|\^/| 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_y1 := proc(x) > return(neg(cos(c(x)))); > end; exact_soln_y1 := proc(x) return neg(cos(c(x))) end proc > exact_soln_y2 := proc(x) > return(neg(sin(c(x)))); > end; exact_soln_y2 := proc(x) return neg(sin(c(x))) end proc > exact_soln_y2p := proc(x) > return(neg(cos(c(x)))); > end; exact_soln_y2p := proc(x) return neg(cos(c(x))) 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 > ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3 > rad_given := sqrt((array_x[1] - array_given_rad_poles[2,1]) * (array_x[1] - array_given_rad_poles[2,1]) + array_given_rad_poles[2,2] * array_given_rad_poles[2,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," "); > if (rad_given < glob_least_given_sing) then # if number 4 > glob_least_given_sing := rad_given; > fi;# end if 4; > elif > (glob_type_given_pole = 3) then # if number 4 > omniout_str(ALWAYS,"NO POLE (given) for Equation 2"); > elif > (glob_type_given_pole = 5) then # if number 5 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 2"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 2"); > fi;# end if 5; > if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," "); > if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6 > glob_least_ratio_sing := array_rad_test_poles[2,1]; > fi;# end if 6; > omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," "); > if (array_rad_test_poles[2,2]< glob_least_3_sing) then # if number 6 > glob_least_3_sing := array_rad_test_poles[2,2]; > fi;# end if 6; > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," "); > if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6 > glob_least_6_sing := array_rad_test_poles[2,3]; > fi;# end if 6; > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2"); > fi;# end if 5 > ; > 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; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_x[1] - array_given_rad_poles[2, 1])* (array_x[1] - array_given_rad_poles[2, 1]) + array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[2, 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 2") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2") end if; if array_rad_test_poles[2, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 2 ", 4, array_rad_test_poles[2, 1], 4, " "); if array_rad_test_poles[2, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[2, 1] end if; omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[2, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 2] and array_rad_test_poles[2, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_rad_test_poles[2, 2], 4, " "); if array_rad_test_poles[2, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[2, 2] end if; omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 3] and array_rad_test_poles[2, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_rad_test_poles[2, 3], 4, " "); if array_rad_test_poles[2, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[2, 3] end if; omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[2, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 2") 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 5 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 5; > 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_2, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1[1]) < min_size) then # if number 5 > min_size := float_abs(array_y1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > if (float_abs(array_y2[1]) < min_size) then # if number 5 > min_size := float_abs(array_y2[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > if (min_size < glob__1) then # if number 5 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > 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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[1]) < min_size then min_size := float_abs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if float_abs(array_y2[1]) < min_size then min_size := float_abs(array_y2[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_2, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 5 > max_estimated_step_error := est_tmp; > fi;# end if 5; > est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 5 > max_estimated_step_error := est_tmp; > fi;# end if 5; > 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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[no_terms - 3] + array_y1[no_terms - 2]*hn_div_ho + array_y1[no_terms - 1]*hn_div_ho_2 + array_y1[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; est_tmp := float_abs(array_y2[no_terms - 3] + array_y2[no_terms - 2]*hn_div_ho + array_y2[no_terms - 1]*hn_div_ho_2 + array_y2[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_2, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5 > est_tmp := c(glob_prec) * c(float_abs(array_y1[1])); > fi;# end if 5; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5 > array_max_est_error[1] := c(est_tmp); > fi;# end if 5 > ; > est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5 > est_tmp := c(glob_prec) * c(float_abs(array_y2[1])); > fi;# end if 5; > if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5 > array_max_est_error[2] := c(est_tmp); > fi;# end if 5 > ; > 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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[no_terms - 3])) + c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y1[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if; est_tmp := c(float_abs(array_y2[no_terms - 3])) + c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y2[1])) end if; if c(array_max_est_error[2]) <= c(est_tmp) then array_max_est_error[2] := 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_2, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 5 > ret := true; > else > ret := false; > fi;# end if 5; > 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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_2, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 5 > if (iter >= 0) then # if number 6 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > closed_form_val_y := evalf(exact_soln_y1(ind_var)); > omniout_float(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7 > relerr := abserr*glob__100/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 8 > glob_good_digits := -int_trunc(log10(c(relerr))) + 3; > else > glob_good_digits := Digits; > fi;# end if 8; > else > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 7; > if (glob_good_digits < glob_min_good_digits) then # if number 7 > glob_min_good_digits := glob_good_digits; > fi;# end if 7; > if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7 > glob_min_apfp_est_good_digits := glob_apfp_est_good_digits; > fi;# end if 7; > if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7 > est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*36*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 8 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 8; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 7; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 7 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 7; > 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," "); > ; > closed_form_val_y := evalf(exact_soln_y2(ind_var)); > omniout_float(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7 > relerr := abserr*glob__100/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 8 > glob_good_digits := -int_trunc(log10(c(relerr))) + 3; > else > glob_good_digits := Digits; > fi;# end if 8; > else > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 7; > if (glob_good_digits < glob_min_good_digits) then # if number 7 > glob_min_good_digits := glob_good_digits; > fi;# end if 7; > if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7 > glob_min_apfp_est_good_digits := glob_apfp_est_good_digits; > fi;# end if 7; > if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7 > est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*36*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 8 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 8; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 7; > array_est_digits[2] := glob_est_digits; > if (glob_iter = 1) then # if number 7 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 7; > array_est_rel_error[2] := 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 6; > #BOTTOM DISPLAY ALOT > fi;# end if 5; > 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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1(ind_var)); omniout_float(ALWAYS, "y1[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "y1[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)*36*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, " "); closed_form_val_y := evalf(exact_soln_y2(ind_var)); omniout_float(ALWAYS, "y2[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "y2[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[2]*100.0* sqrt(glob_iter)*36*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[2] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; array_est_rel_error[2] := 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_2, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 5 > 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 5; > 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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_2, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1_higher[1,last_no-1],array_y1_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[1,1]) then # if number 8 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_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 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[2,1] := glob_larger_float; > array_ord_test_poles[2,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 2 - 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_y2_higher[1,last_no-1],array_y2_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[2,1]) then # if number 10 > array_rad_test_poles[2,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[2,1] := rad_c; > array_ord_test_poles[2,1] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test2 > 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_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 9 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 9; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 10 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 11 > found_sing := 0; > fi;# end if 11; > 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 11 > if (rad_c < array_rad_test_poles[1,2]) then # if number 12 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 13 > glob_min_pole_est := rad_c; > fi;# end if 13; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 12; > fi;# end if 11; > #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[2,2] := glob_larger_float; > array_ord_test_poles[2,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 2 - 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_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 11 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 11; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 12 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 13 > found_sing := 0; > fi;# end if 13; > 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 13 > if (rad_c < array_rad_test_poles[2,2]) then # if number 14 > array_rad_test_poles[2,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[2,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 15 > glob_min_pole_est := rad_c; > fi;# end if 15; > array_ord_test_poles[2,2] := tmp_ord; > fi;# end if 14; > fi;# end if 13; > #BOTTOM general radius test2 > 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_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 13 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 13; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 14 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 15 > found_sing := 0; > fi;# end if 15; > 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 15 > if (rad_c < array_rad_test_poles[1,3]) then # if number 16 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 17 > glob_min_pole_est := rad_c; > fi;# end if 17; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 16; > fi;# end if 15; > #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[2,3] := glob_larger_float; > array_ord_test_poles[2,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 2 - 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_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 15 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 15; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 16 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 17 > found_sing := 0; > fi;# end if 17; > 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 17 > if (rad_c < array_rad_test_poles[2,3]) then # if number 18 > array_rad_test_poles[2,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[2,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 19 > glob_min_pole_est := rad_c; > fi;# end if 19; > array_ord_test_poles[2,3] := tmp_ord; > fi;# end if 18; > fi;# end if 17; > #BOTTOM general radius test2 > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17 > 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 18 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 18; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_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 17; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 17 > display_poles(); > fi;# end if 17 > 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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 1], array_y1_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[2, 1] := glob_larger_float; array_ord_test_poles[2, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 12; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1], array_y2_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[2, 1] then array_rad_test_poles[2, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[2, 1] := rad_c; array_ord_test_poles[2, 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_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_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[2, 2] := glob_larger_float; array_ord_test_poles[2, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 12; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_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[2, 2] then array_rad_test_poles[2, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[2, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[2, 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_y1_higher[1, last_no - 5], array_y1_higher[1, last_no - 4], array_y1_higher[1, last_no - 3], array_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 5], array_y1_higher[1, last_no - 4], array_y1_higher[1, last_no - 3], array_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_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; 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[2, 3] := glob_larger_float; array_ord_test_poles[2, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 12; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5], array_y2_higher[1, last_no - 4], array_y2_higher[1, last_no - 3], array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_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[2, 3] then array_rad_test_poles[2, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y2_higher[1, last_no - 5], array_y2_higher[1, last_no - 4], array_y2_higher[1, last_no - 3], array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[2, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[2, 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_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_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_2, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre neg FULL $eq_no = 1 > array_tmp1[1] := neg(array_y2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y1_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre diff $eq_no = 2 i = 1 order_d = 1 > array_tmp4[1] := array_y1_higher[2,1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[2,2] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(1); > array_y2_higher[3,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre neg FULL $eq_no = 1 > array_tmp1[2] := neg(array_y2[2]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y1_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre diff $eq_no = 2 i = 2 order_d = 1 > array_tmp4[2] := array_y1_higher[2,2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[2,3] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[3,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre neg FULL $eq_no = 1 > array_tmp1[3] := neg(array_y2[3]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y1_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre diff $eq_no = 2 i = 3 order_d = 1 > array_tmp4[3] := array_y1_higher[2,3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[2,4] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[3,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre neg FULL $eq_no = 1 > array_tmp1[4] := neg(array_y2[4]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y1_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre diff $eq_no = 2 i = 4 order_d = 1 > array_tmp4[4] := array_y1_higher[2,4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[2,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[3,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre neg FULL $eq_no = 1 > array_tmp1[5] := neg(array_y2[5]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y1_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre diff $eq_no = 2 i = 5 order_d = 1 > array_tmp4[5] := array_y1_higher[2,5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,7]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6)); > if (7 <= ATS_MAX_TERMS) then # if number 3 > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(6); > array_y2_higher[2,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[3,5] := 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 neg FULL $eq_no = 1 > array_tmp1[kkk] := neg(array_y2[kkk]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y1[kkk + order_d] := c(temporary); > array_y1_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_y1_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; > #emit diff $eq_no = 2 > if (kkk <= ATS_MAX_TERMS) then # if number 1 > array_tmp4[kkk] := array_y1_higher[2,kkk]; > fi;# end if 1; > #emit assign $eq_no = 2 > order_d := 2; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y2[kkk + order_d] := c(temporary); > array_y2_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_y2_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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := neg(array_y2[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y1_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y1[2] := temporary; array_y1_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y1_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp4[1] := array_y1_higher[2, 1]; if not array_y2_set_initial[2, 3] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp4[1])*expt(glob_h, c(2))*c(factorial_3(0, 2)); if 3 <= ATS_MAX_TERMS then array_y2[3] := temporary; array_y2_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[2, 2] := c(temporary); temporary := c(temporary)*c(1)/c(glob_h); array_y2_higher[3, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := neg(array_y2[2]); array_tmp2[2] := array_tmp1[2]; if not array_y1_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y1[3] := temporary; array_y1_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y1_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp4[2] := array_y1_higher[2, 2]; if not array_y2_set_initial[2, 4] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp4[2])*expt(glob_h, c(2))*c(factorial_3(1, 3)); if 4 <= ATS_MAX_TERMS then array_y2[4] := temporary; array_y2_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[2, 3] := c(temporary); temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[3, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := neg(array_y2[3]); array_tmp2[3] := array_tmp1[3]; if not array_y1_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y1[4] := temporary; array_y1_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y1_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp4[3] := array_y1_higher[2, 3]; if not array_y2_set_initial[2, 5] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp4[3])*expt(glob_h, c(2))*c(factorial_3(2, 4)); if 5 <= ATS_MAX_TERMS then array_y2[5] := temporary; array_y2_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[2, 4] := c(temporary); temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[3, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := neg(array_y2[4]); array_tmp2[4] := array_tmp1[4]; if not array_y1_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y1[5] := temporary; array_y1_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y1_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp4[4] := array_y1_higher[2, 4]; if not array_y2_set_initial[2, 6] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp4[4])*expt(glob_h, c(2))*c(factorial_3(3, 5)); if 6 <= ATS_MAX_TERMS then array_y2[6] := temporary; array_y2_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[2, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[3, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := neg(array_y2[5]); array_tmp2[5] := array_tmp1[5]; if not array_y1_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y1[6] := temporary; array_y1_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y1_higher[2, 5] := c(temporary) end if end if; kkk := 6; array_tmp4[5] := array_y1_higher[2, 5]; if not array_y2_set_initial[2, 7] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp4[5])*expt(glob_h, c(2))*c(factorial_3(4, 6)); if 7 <= ATS_MAX_TERMS then array_y2[7] := temporary; array_y2_higher[1, 7] := temporary end if; temporary := c(temporary)*c(6)/c(glob_h); array_y2_higher[2, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[3, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := neg(array_y2[kkk]); array_tmp2[kkk] := array_tmp1[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y1_set_initial[1, kkk + order_d] then temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y1[kkk + order_d] := c(temporary); array_y1_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_y1_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; if kkk <= ATS_MAX_TERMS then array_tmp4[kkk] := array_y1_higher[2, kkk] end if; order_d := 2; if kkk + order_d <= ATS_MAX_TERMS then if not array_y2_set_initial[2, kkk + order_d] then temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y2[kkk + order_d] := c(temporary); array_y2_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_y2_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_2, > #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1_init:= Array(0..(30),[]); > array_y2_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(3),[]); > array_last_rel_error:= Array(0..(3),[]); > array_est_rel_error:= Array(0..(3),[]); > array_max_est_error:= Array(0..(3),[]); > array_type_pole:= Array(0..(3),[]); > array_type_real_pole:= Array(0..(3),[]); > array_type_complex_pole:= Array(0..(3),[]); > array_est_digits:= Array(0..(3),[]); > array_y1:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_y2:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y1_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y1_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y1_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y1_set_initial := Array(0..(3) ,(0..30+ 1),[]); > array_y2_higher := Array(0..(3) ,(0..30+ 1),[]); > array_y2_higher_work := Array(0..(3) ,(0..30+ 1),[]); > array_y2_higher_work2 := Array(0..(3) ,(0..30+ 1),[]); > array_y2_set_initial := Array(0..(3) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(3) ,(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_y1_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y2_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 <= 3) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) 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_y1[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_y2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y1_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_y1_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_y1_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 <=3) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y1_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 <=3) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y2_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 <=3) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y2_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 <=3) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y2_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 <=3) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y2_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 <=3) 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 <=3) 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 <=3) 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 <=3) 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_y1); > zero_ats_ar(array_x); > zero_ats_ar(array_y2); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2); > array_const_2[1] := c(2); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := true; > array_y2_set_initial[2,3] := false; > array_y2_set_initial[2,4] := false; > array_y2_set_initial[2,5] := false; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := 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 := 2; > 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/mtest5postode.ode#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; "); > omniout_str(ALWAYS,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; "); > 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(0.5);"); > omniout_str(ALWAYS,"x_end := c(5.0);"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 3;"); > 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(0.005);"); > 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_y1 := proc(x)"); > omniout_str(ALWAYS,"return(neg(cos(c(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(neg(sin(c(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return(neg(cos(c(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(0.5); > x_end := c(5.0); > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > glob_look_poles := true; > glob_type_given_pole := 3; > #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(0.005); > 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 17 > #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 18 > glob_display_interval := c(display_max); > fi;# end if 18; > 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_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_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 18 > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 18; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 2; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_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 18 > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 18; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > if (glob_subiter_method = 1 ) then # if number 18 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 19 > subiter := 1; > while (subiter <= 3) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 3 + ATS_MAX_TERMS) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 19; > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 19 > 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 19; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 19 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 19; > if (glob_look_poles) then # if number 19 > check_for_pole(); > fi;# end if 19; > if ( not found_h) then # if number 19 > 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 20 > 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 20; > fi;# end if 19; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 19 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 19; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 19 > 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 19; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 18; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 18 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 18; > #BEGIN SOLUTION CODE > if (found_h) then # if number 18 > 