] = 28.44 y[1] (closed_form) = 3.444969073582935431455840997357 y[1] (numeric) = 3.4449690735829354314558409973555 absolute error = 1.5e-30 relative error = 4.3541755178659035862579366563761e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.45 y[1] (closed_form) = 3.456102440378647542723444198876 y[1] (numeric) = 3.4561024403786475427234441988746 absolute error = 1.4e-30 relative error = 4.0508058547206061163685592030415e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.46 y[1] (closed_form) = 3.467239091246668275397756759838 y[1] (numeric) = 3.4672390912466682753977567598344 absolute error = 3.6e-30 relative error = 1.0382900934315425821583948152754e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.47 y[1] (closed_form) = 3.478379025108838592503365281913 y[1] (numeric) = 3.4783790251088385925033652819124 absolute error = 6e-31 relative error = 1.7249414042255673403542648099004e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.48 y[1] (closed_form) = 3.48952224088770714271963721039 y[1] (numeric) = 3.4895222408877071427196372103863 absolute error = 3.7e-30 relative error = 1.0603170705278981007282027028926e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.49 y[1] (closed_form) = 3.500668737506529563839672026106 y[1] (numeric) = 3.5006687375065295638396720261025 absolute error = 3.5e-30 relative error = 9.9980896864094433142912663474796e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.5 y[1] (closed_form) = 3.511818513889267787143048582135 y[1] (numeric) = 3.5118185138892677871430485821314 absolute error = 3.6e-30 relative error = 1.0251099211881177211638720074845e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.51 y[1] (closed_form) = 3.522971568960589342680870558484 y[1] (numeric) = 3.5229715689605893426808705584816 absolute error = 2.4e-30 relative error = 6.8124307932127062747526791435882e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.52 y[1] (closed_form) = 3.534127901645866665471614954216 y[1] (numeric) = 3.5341279016458666654716149542152 absolute error = 8e-31 relative error = 2.2636419005306364982862709085764e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.53 y[1] (closed_form) = 3.545287510871176402606291475531 y[1] (numeric) = 3.5452875108711764026062914755285 absolute error = 2.5e-30 relative error = 7.0516142691786370940645549565015e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.54 y[1] (closed_form) = 3.556450395563298721261423610831 y[1] (numeric) = 3.5564503955632987212614236108279 absolute error = 3.1e-30 relative error = 8.7165562715770635677367286391832e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.55 y[1] (closed_form) = 3.567616554649716617618365109599 y[1] (numeric) = 3.567616554649716617618365109596 absolute error = 3.0e-30 relative error = 8.4089754435354458547537781656749e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.56 y[1] (closed_form) = 3.57878598705861522668746850089 y[1] (numeric) = 3.5787859870586152266874685008869 absolute error = 3.1e-30 relative error = 8.6621552985007442982301815116206e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2717.6MB, alloc=44.3MB, time=28.42 TOP MAIN SOLVE Loop x[1] = 28.57 y[1] (closed_form) = 3.589958691718881133035625199659 y[1] (numeric) = 3.5899586917188811330356251996569 absolute error = 2.1e-30 relative error = 5.8496494816059144878895439643173e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.58 y[1] (closed_form) = 3.601134667560101682415699654837 y[1] (numeric) = 3.6011346675601016824156996548328 absolute error = 4.2e-30 relative error = 1.1662990661900603482283179353325e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.59 y[1] (closed_form) = 3.612313913512564294296382892065 y[1] (numeric) = 3.6123139135125642942963828920635 absolute error = 1.5e-30 relative error = 4.1524630359198784600207340432195e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.6 y[1] (closed_form) = 3.623496428507255775290993696513 y[1] (numeric) = 3.6234964285072557752909936965107 absolute error = 2.3e-30 relative error = 6.3474603753025181859506056397456e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.61 y[1] (closed_form) = 3.634682211475861633483758566832 y[1] (numeric) = 3.6346822114758616334837585668288 absolute error = 3.2e-30 relative error = 8.8040709305935193423876730473379e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.62 y[1] (closed_form) = 3.645871261350765393652104450683 y[1] (numeric) = 3.6458712613507653936521044506799 absolute error = 3.1e-30 relative error = 8.5027686875906732665524225607639e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.63 y[1] (closed_form) = 3.657063577065047913383501144742 y[1] (numeric) = 3.6570635770650479133835011447396 absolute error = 2.4e-30 relative error = 6.5626422659189973973809308403871e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.64 y[1] (closed_form) = 3.6682591575524867000853931082 y[1] (numeric) = 3.6682591575524867000853931081974 absolute error = 2.6e-30 relative error = 7.0878307347694485116181774269769e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.65 