|\^/| 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(0.0)); > end; exact_soln_y := proc(x) return c(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_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > 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)*24*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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if 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)*24*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_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > 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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); 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_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > #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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; 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_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre tanh $eq_no = 1 > array_tmp4_a1[1] := sinh(array_tmp3[1]); > array_tmp4_a2[1] := cosh(array_tmp3[1]); > array_tmp4[1] := (array_tmp4_a1[1] / array_tmp4_a2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2; > #emit pre tanh $eq_no = 1 > array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[2] := att(1,array_tmp4_a1,array_tmp3,1); > array_tmp4[2] := (array_tmp4_a1[2] - ats(2,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0; > array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre tanh $eq_no = 1 > array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[3] := att(2,array_tmp4_a1,array_tmp3,1); > array_tmp4[3] := (array_tmp4_a1[3] - ats(3,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0; > array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre tanh $eq_no = 1 > array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[4] := att(3,array_tmp4_a1,array_tmp3,1); > array_tmp4[4] := (array_tmp4_a1[4] - ats(4,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0; > array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre tanh $eq_no = 1 > array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[5] := att(4,array_tmp4_a1,array_tmp3,1); > array_tmp4[5] := (array_tmp4_a1[5] - ats(5,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0; > array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2; > array_tmp4_a1[kkk] := att(kkk-1 ,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[kkk] := att(kkk-1,array_tmp4_a1,array_tmp3,1); > array_tmp4[kkk] := (array_tmp4_a1[kkk] - ats(kkk ,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_a1[1] := sinh(array_tmp3[1]); array_tmp4_a2[1] := cosh(array_tmp3[1]); array_tmp4[1] := array_tmp4_a1[1]/array_tmp4_a2[1]; array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2); array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[2] := att(1, array_tmp4_a1, array_tmp3, 1); array_tmp4[2] := ( array_tmp4_a1[2] - ats(2, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := 0; array_tmp3[3] := neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[3] := att(2, array_tmp4_a1, array_tmp3, 1); array_tmp4[3] := ( array_tmp4_a1[3] - ats(3, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := 0; array_tmp3[4] := neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[4] := att(3, array_tmp4_a1, array_tmp3, 1); array_tmp4[4] := ( array_tmp4_a1[4] - ats(4, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := 0; array_tmp3[5] := neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[5] := att(4, array_tmp4_a1, array_tmp3, 1); array_tmp4[5] := ( array_tmp4_a1[5] - ats(5, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := 0; array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/( array_tmp3[1]*glob__2); array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[kkk] := att(kkk - 1, array_tmp4_a1, array_tmp3, 1); array_tmp4[kkk] := ( array_tmp4_a1[kkk] - ats(kkk, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 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_g:= Array(0..(30),[]); > array_tmp4_a1:= Array(0..(30),[]); > array_tmp4_a2:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_tmp5:= 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_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4_a1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4_a2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_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_g); > zero_ats_ar(array_tmp4_a1); > zero_ats_ar(array_tmp4_a2); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_const_3D0); > array_const_3D0[1] := c(3.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_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/tanh_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; "); > 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(0.1);"); > omniout_str(ALWAYS,"x_end := c(5.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_h := 0.1;"); > 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(-1.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#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(1.0000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(c(0.0));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(0.1); > x_end := c(5.0) ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_h := 0.1; > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(-1.5); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(0.5); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=100000; > glob_upper_ratio_limit:=c(1.0000001); > glob_lower_ratio_limit:=c(0.9999999); > 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 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2015-05-02T18:39:08-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"tanh_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; ") > ; > 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,"tanh_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"tanh_sqrt maple results") > ; > logitem_str(html_log_file,"??") > ; > 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_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 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_g := Array(0 .. 30, []); array_tmp4_a1 := Array(0 .. 30, []); array_tmp4_a2 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_tmp5 := 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_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4_a1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4_a2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_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_g); zero_ats_ar(array_tmp4_a1); zero_ats_ar(array_tmp4_a2); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_const_3D0); array_const_3D0[1] := c(3.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_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/tanh_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh ( sqrt ( 2.0\ * x + 3.0 ) ) ; "); 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(0.1);"); omniout_str(ALWAYS, "x_end := c(5.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_h := 0.1;"); 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(-1.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#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(1.0000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(c(0.0));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(0.1); x_end := c(5.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := 0.1; glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(-1.5); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(0.5); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 100000; glob_upper_ratio_limit := c(1.0000001); glob_lower_ratio_limit := c(0.9999999); 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 ) = tanh ( sqrt ( 2\ .0 * x + 3.0 ) ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2015-05-02T18:39:08-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "tanh_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ta\ nh ( sqrt ( 2.0 * x + 3.0 ) ) ; "); 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, "tanh_sqrt diffeq.mxt"); logitem_str(html_log_file, "tanh_sqrt maple results"); logitem_str(html_log_file, "??"); 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/tanh_sqrtpostode.ode################# diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.1); x_end := c(5.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := 0.1; glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(-1.5); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(0.5); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=100000; glob_upper_ratio_limit:=c(1.0000001); glob_lower_ratio_limit:=c(0.9999999); 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(0.0)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0 y[1] (numeric) = 0 memory used=4.3MB, alloc=40.3MB, time=0.08 absolute error = 0 relative error = -1 % Desired digits = 8 Estimated correct digits = -16 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0 y[1] (numeric) = 0.0094590443916663969645925910802989 absolute error = 0.0094590443916663969645925910802989 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0 y[1] (numeric) = 0.018923925070309697281451477238366 absolute error = 0.018923925070309697281451477238366 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=35.6MB, alloc=44.3MB, time=0.42 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0 y[1] (numeric) = 0.028394563018230195767219458177815 absolute error = 0.028394563018230195767219458177815 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0 y[1] (numeric) = 0.037870880543987960601016329501099 absolute error = 0.037870880543987960601016329501099 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0 y[1] (numeric) = 0.047352801255258205072623974894738 absolute error = 0.047352801255258205072623974894738 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=79.6MB, alloc=52.3MB, time=0.89 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (closed_form) = 0 y[1] (numeric) = 0.056840250032352381573685999439139 absolute error = 0.056840250032352381573685999439139 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (closed_form) = 0 y[1] (numeric) = 0.066333153002385754410140866943441 absolute error = 0.066333153002385754410140866943441 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = 0 y[1] (numeric) = 0.075831437514072853977189514601243 absolute error = 0.075831437514072853977189514601243 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=123.8MB, alloc=52.3MB, time=1.36 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (closed_form) = 0 y[1] (numeric) = 0.085335032113132835949885035836124 absolute error = 0.085335032113132835949885035836124 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0 y[1] (numeric) = 0.094843866518287366485838594619938 absolute error = 0.094843866518287366485838594619938 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = 0 y[1] (numeric) = 0.10435787159783422904159333608539 absolute error = 0.10435787159783422904159333608539 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=167.8MB, alloc=52.3MB, time=1.81 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 0 y[1] (numeric) = 0.11387697934678040125093994777782 absolute error = 0.11387697934678040125093994777782 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 0 y[1] (numeric) = 0.12340112286451888233452467005861 absolute error = 0.12340112286451888233452467005861 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = 0 y[1] (numeric) = 0.13293023633303406359343734141664 absolute error = 0.13293023633303406359343734141664 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=211.9MB, alloc=52.3MB, time=2.28 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = 0 y[1] (numeric) = 0.14246425499562092753056755049755 absolute error = 0.14246425499562092753056755049755 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = 0 y[1] (numeric) = 0.1520031151361038358477312673416 absolute error = 0.1520031151361038358477312673416 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (closed_form) = 0 y[1] (numeric) = 0.16154675405854112375121010292233 absolute error = 0.16154675405854112375121010292233 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=256.0MB, alloc=52.3MB, time=2.73 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (closed_form) = 0 y[1] (numeric) = 0.17109511006740215839467670868918 absolute error = 0.17109511006740215839467670868918 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (closed_form) = 0 y[1] (numeric) = 0.1806481224482039435936014081363 absolute error = 0.1806481224482039435936014081363 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 0 y[1] (numeric) = 0.19020573144859476182384856645736 