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_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y1[term_no] := array_y1_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 19 > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 19; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > order_diff := 2; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y2[term_no] := array_y2_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 19 > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 19; > 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 19 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 19; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > if (glob_subiter_method = 1 ) then # if number 19 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 20 > subiter := 1; > while (subiter <= 3) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 3 + ATS_MAX_TERMS) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 20; > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 20 > check_for_pole(); > fi;# end if 20; > if (reached_interval()) then # if number 20 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 20; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[2,iii] := array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_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_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y1_higher[ord,term_no] := array_y1_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 > #Jump Series array_y2; > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[3,iii] := array_y2_higher[3,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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #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_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y2_higher[ord,term_no] := array_y2_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 20 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 20; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 20 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 20; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) ; "); > omniout_str(INFO,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 20 > logstart(html_log_file); > logitem_str(html_log_file,"2015-05-02T21:41:05-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest5") > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ") > ; > 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 21 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 21; > if (glob_min_good_digits <> -16) then # if number 21 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 21; > if (glob_good_digits <> -16) then # if number 21 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 21; > 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 21 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 22 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 23 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 24 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 25 > 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 26 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 26; > if (glob_least_ratio_sing < glob_large_float) then # if number 26 > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 26; > if (glob_least_3_sing < glob_large_float) then # if number 26 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 26; > if (glob_least_6_sing < glob_large_float) then # if number 26 > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 26; > 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 26 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 26; > log_revs(html_log_file," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"mtest5 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest5 maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > if (array_est_digits[2] <> -16) then # if number 26 > logitem_integer(html_log_file,array_est_digits[2]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 26; > if (glob_min_good_digits <> -16) then # if number 26 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 26; > if (glob_good_digits <> -16) then # if number 26 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 26; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logditto(html_log_file) > ; > if (glob_type_given_pole = 0) then # if number 26 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 4) then # if number 27 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 5) then # if number 28 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 3) then # if number 29 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 1) then # if number 30 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 2) then # if number 31 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > fi;# end if 31; > if (glob_least_ratio_sing < glob_large_float) then # if number 31 > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 31; > if (glob_least_3_sing < glob_large_float) then # if number 31 > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 31; > if (glob_least_6_sing < glob_large_float) then # if number 31 > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 31; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > if (c(glob_percent_done) < glob__100) then # if number 31 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 31; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 30; > if (glob_html_log) then # if number 30 > fclose(html_log_file); > fi;# end if 30 > ; > ;; > fi;# end if 29 > #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_2, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1_init := Array(0 .. 30, []); array_y2_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_est_rel_error := Array(0 .. 3, []); array_max_est_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_est_digits := Array(0 .. 3, []); array_y1 := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_y2 := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y1_higher := Array(0 .. 2, 0 .. 31, []); array_y1_higher_work := Array(0 .. 2, 0 .. 31, []); array_y1_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y1_set_initial := Array(0 .. 3, 0 .. 31, []); array_y2_higher := Array(0 .. 3, 0 .. 31, []); array_y2_higher_work := Array(0 .. 3, 0 .. 31, []); array_y2_higher_work2 := Array(0 .. 3, 0 .. 31, []); array_y2_set_initial := Array(0 .. 3, 0 .. 31, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_rad_test_poles := Array(0 .. 3, 0 .. 5, []); array_ord_test_poles := Array(0 .. 3, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y1_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_y2_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 <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y1[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_y2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y1_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_y1_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_y1_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 30 do array_y1_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 30 do array_y2_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 30 do array_y2_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 30 do array_y2_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 30 do array_y2_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 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 <= 3 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 <= 3 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 <= 3 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_y1); zero_ats_ar(array_x); zero_ats_ar(array_y2); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2); array_const_2[1] := c(2); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := true; array_y2_set_initial[2, 3] := false; array_y2_set_initial[2, 4] := false; array_y2_set_initial[2, 5] := false; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 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 := 2; 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/mtest5postode.ode#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ") ; omniout_str(ALWAYS, "diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; "); 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(0.5);"); omniout_str(ALWAYS, "x_end := c(5.0);"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 3;"); 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(0.005);"); 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_y1 := proc(x)"); omniout_str(ALWAYS, "return(neg(cos(c(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(neg(sin(c(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return(neg(cos(c(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(0.5); x_end := c(5.0); array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); glob_look_poles := true; glob_type_given_pole := 3; 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(0.005); 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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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; order_diff := 2; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + ATS_MAX_TERMS do atomall(); subiter := subiter + 1 end do end if; 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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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; order_diff := 2; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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(); if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + ATS_MAX_TERMS do atomall(); subiter := subiter + 1 end do end if; 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_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 3; ord := 3; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, 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 := 3; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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 := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_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 := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_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 ( y1 , x , 1 ) = neg ( y2 ) ; "); omniout_str(INFO, "diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ") ; 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, "2015-05-02T21:41:05-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest5"); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = neg ( y2 ) ; "); 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, "mtest5 diffeq.mxt"); logitem_str(html_log_file, "mtest5 maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y2 , x , 2 ) = d\ iff ( y1 , x , 1 ) ; "); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); if array_est_digits[2] <> -16 then logitem_integer(html_log_file, array_est_digits[2]) 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"); logditto(html_log_file); if glob_type_given_pole = 0 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 4 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 5 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 3 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 1 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 2 then logditto(html_log_file); logditto(html_log_file) end if; if glob_least_ratio_sing < glob_large_float then logditto(html_log_file) else logditto(html_log_file) end if; if glob_least_3_sing < glob_large_float then logditto(html_log_file) else logditto(html_log_file) end if; if glob_least_6_sing < glob_large_float then logditto(html_log_file) else logditto(html_log_file) end if; logditto(html_log_file); logditto(html_log_file); if c(glob_percent_done) < glob__100 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(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/mtest5postode.ode################# diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.5); x_end := c(5.0); array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); glob_look_poles := true; glob_type_given_pole := 3; #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(0.005); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return(neg(cos(c(x)))); end; exact_soln_y2 := proc(x) return(neg(sin(c(x)))); end; exact_soln_y2p := proc(x) return(neg(cos(c(x)))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop memory used=3.8MB, alloc=40.3MB, time=0.13 x[1] = 0.5 y1[1] (closed_form) = -0.87758256189037271611628158260383 y1[1] (numeric) = -0.87758256189037271611628158260383 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.47942553860420300027328793521557 y2[1] (numeric) = -0.47942553860420300027328793521557 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.51 y1[1] (closed_form) = -0.87274450764575126310580847357551 y1[1] (numeric) = -0.87274450764575126310548553836393 absolute error = 3.2293521158e-22 relative error = 3.7002262260134445518481841751712e-20 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.48817724688290749450013023767457 y2[1] (numeric) = -0.48817724688290749462247640457479 absolute error = 1.2234616690022e-19 relative error = 2.5061833111112924997505687286828e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.52 y1[1] (closed_form) = -0.86781917967764990038784757198851 y1[1] (numeric) = -0.86781917967764990038407895948097 absolute error = 3.76861250754e-21 relative error = 4.3426241269982593838454058926118e-19 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.49688013784373671433445894254775 y2[1] (numeric) = -0.49688013784373671495868242948029 absolute error = 6.2422348693254e-19 relative error = 1.2562858512345111183515164508660e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.53 y1[1] (closed_form) = -0.8628070705147610118066950185642 y1[1] (numeric) = -0.86280707051476101179257348677463 absolute error = 1.412153178957e-20 relative error = 1.6366963452379829633349852656947e-18 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.50553334120484696181366102246608 y2[1] (numeric) = -0.50553334120484696331711860517896 absolute error = 1.50345758271288e-18 relative error = 2.9740028207232815486042843945565e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.54 y1[1] (closed_form) = -0.8577086813638241425379687789178 y1[1] (numeric) = -0.8577086813638241425028247074642 absolute error = 3.514407145360e-20 relative error = 4.0974368357468607183549193653684e-18 