y[1] (closed_form) = 3.67945800174755522888676329826 y[1] (numeric) = 3.6794580017475552288867632982582 absolute error = 1.8e-30 relative error = 4.8920248556855157426998115874053e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.66 y[1] (closed_form) = 3.690660108585422261429874489117 y[1] (numeric) = 3.6906601085854222614298744891149 absolute error = 2.1e-30 relative error = 5.6900390125735535475202801416630e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.67 y[1] (closed_form) = 3.701865477001951165550736382326 y[1] (numeric) = 3.7018654770019511655507363823236 absolute error = 2.4e-30 relative error = 6.4832177584791664132239706189434e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.68 y[1] (closed_form) = 3.71307410593369923584684965647 y[1] (numeric) = 3.7130741059336992358468496564658 absolute error = 4.2e-30 relative error = 1.1311382105970268851201350044224e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.69 y[1] (closed_form) = 3.724285994317917015130780937469 y[1] (numeric) = 3.7242859943179170151307809374667 absolute error = 2.3e-30 relative error = 6.1756803948705143728715167752265e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=2758.8MB, alloc=44.3MB, time=28.84 x[1] = 28.7 y[1] (closed_form) = 3.735501141092547616768125497954 y[1] (numeric) = 3.7355011410925476167681254979492 absolute error = 4.8e-30 relative error = 1.2849681525183823414234321916692e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.71 y[1] (closed_form) = 3.746719545196226047898417314582 y[1] (numeric) = 3.7467195451962260478984173145798 absolute error = 2.2e-30 relative error = 5.8718032493803320564088317781899e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.72 y[1] (closed_form) = 3.757941205568278533537548926501 y[1] (numeric) = 3.7579412055682785335375489264974 absolute error = 3.6e-30 relative error = 9.5797134736055708129445115424227e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.73 y[1] (closed_form) = 3.769166121148721841560266345651 y[1] (numeric) = 3.7691661211487218415602663456489 absolute error = 2.1e-30 relative error = 5.5715241316028460266558150444430e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.74 y[1] (closed_form) = 3.780394290878262608561307071192 y[1] (numeric) = 3.7803942908782626085613070711874 absolute error = 4.6e-30 relative error = 1.2168042923721922900461800875012e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.75 y[1] (closed_form) = 3.791625713698296666593752055045 y[1] (numeric) = 3.7916257136982966665937520550428 absolute error = 2.2e-30 relative error = 5.8022604711532878177537999683015e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.76 y[1] (closed_form) = 3.802860388550908370783165254365 y[1] (numeric) = 3.8028603885509083707831652543631 absolute error = 1.9e-30 relative error = 4.9962391617642340919272839100941e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.77 y[1] (closed_form) = 3.814098314378869927816097188779 y[1] (numeric) = 3.8140983143788699278160971887768 absolute error = 2.2e-30 relative error = 5.7680736537549698702297065633215e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.78 y[1] (closed_form) = 3.825339490125640725301531696337 y[1] (numeric) = 3.8253394901256407253015316963346 absolute error = 2.4e-30 relative error = 6.2739529555353885728345761382688e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.79 y[1] (closed_form) = 3.836583914735366662003857851601 y[1] (numeric) = 3.8365839147353666620038578515967 absolute error = 4.3e-30 relative error = 1.1207887265243351420057705450388e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.8 y[1] (closed_form) = 3.847831587152879478945951772642 y[1] (numeric) = 3.8478315871528794789459517726391 absolute error = 2.9e-30 relative error = 7.5367123906423171988876092190837e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.81 y[1] (closed_form) = 3.859082506323696091380955800778 y[1] (numeric) = 3.8590825063236960913809558007732 absolute error = 4.8e-30 relative error = 1.2438189627027841169943605081225e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.82 y[1] (closed_form) = 3.870336671194017921631345287545 y[1] (numeric) = 3.870336671194017921631345287541 absolute error = 4.0e-30 relative error = 1.0335018216298946166187821313386e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.83 y[1] (closed_form) = 3.881594080710730232793875968064 y[1] (numeric) = 3.8815940807107302327938759680589 absolute error = 5.1e-30 relative error = 1.3138931825313831869078859111598e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2800.0MB, alloc=44.3MB, time=29.28 Radius of convergence (given) for eq 1 = 30.