absolute error = 0.19020573144859476182384856645736 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (closed_form) = 0 y[1] (numeric) = 0.19976787825987273860325063341742 absolute error = 0.19976787825987273860325063341742 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=300.2MB, alloc=52.3MB, time=3.20 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (closed_form) = 0 y[1] (numeric) = 0.2093345049989275942533149571217 absolute error = 0.2093345049989275942533149571217 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (closed_form) = 0 y[1] (numeric) = 0.21890555469059421432602883049816 absolute error = 0.21890555469059421432602883049816 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (closed_form) = 0 y[1] (numeric) = 0.2284809712504070232088739270448 absolute error = 0.2284809712504070232088739270448 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=344.3MB, alloc=52.3MB, time=3.67 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (closed_form) = 0 y[1] (numeric) = 0.23806069946774448611559580178966 absolute error = 0.23806069946774448611559580178966 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (closed_form) = 0 y[1] (numeric) = 0.24764468498935339333326359041076 absolute error = 0.24764468498935339333326359041076 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (closed_form) = 0 y[1] (numeric) = 0.25723287430324289770746041251347 absolute error = 0.25723287430324289770746041251347 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=388.3MB, alloc=52.3MB, time=4.13 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (closed_form) = 0 y[1] (numeric) = 0.26682521472293858236543950956343 absolute error = 0.26682521472293858236543950956343 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (closed_form) = 0 y[1] (numeric) = 0.27642165437208713103980673378394 absolute error = 0.27642165437208713103980673378394 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0 y[1] (numeric) = 0.28602214216940245848145630894161 absolute error = 0.28602214216940245848145630894161 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=432.4MB, alloc=52.3MB, time=4.59 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (closed_form) = 0 y[1] (numeric) = 0.29562662781394443374041633682606 absolute error = 0.29562662781394443374041633682606 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (closed_form) = 0 y[1] (numeric) = 0.30523506177072159492978307895621 absolute error = 0.30523506177072159492978307895621 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (closed_form) = 0 y[1] (numeric) = 0.3148473952566095108372221381185 absolute error = 0.3148473952566095108372221381185 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=476.5MB, alloc=52.3MB, time=5.05 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (closed_form) = 0 y[1] (numeric) = 0.32446358022657669276092916366517 absolute error = 0.32446358022657669276092916366517 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (closed_form) = 0 y[1] (numeric) = 0.33408356936021019955772594759338 absolute error = 0.33408356936021019955772594759338 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (closed_form) = 0 y[1] (numeric) = 0.34370731604853331042100677143895 absolute error = 0.34370731604853331042100677143895 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=520.4MB, alloc=52.3MB, time=5.51 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (closed_form) = 0 y[1] (numeric) = 0.35333477438110786366274681077105 absolute error = 0.35333477438110786366274681077105 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (closed_form) = 0 y[1] (numeric) = 0.36296589913341407605090272669618 absolute error = 0.36296589913341407605090272669618 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (closed_form) = 0 y[1] (numeric) = 0.37260064575450086633301244054403 absolute error = 0.37260064575450086633301244054403 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=564.6MB, alloc=52.3MB, time=5.98 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 0 y[1] (numeric) = 0.38223897035489990872852834161645 absolute error = 0.38223897035489990872852834161645 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = 0 y[1] (numeric) = 0.39188082969479683765499344224117 absolute error = 0.39188082969479683765499344224117 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 0 y[1] (numeric) = 0.40152618117245321401441962750352 absolute error = 0.40152618117245321401441962750352 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 0 y[1] (numeric) = 0.4111749828128730462437026100089 absolute error = 0.4111749828128730462437026100089 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=608.6MB, alloc=52.3MB, time=6.44 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 0 y[1] (numeric) = 0.4208271932567078362543573138409 absolute error = 0.4208271932567078362543573138409 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 0 y[1] (numeric) = 0.43048277174939429157067188765739 absolute error = 0.43048277174939429157067188765739 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = 0 y[1] (numeric) = 0.44014167813051901063101909159334 absolute error = 0.44014167813051901063101909159334 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=652.8MB, alloc=52.3MB, time=6.91 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (closed_form) = 0 y[1] (numeric) = 0.44980387282340460854546402508332 absolute error = 0.44980387282340460854546402508332 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (closed_form) = 0 y[1] (numeric) = 0.45946931682491190579675743191222 absolute error = 0.45946931682491190579675743191222 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (closed_form) = 0 y[1] (numeric) = 0.46913797169545295261631615954322 absolute error = 0.46913797169545295261631615954322 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=696.8MB, alloc=52.3MB, time=7.36 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0 y[1] (numeric) = 0.47880979954920980723944739608592 absolute error = 0.47880979954920980723944739608592 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (closed_form) = 0 y[1] (numeric) = 0.48848476304455412711535027625671 absolute error = 0.48848476304455412711535027625671 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (closed_form) = 0 y[1] (numeric) = 0.49816282537466276858101903338665 absolute error = 0.49816282537466276858101903338665 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=740.7MB, alloc=52.3MB, time=7.83 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (closed_form) = 0 y[1] (numeric) = 0.50784395025832472266127893010453 absolute error = 0.50784395025832472266127893010453 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (closed_form) = 0 y[1] (numeric) = 0.51752810193093484268080799281962 absolute error = 0.51752810193093484268080799281962 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (closed_form) = 0 y[1] (numeric) = 0.52721524513566994341319838614271 absolute error = 0.52721524513566994341319838614271 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=784.8MB, alloc=52.3MB, time=8.30 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (closed_form) = 0 y[1] (numeric) = 0.53690534511484297168627904460778 absolute error = 0.53690534511484297168627904460778 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (closed_form) = 0 y[1] (numeric) = 0.54659836760143106484601293830893 absolute error = 0.54659836760143106484601293830893 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = 0 y[1] (numeric) = 0.55629427881077342638205790327931 absolute error = 0.55629427881077342638205790327931 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=828.9MB, alloc=52.3MB, time=8.75 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (closed_form) = 0 y[1] (numeric) = 0.56599304543243505746032466330383 absolute error = 0.56599304543243505746032466330383 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 0 y[1] (numeric) = 0.57569463462223248921060263933209 absolute error = 0.57569463462223248921060263933209 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (closed_form) = 0 y[1] (numeric) = 0.58539901399441776349501662885362 absolute error = 0.58539901399441776349501662885362 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=873.1MB, alloc=52.3MB, time=9.22 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (closed_form) = 0 y[1] (numeric) = 0.59510615161401700964582169701906 absolute error = 0.59510615161401700964582169701906 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = 0 y[1] (numeric) = 0.60481601598932006141475288038332 absolute error = 0.60481601598932006141475288038332 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (closed_form) = 0 y[1] (numeric) = 0.6145285760645176522227262219586 absolute error = 0.6145285760645176522227262219586 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (closed_form) = 0 y[1] (numeric) = 0.62424380121248281783620372024484 memory used=917.3MB, alloc=52.3MB, time=9.69 absolute error = 0.62424380121248281783620372024484 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (closed_form) = 0 y[1] (numeric) = 0.63396166122769322391937203370401 absolute error = 0.63396166122769322391937203370401 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (closed_form) = 0 y[1] (numeric) = 0.64368212631929122161030029733128 absolute error = 0.64368212631929122161030029733128 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (closed_form) = 0 y[1] (numeric) = 0.65340516710427851743191078602235 absolute error = 0.65340516710427851743191078602235 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=961.3MB, alloc=52.3MB, time=10.14 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (closed_form) = 0 y[1] (numeric) = 0.66313075460084242455914850590862 absolute error = 0.66313075460084242455914850590862 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = 0 y[1] (numeric) = 0.67285886022181074080329241442031 absolute error = 0.67285886022181074080329241442031 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (closed_form) = 0 y[1] (numeric) = 0.68258945576823237472104811865592 absolute error = 0.68258945576823237472104811865592 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1005.4MB, alloc=52.3MB, time=10.61 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (closed_form) = 0 y[1] (numeric) = 0.69232251342308091508517288194017 absolute error = 0.69232251342308091508517288194017 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (closed_form) = 0 y[1] (numeric) = 0.70205800574507841063743464065346 absolute error = 0.70205800574507841063743464065346 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (closed_form) = 0 y[1] (numeric) = 0.71179590566263669665358690575941 absolute error = 0.71179590566263669665358690575941 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1049.5MB, alloc=52.3MB, time=11.08 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (closed_form) = 0 y[1] (numeric) = 0.72153618646791367245110936617181 absolute error = 0.72153618646791367245110936617181 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (closed_form) = 0 y[1] (numeric) = 0.73127882181098199962864832890006 absolute error = 0.73127882181098199962864832890006 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (closed_form) = 0 y[1] (numeric) = 0.74102378569410775460398721562756 absolute error = 0.74102378569410775460398721562756 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1093.7MB, alloc=52.3MB, time=11.53 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (closed_form) = 0 y[1] (numeric) = 0.75077105246613663097533980903667 absolute error = 0.75077105246613663097533980903667 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (closed_form) = 0 y[1] (numeric) = 0.76052059681698534742699009000688 absolute error = 0.76052059681698534742699009000688 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (closed_form) = 0 y[1] (numeric) = 0.77027239377223597539093688932541 absolute error = 0.77027239377223597539093688932541 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1137.8MB, alloc=52.3MB, time=12.00 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (closed_form) = 0 y[1] (numeric) = 0.78002641868783095751538700157011 absolute error = 0.78002641868783095751538700157011 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = 0 y[1] (numeric) = 0.78978264724486664323091542755906 absolute error = 0.78978264724486664323091542755906 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (closed_form) = 0 y[1] (numeric) = 0.79954105544448322139627951601596 absolute error = 0.79954105544448322139627951601596 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1181.8MB, alloc=52.3MB, time=12.47 