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.51413599165311310467728068295824 y2[1] (numeric) = -0.51413599165311310743507928284706 absolute error = 2.75779859988882e-18 relative error = 5.3639477582995262944940503474303e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=46.1MB, alloc=40.3MB, time=0.64 TOP MAIN SOLVE Loop x[1] = 0.55 y1[1] (closed_form) = -0.85252452205950574280498179761777 y1[1] (numeric) = -0.85252452205950574273440606180094 absolute error = 7.057573581683e-20 relative error = 8.2784405598486529461017856040074e-18 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.52268722893065916778837810775729 y2[1] (numeric) = -0.52268722893065917217329975607178 absolute error = 4.38492164831449e-18 relative error = 8.3891884201674330685330582586950e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.56 y1[1] (closed_form) = -0.84725511101341612609452550386632 y1[1] (numeric) = -0.84725511101341612597039309685337 absolute error = 1.2413240701295e-19 relative error = 1.4651125192325264895325116571847e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.53118619792088340385186944111203 y2[1] (numeric) = -0.53118619792088341023429669559359 absolute error = 6.38242725448156e-18 relative error = 1.2015423743054745989141686205183e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.57 y1[1] (closed_form) = -0.84190097516226874013375636391601 y1[1] (numeric) = -0.8419009751622687399342507624485 absolute error = 1.9950560146751e-19 relative error = 2.3697038886201208348803131838359e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.53963204873396924099446349307883 y2[1] (numeric) = -0.53963204873396924974230531821778 absolute error = 8.74784182513895e-18 relative error = 1.6210752948536436743308378172095e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.58 y1[1] (closed_form) = -0.83646264991518693465788732805002 y1[1] (numeric) = -0.8364626499151869343575255969847 absolute error = 3.0036173106532e-19 relative error = 3.5908564607848916429713824811201e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.54802393679187355618269605957646 y2[1] (numeric) = -0.54802393679187356766131418160915 absolute error = 1.147861812203269e-17 relative error = 2.0945468530495951455747038594004e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.59 y1[1] (closed_form) = -0.83094067910016349524799652249068 y1[1] (numeric) = -0.83094067910016349481765515337029 absolute error = 4.3034136912039e-19 relative error = 5.1789661999267178056210022099925e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.55636102291278377572254337887577 y2[1] (numeric) = -0.55636102291278379029467912657126 absolute error = 1.457213574769549e-17 relative error = 2.6191870292070848452730852741073e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=88.4MB, alloc=40.3MB, time=1.14 TOP MAIN SOLVE Loop x[1] = 0.6 y1[1] (closed_form) = -0.82533561490967829724095249895538 y1[1] (numeric) = -0.82533561490967829664789397769655 absolute error = 5.9305852125883e-19 relative error = 7.1856649652000313776752486800948e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.56464247339503535720094544565866 y2[1] (numeric) = -0.56464247339503537522664708787329 absolute error = 1.802570164221463e-17 relative error = 3.1924097976248914864458895037051e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.61 y1[1] (closed_form) = -0.81964801784547951790074657865482 y1[1] (numeric) = -0.81964801784547951710864667733086 absolute error = 7.9209990132396e-19 relative error = 9.6639030910617915562278994840295e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 y2[1] (closed_form) = -0.57286746010048126119097603216272 y2[1] (numeric) = -0.5728674601004812830275266230675 absolute error = 2.183655059090478e-17 relative error = 3.8117980356354395237845522524697e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.62 y1[1] (closed_form) = -0.8138784566625339286839996543607 y1[1] (numeric) = -0.81387845666253392765297544194832 absolute error = 1.03102421241238e-18 relative error = 1.2668036657958661955649213716780e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.58103516053730507584296322758221 y2[1] (numeric) = -0.58103516053730510184480897039341 absolute error = 2.600184574281120e-17 relative error = 4.4750898927986242446081180708582e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.63 y1[1] (closed_form) = -0.80802750831215187252370896577706 y1[1] (numeric) = -0.80802750831215187121034753262817 absolute error = 1.31336143314889e-18 relative error = 1.6253919818798060638192977266428e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.58914475794226951311811209079462 y2[1] (numeric) = -0.58914475794226954363679123076202 absolute error = 3.051867913996740e-17 relative error = 5.1801664579960389493091884246155e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.64 y1[1] (closed_form) = -0.80209575788429261358611077926032 y1[1] (numeric) = -0.80209575788429261194349866995287 absolute error = 1.64261210930745e-18 relative error = 2.0479002577450449332260516025654e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.59719544136239205188354623920793 y2[1] (numeric) = -0.59719544136239208726761849653756 absolute error = 3.538407225732963e-17 relative error = 5.9250405824611366814312749022424e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=130.7MB, alloc=40.3MB, time=1.63 TOP MAIN SOLVE Loop x[1] = 0.65 y1[1] (closed_form) = -0.79608379854905582891760457067991 y1[1] (numeric) = -0.79608379854905582689535791979533 absolute error = 2.02224665088458e-18 relative error = 2.5402434449367408551225738505177e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.60518640573603956037252167860594 y2[1] (numeric) = -0.60518640573603960096749823191523 absolute error = 4.059497655330929e-17 relative error = 6.7078467342532065614957338451980e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.66 y1[1] (closed_form) = -0.78999223149736509278381709123024 y1[1] (numeric) = -0.78999223149736509032811245649967 absolute error = 2.45570463473057e-18 relative error = 3.1085174471601885050348787569082e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.6131168519734337886151454793963 y2[1] (numeric) = -0.61311685197343383476341951021939 absolute error = 4.614827403082309e-17 relative error = 7.5268317747727938882144015083094e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.67 y1[1] (closed_form) = -0.78382166588084928530294214483812 y1[1] (numeric) = -0.78382166588084928235654803199439 absolute error = 2.94639411284373e-18 relative error = 3.7590108070470443262965629400686e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.62098598703655968035744391412659 y2[1] (numeric) = -0.62098598703655973239822172290571 absolute error = 5.204077780877912e-17 relative error = 8.3803465609788859993164508631898e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.68 y1[1] (closed_form) = -0.77757271875092793718239408404432 y1[1] (numeric) = -0.77757271875092793368470315761333 absolute error = 3.49769092643099e-18 relative error = 4.4982171340187800757597783471374e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.62879302401846851370417818742025 y2[1] (numeric) = -0.62879302401846857197341089133588 absolute error = 5.826923270391563e-17 relative error = 9.2668382883020315920013940750138e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=172.9MB, alloc=40.3MB, time=2.13 x[1] = 0.69 y1[1] (closed_form) = -0.77124601499710660197353931549777 y1[1] (numeric) = -0.77124601499710659786060128965914 absolute error = 4.11293802583863e-18 relative error = 5.3328483335554868997847899362401e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.63653718222196794023742920700872 y2[1] (numeric) = -0.63653718222196800506774502991699 absolute error = 6.483031582290827e-17 relative error = 1.0184843499103118012143884050072e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7 y1[1] (closed_form) = -0.76484218728448842625585999019186 y1[1] (numeric) = -0.76484218728448842146041519373708 absolute error = 4.79544479645478e-18 relative error = 6.2698487036660813918096448404091e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.64421768723769105367261435139872 y2[1] (numeric) = -0.64421768723769112539325151605839 absolute error = 7.172063716465967e-17 relative error = 1.1132981690115808403066168144647e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.71 y1[1] (closed_form) = -0.75836187599050816654145794413955 y1[1] (numeric) = -0.75836187599050816099297155345398 absolute error = 5.54848639068557e-18 relative error = 7.3164099704229015659981182788196e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.65183377102153668121012797285284 y2[1] (numeric) = -0.65183377102153676014686820553713 absolute error = 7.893674023268429e-17 relative error = 1.2109949459810392178979787980049e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.72 y1[1] (closed_form) = -0.75180572914089497944548696225195 y1[1] (numeric) = -0.75180572914089497307018389614683 absolute error = 6.37530306610512e-18 relative error = 8.4799873411317571349250139083549e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.65938467197147315361800383264817 y2[1] (numeric) = -0.65938467197147324009310649014807 absolute error = 8.647510265749990e-17 relative error = 1.3114515143178981507874403967467e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.73 y1[1] (closed_form) = -0.74517440234487038879013215855033 y1[1] (numeric) = -0.74517440234487038151103262867123 absolute error = 7.27909952987910e-18 relative error = 9.7683166611382026985518248986490e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = 0.005 y2[1] (closed_form) = -0.66686963500369787373259413076153 y2[1] (numeric) = -0.66686963500369796806473095969727 absolute error = 9.433213682893574e-17 relative error = 1.4145513887195157230037165407874e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=215.1MB, alloc=40.3MB, time=2.61 x[1] = 0.74 y1[1] (closed_form) = -0.73846855872958790979142456069883 y1[1] (numeric) = -0.73846855872958790152838027113811 absolute error = 8.26304428956072e-18 relative error = 1.1189432768506638483955018518998e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.67428791162814506748388115760817 y2[1] (numeric) = -0.6742879116281451699880716958744 absolute error = 1.0250419053826623e-16 relative error = 1.5201843125254636552734446815992e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.75 y1[1] (closed_form) = -0.73168886887382088631183875300008 y1[1] (numeric) = -0.73168886887382087698156974264352 absolute error = 9.33026901035656e-18 relative error = 1.2751689149948728870122353755656e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.68163876002333416673324195277989 y2[1] (numeric) = -0.6816387600233342777207895828575 absolute error = 1.1098754763007761e-16 relative error = 1.6282458413350531006417241428943e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.76 y1[1] (closed_form) = -0.72483601074090517233968836666701 y1[1] (numeric) = -0.72483601074090516185582048770746 absolute error = 1.048386787895955e-17 relative error = 1.4463779011535673177681934720507e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.68892144511055133914775563876973 y2[1] (numeric) = -0.68892144511055145892618430254335 absolute error = 1.1977842866377362e-16 relative error = 1.7386369594657160887759604395207e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.77 y1[1] (closed_form) = -0.71791066961094336337129056532434 y1[1] (numeric) = -0.71791066961094335164439359127968 absolute error = 1.172689697404466e-17 relative error = 1.6334757889027900873028496458726e-15 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.69613523862735674701988373445221 y2[1] (numeric) = -0.69613523862735687589287531907742 absolute error = 1.2887299158462521e-16 relative error = 1.8512637262658571391180507539572e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.78 y1[1] (closed_form) = -0.71091353801227735721626502376456 y1[1] (numeric) = -0.71091353801227734415389138024204 absolute error = 1.306237364352252e-17 relative error = 1.8374067935244377079851141703368e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.70327941920041018436789732511792 y2[1] (numeric) = -0.70327941920041032263522972938561 absolute error = 1.3826733240426769e-16 relative error = 1.9660369496020515175294137162186e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=257.3MB, alloc=40.3MB, time=3.11 x[1] = 0.79 y1[1] (closed_form) = -0.70384531565223609691278086108495 y1[1] (numeric) = -0.70384531565223608241950497244022 absolute error = 1.449327588864473e-17 relative error = 2.0591564035933333794902439746357e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.7103532724176078098140288749692 y2[1] (numeric) = -0.710353272417607957771514765517 absolute error = 1.4795748589054780e-16 relative error = 2.0828718841118457385705296415401e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8 y1[1] (closed_form) = -0.69670670934716542092074998164232 y1[1] (numeric) = -0.69670670934716540489820822658826 absolute error = 1.602254175505406e-17 relative error = 2.2997541921288013144069570993652e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.71735609089952276162717461058139 y2[1] (numeric) = -0.7173560908995229195666008772031 absolute error = 1.5793942626662171e-16 relative error = 2.2016879520542561688252720978024e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.81 y1[1] (closed_form) = -0.6894984329517470175496392406801 y1[1] (numeric) = -0.68949843295174699989657050980866 absolute error = 1.765306873087144e-17 relative error = 2.5602768457788286136792870962349e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.72428717437014251092817685251454 y2[1] (numeric) = -0.72428717437014267913724477171828 absolute error = 1.6820906791920374e-16 relative error = 2.3224084848041438492098598719268e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.82 y1[1] (closed_form) = -0.68222120728761355166655797843693 y1[1] (numeric) = -0.68222120728761353227884482652619 absolute error = 1.938771315191074e-17 relative error = 2.8418514324690569406454688088216e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.73114582972689587938131336468772 y2[1] (numeric) = -0.73114582972689605814357948055216 absolute error = 1.7876226611586444e-16 relative error = 2.4449604832272286675275319837675e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.83 