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.84 y[1] (closed_form) = 3.892854733821401463309007638069 y[1] (numeric) = 3.8928547338214014633090076380671 absolute error = 1.9e-30 relative error = 4.8807369653243507030849725419924e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.85 y[1] (closed_form) = 3.904118629474282562393402584115 y[1] (numeric) = 3.9041186294742825623934025841108 absolute error = 4.2e-30 relative error = 1.0757869825706500050403374642701e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.86 y[1] (closed_form) = 3.91538576661830632633409994215 y[1] (numeric) = 3.9153857666183063263340999421457 absolute error = 4.3e-30 relative error = 1.0982315042008957727750935198158e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.87 y[1] (closed_form) = 3.926656144203086735642969879551 y[1] (numeric) = 3.9266561442030867356429698795471 absolute error = 3.9e-30 relative error = 9.9321149007599274032011514485742e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.88 y[1] (closed_form) = 3.937929761178918293070054209024 y[1] (numeric) = 3.9379297611789182930700542090198 absolute error = 4.2e-30 relative error = 1.0665502572962663486397122904318e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.89 y[1] (closed_form) = 3.949206616496775362474402750277 y[1] (numeric) = 3.9492066164967753624744027502734 absolute error = 3.6e-30 relative error = 9.1157550100365570492251085834363e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.9 y[1] (closed_form) = 3.960486709108311508551017456562 y[1] (numeric) = 3.9604867091083115085510174565602 absolute error = 1.8e-30 relative error = 4.5448959489255883432796697565275e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.91 y[1] (closed_form) = 3.971770037965858837412519018287 y[1] (numeric) = 3.9717700379658588374125190182836 absolute error = 3.4e-30 relative error = 8.5604150479500300117749115208914e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.92 y[1] (closed_form) = 3.983056602022427338024153344901 y[1] (numeric) = 3.9830566020224273380241533448979 absolute error = 3.1e-30 relative error = 7.7829674788602084639721646496847e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.93 y[1] (closed_form) = 3.99434640023170422449075800924 y[1] (numeric) = 3.9943464002317042244907580092374 absolute error = 2.6e-30 relative error = 6.5092001030485965959457003546639e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.94 y[1] (closed_form) = 4.00563943154805327919431141527 y[1] (numeric) = 4.0056394315480532791943114152674 absolute error = 2.6e-30 relative error = 6.4908488255898310324928863952913e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.95 y[1] (closed_form) = 4.016935694926514196780690121041 y[1] (numeric) = 4.0169356949265141967806901210381 absolute error = 2.9e-30 relative error = 7.2194334693053944612076434657786e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.96 y[1] (closed_form) = 4.028235189322801928994262413381 y[1] (numeric) = 4.0282351893228019289942624133787 absolute error = 2.3e-30 relative error = 5.7096964102204259317415021647471e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2841.2MB, alloc=44.3MB, time=29.70 TOP MAIN SOLVE Loop x[1] = 28.97 y[1] (closed_form) = 4.039537913693306030358948889602 y[1] (numeric) = 4.0395379136933060303589488895991 absolute error = 2.9e-30 relative error = 7.1790389444533303499233089033011e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.98 y[1] (closed_form) = 4.05084386699509000470438345418 y[1] (numeric) = 4.050843866995090004704383454176 absolute error = 4.0e-30 relative error = 9.8744857400964063566389007954735e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.99 y[1] (closed_form) = 4.062153048185890652535810785142 y[1] (numeric) = 4.0621530481858906525358107851373 absolute error = 4.7e-30 relative error = 1.1570218906692755525505918465096e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 30.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29 y[1] (closed_form) = 4.073465456224117419246358965598 y[1] (numeric) = 4.0734654562241174192463589655951 absolute error = 2.9e-30 relative error = 7.1192453481320139874521146875920e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.01 y[1] (closed_form) = 4.08478109006885174417032861067 y[1] (numeric) = 4.0847810900688517441703286106658 absolute error = 4.2e-30 relative error = 1.0282068750786363837389662169936e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.01 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.02 y[1] (closed_form) = 4.096099948679846410476142448853 y[1] (numeric) = 4.0960999486798464104761424488507 absolute error = 2.3e-30 relative error = 5.6150973580155901549009345859267e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.02 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.03 y[1] (closed_form) = 4.107422031017524895897601939855 y[1] (numeric) = 4.1074220310175248958976019398519 absolute error = 3.1e-30 relative error = 7.5473130751846362008401028825246e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.03 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.04 y[1] (closed_form) = 4.118747336042980724302100127793 y[1] (numeric) = 4.1187473360429807243021001277889 absolute error = 4.1e-30 relative error = 9.9544829179519617695076650665176e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.04 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.05 