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (closed_form) = 0 y[1] (numeric) = 0.80930161960284898219687442919533 absolute error = 0.80930161960284898219687442919533 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (closed_form) = 0 y[1] (numeric) = 0.81906431634623689120659402557597 absolute error = 0.81906431634623689120659402557597 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (closed_form) = 0 y[1] (numeric) = 0.82882912260619150785372655581346 absolute error = 0.82882912260619150785372655581346 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=1225.8MB, alloc=52.3MB, time=12.92 x[1] = 0.97 y[1] (closed_form) = 0 y[1] (numeric) = 0.83859601561478432849721269939143 absolute error = 0.83859601561478432849721269939143 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = 0 y[1] (numeric) = 0.84836497289995568096335999851797 absolute error = 0.84836497289995568096335999851797 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (closed_form) = 0 y[1] (numeric) = 0.85813597228094134275572692723828 absolute error = 0.85813597228094134275572692723828 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 0 y[1] (numeric) = 0.86790899186378209927174953367205 absolute error = 0.86790899186378209927174953367205 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1270.0MB, alloc=52.3MB, time=13.39 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 0 y[1] (numeric) = 0.87768401003691450127682794266353 absolute error = 0.87768401003691450127682794266353 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = 0 y[1] (numeric) = 0.8874610054668411226367698820163 absolute error = 0.8874610054668411226367698820163 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = 0 y[1] (numeric) = 0.8972399570938786599282098282229 absolute error = 0.8972399570938786599282098282229 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1314.1MB, alloc=52.3MB, time=13.86 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = 0 y[1] (numeric) = 0.90702084412798225506819296638869 absolute error = 0.90702084412798225506819296638869 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = 0 y[1] (numeric) = 0.91680364604464446056168664407852 absolute error = 0.91680364604464446056168664407852 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (closed_form) = 0 y[1] (numeric) = 0.92658834258086730439140092392899 absolute error = 0.92658834258086730439140092392899 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1358.1MB, alloc=52.3MB, time=14.31 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = 0 y[1] (numeric) = 0.93637491373120594799893658565372 absolute error = 0.93637491373120594799893658565372 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = 0 y[1] (numeric) = 0.94616333974388246625987504146807 absolute error = 0.94616333974388246625987504146807 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = 0 y[1] (numeric) = 0.9559536011169683128669285818956 absolute error = 0.9559536011169683128669285818956 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1402.1MB, alloc=52.3MB, time=14.78 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 0 y[1] (numeric) = 0.96574567859463406813267280495381 absolute error = 0.96574567859463406813267280495381 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = 0 y[1] (numeric) = 0.97553955316346509893375561656632 absolute error = 0.97553955316346509893375561656632 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = 0 y[1] (numeric) = 0.98533520604884179236799982859837 absolute error = 0.98533520604884179236799982859837 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1446.3MB, alloc=52.3MB, time=15.25 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = 0 y[1] (numeric) = 0.99513261871138305570981361054384 absolute error = 0.99513261871138305570981361054384 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = 0 y[1] (numeric) = 1.0049317728434518054522936680356 absolute error = 1.0049317728434518054522936680356 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = 0 y[1] (numeric) = 1.0147326503657211976400527456242 absolute error = 1.0147326503657211976400527456242 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1490.3MB, alloc=52.3MB, time=15.70 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = 0 y[1] (numeric) = 1.0245352334238003803480609789697 absolute error = 1.0245352334238003803480609789697 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = 0 y[1] (numeric) = 1.034339504384918577070854567984 absolute error = 1.034339504384918577070854567984 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = 0 y[1] (numeric) = 1.0441454458346663369748160199549 absolute error = 1.0441454458346663369748160199549 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=1534.3MB, alloc=52.3MB, time=16.17 x[1] = 1.19 y[1] (closed_form) = 0 y[1] (numeric) = 1.0539530405737928144546598889351 absolute error = 1.0539530405737928144546598889351 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 0 y[1] (numeric) = 1.0637622716150579662438941225024 absolute error = 1.0637622716150579662438941225024 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = 0 y[1] (numeric) = 1.0735731221801385794773563139946 absolute error = 1.0735731221801385794773563139946 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = 0 y[1] (numeric) = 1.0833855756965870686108141805787 absolute error = 1.0833855756965870686108141805787 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1578.5MB, alloc=52.3MB, time=16.64 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = 0 y[1] (numeric) = 1.0931996157948420029863412093179 absolute error = 1.0931996157948420029863412093179 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = 0 y[1] (numeric) = 1.1030152263052893501104261000608 absolute error = 1.1030152263052893501104261000608 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = 0 y[1] (numeric) = 1.1128323912553734424016865325324 absolute error = 1.1128323912553734424016865325324 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1622.6MB, alloc=52.3MB, time=17.09 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = 0 y[1] (numeric) = 1.1226510948667566972832349484374 absolute error = 1.1226510948667566972832349484374 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (closed_form) = 0 y[1] (numeric) = 1.1324713215525271420572689254916 absolute error = 1.1324713215525271420572689254916 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = 0 y[1] (numeric) = 1.1422930559144528160219129948723 absolute error = 1.1422930559144528160219129948723 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1666.8MB, alloc=52.3MB, time=17.56 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = 0 y[1] (numeric) = 1.1521162827402821427878204262658 absolute error = 1.1521162827402821427878204262658 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 0 y[1] (numeric) = 1.1619409870010893857391834248505 absolute error = 1.1619409870010893857391834248505 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = 0 y[1] (numeric) = 1.1717671538486643190747779227017 absolute error = 1.1717671538486643190747779227017 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1710.9MB, alloc=52.3MB, time=18.03 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = 0 y[1] (numeric) = 1.1815947686129452658732282873315 absolute error = 1.1815947686129452658732282873315 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = 0 y[1] (numeric) = 1.191423816799494673166140136492 absolute error = 1.191423816799494673166140136492 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = 0 y[1] (numeric) = 1.2012542840870164120860312889118 absolute error = 1.2012542840870164120860312889118 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1755.0MB, alloc=52.3MB, time=18.48 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = 0 y[1] (numeric) = 1.2110861563249140087956135295266 absolute error = 1.2110861563249140087956135295266 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = 0 y[1] (numeric) = 1.2209194195308890291130829075782 absolute error = 1.2209194195308890291130829075782 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = 0 y[1] (numeric) = 1.230754059888578856536437729193 absolute error = 1.230754059888578856536437729193 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1799.0MB, alloc=52.3MB, time=18.95 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = 0 y[1] (numeric) = 1.2405900637452331197498799151954 absolute error = 1.2405900637452331197498799151954 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = 0 y[1] (numeric) = 1.2504274176094280416781420591654 absolute error = 1.2504274176094280416781420591654 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 0 y[1] (numeric) = 1.2602661081488179977508622070656 absolute error = 1.2602661081488179977508622070656 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=1843.1MB, alloc=52.3MB, time=19.41 x[1] = 1.41 y[1] (closed_form) = 0 y[1] (numeric) = 1.2701061221879235862593226745478 absolute error = 1.2701061221879235862593226745478 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = 0 y[1] (numeric) = 1.2799474467059555285420889759938 absolute error = 1.2799474467059555285420889759938 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = 0 y[1] (numeric) = 1.2897900688346737312341404541552 absolute error = 1.2897900688346737312341404541552 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = 0 y[1] (numeric) = 1.2996339758562808569654950115103 absolute error = 1.2996339758562808569654950115103 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1887.2MB, alloc=52.3MB, time=19.88 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = 0 y[1] (numeric) = 1.309479155201349763709334700212 absolute error = 1.309479155201349763709334700212 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = 0 y[1] (numeric) = 1.3193255944467841864652029013812 absolute error = 1.3193255944467841864652029013812 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = 0 y[1] (numeric) = 1.3291732813138120481286701200956 absolute error = 1.3291732813138120481286701200956 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1931.4MB, alloc=52.3MB, time=20.34 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = 0 y[1] (numeric) = 1.3390222036660107992534018623341 absolute error = 1.3390222036660107992534018623341 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = 0 y[1] (numeric) = 1.3488723495073641989630097776376 absolute error = 1.3488723495073641989630097776376 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 2.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 0 y[1] (numeric) = 1.3587237069803499615263885948298 absolute error = 1.3587237069803499615263885948298 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1975.5MB, alloc=52.3MB, time=20.81 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = 0 y[1] (numeric) = 1.3685762643640577050791675399114 absolute error = 1.3685762643640577050791675399114 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = 0 y[1] (numeric) = 1.3784300100723366506629433036456 absolute error = 1.3784300100723366506629433036456 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = 0 y[1] (numeric) = 1.3882849326519725311704029331636 absolute error = 1.3882849326519725311704029331636 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2019.5MB, alloc=52.3MB, time=21.27 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = 0 y[1] (numeric) = 1.3981410207808931809353701432739 absolute error = 1.3981410207808931809353701432739 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = 0 y[1] (numeric) = 1.407998263266402287599095163678 absolute error = 1.407998263266402287599095163678 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = 0 y[1] (numeric) = 1.4178566490434407985244372373847 absolute error = 1.4178566490434407985244372373847 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2063.7MB, alloc=52.3MB, time=21.73 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = 0 y[1] (numeric) = 1.4277161671728754844244505141357 absolute error = 1.4277161671728754844244505141357 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = 0 y[1] (numeric) = 1.4375768068398141730275839285505 absolute error = 1.4375768068398141730275839285505 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = 0 y[1] (numeric) = 1.4474385573519471755243704028864 absolute error = 1.4474385573519471755243704028864 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2107.9MB, alloc=52.3MB, time=22.19 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = 0 y[1] (numeric) = 1.4573014081379144382360637209078 absolute error = 1.4573014081379144382360637209078 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = 0 y[1] (numeric) = 1.4671653487456979614199680769783 absolute