y1[1] (closed_form) = -0.67487576007126710211246291786445 y1[1] (numeric) = -0.6748757600712670808831733037531 absolute error = 2.122928961411135e-17 relative error = 3.1456589301517556413848587084164e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.73793137110996271872858022613808 y2[1] (numeric) = -0.7379313711099629083233979574136 absolute error = 1.8959481773127552e-16 relative error = 2.5692743953424237906920723923232e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=299.7MB, alloc=40.3MB, time=3.59 TOP MAIN SOLVE Loop x[1] = 0.84 y1[1] (closed_form) = -0.66746282584130811792267103687086 y1[1] (numeric) = -0.66746282584130809474210064359324 absolute error = 2.318057039327762e-17 relative error = 3.4729380417642750851648569734907e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.74464311997085932125657267062965 y2[1] (numeric) = -0.74464311997085952195903465292729 absolute error = 2.0070246198229764e-16 relative error = 2.6952839098298777037497925448154e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.85 y1[1] (closed_form) = -0.65998314588498217039541602946147 y1[1] (numeric) = -0.65998314588498214515113115724875 absolute error = 2.524428487221272e-17 relative error = 3.8249893242898265925422890335556e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.75128040514029270271207152423547 y2[1] (numeric) = -0.75128040514029291479295269604176 absolute error = 2.1208088117180629e-16 relative error = 2.8229257640787623297613503446970e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.86 y1[1] (closed_form) = -0.65243746816405184627203066422386 y1[1] (numeric) = -0.65243746816405181884891168888959 absolute error = 2.742311897533427e-17 relative error = 4.2031796629495343699054348702919e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.75784256289527697229458872952865 y2[1] (numeric) = -0.75784256289527719602029017067798 absolute error = 2.2372570144114933e-16 relative error = 2.9521395655902877726300950701850e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.87 y1[1] (closed_form) = -0.64482654724000119477766380548283 y1[1] (numeric) = -0.64482654724000116505794919462574 absolute error = 2.971971461085709e-17 relative error = 4.6089471250934031152884661403963e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.76432893702550507814480282372285 y2[1] (numeric) = -0.76432893702550531377729635485208 absolute error = 2.3563249353112923e-16 relative error = 3.0828676256603163518555243350441e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.88 y1[1] (closed_form) = -0.63715114419858020801549860572209 y1[1] (numeric) = -0.63715114419858017587882948509413 absolute error = 3.213666912062796e-17 relative error = 5.0438062323579472521334600948066e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.77073887889896929120964513075599 y2[1] (numeric) = -0.77073887889896953900641868215717 absolute error = 2.4779677355140118e-16 relative error = 3.2150548043636852341591799058724e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=342.0MB, alloc=40.3MB, time=4.09 TOP MAIN SOLVE Loop x[1] = 0.89 y1[1] (closed_form) = -0.62941202657369688020355305738025 y1[1] (numeric) = -0.62941202657369684552701831968423 absolute error = 3.467653473769602e-17 relative error = 5.5093536941871253246548649142518e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.77707174752682386549033371297318 y2[1] (numeric) = -0.777071747526824125704337471151 absolute error = 2.6021400375817782e-16 relative error = 3.3486483659502168513176134997002e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9 y1[1] (closed_form) = -0.62160996827066445648471615140713 y1[1] (numeric) = -0.62160996827066441914289809970584 absolute error = 3.734181805170129e-17 relative error = 6.0072746509498915751721578961118e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.78332690962748338846138231571355 y2[1] (numeric) = -0.78332690962748366134097565584318 absolute error = 2.7287959334012963e-16 relative error = 3.4835978438414612422175765248176e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.91 y1[1] (closed_form) = -0.61374574948881154652117822617468 y1[1] (numeric) = -0.61374574948881150638619874401201 absolute error = 4.013497948216267e-17 relative error = 6.5393494807240733606853901621824e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.78950373968995041187895751787155 y2[1] (numeric) = -0.78950373968995069766785673024088 absolute error = 2.8578889921236933e-16 relative error = 3.6198549144884707263009061910640e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.92 y1[1] (closed_form) = -0.60582015664346284179740470667438 y1[1] (numeric) = -0.60582015664346279873897194692865 absolute error = 4.305843275974573e-17 relative error = 7.1074612304599284390322854696983e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.79560162003636603026827610248162 y2[1] (numeric) = -0.79560162003636632920550292088893 absolute error = 2.9893722681840731e-16 relative error = 3.7573732794151831284501100047096e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.93 y1[1] (closed_form) = -0.59783398228729823849490708443298 y1[1] (numeric) = -0.5978339822872981923803626688435 absolute error = 4.611454441558948e-17 relative error = 7.7136037398135779325836842010606e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.80161994088377715208431921591065 y2[1] (numeric) = -0.80161994088377746440415015587486 absolute error = 3.1231983093996421e-16 relative error = 3.8961085548300487350663293960176e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=384.4MB, alloc=40.3MB, time=4.59 TOP MAIN SOLVE Loop x[1] = 0.94 y1[1] (closed_form) = -0.58978802503109822996098981522402 y1[1] (numeric) = -0.58978802503109818065535653645395 absolute error = 4.930563327877007e-17 relative error = 8.3598905345984757857814331120507e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.80755810040511428687021979863415 y2[1] (numeric) = -0.80755810040511461280213631315971 absolute error = 3.2593191651452556e-16 relative error = 4.0360181682410305561640507508809e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.95 y1[1] (closed_form) = -0.58168308946388349416618097376046 y1[1] (numeric) = -0.58168308946388344153221099178233 absolute error = 5.263396998197813e-17 relative error = 9.0485645767163316088161156322470e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.81341550478937375068542210210256 y2[1] (numeric) = -0.81341550478937409045406156262509 absolute error = 3.3976863946052253e-16 relative error = 4.1770612615566309455570215964709e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.96 y1[1] (closed_form) = -0.57351998607245666212505080035186 y1[1] (numeric) = -0.57351998607245660602327432486609 absolute error = 5.610177647548577e-17 relative error = 9.7820089688030597790592429370456e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = -0.81919156830099827163322214643043 y2[1] (numeric) = -0.81919156830099862545832965645197 absolute error = 3.5382510751002154e-16 relative error = 4.3191986001986584003750040509333e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.97 y1[1] (closed_form) = -0.56529953116035431303652775484986 y1[1] (numeric) = -0.56529953116035425332530220537251 absolute error = 5.971122554947735e-17 relative error = 1.0562758724903224943410670389312e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.82488571333845005747662003785634 y2[1] (numeric) = -0.82488571333845042557300108666113 absolute error = 3.6809638104880479e-16 relative error = 4.4623924877915189519396160642904e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=426.7MB, alloc=40.3MB, time=5.09 x[1] = 0.98 y1[1] (closed_form) = -0.55702254676621730087665826735994 y1[1] (numeric) = -0.55702254676621723741221790254233 absolute error = 6.346444036481761e-17 relative error = 1.1393513733556942342461057641466e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.83049737049197046808453328771915 y2[1] (numeric) = -0.83049737049197085066200725144165 absolute error = 3.8257747396372250e-16 relative error = 4.6066066860282899539986761447451e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.99 y1[1] (closed_form) = -0.54868986058158757534312640865361 y1[1] (numeric) = -0.54868986058158750797963241632449 absolute error = 6.736349399232912e-17 relative error = 1.2277153057088885005841411709393e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.83602597860052051678925941154711 y2[1] (numeric) = -0.83602597860052091405261390874406 absolute error = 3.9726335449719695e-16 relative error = 4.7518063393460870439762923618054e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1 y1[1] (closed_form) = -0.54030230586813971740093660744298 y1[1] (numeric) = -0.54030230586813964599052764679291 absolute error = 7.141040896065007e-17 relative error = 1.3216750731039396094001183947532e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.8414709848078965066525023216303 y2[1] (numeric) = -0.84147098480789691880144843038729 absolute error = 4.1214894610875699e-16 relative error = 4.8979579040725744377761634590610e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.01 y1[1] (closed_form) = -0.53186072137435546620673135577918 y1[1] (numeric) = -0.53186072137435539059957454303717 absolute error = 7.560715681274201e-17 relative error = 1.4215593251061899645515388035885e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.84683184461801519012309878478201 y2[1] (numeric) = -0.84683184461801561735222712826342 absolute error = 4.2722912834348141e-16 relative error = 5.0450290817322045495453866364557e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.02 y1[1] (closed_form) = -0.52336595125164956988961380803381 y1[1] (numeric) = -0.52336595125164948993395613691772 absolute error = 7.995565767111609e-17 relative error = 1.5277198961816124053016428996346e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.85210802194936292361654998545538 y2[1] (numeric) = -0.85210802194936336611528769268327 absolute error = 4.4249873770722789e-16 relative error = 5.1929887562251311234661384890864e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=469.0MB, alloc=40.3MB, time=5.59 x[1] = 1.03 y1[1] (closed_form) = -0.51481884496995534753350229983735 y1[1] (numeric) = -0.51481884496995526307572248799238 absolute error = 8.445777981184497e-17 relative error = 1.6405339594119538741244400210185e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.85729898918860337214627438529442 y2[1] (numeric) = -0.85729898918860383009884293381836 absolute error = 4.5795256854852394e-16 relative error = 5.3418069346139828455781017971686e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.04 y1[1] (closed_form) = -0.50622025723277840373447342099217 y1[1] (numeric) = -0.50622025723277831461913417356576 absolute error = 8.911533924742641e-17 relative error = 1.7604064233732936191908478098756e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.86240422724333840328079169211617 y2[1] (numeric) = -0.86240422724333887686616563911114 absolute error = 4.7358537394699497e-16 relative error = 5.4914546912739887158931732549270e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.05 y1[1] (closed_form) = -0.4975710478917269902908495728121 y1[1] (numeric) = -0.49757104789172689636075025424872 absolute error = 9.393009931856338e-17 relative error = 1.8877726048683375596555563771219e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.86742322559401689438140948500027 y2[1] (numeric) = -0.86742322559401738377327609320416 absolute error = 4.8939186660820389e-16 relative error = 5.6419041151805135712186831706148e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.06 y1[1] (closed_form) = -0.48887208186052756191863753995641 y1[1] (numeric) = -0.48887208186052746301486724503245 absolute error = 9.890377029492396e-17 relative error = 2.0231012153224295982325836801306e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.87235548234498626228294592199742 y2[1] (numeric) = -0.87235548234498676764966568677314 absolute error = 5.0536671976477572e-16 relative error = 5.7931282601250478925903672582800e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.07 y1[1] (closed_form) = -0.48012422902853412436509306817592 y1[1] (numeric) = -0.48012422902853402032708408323237 absolute error = 1.0403800898494355e-16 relative error = 2.1668977046930180468102448328813e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.87720050427468161030706325777682 y2[1] (numeric) = -0.87720050427468213181163134145674 absolute error = 5.2150456808367992e-16 relative error = 5.9451010976662517479068213307339e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=511.4MB, alloc=40.3MB, time=6.08 x[1] = 1.08 y1[1] (closed_form) = -0.47132836417374002391352478852603 y1[1] (numeric) = -0.47132836417373991457910643379604 absolute error = 1.0933441835472999e-16 relative error = 2.3197080138895985775946767566853e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.88195780688494747373533498762476 y2[1] (numeric) = -0.8819578068849480115353435671669 absolute error = 5.3780000857954214e-16 relative error = 6.0977974726369063184415641737374e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.09 y1[1] (closed_form) = -0.46248536687530087702789707387514 y1[1] (numeric) = -0.46248536687530076223334991774361 absolute error = 1.1479454715613153e-16 relative error = 2.4821227951863692925635956593462e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.88662691444948723160860062863605 y2[1] (numeric) = -0.88662691444948778585620216249263 absolute error = 5.5424760153385658e-16 relative error = 6.2511930610407054897297188121003e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.1 y1[1] (closed_form) = -0.45359612142557738777137005178472 y1[1] (numeric) = -0.45359612142557726735148048775891 absolute error = 1.2041988956402581e-16 relative error = 2.6547821702171100332160768836356e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.8912073600614353399518025778717 y2[1] (numeric) = -0.89120736006143591079367399784053 absolute error = 5.7084187141996883e-16 relative error = 6.4052643301848165935186405535349e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.11 y1[1] (closed_form) = -0.44466151674170684864373751193357 y1[1] (numeric) = -0.44466151674170672243185268904661 absolute error = 1.2621188482288696e-16 relative error = 2.8383811072231915246552710216202e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.89569868568004762924062595933937 