y[1] (closed_form) = 4.130075862717976818094442539865 y[1] (numeric) = 4.1300758627179768180944425398614 absolute error = 3.6e-30 relative error = 8.7165469101840244562207824882414e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.05 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.06 y[1] (closed_form) = 4.141407610004944851454930545708 y[1] (numeric) = 4.141407610004944851454930545706 absolute error = 2.0e-30 relative error = 4.8292759089164179007232600360749e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.06 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.07 y[1] (closed_form) = 4.152742576866984604410364192021 y[1] (numeric) = 4.1527425768669846044103641920193 absolute error = 1.7e-30 relative error = 4.0936801849214460685350542055092e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.07 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.08 y[1] (closed_form) = 4.164080762267863317736624120493 y[1] (numeric) = 4.1640807622678633177366241204906 absolute error = 2.4e-30 relative error = 5.7635769741720847895667812746347e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.08 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.09 y[1] (closed_form) = 4.175422165172015048691494764723 y[1] (numeric) = 4.1754221651720150486914947647181 absolute error = 4.9e-30 relative error = 1.1735340298932705614707065175519e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.09 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2882.3MB, alloc=44.3MB, time=30.14 TOP MAIN SOLVE Loop x[1] = 29.1 y[1] (closed_form) = 4.18676678454454002757639360359 y[1] (numeric) = 4.1867667845445400275763936035858 absolute error = 4.2e-30 relative error = 1.0031607242859359685637989066235e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.11 y[1] (closed_form) = 4.198114619351204015125673824573 y[1] (numeric) = 4.1981146193512040151256738245688 absolute error = 4.2e-30 relative error = 1.0004491017563230229980306161283e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.11 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.12 y[1] (closed_form) = 4.209465668558437660722170320636 y[1] (numeric) = 4.2094656685584376607221703206333 absolute error = 2.7e-30 relative error = 6.4141157395984530478364235277769e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.12 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.13 y[1] (closed_form) = 4.220819931133335861437661508815 y[1] (numeric) = 4.2208199311333358614376615088115 absolute error = 3.5e-30 relative error = 8.2922277119275545504888042219933e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.13 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.14 y[1] (closed_form) = 4.232177406043657121896922017181 y[1] (numeric) = 4.232177406043657121896922017179 absolute error = 2.0e-30 relative error = 4.7256998185944404493546791193964e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.14 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.15 y[1] (closed_form) = 4.243538092257822914964043839862 y[1] (numeric) = 4.2435380922578229149640438398603 absolute error = 1.7e-30 relative error = 4.0060910566623324012240140252235e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.15 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.16 y[1] (closed_form) = 4.25490198874491704324970610685 y[1] (numeric) = 4.2549019887449170432497061068478 absolute error = 2.2e-30 relative error = 5.1705068784649996276228172791774e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.16 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.17 y[1] (closed_form) = 4.26626909447468500143807615686 y[1] (numeric) = 4.266269094474685001438076156858 absolute error = 2.0e-30 relative error = 4.6879368265593765897466035808278e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.17 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.18 y[1] (closed_form) = 4.277639408417533339432027137177 y[1] (numeric) = 4.2776394084175333394320271371756 absolute error = 1.4e-30 relative error = 3.2728331360635068871835140721878e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.18 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.19 y[1] (closed_form) = 4.289012929544529026315359884481 y[1] (numeric) = 4.2890129295445290263153598844794 absolute error = 1.6e-30 relative error = 3.7304620580146204375880782418794e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.19 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.2 y[1] (closed_form) = 4.300389656827398815130719365 y[1] (numeric) = 4.3003896568273988151307193649992 absolute error = 8e-31 relative error = 1.8602965401749149884169237392042e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.21 y[1] (closed_form) = 4.311769589238528608471898471052 y[1] (numeric) = 4.3117695892385286084718984710504 absolute error = 1.6e-30 relative error = 3.7107734234995724348150330148726e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.21 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.22 y[1] (closed_form) = 4.323152725750962824889224484039 