error = 1.4671653487456979614199680769783 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = 0 y[1] (numeric) = 1.4770303688410390363848182459045 absolute error = 1.4770303688410390363848182459045 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = 0 y[1] (numeric) = 1.4868964582058798611379724356584 absolute error = 1.4868964582058798611379724356584 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2152.1MB, alloc=52.3MB, time=22.66 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (closed_form) = 0 y[1] (numeric) = 1.4967636067368291036296871786378 absolute error = 1.4967636067368291036296871786378 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (closed_form) = 0 y[1] (numeric) = 1.5066318044436509903035178889285 absolute error = 1.5066318044436509903035178889285 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = 0 y[1] (numeric) = 1.5165010414477775061109500964569 absolute error = 1.5165010414477775061109500964569 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2196.3MB, alloc=52.3MB, time=23.13 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = 0 y[1] (numeric) = 1.5263713079808433004075957108723 absolute error = 1.5263713079808433004075957108723 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (closed_form) = 0 y[1] (numeric) = 1.5362425943832429012224317648332 absolute error = 1.5362425943832429012224317648332 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (closed_form) = 0 y[1] (numeric) = 1.54611489110270984828523077953 absolute error = 1.54611489110270984828523077953 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2240.6MB, alloc=52.3MB, time=23.59 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 0 y[1] (numeric) = 1.5559881886929173629150200315644 absolute error = 1.5559881886929173629150200315644 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = 0 y[1] (numeric) = 1.565862477812100180418476261851 absolute error = 1.565862477812100180418476261851 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = 0 y[1] (numeric) = 1.5757377492216971780258579754497 absolute error = 1.5757377492216971780258579754497 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2284.8MB, alloc=52.3MB, time=24.06 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (closed_form) = 0 y[1] (numeric) = 1.5856139937850144386075287797988 absolute error = 1.5856139937850144386075287797988 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = 0 y[1] (numeric) = 1.5954912024659083974703491291971 absolute error = 1.5954912024659083974703491291971 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = 0 y[1] (numeric) = 1.6053693663274887264341182578679 absolute error = 1.6053693663274887264341182578679 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2328.8MB, alloc=52.3MB, time=24.53 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = 0 y[1] (numeric) = 1.6152484765308406161376350496072 absolute error = 1.6152484765308406161376350496072 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = 0 y[1] (numeric) = 1.6251285243337661241255154896659 absolute error = 1.6251285243337661241255154896659 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = 0 y[1] (numeric) = 1.6350095010895442627242549161829 absolute error = 1.6350095010895442627242549161829 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = 0 y[1] (numeric) = 1.6448913982457095070326585772342 absolute error = 1.6448913982457095070326585772342 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2373.0MB, alloc=52.3MB, time=25.02 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 0 y[1] (numeric) = 1.6547742073428484095310931947137 absolute error = 1.6547742073428484095310931947137 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = 0 y[1] (numeric) = 1.6646579200134140138593534275841 absolute error = 1.6646579200134140138593534275841 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = 0 y[1] (numeric) = 1.6745425279805577662275199709448 absolute error = 1.6745425279805577662275199709448 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2417.3MB, alloc=52.3MB, time=25.48 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = 0 y[1] (numeric) = 1.6844280230569786287111543281251 absolute error = 1.6844280230569786287111543281251 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = 0 y[1] (numeric) = 1.6943143971437891043445895020252 absolute error = 1.6943143971437891043445895020252 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = 0 y[1] (numeric) = 1.7042016422293978894669154877553 absolute error = 1.7042016422293978894669154877553 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2461.4MB, alloc=52.3MB, time=25.95 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = 0 y[1] (numeric) = 1.7140897503884088741974244405897 absolute error = 1.7140897503884088741974244405897 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = 0 y[1] (numeric) = 1.7239787137805362172235973511566 absolute error = 1.7239787137805362172235973511566 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = 0 y[1] (numeric) = 1.733868524649535226277932472328 absolute error = 1.733868524649535226277932472328 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2505.5MB, alloc=52.3MB, time=26.42 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = 0 y[1] (numeric) = 1.743759175322148780762714106507 absolute error = 1.743759175322148780762714106507 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 0 y[1] (numeric) = 1.7536506582070690379568072462641 absolute error = 1.7536506582070690379568072462641 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = 0 y[1] (numeric) = 1.7635429657939141691082796037874 absolute error = 1.7635429657939141691082796037874 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2549.7MB, alloc=52.3MB, time=26.89 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = 0 y[1] (numeric) = 1.773436090652219876483572409907 absolute error = 1.773436090652219876483572409907 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = 0 y[1] (numeric) = 1.7833300254304454471104755387924 absolute error = 1.7833300254304454471104755387924 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = 0 y[1] (numeric) = 1.7932247628549941035206592481242 absolute error = 1.7932247628549941035206592481242 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = 0 y[1] (numeric) = 1.8031202957292474162702618082276 absolute error = 1.8031202957292474162702618082276 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2593.9MB, alloc=52.3MB, time=27.36 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = 0 y[1] (numeric) = 1.8130166169326135473962583902714 absolute error = 1.8130166169326135473962583902714 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = 0 y[1] (numeric) = 1.8229137194195890982542134830818 absolute error = 1.8229137194195890982542134830818 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = 0 y[1] (numeric) = 1.8328115962188343393816629320941 absolute error = 1.8328115962188343393816629320941 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2638.0MB, alloc=52.3MB, time=27.83 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = 0 y[1] (numeric) = 1.842710240432261604142844551996 absolute error = 1.842710240432261604142844551996 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 0 y[1] (numeric) = 1.8526096452341366319368077624516 absolute error = 1.8526096452341366319368077624516 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = 0 y[1] (numeric) = 1.8625098038701926506940413987702 absolute error = 1.8625098038701926506940413987702 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2682.2MB, alloc=52.3MB, time=28.30 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = 0 y[1] (numeric) = 1.8724107096567569922485736986585 absolute error = 1.8724107096567569922485736986585 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = 0 y[1] (numeric) = 1.8823123559798900379548801574196 absolute error = 1.8823123559798900379548801574196 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = 0 y[1] (numeric) = 1.8922147362945362956236972592369 absolute error = 1.8922147362945362956236972592369 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2726.3MB, alloc=52.3MB, time=28.76 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = 0 y[1] (numeric) = 1.9021178441236874124797511945834 absolute error = 1.9021178441236874124797511945834 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = 0 y[1] (numeric) = 1.9120216730575569323991943624664 absolute error = 1.9120216730575569323991943624664 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = 0 y[1] (numeric) = 1.9219262167527666091668793840267 absolute error = 1.9219262167527666091668793840267 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2770.4MB, alloc=52.3MB, time=29.23 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = 0 y[1] (numeric) = 1.9318314689315440909051292087401 absolute error = 1.9318314689315440909051292087401 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = 0 y[1] (numeric) = 1.941737423380931794167980544996 absolute error = 1.941737423380931794167980544996 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 0 y[1] (numeric) = 1.9516440739520067894695444551303 absolute error = 1.9516440739520067894695444551303 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = 0 y[1] (numeric) = 1.9615514145591115232236620553439 absolute error = 1.9615514145591115232236620553439 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2814.6MB, alloc=52.3MB, time=29.70 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = 0 y[1] (numeric) = 1.971459439179095204215916807111 absolute error = 1.971459439179095204215916807111 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = 0 y[1] (numeric) = 1.9813681418505656858097432683785 absolute error = 1.9813681418505656858097432683785 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = 0 y[1] (numeric) = 1.9912775166731516781072552022003 absolute error = 1.9912775166731516781072552022003 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2858.8MB, alloc=52.3MB, time=30.17 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = 0 y[1] (numeric) = 2.0011875578067751272438788095546 absolute error = 2.0011875578067751272438788095546 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = 0 y[1] (numeric) = 2.0110982594709336018952610636639 absolute error = 2.0110982594709336018952610636639 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = 0 y[1] (numeric) = 2.0210096159439925299165373888949 absolute error = 2.0210096159439925299165373888949 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2902.9MB, alloc=52.3MB, time=30.64 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = 0 y[1] (numeric) = 2.0309216215624871308191640501276 absolute error = 2.0309216215624871308191640501276 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = 0 y[1] (numeric) = 2.0408342707204338925203943391798 absolute error = 2.0408342707204338925203943391798 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 0 y[1] (numeric) = 2.0507475578686514434763194692157 absolute error = 2.0507475578686514434763194692157 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2947.1MB, alloc=52.3MB, time=31.11 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = 0 y[1] (numeric) = 2.060661477514090673932391089045 absolute error = 2.060661477514090673932391089045 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = 0 y[1] (numeric) = 2.070576024219173962596649926063 absolute error = 2.070576024219173962596649926063 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = 0 y[1] (numeric) = 2.0804911926011433675616337814748 absolute error = 2.0804911926011433675616337814748 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2991.2MB, alloc=52.3MB, time=31.58 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = 0 y[1] (numeric) = 2.0904069773314176427722302944547 absolute error = 2.0904069773314176427722302944547 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = 0 y[1] (numeric) = 2.1003233731349579437596514748995 absolute error = 2.1003233731349579437596514748995 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = 0 y[1] (numeric) = 2.1102403747896420887372881346625 absolute error = 2.1102403747896420887372881346625 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=3035.3MB, alloc=52.3MB, time=32.05 x[1] = 2.27 y[1] (closed_form) = 0 y[1] (numeric) = 2.1201579771256472434834781009749 absolute error = 2.1201579771256472434834781009749 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = 0 y[1] (numeric) = 2.1300761750248409007201931232523 absolute error = 2.1300761750248409007201931232523 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = 0 y[1] (numeric) = 2.1399949634201800269362925455694 absolute error = 2.1399949634201800269362925455694 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 0 y[1] (numeric) = 2.1499143372951182518002607995841 absolute error = 2.1499143372951182518002607995841 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3079.5MB, alloc=52.3MB, time=32.52 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = 0 y[1] (numeric) = 2.1598342916830209774611716928872 absolute error = 2.1598342916830209774611716928872 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = 0 y[1] (numeric) = 2.1697548216665882871489144542358 absolute error = 2.1697548216665882871489144542358 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = 0 y[1] (numeric) = 2.1796759223772855345563622579819 absolute error = 2.1796759223772855345563622579819 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3123.7MB, alloc=52.3MB, time=32.98 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = 0 y[1] (numeric) = 2.189597588994781497518030324346 absolute error = 2.189597588994781497518030324346 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = 0 y[1] (numeric) = 2.1995198167463939814927041860841 absolute error = 2.1995198167463939814927041860841 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = 0 y[1] (numeric) = 2.2094426009065427603123460196807 absolute error = 2.2094426009065427603123460196807 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3167.7MB, alloc=52.3MB, time=33.45 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = 0 y[1] (numeric) = 2.2193659367962097435771154492173 absolute error = 2.2193659367962097435771154492173 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = 0 y[1] (numeric) = 2.2292898197824062619573595192977 absolute error = 2.2292898197824062619573595192977 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = 0 y[1] (numeric) = 2.2392142452776473635087048416433 absolute error = 2.2392142452776473635087048416433 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3211.9MB, alloc=52.3MB, time=33.92 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 0 y[1] (numeric) = 2.2491392087394330159166756214741 absolute error = 2.2491392087394330159166756214741 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = 0 y[1] (numeric) = 2.259064705669736111363299322179 absolute error = 2.259064705669736111363299322179 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = 0 y[1] (numeric) = 2.2689907316144971724506651122949 absolute error = 2.2689907316144971724506651122949 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=3256.1MB, alloc=52.3MB, time=34.39 x[1] = 2.43 y[1] (closed_form) = 0 y[1] (numeric) = 2.2789172821631256593260703925594 absolute error = 2.2789172821631256593260703925594 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = 0 y[1] (numeric) = 2.2888443529480077798309129272032 absolute error = 2.2888443529480077798309129272032 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = 0 y[1] (numeric) = 2.2987719396440207061415299816624 absolute error = 2.2987719396440207061415299816624 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = 0 y[1] (numeric) = 2.3087000379680531029854056459474 absolute error = 2.3087000379680531029854056459474 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3300.3MB, alloc=52.3MB, time=34.86 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = 0 y[1] (numeric) = 2.3186286436785318741012024983722 absolute error = 2.3186286436785318741012024983722 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = 0 y[1] (numeric) = 2.3285577525749550351665486624099 absolute error = 2.3285577525749550351665486624099 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = 0 y[1] (numeric) = 2.338487360497430622944036641962 absolute error = 2.338487360497430622944036641962 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3344.4MB, alloc=52.3MB, time=35.33 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 0 y[1] (numeric) = 2.3484174633262215518940627398856 absolute error = 2.3484174633262215518940627398856 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = 0 y[1] (numeric) = 2.3583480569812963309735385080416 absolute error = 2.3583480569812963309735385080416 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = 0 y[1] (numeric) = 2.3682791374218855547827084997251 absolute error = 2.3682791374218855547827084997251 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3388.5MB, alloc=52.3MB, time=35.80 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = 0 y[1] (numeric) = 2.3782107006460440846388686962689 absolute error = 2.3782107006460440846388686962689 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = 0 y[1] (numeric) = 2.3881427426902188365462419184221 absolute error = 2.3881427426902188365462419184221 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = 0 y[1] (numeric) = 2.3980752596288220943961626378839 absolute error = 2.3980752596288220943961626378839 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3432.7MB, alloc=52.3MB, time=36.25 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = 0 y[1] (numeric) = 2.4080082475738102680715742716492 absolute error = 2.4080082475738102680715742716492 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = 0 y[1] (numeric) = 2.4179417026742680174451560285214 absolute error = 2.4179417026742680174451560285214 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = 0 y[1] (numeric) = 2.4278756211159976645516710847228 absolute error = 2.4278756211159976645516710847228 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=3476.9MB, alloc=52.3MB, time=36.73 x[1] = 2.59 y[1] (closed_form) = 0 y[1] (numeric) = 2.4378099991211138174828496166794 absolute error = 2.4378099991211138174828496166794 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 0 y[1] (numeric) = 2.4477448329476431307977645269887 absolute error = 2.4477448329476431307977645269887 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = 0 y[1] (numeric) = 2.4576801188891291284636895303057 absolute error = 2.4576801188891291284636895303057 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = 0 y[1] (numeric) = 2.4676158532742420165423032935065 absolute error = 2.4676158532742420165423032935065 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3521.1MB, alloc=52.3MB, time=37.19 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = 0 y[1] (numeric) = 2.4775520324663934140142641798559 absolute error = 2.4775520324663934140142641798559 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = 0 y[1] (numeric) = 2.4874886528633559312920626596747 absolute error = 2.4874886528633559312920626596747 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = 0 y[1] (numeric) = 2.4974257108968875271070878844687 absolute error = 2.4974257108968875271070878844687 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3565.1MB, alloc=52.3MB, time=37.66 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = 0 y[1] (numeric) = 2.507363203032360575572437206133 absolute error = 2.507363203032360575572437206133 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = 0 y[1] (numeric) = 2.5173011257683955763185593740866 absolute error = 2.5173011257683955763185593740866 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = 0 y[1] (numeric) = 2.5272394756364994416747516830629 absolute error = 2.5272394756364994416747516830629 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3609.3MB, alloc=52.3MB, time=38.13 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = 0 y[1] (numeric) = 2.5371782492007082959262177127645 absolute error = 2.5371782492007082959262177127645 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 0 y[1] (numeric) = 2.547117443057234722714216262174 absolute error = 2.547117443057234722714216262174 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = 0 y[1] (numeric) = 2.5570570538341193976661661264583 absolute error = 2.5570570538341193976661661264583 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3653.5MB, alloc=52.3MB, time=38.59 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = 0 y[1] (numeric) = 2.5669970781908870443437799055762 absolute error = 2.5669970781908870443437799055762 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = 0 y[1] (numeric) = 2.5769375128182066525807395966666 absolute error = 2.5769375128182066525807395966666 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = 0 y[1] (numeric) = 2.5868783544375558992474461321102 absolute error = 2.5868783544375558992474461321102 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=3697.6MB, alloc=52.3MB, time=39.06 x[1] = 2.75 y[1] (closed_form) = 0 y[1] (numeric) = 2.5968195998008897124293155878395 absolute error = 2.5968195998008897124293155878395 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = 0 y[1] (numeric) = 2.6067612456903129209372904656265 absolute error = 2.6067612456903129209372904656265 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = 0 y[1] (numeric) = 2.6167032889177569319850120423118 absolute error = 2.6167032889177569319850120423118 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = 0 y[1] (numeric) = 2.6266457263246603807667790697188 absolute error = 2.6266457263246603807667790697188 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3741.9MB, alloc=52.3MB, time=39.53 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = 0 y[1] (numeric) = 2.6365885547816536965543120543067 absolute error = 2.6365885547816536965543120543067 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 0 y[1] (numeric) = 2.646531771188247530798757219499 absolute error = 2.646531771188247530798757219499 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = 0 y[1] (numeric) = 2.6564753724725249935775998065618 absolute error = 2.6564753724725249935775998065618 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3786.0MB, alloc=52.3MB, time=40.00 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = 0 y[1] (numeric) = 2.6664193555908376455645059804724 absolute error = 2.6664193555908376455645059804724 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = 0 y[1] (numeric) = 2.6763637175275051935238634297123 absolute error = 2.6763637175275051935238634297123 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = 0 y[1] (numeric) = 2.6863084552945188381412238574207 absolute error = 2.6863084552945188381412238574207 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3830.1MB, alloc=52.3MB, time=40.47 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = 0 y[1] (numeric) = 2.6962535659312482237962410901294 absolute error = 2.6962535659312482237962410901294 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = 0 y[1] (numeric) = 2.7061990465041519406663158106579 absolute error = 2.7061990465041519406663158106579 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = 0 y[1] (numeric) = 2.716144894106491530317265615541 absolute error = 2.716144894106491530317265615541 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3874.3MB, alloc=52.3MB, time=40.94 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = 0 y[1] (numeric) = 2.7260911058580489466921953270627 absolute error = 2.7260911058580489466921953270627 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = 0 y[1] (numeric) = 2.7360376789048474251515999656415 absolute error = 2.7360376789048474251515999656415 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 0 y[1] (numeric) = 2.7459846104188757129468389312945 absolute error = 2.7459846104188757129468389312945 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=3918.5MB, alloc=52.3MB, time=41.41 x[1] = 2.91 y[1] (closed_form) = 0 y[1] (numeric) = 2.755931897597815615225717006533 absolute error = 2.755931897597815615225717006533 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = 0 y[1] (numeric) = 2.7658795376647728113732329803053 absolute error = 2.7658795376647728113732329803053 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = 0 y[1] (numeric) = 2.775827527868010897182842270974 absolute error = 2.775827527868010897182842270974 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = 0 y[1] (numeric) = 2.7857758654806886090340533396562 absolute error = 2.7857758654806886090340533396562 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3962.7MB, alloc=52.3MB, time=41.88 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = 0 y[1] (numeric) = 2.7957245478006001869210616631075 absolute error = 2.7957245478006001869210616631075 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = 0 y[1] (numeric) = 2.8056735721499188338346376993147 absolute error = 2.8056735721499188338346376993147 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = 0 y[1] (numeric) = 2.8156229358749432296458402468522 absolute error = 2.8156229358749432296458402468522 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4006.9MB, alloc=52.3MB, time=42.34 