y2[1] (numeric) = -0.89569868568004821681793379303834 absolute error = 5.8757730783369897e-16 relative error = 6.5599885009051733419857247961272e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.12 y1[1] (closed_form) = -0.43568244627671216761398879396113 y1[1] (numeric) = -0.43568244627671203544207189127442 absolute error = 1.3217191690268671e-16 relative error = 3.0336755137190268454408353246556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.90010044217650499711910324733915 y2[1] (numeric) = -0.9001004421765056015674696768124 absolute error = 6.0444836642947325e-16 relative error = 6.7153435117515927325858333938494e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=553.7MB, alloc=40.3MB, time=6.58 TOP MAIN SOLVE Loop x[1] = 1.13 y1[1] (closed_form) = -0.42665980793015731037121583565354 y1[1] (numeric) = -0.42665980793015717206990167146994 absolute error = 1.3830131416418360e-16 relative error = 3.2414891581918827498526988527455e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.9044121893788259160370815224114 y2[1] (numeric) = -0.9044121893788265374865513842438 absolute error = 6.2144946986183240e-16 relative error = 6.8713079850091388564932312552855e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.14 y1[1] (closed_form) = -0.41759450395835809217518674082258 y1[1] (numeric) = -0.41759450395835794757383770716876 absolute error = 1.4460134903365382e-16 relative error = 3.4627215555517285539736870339470e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.9086334961158832645942155781022 y2[1] (numeric) = -0.90863349611588390316922431028586 absolute error = 6.3857500873218366e-16 relative error = 7.0278611944407397255727009028837e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.15 y1[1] (closed_form) = -0.40848744088415729815257671880992 y1[1] (numeric) = -0.40848744088415714707933903169487 absolute error = 1.5107323768711505e-16 relative error = 3.6983569766581346734044292890777e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.91276394026052108094403304975368 y2[1] (numeric) = -0.91276394026052173676337559041657 absolute error = 6.5581934254066289e-16 relative error = 7.1849830346439730663001578202719e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.16 y1[1] (closed_form) = -0.39933952940627315445163962339401 y1[1] (numeric) = -0.39933952940627299673349987929998 absolute error = 1.5771813974409403e-16 relative error = 3.9494747734737142071243823540473e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.91680310877176692661866166687433 y2[1] (numeric) = -0.91680310877176759979546230984707 absolute error = 6.7317680064297274e-16 relative error = 7.3426539919222327673761889430043e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.17 y1[1] (closed_form) = -0.3901516843082302153326619350505 y1[1] (numeric) = -0.39015168430823005079550396406376 absolute error = 1.6453715797098674e-16 relative error = 4.2172612496271579771351958049070e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.92075059773613563957301300896203 y2[1] (numeric) = -0.92075059773613633021469622102345 absolute error = 6.9064168321206142e-16 relative error = 7.5008551165772064347778327730607e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=596.1MB, alloc=40.3MB, time=7.08 TOP MAIN SOLVE Loop x[1] = 1.18 y1[1] (closed_form) = -0.38092482436688177302959946671276 y1[1] (numeric) = -0.38092482436688160149826147265367 absolute error = 1.7153133799405909e-16 relative error = 4.5030233532076494657158002309811e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.92460601240802034610753802587476 y2[1] (numeric) = -0.92460601240802105431580023038186 absolute error = 7.0820826220450710e-16 relative error = 7.6595679965358168307251222955859e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.19 y1[1] (closed_form) = -0.37165987226053293806567955835047 y1[1] (numeric) = -0.37165987226053275936401153621613 absolute error = 1.7870166802213434e-16 relative error = 4.8082045267686250180387236641280e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.92836896724916669260202111160267 y2[1] (numeric) = -0.92836896724916741847280344307365 absolute error = 7.2587078233147098e-16 relative error = 7.8187747322305007204854930252152e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.2 y1[1] (closed_form) = -0.36235775447667357763837335562308 y1[1] (numeric) = -0.36235775447667339158929477661077 absolute error = 1.8604907857901231e-16 relative error = 5.1344031217907614994720519227901e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.93203908596722634967013443549483 y2[1] (numeric) = -0.93203908596722709329359646957751 absolute error = 7.4362346203408268e-16 relative error = 7.9784579126570127444215038305492e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.21 y1[1] (closed_form) = -0.35301940121933033870301071366479 y1[1] (numeric) = -0.35301940121933014512856846800064 absolute error = 1.9357444224566415e-16 relative error = 5.4833938751540934831523274630999e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.93561600155338593341646488854361 y2[1] (numeric) = -0.93561600155338669487695935166377 absolute error = 7.6146049446312016e-16 relative error = 8.1386005925388342245699825255889e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.22 y1[1] (closed_form) = -0.3436457463160470204755229744352 y1[1] (numeric) = -0.34364574631604681919694956219054 absolute error = 2.0127857341224466e-16 relative error = 5.8571530586364681125685989010690e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.93909935631906758093524527188837 y2[1] (numeric) = -0.93909935631906836031129373473432 absolute error = 7.7937604846284595e-16 relative error = 8.2991862705318032535530963592919e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=638.4MB, alloc=40.3MB, time=7.56 TOP MAIN SOLVE Loop x[1] = 1.23 y1[1] (closed_form) = -0.33423772712450259823954724549766 y1[1] (numeric) = -0.33423772712450238907731920553442 absolute error = 2.0916222803996324e-16 relative error = 6.2578880558881645265308259847481e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.94248880193169751002382356538924 y2[1] (numeric) = -0.94248880193169830738809312425052 absolute error = 7.9736426955886128e-16 relative error = 8.4601988684067839443739232621093e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.24 y1[1] (closed_form) = -0.32479628443877623657769341569738 y1[1] (numeric) = -0.32479628443877601935158998284447 absolute error = 2.1722610343285291e-16 relative error = 6.6880723037889248282901897108805e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.94578399944953898628470596308179 y2[1] (numeric) = -0.94578399944953980170398691292043 absolute error = 8.1541928094983864e-16 relative error = 8.6216227111520744455938910049427e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.25 y1[1] (closed_form) = -0.31532236239526866544753855243804 y1[1] (numeric) = -0.31532236239526843997670053296266 absolute error = 2.2547083801947538e-16 relative error = 7.1504867687385598031909555303326e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.94898461935558621434849084703605 y2[1] (numeric) = -0.94898461935558704788367535002912 absolute error = 8.3353518450299307e-16 relative error = 8.7834425079408580273877927189512e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.26 y1[1] (closed_form) = -0.30581690837828932688634248917648 y1[1] (numeric) = -0.30581690837828909298933134457746 absolute error = 2.3389701114459902e-16 relative error = 7.6482694297358192686319567607654e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.95209034159051576385681622142542 y2[1] (numeric) = -0.95209034159051661556287797457715 absolute error = 8.5170606175315173e-16 relative error = 8.9456433339123370998300256496336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=680.7MB, alloc=40.3MB, time=8.06 x[1] = 1.27 y1[1] (closed_form) = -0.29628087292531873355113701608796 y1[1] (numeric) = -0.29628087292531849104599414520301 absolute error = 2.4250514287088495e-16 relative error = 8.1849746315554894808764102704864e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.95510085558469223509018174218289 y2[1] (numeric) = -0.95510085558469310501615664746397 absolute error = 8.6992597490528108e-16 relative error = 9.1082106127182880379450926577764e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.28 y1[1] (closed_form) = -0.28671520963195551277938689359259 y1[1] (numeric) = -0.28671520963195526148369310297764 absolute error = 2.5129569379061495e-16 relative error = 8.7646446839423993529065060680643e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.95801586028922496370075385916029 y2[1] (numeric) = -0.95801586028922585188972169949055 absolute error = 8.8818896784033026e-16 relative error = 9.2711300997896426614726128826799e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.29 y1[1] (closed_form) = -0.27712087505655764138660609006118 y1[1] (numeric) = -0.27712087505655738111754124256722 absolute error = 2.6026906484749396e-16 relative error = 9.3918967596495791633441953132261e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = -0.96083506420607265890556129128537 y2[1] (numeric) = -0.96083506420607356539462841553423 absolute error = 9.0648906712424886e-16 relative error = 9.4343878662803663119118224459539e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.3 y1[1] (closed_form) = -0.26749882862458740699798410929287 y1[1] (numeric) = -0.26749882862458713757238694073491 absolute error = 2.6942559716855796e-16 relative error = 1.0072029046029005760475196381169e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.96355818541719296470134863003955 y2[1] (numeric) = -0.96355818541719388952163165007642 absolute error = 9.2482028302003687e-16 relative error = 9.5979702836483746150205662473617e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.31 y1[1] (closed_form) = -0.2578500325326696613381769786162 y1[1] (numeric) = -0.25785003253266938257260507239934 absolute error = 2.7876557190621686e-16 relative error = 1.0811151318000985506042633978600e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.9661849516127340291692578059375 y2[1] (numeric) = -0.96618495161273497234586830862169 absolute error = 9.4317661050268419e-16 relative error = 9.7618640088355253565358474166116e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=723.1MB, alloc=40.3MB, time=8.56 x[1] = 1.32 y1[1] (closed_form) = -0.24817545165237295957398272942735 y1[1] (numeric) = -0.2481754516523726712847726389666 absolute error = 2.8828921009046075e-16 relative error = 1.1616346748681508358072985353728e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.96871510011826526273589984597277 y2[1] (numeric) = -0.96871510011826622428793012282929 absolute error = 9.6155203027685652e-16 relative error = 9.9260559700108500247135815468722e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.33 y1[1] (closed_form) = -0.23847605343372320751578498601058 y1[1] (numeric) = -0.2384760534337229095191124947545 absolute error = 2.9799667249125608e-16 relative error = 1.2495874038525831485886553982209e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.9711483779210445623376830377638 y2[1] (numeric) = -0.97114837792104554227819283494793 absolute error = 9.7994050979718413e-16 relative error = 1.0090533352843167470254415518034e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.34 y1[1] (closed_form) = -0.22875280780845946523263949230014 y1[1] (numeric) = -0.22875280780845915734458000114307 absolute error = 3.0788805949115707e-16 relative error = 1.3459422091507596291744715231051e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.97348454169531937478787034808955 y2[1] (numeric) = -0.97348454169532037312387463909938 absolute error = 9.9833600429100983e-16 relative error = 1.0255283587271059631368484770977e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.35 y1[1] (closed_form) = -0.21900668709304158142002217301063 y1[1] (numeric) = -0.21900668709304126345661120485418 absolute error = 3.1796341096815645e-16 relative error = 1.4518433897549194241863339944963e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.97572335782665906926111353926522 y2[1] (numeric) = -0.97572335782666008599357132271681 absolute error = 1.01673245778345159e-15 relative error = 1.0420294334739887838738157856905e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.36 y1[1] (closed_form) = -0.20923866589141935767597525239186 y1[1] (numeric) = -0.20923866589141902945326906359423 absolute error = 3.2822270618879763e-16 relative error = 1.5686522602811991737911665884099e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.97786460243531618567849243942663 y2[1] (numeric) = -0.97786460243531722080229656406227 absolute error = 1.03512380412463564e-15 relative error = 1.0585553475877117021959105427024e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=765.5MB, alloc=40.3MB, time=9.06 x[1] = 1.37 y1[1] (closed_form) = -0.19944972099757296568819838964531 y1[1] (numeric) = -0.19944972099757262702233467807572 absolute error = 3.3866586371156959e-16 relative error = 1.6980011905641657786574653324711e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.97990806139861422288768850489193 y2[1] (numeric) = -0.97990806139861527639165652384675 absolute error = 1.05350396801895482e-15 relative error = 1.0751049098578674839927332246483e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.38 y1[1] (closed_form) = -0.1896408312978343632091500735982 y1[1] (numeric) = -0.18964083129783401391640877299446 absolute error = 3.4929274130060374e-16 relative error = 1.8418646391189519628848068909641e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98185353037235972787813108520605 y2[1] (numeric) = -0.98185353037236079974499714141322 absolute error = 1.07186686605620717e-15 relative error = 1.0916769486480439078022012996134e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.39 y1[1] (closed_form) = -0.17981297767299947659616321780405 y1[1] (numeric) = -0.17981297767299911649302736811297 absolute error = 3.6010313584969108e-16 relative error = 2.0026537600893296352940251497733e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98370081481127654484003822444291 y2[1] (numeric) = -0.98370081481127763504644596891219 absolute error = 1.09020640774446928e-15 relative error = 1.1082703107790206337293940355464e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.4 y1[1] (closed_form) = -0.16996714290024093861674803520365 y1[1] (numeric) = -0.16996714290024056751996471856759 