y[1] (numeric) = 4.3231527257509628248892244840368 absolute error = 2.2e-30 relative error = 5.0888787409606125458289235796190e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2923.5MB, alloc=44.3MB, time=30.56 TOP MAIN SOLVE Loop x[1] = 29.23 y[1] (closed_form) = 4.334539065338403766106726021433 y[1] (numeric) = 4.3345390653384037661067260214307 absolute error = 2.3e-30 relative error = 5.3062158751600400131750906938961e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.24 y[1] (closed_form) = 4.345928606975210985049780787025 y[1] (numeric) = 4.3459286069752109850497807870235 absolute error = 1.5e-30 relative error = 3.4515063077485937728529178774065e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.25 y[1] (closed_form) = 4.357321349636400654681946939931 y[1] (numeric) = 4.3573213496364006546819469399302 absolute error = 8e-31 relative error = 1.8359903615251064495072837028273e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.26 y[1] (closed_form) = 4.368717292297644937649683388427 y[1] (numeric) = 4.3687172922976449376496833884262 absolute error = 8e-31 relative error = 1.8312011203161534895491397537157e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.27 y[1] (closed_form) = 4.380116433935271356733666799715 y[1] (numeric) = 4.380116433935271356733666799711 absolute error = 4.0e-30 relative error = 9.1321773298301123308968796708340e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.28 y[1] (closed_form) = 4.39151877352626216610541559615 y[1] (numeric) = 4.3915187735262621661054155961466 absolute error = 3.4e-30 relative error = 7.7421962089664452067813537035016e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.29 y[1] (closed_form) = 4.402924310048253723387933682429 y[1] (numeric) = 4.4029243100482537233879336824273 absolute error = 1.7e-30 relative error = 3.8610702348897950927764742105523e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.3 y[1] (closed_form) = 4.41433304247953586251908911651 y[1] (numeric) = 4.4143330424795358625190891165072 absolute error = 2.8e-30 relative error = 6.3429740643837711738061280579363e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.31 y[1] (closed_form) = 4.425744969799051267416445399966 y[1] (numeric) = 4.4257449697990512674164453999623 absolute error = 3.7e-30 relative error = 8.3601744457679328185633089294492e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.32 y[1] (closed_form) = 4.437160090986394846442265520811 y[1] (numeric) = 4.4371600909863948464422655208105 absolute error = 5e-31 relative error = 1.1268468789658846962761940834014e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.32 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.33 y[1] (closed_form) = 4.448578405021813107667411333667 y[1] (numeric) = 4.4485784050218131076674113336655 absolute error = 1.5e-30 relative error = 3.3718636908966537983881249187220e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.33 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.34 y[1] (closed_form) = 4.459999910886203534932863308473 y[1] (numeric) = 4.4599999108862035349328633084721 absolute error = 9e-31 relative error = 2.0179372600506839173614125172966e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.34 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.35 y[1] (closed_form) = 4.471424607561113964707588119989 y[1] (numeric) = 4.4714246075611139647075881199864 absolute error = 2.6e-30 relative error = 5.8147016402858226049538547398316e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.35 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2964.7MB, alloc=44.3MB, time=31.00 TOP MAIN SOLVE Loop x[1] = 29.36 y[1] (closed_form) = 4.482852494028741963741483985621 y[1] (numeric) = 4.4828524940287419637414839856194 absolute error = 1.6e-30 relative error = 3.5691560276213307514789730881710e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.36 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.37 y[1] (closed_form) = 4.494283569271934207512136089291 y[1] (numeric) = 4.4942835692719342075121360892897 absolute error = 1.3e-30 relative error = 2.8925633640215489201870078247839e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.37 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.38 y[1] (closed_form) = 4.505717832274185859464116853533 y[1] (numeric) = 4.5057178322741858594641168535309 absolute error = 2.1e-30 relative error = 4.6607445875945144492811344780457e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.38 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.39 y[1] (closed_form) = 4.517155282019639951039568241296 y[1] (numeric) = 4.517155282019639951039568241293 absolute error = 3.0e-30 relative error = 6.6413479561824733948350991439319e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.39 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.4 y[1] (closed_form) = 4.528595917493086762498805682677 y[1] (numeric) = 4.5285959174930867624988056826753 absolute error = 1.7e-30 relative error = 3.7539229177706716334979174036026e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.41 