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = 0 y[1] (numeric) = 2.8255726363458470582755330860069 absolute error = 2.8255726363458470582755330860069 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = 0 y[1] (numeric) = 2.8355226709564315075583457072423 absolute error = 2.8355226709564315075583457072423 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 0 y[1] (numeric) = 2.8454730371238807018238389851333 absolute error = 2.8454730371238807018238389851333 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4051.0MB, alloc=52.3MB, time=42.81 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = 0 y[1] (numeric) = 2.8554237322885200278214104348476 absolute error = 2.8554237322885200278214104348476 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = 0 y[1] (numeric) = 2.8653747539135773152090937638452 absolute error = 2.8653747539135773152090937638452 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = 0 y[1] (numeric) = 2.8753260994849468334100624424716 absolute error = 2.8753260994849468334100624424716 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4095.1MB, alloc=52.3MB, time=43.28 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = 0 y[1] (numeric) = 2.8852777665109560672145217583088 absolute error = 2.8852777665109560672145217583088 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = 0 y[1] (numeric) = 2.8952297525221352340689493266436 absolute error = 2.8952297525221352340689493266436 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = 0 y[1] (numeric) = 2.9051820550709895065494976640026 absolute error = 2.9051820550709895065494976640026 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=4139.3MB, alloc=52.3MB, time=43.75 x[1] = 3.07 y[1] (closed_form) = 0 y[1] (numeric) = 2.9151346717317739040619779602 absolute error = 2.9151346717317739040619779602 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = 0 y[1] (numeric) = 2.9250876001002708183473718588572 absolute error = 2.9250876001002708183473718588572 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = 0 y[1] (numeric) = 2.935040837793570137899434691882 absolute error = 2.935040837793570137899434691882 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = 0 y[1] (numeric) = 2.9449943824498519369198226632876 absolute error = 2.9449943824498519369198226632876 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4183.4MB, alloc=52.3MB, time=44.22 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = 0 y[1] (numeric) = 2.9549482317281716949464581076664 absolute error = 2.9549482317281716949464581076664 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = 0 y[1] (numeric) = 2.9649023833082480137926981085287 absolute error = 2.9649023833082480137926981085287 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = 0 y[1] (numeric) = 2.9748568348902527989284462561672 absolute error = 2.9748568348902527989284462561672 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4227.5MB, alloc=52.3MB, time=44.69 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = 0 y[1] (numeric) = 2.9848115841946038729197958816374 absolute error = 2.9848115841946038729197958816374 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = 0 y[1] (numeric) = 2.9947666289617599890212634411398 absolute error = 2.9947666289617599890212634411398 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = 0 y[1] (numeric) = 3.0047219669520182134843076177148 absolute error = 3.0047219669520182134843076177148 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4271.6MB, alloc=52.3MB, time=45.16 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = 0 y[1] (numeric) = 3.0146775959453136456077750486308 absolute error = 3.0146775959453136456077750486308 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = 0 y[1] (numeric) = 3.0246335137410214450103064533066 absolute error = 3.0246335137410214450103064533066 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = 0 y[1] (numeric) = 3.0345897181577611360517136473396 absolute error = 3.0345897181577611360517136473396 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4315.7MB, alloc=52.3MB, time=45.63 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = 0 y[1] (numeric) = 3.0445462070332031597700321052262 absolute error = 3.0445462070332031597700321052262 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = 0 y[1] (numeric) = 3.0545029782238776441334963604395 absolute error = 3.0545029782238776441334963604395 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = 0 y[1] (numeric) = 3.0644600296049853638322050071433 absolute error = 3.0644600296049853638322050071433 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4359.9MB, alloc=52.3MB, time=46.09 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = 0 y[1] (numeric) = 3.0744173590702108612528642664233 absolute error = 3.0744173590702108612528642664233 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = 0 y[1] (numeric) = 3.0843749645315377006918474022697 absolute error = 3.0843749645315377006918474022697 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = 0 y[1] (numeric) = 3.0943328439190658282670026995082 absolute error = 3.0943328439190658282670026995082 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = 0 y[1] (numeric) = 3.1042909951808310103873038601468 absolute error = 3.1042909951808310103873038601468 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4404.0MB, alloc=52.3MB, time=46.56 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = 0 y[1] (numeric) = 3.1142494162826263240316798312146 absolute error = 3.1142494162826263240316798312146 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = 0 y[1] (numeric) = 3.1242081052078256724743002727561 absolute error = 3.1242081052078256724743002727561 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = 0 y[1] (numeric) = 3.1341670599572093004733399157081 absolute error = 3.1341670599572093004733399157081 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4448.1MB, alloc=52.3MB, time=47.03 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = 0 y[1] (numeric) = 3.1441262785487912833139095792737 absolute error = 3.1441262785487912833139095792737 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = 0 y[1] (numeric) = 3.1540857590176489644635311224356 absolute error = 3.1540857590176489644635311224356 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = 0 y[1] (numeric) = 3.1640454994157543169603535184931 absolute error = 3.1640454994157543169603535184931 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4492.3MB, alloc=52.3MB, time=47.50 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = 0 y[1] (numeric) = 3.1740054978118072040103609508583 absolute error = 3.1740054978118072040103609508583 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = 0 y[1] (numeric) = 3.1839657522910705146202127233122 absolute error = 3.1839657522910705146202127233122 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = 0 y[1] (numeric) = 3.1939262609552071504371782956452 absolute error = 3.1939262609552071504371782956452 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4536.4MB, alloc=52.3MB, time=47.97 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = 0 y[1] (numeric) = 3.2038870219221188403069864207637 absolute error = 3.2038870219221188403069864207637 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = 0 y[1] (numeric) = 3.2138480333257867593943908242646 absolute error = 3.2138480333257867593943908242646 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = 0 y[1] (numeric) = 3.2238092933161139300399599512377 absolute error = 3.2238092933161139300399599512377 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4580.6MB, alloc=52.3MB, time=48.44 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = 0 y[1] (numeric) = 3.2337708000587693818501170317338 absolute error = 3.2337708000587693818501170317338 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = 0 y[1] (numeric) = 3.2437325517350340488358793524416 absolute error = 3.2437325517350340488358793524416 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = 0 y[1] (numeric) = 3.2536945465416483817291607130775 absolute error = 3.2536945465416483817291607130775 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = 0 y[1] (numeric) = 3.2636567826906616539139954519398 absolute error = 3.2636567826906616539139954519398 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4624.8MB, alloc=52.3MB, time=48.91 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = 0 y[1] (numeric) = 3.2736192584092829397137013557087 absolute error = 3.2736192584092829397137013557087 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = 0 y[1] (numeric) = 3.2835819719397337440739058173429 absolute error = 3.2835819719397337440739058173429 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = 0 y[1] (numeric) = 3.2935449215391022629755967833625 absolute error = 3.2935449215391022629755967833625 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4668.9MB, alloc=52.3MB, time=49.38 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = 0 y[1] (numeric) = 3.3035081054791992542020077982099 absolute error = 3.3035081054791992542020077982099 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = 0 y[1] (numeric) = 3.3134715220464154983682837506409 absolute error = 3.3134715220464154983682837506409 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = 0 y[1] (numeric) = 3.3234351695415808304035782099504 absolute error = 3.3234351695415808304035782099504 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4713.1MB, alloc=52.3MB, time=49.83 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = 0 y[1] (numeric) = 3.3333990462798247219515805063304 absolute error = 3.3333990462798247219515805063304 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 4.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = 0 y[1] (numeric) = 3.3433631505904383954275355309446 absolute error = 3.3433631505904383954275355309446 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = 0 y[1] (numeric) = 3.3533274808167384507376747808828 absolute error = 3.3533274808167384507376747808828 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4757.2MB, alloc=52.3MB, time=50.30 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = 0 y[1] (numeric) = 3.3632920353159319859306952562641 absolute error = 3.3632920353159319859306952562641 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = 0 y[1] (numeric) = 3.3732568124589831933105738943647 absolute error = 3.3732568124589831933105738943647 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = 0 y[1] (numeric) = 3.3832218106304814127956584476616 absolute error = 3.3832218106304814127956584476616 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4801.4MB, alloc=52.3MB, time=50.77 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = 0 y[1] (numeric) = 3.3931870282285106245606989406294 absolute error = 3.3931870282285106245606989406294 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = 0 y[1] (numeric) = 3.4031524636645203632463436742591 absolute error = 3.4031524636645203632463436742591 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = 0 y[1] (numeric) = 3.4131181153631980362646855520214 absolute error = 3.4131181153631980362646855520214 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = 0 y[1] (numeric) = 3.4230839817623426289697724300176 absolute error = 3.4230839817623426289697724300176 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4845.6MB, alloc=52.3MB, time=51.25 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = 0 y[1] (numeric) = 3.4330500613127397796986522145381 absolute error = 3.4330500613127397796986522145381 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = 0 y[1] (numeric) = 3.4430163524780382079215713468452 absolute error = 3.4430163524780382079215713468452 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = 0 y[1] (numeric) = 3.4529828537346274789694447931627 absolute error = 3.4529828537346274789694447931627 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4889.8MB, alloc=52.3MB, time=51.72 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = 0 y[1] (numeric) = 3.4629495635715170890327262467211 absolute error = 3.4629495635715170890327262467211 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = 0 y[1] (numeric) = 3.4729164804902168543483874033856 absolute error = 3.4729164804902168543483874033856 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = 0 y[1] (numeric) = 3.4828836030046185887109222758735 absolute error = 3.4828836030046185887109222758735 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4934.0MB, alloc=52.3MB, time=52.19 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = 0 y[1] (numeric) = 3.4928509296408790536591828961212 absolute error = 3.4928509296408790536591828961212 