absolute error = 3.7109678331663606e-16 relative error = 2.1833442451547498952380615176967e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.9854497299884601806594745788061 y2[1] (numeric) = -0.98544972998846128917597112336468 absolute error = 1.10851649654455858e-15 relative error = 1.1248838604456663015460116862853e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.41 y1[1] (closed_form) = -0.16010431155483119016356254936092 y1[1] (numeric) = -0.16010431155483080789020388139849 absolute error = 3.8227335866796243e-16 relative error = 2.3876518686821537366525157708097e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98710010101385034142908886194224 y2[1] (numeric) = -0.98710010101385146822011976788094 absolute error = 1.12679103090593870e-15 relative error = 1.1415164781652963350577953034665e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=807.9MB, alloc=40.3MB, time=9.56 TOP MAIN SOLVE Loop x[1] = 1.42 y1[1] (closed_form) = -0.15022546991168577348698210297591 y1[1] (numeric) = -0.15022546991168537985450626899114 absolute error = 3.9363247583398477e-16 relative error = 2.6202778800784752693954015276730e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.9886517628517197927362734733357 y2[1] (numeric) = -0.9886517628517209377601787772572 absolute error = 1.14502390530392150e-15 relative error = 1.1581670597553516441426143364067e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.43 y1[1] (closed_form) = -0.14033160584673666253389762457492 y1[1] (numeric) = -0.140331605846736257360209950317 absolute error = 4.0517368767425792e-16 relative error = 2.8872589694211072150233790819996e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99010456033717779485729149548183 y2[1] (numeric) = -0.99010456033717895806630277350144 absolute error = 1.16320901127801961e-15 relative error = 1.1748345153383512331222673381290e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.44 y1[1] (closed_form) = -0.13042370873814549297752015612917 y1[1] (numeric) = -0.13042370873814507608103420271418 absolute error = 4.1689648595341499e-16 relative error = 3.1964777722310220548617344683725e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99145834819168646252760446395798 y2[1] (numeric) = -0.99145834819168764386784293526057 absolute error = 1.18134023847130259e-15 relative error = 1.1915177683721563298007106601630e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.45 y1[1] (closed_form) = -0.12050276936736657053286662724802 y1[1] (numeric) = -0.1205027693673661417325652998446 absolute error = 4.2880030132740342e-16 relative error = 3.5584269438667946056899834801837e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99271299103758849766535413432301 y2[1] (numeric) = -0.99271299103758969707682980493312 absolute error = 1.19941147567061011e-15 relative error = 1.2082157547036624757186010267455e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.46 y1[1] (closed_form) = -0.11056977982006955117464810912337 y1[1] (numeric) = -0.11056977982006911029014476899657 absolute error = 4.4088450334012680e-16 relative error = 3.9873870062649951340921252305353e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99386836341164484228683230125003 y2[1] (numeric) = -0.9938683634116460597034441487252 absolute error = 1.21741661184747517e-15 relative error = 1.2249274216441077264721174583670e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=850.3MB, alloc=40.3MB, time=10.05 TOP MAIN SOLVE Loop x[1] = 1.47 y1[1] (closed_form) = -0.10062573338693170090697460146241 y1[1] (numeric) = -0.1006257333869312477585741709635 absolute error = 4.5314840043049891e-16 relative error = 4.5033053194059945189051393372464e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99492434977758089785992846273557 y2[1] (numeric) = -0.9949243497775821332094656623458 absolute error = 1.23534953719961023e-15 relative error = 1.2416517270642509576776363554337e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.48 y1[1] (closed_form) = -0.090671624464309655776226540647838 y1[1] (numeric) = -0.090671624464309190184986590733144 absolute error = 4.65591239949914694e-16 relative error = 5.1349167140286721021976507079574e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99588084453764005648407513256269 y2[1] (numeric) = -0.99588084453764130968821932537183 absolute error = 1.25320414419280914e-15 relative error = 1.2583876385077345045848072378386e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.49 y1[1] (closed_form) = -0.080708448454800614868318484563714 y1[1] (numeric) = -0.080708448454800136656110294421809 absolute error = 4.78212208190141905e-16 relative error = 5.9251815311250403605571362910167e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.9967377520431433885532007170437 y2[1] (numeric) = -0.99673775204314465952752932016119 absolute error = 1.27097432860311749e-15 relative error = 1.2751341323209997996261574817625e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.5 y1[1] (closed_form) = -0.070737201667702910088189851434269 y1[1] (numeric) = -0.070737201667702419077759429799275 absolute error = 4.91010430421634994e-16 relative error = 6.9413324084859838455361672885849e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99749498660405443094172337114149 y2[1] (numeric) = -0.9974949866040557195957139302657 absolute error = 1.28865399055912421e-15 relative error = 1.2918901927981743406478691874976e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.51 y1[1] (closed_form) = -0.060758881219385906581595514916193 y1[1] (numeric) = -0.06075888121938540259662457264418 absolute error = 5.03984970942272013e-16 relative error = 8.2948362581348698729851877625525e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99815247249754811924273786483671 y2[1] (numeric) = -0.99815247249754942547977344906345 absolute error = 1.30623703558422674e-15 relative error = 1.3086548113393922445549235121322e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=892.7MB, alloc=40.3MB, time=10.55 TOP MAIN SOLVE Loop x[1] = 1.52 y1[1] (closed_form) = -0.050774484933579196726129270152727 y1[1] (numeric) = -0.050774484933578679591296133639337 absolute error = 5.17134833136513390e-16 relative error = 1.0184935087239288784251858388878e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.99871014397558300717231239411685 y2[1] (numeric) = -0.99871014397558433088968803283938 absolute error = 1.32371737563872253e-15 relative error = 1.3254269856210506971695811656900e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.53 y1[1] (closed_form) = -0.040785011241591058688989007076121 y1[1] (numeric) = -0.040785011241590528230029462095993 absolute error = 5.30458959544980128e-16 relative error = 1.3006223202999574888971811692732e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.99916794527147601592426506870898 y2[1] (numeric) = -0.99916794527147735701319523028833 absolute error = 1.34108893016157935e-15 relative error = 1.3422057187765393023249765822175e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.54 y1[1] (closed_form) = -0.030791459082466157622476807076397 y1[1] (numeric) = -0.030791459082465613666244862628908 absolute error = 5.43956231944447489e-16 relative error = 1.7665815396653194379974655803084e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.99952583060547905600596353844003 y2[1] (numeric) = -0.99952583060548041435159065017688 absolute error = 1.35834562711173685e-15 relative error = 1.3589900185860097846846198577449e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.55 y1[1] (closed_form) = -0.020794827803092473643912774695556 y1[1] (numeric) = -0.020794827803091916018441336446821 absolute error = 5.57625471438248735e-16 relative error = 2.6815584948259213057845291582525e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.99978376418935696389761134763447 y2[1] (numeric) = -0.99978376418935833937901535642645 absolute error = 1.37548140400879198e-15 relative error = 1.3757788966737798165838663316307e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=934.9MB, alloc=40.3MB, time=11.05 x[1] = 1.56 y1[1] (closed_form) = -0.010796117058267445823920663760906 y1[1] (numeric) = -0.010796117058266874358482106678886 absolute error = 5.71465438557082020e-16 relative error = 5.2932497440778067989133939573696e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.99994172022996629574517002341348 y2[1] (numeric) = -0.99994172022996768823537899633439 absolute error = 1.39249020897292091e-15 relative error = 1.3925713677119866855905255719729e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.57 y1[1] (closed_form) = -0.00079632671073332548540853364535419 y1[1] (numeric) = -0.0007963267107327400105751634332882 absolute error = 5.8547483337021206599e-16 relative error = 7.3521938355057430469211841592773e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.005 y2[1] (closed_form) = -0.99999968293183462021052992382333 y2[1] (numeric) = -0.9999996829318360295765316877133 absolute error = 1.40936600176388997e-15 relative error = 1.4093664486291241846657074570751e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.58 y1[1] (closed_form) = 0.0092035432688082648053890569827275 y1[1] (numeric) = 0.0092035432688088644576846640395094 absolute error = 5.996522956070567819e-16 relative error = 6.5154503878885299928609214286101e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.99995764649874005255179423225172 y2[1] (numeric) = -0.99995764649874147865454905126018 absolute error = 1.42610275481900846e-15 relative error = 1.4261631578221101693744816494361e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.59 y1[1] (closed_form) = 0.019202492901692568095027346243403 y1[1] (numeric) = 0.019202492901693182091432135390902 absolute error = 6.13996404789147499e-16 relative error = 3.1974827848264843026711132602877e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.99981561513429087198158434374551 y2[1] (numeric) = -0.99981561513429231467603863362147 absolute error = 1.44269445428987596e-15 relative error = 1.4429605143705417466301368803428e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.6 y1[1] (closed_form) = 0.029199522301288726205770462946499 y1[1] (numeric) = 0.029199522301289354711450835396533 absolute error = 6.28505680372450034e-16 relative error = 2.1524519267382357894036955155617e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.99957360304150516434211382554623 y2[1] (numeric) = -0.99957360304150662347721490332352 absolute error = 1.45913510107777729e-15 relative error = 1.4597575372518013698654311496551e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=977.2MB, alloc=40.3MB, time=11.55 x[1] = 1.61 y1[1] (closed_form) = 0.039193631772987609585327609601018 y1[1] (numeric) = 0.039193631772988252763909509633355 absolute error = 6.43178581900032337e-16 relative error = 1.6410282813936964708262986939996e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.9992316344213905321324131478443 y2[1] (numeric) = -0.99923163442139200755112501542231 absolute error = 1.47541871186757801e-15 relative error = 1.4765532445556787211911281193334e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.62 y1[1] (closed_form) = 0.049183821914170445143744274712327 y1[1] (numeric) = 0.049183821914171103157253439775287 absolute error = 6.58013509165062960e-16 relative error = 1.3378657525097321227972055325818e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.9987897434705240139155188912468 y2[1] (numeric) = -0.99878974347052550545483905122054 absolute error = 1.49153932015997374e-15 relative error = 1.4933466526971715996142568250978e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.63 y1[1] (closed_form) = 0.059169093714148245297971697419802 y1[1] (numeric) = 0.059169093714148918306774081542996 absolute error = 6.73008802384123194e-16 relative error = 1.1374330079069579900312479703400e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = -0.9982479743776324551116699849331 y2[1] (numeric) = -0.99824797437763396260264728687983 absolute error = 1.50749097730194673e-15 relative error = 1.5101367756261232060020048491517e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.64 y1[1] (closed_form) = 0.069148448654062044364492707456605 y1[1] (numeric) = 0.069148448654062732527235088270792 absolute error = 6.88162742380814187e-16 relative error = 9.9519621303953704146128034148765e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99760638131917367213758197436794 y2[1] (numeric) = -0.99760638131917519540533548965101 absolute error = 1.52326775351528307e-15 relative error = 1.5269226240323432424172159853415e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.65 y1[1] (closed_form) = 0.079120888806733952359614597341276 y1[1] (numeric) = 0.079120888806734655833165376980197 absolute error = 7.03473550779638921e-16 relative error = 8.8911229561385630262268642443368e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99686502845391885177170304020219 y2[1] (numeric) = -0.99686502845392039063544196320683 absolute error = 1.53886373892300464e-15 relative error = 1.5437032045448470220751937198581e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1019.7MB, alloc=40.3MB, time=12.03 x[1] = 1.66 y1[1] (closed_form) = 0.089085416936459041185257931650621 y1[1] (numeric) = 0.089085416936459760124648141788099 absolute error = 7.18939390210137478e-16 relative error = 8.0702253515064910644776044589581e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99602398991653672750100059061296 y2[1] (numeric) = -0.99602398991653828177404516418237 absolute error = 1.55427304457356941e-15 relative error = 1.5604775189238283009533756200677e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.67 y1[1] (closed_form) = 0.099041036598728084094782342448611 y1[1] (numeric) = 0.099041036598728818653146863701143 absolute error = 7.34558364521252532e-16 relative error = 7.4167071523833986183405718279687e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99508334981018017442629724653424 y2[1] (numeric) = -0.99508334981018174391610070922899 absolute error = 1.56948980346269475e-15 relative error = 1.5772445632439604560583186874726e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.68 y1[1] (closed_form) = 0.10898675223987117624800473417282 y1[1] (numeric) = 0.10898675223987192657652374007341 absolute error = 7.5032851900590059e-16 relative error = 6.8845846268956356967827893050854e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99404320219807596406048786919357 