y[1] (closed_form) = 4.540039737679963204529685630248 y[1] (numeric) = 4.5400397376799632045296856302452 absolute error = 2.8e-30 relative error = 6.1673468995468466400204780809192e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.41 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.42 y[1] (closed_form) = 4.551486741566352200644481149648 y[1] (numeric) = 4.5514867415663522006444811496456 absolute error = 2.4e-30 relative error = 5.2730022875427780028870273067508e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.42 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.43 y[1] (closed_form) = 4.562936928138982070363012349895 y[1] (numeric) = 4.5629369281389820703630123498927 absolute error = 2.3e-30 relative error = 5.0406131757294904131837337613309e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.43 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.44 y[1] (closed_form) = 4.57439029638522591318078085012 y[1] (numeric) = 4.5743902963852259131807808501177 absolute error = 2.3e-30 relative error = 5.0279924776368682219538008136403e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.44 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.45 y[1] (closed_form) = 4.585846845293100993320859866544 y[1] (numeric) = 4.5858468452931009933208598665403 absolute error = 3.7e-30 relative error = 8.0683025945309720641422121512274e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.45 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.46 y[1] (closed_form) = 4.597306573851268125268293885176 y[1] (numeric) = 4.5973065738512681252682938851722 absolute error = 3.8e-30 relative error = 8.2657093647262547015432422289204e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.46 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.47 y[1] (closed_form) = 4.608769481049031060085764262175 y[1] (numeric) = 4.6087694810490310600857642621729 absolute error = 2.1e-30 relative error = 4.5565307803635380967593594949233e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.47 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.48 y[1] (closed_form) = 4.620235565876335872509279464906 y[1] (numeric) = 4.6202355658763358725092794649023 absolute error = 3.7e-30 relative error = 8.0082496817415160362887014296610e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.48 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3005.9MB, alloc=44.3MB, time=31.42 TOP MAIN SOLVE Loop x[1] = 29.49 y[1] (closed_form) = 4.631704827323770348822651032587 y[1] (numeric) = 4.6317048273237703488226510325851 absolute error = 1.9e-30 relative error = 4.1021612361637314297793250358252e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.49 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.5 y[1] (closed_form) = 4.64317726438256337550951869609 y[1] (numeric) = 4.6431772643825633755095186960869 absolute error = 3.1e-30 relative error = 6.6764627398136376379778390740554e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.51 y[1] (closed_form) = 4.654652876044584328681690451673 y[1] (numeric) = 4.6546528760445843286816904516694 absolute error = 3.6e-30 relative error = 7.7341965037341220718321803313780e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.52 y[1] (closed_form) = 4.666131661302342464282565733704 y[1] (numeric) = 4.6661316613023424642825657337035 absolute error = 5e-31 relative error = 1.0715514183764958499233765303549e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.53 y[1] (closed_form) = 4.677613619148986309064412176225 y[1] (numeric) = 4.6776136191489863090644121762236 absolute error = 1.4e-30 relative error = 2.9929791427593513435966237869170e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.54 y[1] (closed_form) = 4.689098748578303052338268792909 y[1] (numeric) = 4.6890987485783030523382687929068 absolute error = 2.2e-30 relative error = 4.6917331409730329705180015281701e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.55 y[1] (closed_form) = 4.700587048584717938495250739561 y[1] (numeric) = 4.7005870485847179384952507395583 absolute error = 2.7e-30 relative error = 5.7439634073215021881834566574706e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.56 y[1] (closed_form) = 4.712078518163293660298033152513 y[1] (numeric) = 4.7120785181632936602980331525091 absolute error = 3.9e-30 relative error = 8.2766023209650776265308437842898e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.57 y[1] (closed_form) = 4.723573156309729752941293880494 y[1] (numeric) = 4.7235731563097297529412938804926 absolute error = 1.4e-30 relative error = 2.9638579813882753379910874155459e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.58 y[1] (closed_form) = 4.73507096202036198887989724657 y[1] (numeric) = 4.735070962020361988879897246568 absolute error = 2.0e-30 relative error = 4.2238015354824570420247090046400e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.59 y[1] (closed_form) = 4.746571934292161773423603290526 y[1] (numeric) = 4.7465719342921617734236032905216 absolute error = 4.4e-30 relative error = 9.2698479258508388573420297609326e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.6 y[1] (closed_form) = 4.758076072122735541097089250916 y[1] (numeric) = 4.758076072122735541097089250915 absolute error = 1.0e-30 relative error = 2.1016898108437909741447799531745e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.61 y[1] (closed_form) = 4.769583374510324152764072349574 y[1] (numeric) = 4.7695833745103241527640723495719 absolute error = 2.1e-30 relative error = 4.4029002852174680618638249869654e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3047.1MB, alloc=44.3MB, time=31.86 TOP MAIN SOLVE Loop x[1] = 29.62 y[1] (closed_form) = 4.781093840453802293514325239817 y[1] (numeric) = 4.7810938404538022935143252398138 absolute error = 3.2e-30 relative error = 6.6930290573344379417626343471113e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.63 y[1] (closed_form) = 4.792607468952677871312377773189 y[1] (numeric) = 4.792607468952677871312377773187 absolute error = 2.0e-30 relative error = 4.1730936926429681856235397809514e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.64 y[1] (closed_form) = 4.804124259007091416406701027788 y[1] (numeric) = 4.804124259007091416406701027784 absolute error = 4.0e-30 relative error = 8.3261793083318654425852894646880e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.65 y[1] (closed_form) = 4.815644209617815481498171824554 y[1] (numeric) = 4.8156442096178154814981718245517 absolute error = 2.3e-30 relative error = 4.7761003510318200216405747846016e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.66 y[1] (closed_form) = 4.827167319786254042666618236228 y[1] (numeric) = 4.8271673197862540426666182362261 absolute error = 1.9e-30 relative error = 3.9360558152024686847478235015399e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.67 y[1] (closed_form) = 4.838693588514441901054248866742 y[1] (numeric) = 4.8386935885144419010542488667379 absolute error = 4.1e-30 relative error = 8.4733615076022350100729730295719e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.68 y[1] (closed_form) = 4.850223014805044085304770947121 y[1] (numeric) = 4.8502230148050440853047709471169 absolute error = 4.1e-30 relative error = 8.4532195478124844840899286840753e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.69 y[1] (closed_form) = 4.861755597661355254757004557097 y[1] (numeric) = 4.8617555976613552547570045570949 absolute error = 2.1e-30 relative error = 4.3194273299343977775456383933247e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.7 y[1] (closed_form) = 4.873291336087299103391802539778 y[1] (numeric) = 4.8732913360872991033918025397746 absolute error = 3.4e-30 relative error = 6.9768043105130973928606806936565e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.71 y[1] (closed_form) = 4.884830229087427764531087929926 y[1] (numeric) = 4.8848302290874277645310879299228 absolute error = 3.2e-30 relative error = 6.5508929684907725115706225128010e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.72 y[1] (closed_form) = 4.896372275666921216287822964655 y[1] (numeric) = 4.8963722756669212162878229646521 absolute error = 2.9e-30 relative error = 5.9227522678614119172028040551817e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.73 y[1] (closed_form) = 4.907917474831586687765725988508 y[1] (numeric) = 4.9079174748315866877657259885059 absolute error = 2.1e-30 relative error = 4.2788005519022316024854705801739e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.74 y[1] (closed_form) = 4.91946582558785806600755480327 y[1] (numeric) = 4.9194658255878580660075548032667 absolute error = 3.3e-30 relative error = 6.7080453793083563938832475230146e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3088.2MB, alloc=44.3MB, time=32.28 TOP MAIN SOLVE Loop x[1] = 29.75 y[1] (closed_form) = 4.93101732694279530369077724617 y[1] (numeric) = 4.9310173269427953036907772461666 absolute error = 3.4e-30 relative error = 6.8951288843026273458153438995076e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.76 y[1] (closed_form) = 4.942571977904083827569452008626 y[1] (numeric) = 4.942571977904083827569452008623 absolute error = 3.0e-30 relative error = 6.0697143378216643478551830569372e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.77 y[1] (closed_form) = 4.954129777480033947661144931151 y[1] (numeric) = 4.9541297774800339476611449311495 absolute error = 1.5e-30 relative error = 3.0277769605845681246418278771084e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.78 y[1] (closed_form) = 4.965690724679580267177708228728 y[1] (numeric) = 4.9656907246795802671777082287234 absolute error = 4.6e-30 relative error = 9.2635652420677546525705582565882e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.79 y[1] (closed_form) = 4.977254818512281093198752314637 y[1] (numeric) = 4.9772548185122810931987523146341 absolute error = 2.9e-30 relative error = 5.8265049826539123474626322397724e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.8 y[1] (closed_form) = 4.988822057988317848086642099704 