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = 0 y[1] (numeric) = 3.5028184589373041659034817234371 absolute error = 3.5028184589373041659034817234371 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = 0 y[1] (numeric) = 3.5127861894442344467668179208228 absolute error = 3.5127861894442344467668179208228 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4978.2MB, alloc=52.3MB, time=52.66 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = 0 y[1] (numeric) = 3.5227541197239316986203526871164 absolute error = 3.5227541197239316986203526871164 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = 0 y[1] (numeric) = 3.5327222483504668934964253725957 absolute error = 3.5327222483504668934964253725957 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = 0 y[1] (numeric) = 3.5426905739096092592625185441039 absolute error = 3.5426905739096092592625185441039 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5022.4MB, alloc=52.3MB, time=53.13 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = 0 y[1] (numeric) = 3.5526590949987165489366969546077 absolute error = 3.5526590949987165489366969546077 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = 0 y[1] (numeric) = 3.5626278102266264789192120500737 absolute error = 3.5626278102266264789192120500737 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = 0 y[1] (numeric) = 3.5725967182135493221062288569873 absolute error = 3.5725967182135493221062288569873 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = 0 y[1] (numeric) = 3.582565817590961642040043602344 absolute error = 3.582565817590961642040043602344 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5066.7MB, alloc=52.3MB, time=53.59 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = 0 y[1] (numeric) = 3.5925351070015011544357651296181 absolute error = 3.5925351070015011544357651296181 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = 0 y[1] (numeric) = 3.6025045850988627026072771504931 absolute error = 3.6025045850988627026072771504931 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = 0 y[1] (numeric) = 3.6124742505476953334954268473402 absolute error = 3.6124742505476953334954268473402 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5110.9MB, alloc=52.3MB, time=54.06 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = 0 y[1] (numeric) = 3.6224441020235004611788427388431 absolute error = 3.6224441020235004611788427388431 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = 0 y[1] (numeric) = 3.6324141382125311049226146689505 absolute error = 3.6324141382125311049226146689505 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = 0 y[1] (numeric) = 3.6423843578116921889923141259143 absolute error = 3.6423843578116921889923141259143 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5155.0MB, alloc=52.3MB, time=54.53 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = 0 y[1] (numeric) = 3.6523547595284418916305359274453 absolute error = 3.6523547595284418916305359274453 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = 0 y[1] (numeric) = 3.662325342080694030760343954181 absolute error = 3.662325342080694030760343954181 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = 0 y[1] (numeric) = 3.6722961041967214741447446757191 absolute error = 3.6722961041967214741447446757191 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5199.2MB, alloc=52.3MB, time=55.00 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = 0 y[1] (numeric) = 3.6822670446150605618936325694785 absolute error = 3.6822670446150605618936325694785 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = 0 y[1] (numeric) = 3.692238162084416529369590353609 absolute error = 3.692238162084416529369590353609 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = 0 y[1] (numeric) = 3.7022094553635699187015227186849 absolute error = 3.7022094553635699187015227186849 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5243.4MB, alloc=52.3MB, time=55.47 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = 0 y[1] (numeric) = 3.7121809232212839672703927465246 absolute error = 3.7121809232212839672703927465246 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = 0 y[1] (numeric) = 3.7221525644362129616843525787292 absolute error = 3.7221525644362129616843525787292 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = 0 y[1] (numeric) = 3.7321243777968115459113506187767 absolute error = 3.7321243777968115459113506187767 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = 0 y[1] (numeric) = 3.7420963621012449723858924544466 absolute error = 3.7420963621012449723858924544466 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5287.7MB, alloc=52.3MB, time=55.94 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = 0 y[1] (numeric) = 3.7520685161573002850530669772861 absolute error = 3.7520685161573002850530669772861 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = 0 y[1] (numeric) = 3.7620408387822984234572574406947 absolute error = 3.7620408387822984234572574406947 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = 0 y[1] (numeric) = 3.7720133288030072371251734203485 absolute error = 3.7720133288030072371251734203485 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5331.8MB, alloc=52.3MB, time=56.41 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = 0 y[1] (numeric) = 3.7819859850555553996329972083653 absolute error = 3.7819859850555553996329972083653 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = 0 y[1] (numeric) = 3.7919588063853472118855698913198 absolute error = 3.7919588063853472118855698913198 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = 0 y[1] (numeric) = 3.8019317916469782842716804657253 absolute error = 3.8019317916469782842716804657253 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5376.1MB, alloc=52.3MB, time=56.87 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = 0 y[1] (numeric) = 3.8119049397041520874936975057695 absolute error = 3.8119049397041520874936975057695 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = 0 y[1] (numeric) = 3.8218782494295973620020282395376 absolute error = 3.8218782494295973620020282395376 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = 0 y[1] (numeric) = 3.8318517197049863760952349943783 absolute error = 3.8318517197049863760952349943783 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5420.3MB, alloc=52.3MB, time=57.34 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = 0 y[1] (numeric) = 3.8418253494208540228751138924715 absolute error = 3.8418253494208540228751138924715 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = 0 y[1] (numeric) = 3.8517991374765177463726749473212 absolute error = 3.8517991374765177463726749473212 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = 0 y[1] (numeric) = 3.8617730827799982872857853541185 absolute error = 3.8617730827799982872857853541185 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=5464.5MB, alloc=52.3MB, time=57.81 x[1] = 4.03 y[1] (closed_form) = 0 y[1] (numeric) = 3.8717471842479412388922773046248 absolute error = 3.8717471842479412388922773046248 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = 0 y[1] (numeric) = 3.8817214408055394038236061223124 absolute error = 3.8817214408055394038236061223124 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = 0 y[1] (numeric) = 3.8916958513864559425037014560435 absolute error = 3.8916958513864559425037014560435 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = 0 y[1] (numeric) = 3.9016704149327483041755107678256 absolute error = 3.9016704149327483041755107678256 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5508.7MB, alloc=52.3MB, time=58.28 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = 0 y[1] (numeric) = 3.9116451303947929315539170153867 absolute error = 3.9116451303947929315539170153867 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = 0 y[1] (numeric) = 3.9216199967312107302582474213535 absolute error = 3.9216199967312107302582474213535 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = 0 y[1] (numeric) = 3.9315950129087932942905032486768 absolute error = 3.9315950129087932942905032486768 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5552.8MB, alloc=52.3MB, time=58.75 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = 0 y[1] (numeric) = 3.941570177902429878936756839009 absolute error = 3.941570177902429878936756839009 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = 0 y[1] (numeric) = 3.9515454906950351125789066589187 absolute error = 3.9515454906950351125789066589187 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = 0 y[1] (numeric) = 3.9615209502774774390121781575556 absolute error = 3.9615209502774774390121781575556 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5597.1MB, alloc=52.3MB, time=59.22 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = 0 y[1] (numeric) = 3.9714965556485082819704318733625 absolute error = 3.9714965556485082819704318733625 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = 0 y[1] (numeric) = 3.981472305814691923666514034386 absolute error = 3.981472305814691923666514034386 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = 0 y[1] (numeric) = 3.991448199790336089258582074786 absolute error = 3.991448199790336089258582074786 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5641.2MB, alloc=52.3MB, time=59.69 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = 0 y[1] (numeric) = 4.001424236597423229255580845284 absolute error = 4.001424236597423229255580845284 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = 0 y[1] (numeric) = 4.0114004152655424919758572484674 absolute error = 4.0114004152655424919758572484674 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = 0 y[1] (numeric) = 4.021376734831822378272303624172 absolute error = 4.021376734831822378272303624172 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=5685.4MB, alloc=52.3MB, time=60.17 x[1] = 4.19 y[1] (closed_form) = 0 y[1] (numeric) = 4.0313531943408640708354351176427 absolute error = 4.0313531943408640708354351176427 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 0 y[1] (numeric) = 4.0413297928446754304824547916651 absolute error = 4.0413297928446754304824547916651 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = 0 y[1] (numeric) = 4.0513065294026056519356633436612 absolute error = 4.0513065294026056519356633436612 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = 0 y[1] (numeric) = 4.0612834030812805716875485590752 absolute error = 4.0612834030812805716875485590752 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5729.6MB, alloc=52.3MB, time=60.64 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = 0 y[1] (numeric) = 4.0712604129545386206425633278138 absolute error = 4.0712604129545386206425633278138 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = 0 y[1] (numeric) = 4.0812375581033674143169900872548 absolute error = 4.0812375581033674143169900872548 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = 0 y[1] (numeric) = 4.0912148376158409734684135173218 absolute error = 4.0912148376158409734684135173218 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5773.8MB, alloc=52.3MB, time=61.11 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = 0 y[1] (numeric) = 4.1011922505870575681152014580639 absolute error = 4.1011922505870575681152014580639 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = 0 y[1] (numeric) = 4.1111697961190781779940452854558 absolute error = 4.1111697961190781779940452854558 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = 0 y[1] (numeric) = 4.1211474733208655625900539896213 absolute error = 4.1211474733208655625900539896213 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5818.0MB, alloc=52.3MB, time=61.58 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = 0 y[1] (numeric) = 4.1311252813082239339591492653467 absolute error = 4.1311252813082239339591492653467 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 0 y[1] (numeric) = 4.1411032192037392256465900583127 absolute error = 4.1411032192037392256465900583127 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = 0 y[1] (numeric) = 4.1510812861367199510883819247767 absolute error = 4.1510812861367199510883819247767 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5862.2MB, alloc=52.3MB, time=62.06 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = 0 y[1] (numeric) = 4.1610594812431386449641166778556 absolute error = 4.1610594812431386449641166778556 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = 0 y[1] (numeric) = 4.1710378036655738810504582432166 absolute error = 4.1710378036655738810504582432166 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = 0 y[1] (numeric) = 4.1810162525531528602040582819014 