y[1] (numeric) = 4.988822057988317848086642099702 absolute error = 2.0e-30 relative error = 4.0089623898240936834097167144507e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.81 y[1] (closed_form) = 5.000392442118494481641851847771 y[1] (numeric) = 5.0003924421184944816418518477689 absolute error = 2.1e-30 relative error = 4.1996703744922511495764513579777e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.82 y[1] (closed_form) = 5.011965969914236883997514867516 y[1] (numeric) = 5.0119659699142368839975148675126 absolute error = 3.4e-30 relative error = 6.7837651341000219991775870532131e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.83 y[1] (closed_form) = 5.023542640387592299252006514963 y[1] (numeric) = 5.0235426403875922992520065149588 absolute error = 4.2e-30 relative error = 8.3606337213770485190362811674404e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.84 y[1] (closed_form) = 5.035122452551228739838401170559 y[1] (numeric) = 5.0351224525512287398384011705544 absolute error = 4.6e-30 relative error = 9.1358254806082063548870335757584e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.85 y[1] (closed_form) = 5.04670540541843440162964603935 y[1] (numeric) = 5.0467054054184344016296460393464 absolute error = 3.6e-30 relative error = 7.1333666437807764205734759722228e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.86 y[1] (closed_form) = 5.058291498003117079778296802692 y[1] (numeric) = 5.058291498003117079778296802688 absolute error = 4.0e-30 relative error = 7.9078084004828443618383594668792e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.87 y[1] (closed_form) = 5.069880729319803585289662324984 y[1] (numeric) = 5.0698807293198035852896623249809 absolute error = 3.1e-30 relative error = 6.1145422654073145674424734158866e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3129.4MB, alloc=44.3MB, time=32.72 TOP MAIN SOLVE Loop x[1] = 29.88 y[1] (closed_form) = 5.081473098383639162327207789276 y[1] (numeric) = 5.081473098383639162327207789273 absolute error = 3.0e-30 relative error = 5.9037998271687536502151261073686e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.89 y[1] (closed_form) = 5.09306860421038690624906780108 y[1] (numeric) = 5.0930686042103869062490678010774 absolute error = 2.6e-30 relative error = 5.1049773762140313795283890219943e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.9 y[1] (closed_form) = 5.10466724581642718237452316057 y[1] (numeric) = 5.1046672458164271823745231605673 absolute error = 2.7e-30 relative error = 5.2892771849385630876910879401999e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.91 y[1] (closed_form) = 5.11626902221875704547929715936 y[1] (numeric) = 5.1162690222187570454792971593571 absolute error = 2.9e-30 relative error = 5.6681929496005385889457638977972e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.92 y[1] (closed_form) = 5.127873932434989660018529409394 y[1] (numeric) = 5.127873932434989660018529409391 absolute error = 3.0e-30 relative error = 5.8503778359766326123769036461493e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.93 y[1] (closed_form) = 5.139481975483353721076287358078 y[1] (numeric) = 5.1394819754833537210762873580757 absolute error = 2.3e-30 relative error = 4.4751591910849955170005862931202e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.94 y[1] (closed_form) = 5.15109315038269287604047778568 y[1] (numeric) = 5.1510931503826928760404777856778 absolute error = 2.2e-30 relative error = 4.2709381014330021220004042403107e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.95 y[1] (closed_form) = 5.162707456152465147002022718222 y[1] (numeric) = 5.1627074561524651470020227182183 absolute error = 3.7e-30 relative error = 7.1667822192610627549392718204609e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.96 y[1] (closed_form) = 5.174324891812742353877166321615 y[1] (numeric) = 5.1743248918127423538771663216107 absolute error = 4.3e-30 relative error = 8.3102628650238532920414775256393e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.97 y[1] (closed_form) = 5.185945456384209538251781470644 y[1] (numeric) = 5.1859454563842095382517814706428 absolute error = 1.2e-30 relative error = 2.3139464348255497172233119599933e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.98 y[1] (closed_form) = 5.197569148888164387946546809591 y[1] (numeric) = 5.1975691488881643879465468095893 absolute error = 1.7e-30 relative error = 3.2707597557670872305629839488441e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.99 y[1] (closed_form) = 5.20919596834651666230186723979 y[1] (numeric) = 5.2091959683465166623018672397859 absolute error = 4.1e-30 relative error = 7.8706964086463549513529401057248e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 31.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; Iterations = 10000 Total Elapsed Time = 33 Seconds Elapsed Time(since restart) = 32 Seconds Time to Timeout = 2 Minutes 27 Seconds Percent Done = 100 % > quit memory used=3168.9MB, alloc=44.3MB, time=33.11