absolute error = 4.1810162525531528602040582819014 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=5906.4MB, alloc=52.3MB, time=62.53 x[1] = 4.35 y[1] (closed_form) = 0 y[1] (numeric) = 4.1909948270614945621811665321628 absolute error = 4.1909948270614945621811665321628 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = 0 y[1] (numeric) = 4.2009735263526534550786122774426 absolute error = 4.2009735263526534550786122774426 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = 0 y[1] (numeric) = 4.210952349595063756257190898574 absolute error = 4.210952349595063756257190898574 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = 0 y[1] (numeric) = 4.2209312959634842386838088870709 absolute error = 4.2209312959634842386838088870709 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5950.5MB, alloc=52.3MB, time=63.00 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = 0 y[1] (numeric) = 4.2309103646389435767030374972388 absolute error = 4.2309103646389435767030374972388 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = 0 y[1] (numeric) = 4.2408895548086862253220146588628 absolute error = 4.2408895548086862253220146588628 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = 0 y[1] (numeric) = 4.2508688656661188271649318716363 absolute error = 4.2508688656661188271649318716363 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5994.7MB, alloc=52.3MB, time=63.47 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = 0 y[1] (numeric) = 4.260848296410757141324662325237 absolute error = 4.260848296410757141324662325237 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = 0 y[1] (numeric) = 4.2708278462481734884094429628649 absolute error = 4.2708278462481734884094429628649 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = 0 y[1] (numeric) = 4.2808075143899447061519309232431 absolute error = 4.2808075143899447061519309232431 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6039.0MB, alloc=52.3MB, time=63.94 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = 0 y[1] (numeric) = 4.2907873000536006100164278169306 absolute error = 4.2907873000536006100164278169306 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = 0 y[1] (numeric) = 4.3007672024625729533076174501867 absolute error = 4.3007672024625729533076174501867 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = 0 y[1] (numeric) = 4.3107472208461448813508075128294 absolute error = 4.3107472208461448813508075128294 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6083.3MB, alloc=52.3MB, time=64.41 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = 0 y[1] (numeric) = 4.3207273544394008743794167851912 absolute error = 4.3207273544394008743794167851912 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = 0 y[1] (numeric) = 4.330707602483177173830319767229 absolute error = 4.330707602483177173830319767229 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 5.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = 0 y[1] (numeric) = 4.3406879642240126868116632519126 absolute error = 4.3406879642240126868116632519126 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = 0 y[1] (numeric) = 4.3506684389141003635709170087004 absolute error = 4.3506684389141003635709170087004 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6127.6MB, alloc=52.3MB, time=64.88 Radius of convergence (given) for eq 1 = 6.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = 0 y[1] (numeric) = 4.3606490258112390428532259600486 absolute error = 4.3606490258112390428532259600486 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = 0 y[1] (numeric) = 4.3706297241787857601016063721631 absolute error = 4.3706297241787857601016063721631 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = 0 y[1] (numeric) = 4.380610533285608513511185790738 absolute error = 4.380610533285608513511185790738 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6171.8MB, alloc=52.3MB, time=65.34 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = 0 y[1] (numeric) = 4.3905914524060394830095376890936 absolute error = 4.3905914524060394830095376890936 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = 0 y[1] (numeric) = 4.4005724808198286972942188250604 absolute error = 4.4005724808198286972942188250604 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = 0 y[1] (numeric) = 4.4105536178120981441168917017359 absolute error = 4.4105536178120981441168917017359 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6215.9MB, alloc=52.3MB, time=65.81 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = 0 y[1] (numeric) = 4.4205348626732963190609176892017 absolute error = 4.4205348626732963190609176892017 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = 0 y[1] (numeric) = 4.4305162146991532081160495016836 absolute error = 4.4305162146991532081160495016836 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = 0 y[1] (numeric) = 4.4404976731906356994098458717608 absolute error = 4.4404976731906356994098458717608 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6260.1MB, alloc=52.3MB, time=66.28 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = 0 y[1] (numeric) = 4.4504792374539034195106872795022 absolute error = 4.4504792374539034195106872795022 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = 0 y[1] (numeric) = 4.4604609068002649897718001673489 absolute error = 4.4604609068002649897718001673489 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = 0 y[1] (numeric) = 4.4704426805461346982395087197807 absolute error = 4.4704426805461346982395087197807 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6304.3MB, alloc=52.3MB, time=66.75 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = 0 y[1] (numeric) = 4.4804245580129895827020383628785 absolute error = 4.4804245580129895827020383628785 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = 0 y[1] (numeric) = 4.4904065385273269205076038322158 absolute error = 4.4904065385273269205076038322158 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = 0 y[1] (numeric) = 4.5003886214206221208322369970746 absolute error = 4.5003886214206221208322369970746 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = 0 y[1] (numeric) = 4.5103708060292870151288554861473 absolute error = 4.5103708060292870151288554861473 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6348.5MB, alloc=52.3MB, time=67.23 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = 0 y[1] (numeric) = 4.520353091694628541539452251023 absolute error = 4.520353091694628541539452251023 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (closed_form) = 0 y[1] (numeric) = 4.5303354777628078191020080929565 absolute error = 4.5303354777628078191020080929565 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 0 y[1] (numeric) = 4.5403179635847996076328032799821 absolute error = 4.5403179635847996076328032799821 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6392.6MB, alloc=52.3MB, time=67.70 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = 0 y[1] (numeric) = 4.5503005485163521492132399625497 absolute error = 4.5503005485163521492132399625497 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = 0 y[1] (numeric) = 4.5602832319179473872580932789567 absolute error = 4.5602832319179473872580932789567 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = 0 y[1] (numeric) = 4.570266013154761559189294807165 absolute error = 4.570266013154761559189294807165 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6436.8MB, alloc=52.3MB, time=68.17 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = 0 y[1] (numeric) = 4.5802488915966261587859262075247 absolute error = 4.5802488915966261587859262075247 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = 0 y[1] (numeric) = 4.5902318666179892643270722143866 absolute error = 4.5902318666179892643270722143866 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = 0 y[1] (numeric) = 4.600214937597877228689559141369 absolute error = 4.600214937597877228689559141369 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6481.1MB, alloc=52.3MB, time=68.64 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = 0 y[1] (numeric) = 4.6101981039198567276073962000459 absolute error = 4.6101981039198567276073962000459 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = 0 y[1] (numeric) = 4.6201813649719971623439504993242 absolute error = 4.6201813649719971623439504993242 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = 0 y[1] (numeric) = 4.6301647201468334130715307686094 absolute error = 4.6301647201468334130715307686094 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6525.2MB, alloc=52.3MB, time=69.11 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 0 y[1] (numeric) = 4.6401481688413289392961376815744 absolute error = 4.6401481688413289392961376815744 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = 0 y[1] (numeric) = 4.6501317104568392237076680743231 absolute error = 4.6501317104568392237076680743231 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = 0 y[1] (numeric) = 4.6601153443990755558778441552868 absolute error = 4.6601153443990755558778441552868 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = 0 y[1] (numeric) = 4.6700990700780691522695846775415 absolute error = 4.6700990700780691522695846775415 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6569.5MB, alloc=52.3MB, time=69.58 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = 0 y[1] (numeric) = 4.6800828869081356090624505525935 absolute error = 4.6800828869081356090624505525935 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = 0 y[1] (numeric) = 4.6900667943078396843391899771867 absolute error = 4.6900667943078396843391899771867 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = 0 y[1] (numeric) = 4.7000507916999604062182851563009 absolute error = 4.7000507916999604062182851563009 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6613.7MB, alloc=52.3MB, time=70.05 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = 0 y[1] (numeric) = 4.7100348785114565035567713589851 absolute error = 4.7100348785114565035567713589851 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = 0 y[1] (numeric) = 4.7200190541734321558864664513521 absolute error = 4.7200190541734321558864664513521 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = 0 y[1] (numeric) = 4.7300033181211030592851222167438 absolute error = 4.7300033181211030592851222167438 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6657.9MB, alloc=52.3MB, time=70.52 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = 0 y[1] (numeric) = 4.7399876697937628049218945938114 absolute error = 4.7399876697937628049218945938114 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = 0 y[1] (numeric) = 4.7499721086347495670539352310903 absolute error = 4.7499721086347495670539352310903 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = 0 y[1] (numeric) = 4.7599566340914130972878381603764 absolute error = 4.7599566340914130972878381603764 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6702.1MB, alloc=52.3MB, time=70.98 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = 0 y[1] (numeric) = 4.7699412456150820219561395180839 absolute error = 4.7699412456150820219561395180839 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = 0 y[1] (numeric) = 4.7799259426610314394950715811355 absolute error = 4.7799259426610314394950715811355 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = 0 y[1] (numeric) = 4.7899107246884508147453213209227 absolute error = 4.7899107246884508147453213209227 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6746.2MB, alloc=52.3MB, time=71.45 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = 0 y[1] (numeric) = 4.7998955911604121671326445079944 absolute error = 4.7998955911604121671326445079944 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = 0 y[1] (numeric) = 4.8098805415438385497198453188144 absolute error = 4.8098805415438385497198453188144 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = 0 y[1] (numeric) = 4.8198655753094728161558545081845 absolute error = 4.8198655753094728161558545081845 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 0 y[1] (numeric) = 4.8298506919318466725814325287385 absolute error = 4.8298506919318466725814325287385 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 Radius of convergence (given) for eq 1 = 6.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6790.4MB, alloc=52.3MB, time=71.92 Finished! diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 4900 Total Elapsed Time = 1 Minutes 12 Seconds Elapsed Time(since restart) = 1 Minutes 11 Seconds Time to Timeout = 1 Minutes 48 Seconds Percent Done = 100 % > quit memory used=6802.3MB, alloc=52.3MB, time=72.05