y2[1] (numeric) = -0.99404320219807754856865942185161 absolute error = 1.58450817155265804e-15 relative error = 1.5940033270675938833848201133277e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.69 y1[1] (closed_form) = 0.11892156929661227207639046983309 y1[1] (numeric) = 0.11892156929661303832423110555608 absolute error = 7.6624784063572299e-16 relative error = 6.4433041471607215948473484024900e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99290365109411852003714929394559 y2[1] (numeric) = -0.99290365109412011935947808287494 absolute error = 1.59932232878892935e-15 relative error = 1.6107527926063872243875771214457e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.7 y1[1] (closed_form) = 0.12884449429552468408764285733487 y1[1] (numeric) = 0.12884449429552546640190116332424 absolute error = 7.8231425830598937e-16 relative error = 6.0717709560148621979235107554312e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99166481045246861534613339864788 y2[1] (numeric) = -0.99166481045247022927261351263938 absolute error = 1.61392648011399150e-15 relative error = 1.6274919338698753242992424097909e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1062.1MB, alloc=40.3MB, time=12.53 TOP MAIN SOLVE Loop x[1] = 1.71 y1[1] (closed_form) = 0.13875453495237759764268978305111 y1[1] (numeric) = 0.13875453495237839616833287367558 absolute error = 7.9852564309062447e-16 relative error = 5.7549516732169445425968455525203e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.99032680415615805121775222386113 y2[1] (numeric) = -0.99032680415615967953260870206399 absolute error = 1.62831485647820286e-15 relative error = 1.6442197157994369638478991599590e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.72 y1[1] (closed_form) = 0.14865070027136366713637828033119 y1[1] (numeric) = 0.14865070027136448201618678765963 absolute error = 8.1487980850732844e-16 relative error = 5.4818430523351414197999658450081e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98888976600470145717817065708548 y2[1] (numeric) = -0.98888976600470309965988650464395 absolute error = 1.64248171584755847e-15 relative error = 1.6609350933860808655418165784185e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.73 y1[1] (closed_form) = 0.15853200064419777090494835134257 y1[1] (numeric) = 0.158532000644198602279459144101 absolute error = 8.3137451079275843e-16 relative error = 5.2442062638107917940057553795526e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98735383970071645108567767622206 y2[1] (numeric) = -0.98735383970071810750702188442807 absolute error = 1.65642134420820601e-15 relative error = 1.6776370107704196181314151438421e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.74 y1[1] (closed_form) = 0.16839744794907701506737731534509 y1[1] (numeric) = 0.16839744794907786307482650308369 absolute error = 8.4800744918773860e-16 relative error = 5.0357500040272226784549186518922e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98571917883555349712068269566555 y2[1] (numeric) = -0.98571917883555516724873926323827 absolute error = 1.67012805656757272e-15 relative error = 1.6943244003231456272357238292061e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.75 y1[1] (closed_form) = 0.17824605564949209038267694394263 y1[1] (numeric) = 0.17824605564949295515894317640649 absolute error = 8.6477626623246386e-16 relative error = 4.8515871113186567040487514422913e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98398594687393689873166293696799 y2[1] (numeric) = -0.98398594687393858232786088892858 absolute error = 1.68359619795196059e-15 relative error = 1.7109961817042637855110776780037e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1104.2MB, alloc=40.3MB, time=13.03 TOP MAIN SOLVE Loop x[1] = 1.76 y1[1] (closed_form) = 0.1880768388928801010698001765041 y1[1] (numeric) = 0.18807683889288098274834824816538 absolute error = 8.8167854807166128e-16 relative error = 4.6878634990979657214567870290703e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98215431713761846242496809945596 y2[1] (numeric) = -0.98215431713762015924511249992271 absolute error = 1.69682014440046675e-15 relative error = 1.7276512608992686837301609436934e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.77 y1[1] (closed_form) = 0.19788881460910900038948584173039 y1[1] (numeric) = 0.19788881460910989910131061140216 absolute error = 8.9871182476967177e-16 relative error = 4.5414988540150831504850861020245e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.98022447278804546701848144889842 y2[1] (numeric) = -0.98022447278804717681278540398556 absolute error = 1.70979430395508714e-15 relative error = 1.7442885292303827233642692781706e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.78 y1[1] (closed_form) = 0.20768100160878378462655329031263 y1[1] (numeric) = 0.20768100160878470050012392572567 absolute error = 9.1587357063541304e-16 relative error = 4.4100017023255560745718155323298e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.9781966068080446715477686473056 y2[1] (numeric) = -0.97819660680804639406088629416708 absolute error = 1.72251311764686148e-15 relative error = 1.7609068623408923101431634014362e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.79 y1[1] (closed_form) = 0.21745242068136461493517026446461 y1[1] (numeric) = 0.21745242068136554809637482164836 absolute error = 9.3316120455718375e-16 relative error = 4.2913350958946323284329136568420e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.97607092198252419340866043310862 y2[1] (numeric) = -0.9760709219825259283797209110271 absolute error = 1.73497106047791848e-15 relative error = 1.7775051191505342433276490215313e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.8 y1[1] (closed_form) = 0.22720209469308705531667430653058 y1[1] (numeric) = 0.22720209469308800588876465379747 absolute error = 9.5057209034726689e-16 relative error = 4.1838174583352086879091770845113e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.97384763087819518653237317884336 y2[1] (numeric) = -0.97384763087819693369501557812343 absolute error = 1.74716264239928007e-15 relative error = 1.7940821407797909512019781659016e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1146.3MB, alloc=40.3MB, time=13.51 TOP MAIN SOLVE Loop x[1] = 1.81 y1[1] (closed_form) = 0.23692904868467463478774985084198 y1[1] (numeric) = 0.23692904868467560289128694713147 absolute error = 9.6810353709628949e-16 relative error = 4.0860483021004493338202645402024e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.97152695582231534740845126909038 y2[1] (numeric) = -0.97152695582231710649086055337514 absolute error = 1.75908240928428476e-15 relative error = 1.8106367494408535194507656290462e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.82 y1[1] (closed_form) = 0.24663230996883396256417104483087 y1[1] (numeric) = 0.24663230996883494831697058212497 absolute error = 9.8575279953729410e-16 relative error = 3.9968518304104605506554834438456e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.96910912888045637458721531849805 y2[1] (numeric) = -0.96910912888045814531215921598812 absolute error = 1.77072494389749007e-15 relative error = 1.8271677472929019604238031006471e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.83 y1[1] (closed_form) = 0.25631090822752264682983758361853 y1[1] (numeric) = 0.2563109082275236503469160030945 absolute error = 1.00351707841947597e-15 relative error = 3.9152335940718982577193468845820e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.96659439183329760489723892974281 y2[1] (numeric) = -0.96659439183329938698210578865769 absolute error = 1.78208486685891488e-15 relative error = 1.8436739152592349588783869317649e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.84 y1[1] (closed_form) = 0.2659638756089802903802829832816 y1[1] (numeric) = 0.26596387560898131177380387482054 absolute error = 1.02139352089153894e-15 relative error = 3.8403468085763279894767466169304e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.96398299615244814699489367172712 y2[1] (numeric) = -0.96398299615244994015173127521027 absolute error = 1.79315683760348315e-15 relative error = 1.8601540118036543849736280184394e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1188.2MB, alloc=40.3MB, time=14.00 x[1] = 1.85 y1[1] (closed_form) = 0.2755902468245128601219498354748 y1[1] (numeric) = 0.27559024682451389950117073009588 absolute error = 1.03937922089462108e-15 relative error = 3.7714659095191596007716718885857e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.96127520297529993001245916863613 y2[1] (numeric) = -0.96127520297530173394801450416673 absolute error = 1.80393555533553060e-15 relative error = 1.8766067716633723658002008750864e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.86 y1[1] (closed_form) = 0.28518905924502075207093548828912 y1[1] (numeric) = 0.2851890592450218095421550530293 absolute error = 1.05747121956474018e-15 relative error = 3.7079655943470526385794199191822e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.9584712830789141819789777659032 y2[1] (numeric) = -0.95847128307891599639473774414038 absolute error = 1.81441575997823718e-15 relative error = 1.8930309045355615466130264953029e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.87 y1[1] (closed_form) = 0.29475935299726089912514806480989 y1[1] (numeric) = 0.2947593529972619747916537095175 absolute error = 1.07566650564470761e-15 relative error = 3.6493040668830054799387484247865e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.95557151685294394934425049217263 y2[1] (numeric) = -0.95557151685294577393648361002094 absolute error = 1.82459223311784831e-15 relative error = 1.9094250937145093068995694351545e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.88 y1[1] (closed_form) = 0.30430017105983329547931375952224 y1[1] (numeric) = 0.30430017105983438944132966498004 absolute error = 1.09396201590545780e-15 relative error = 3.5950095331703133757058283732834e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.95257619427159536533145742581513 y2[1] (numeric) = -0.9525761942715971997912563683637 absolute error = 1.83445979894254857e-15 relative error = 1.9257879946761649557190090671846e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.89 y1[1] (closed_form) = 0.31381055935888233911038241555123 y1[1] (numeric) = 0.31381055935888345146501799229029 absolute error = 1.11235463557673906e-15 relative error = 3.5446692356346743365726478694684e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.94948561486463047096820167213832 y2[1] (numeric) = -0.94948561486463231498152684799082 absolute error = 1.84401332517585250e-15 relative error = 1.9421182336066841103299968495105e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1230.3MB, alloc=40.3MB, time=14.50 x[1] = 1.9 y1[1] (closed_form) = 0.32328956686350342227883369508031 y1[1] (numeric) = 0.32328956686350455312003248219075 absolute error = 1.13084119878711044e-15 relative error = 3.4979204858304772187610357816051e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.94630008768741448848970961163496 y2[1] (numeric) = -0.94630008768741634173743361601219 absolute error = 1.85324772400437723e-15 relative error = 1.9584144058713742810181636352718e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.91 y1[1] (closed_form) = 0.33273624568084522946633893939753 y1[1] (numeric) = 0.33273624568084637888482795258509 absolute error = 1.14941848901318756e-15 relative error = 3.4544432833316560691535282658795e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.94301993129001054236188657694821 y2[1] (numeric) = -0.94301993129001240451983957681128 absolute error = 1.86215795299986307e-15 relative error = 1.9746750744202314008980261440447e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.92 y1[1] (closed_form) = 0.34214965115089823259923660315905 y1[1] (numeric) = 0.3421496511508994006824761412385 absolute error = 1.16808323953807945e-15 relative error = 3.4139542028143696531801398076119e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.93964547368532491842637133968703 y2[1] (numeric) = -0.9396454736853267891653873749953 absolute error = 1.87073901603530827e-15 relative error = 1.9908987681260246268848559481827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.93 y1[1] (closed_form) = 0.35152884194095990478728906471187 y1[1] (numeric) = 0.35152884194096109161942298366845 absolute error = 1.18683213391895658e-15 relative error = 3.3762013021915505480448394879190e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.93617705231630604661512937274878 y2[1] (numeric) = -0.93617705231630792560109356783412 absolute error = 1.87898596419508534e-15 relative error = 2.0070839800506374098193807162640e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.94 y1[1] (closed_form) = 0.36087288013976720613506768584073 y1[1] (numeric) = 0.36087288013976841179687414953031 absolute error = 1.20566180646368958e-15 relative error = 3.3409598582102732541401787527981e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.9326150140222004873089793388657 y2[1] (numeric) = -0.93261501402220237420287601777236 absolute error = 1.88689389667890666e-15 relative error = 2.0232291656351030893709813652528e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1272.3MB, alloc=40.3MB, time=14.98 TOP MAIN SOLVE Loop x[1] = 1.95 y1[1] (closed_form) = 0.37018083135128692845582845913069 y1[1] (numeric) = 0.3701808313512881530246711756269 absolute error = 1.22456884271649621e-15 relative error = 3.3080287767640484381728182549753e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.92895971500386929571329703509148 y2[1] (numeric) = -0.9289597150038711901712587345998 absolute error = 1.89445796169950832e-15 relative error = 2.0393327408084833243473894257426e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.96 y1[1] (closed_form) = 0.37945176478815451993156521544745 y1[1] (numeric) = 0.37945176478815576348134516798068 absolute error = 1.24354977995253323e-15 relative error = 3.2772275565691441045606780819252e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.92521152078816823258555628949003 y2[1] (numeric) = -0.92521152078817013425891366341147 absolute error = 1.90167335737392144e-15 relative error = 2.0553930800104238962130533251216e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.97 y1[1] (closed_form) = 0.38868475336475204591463981387931 y1[1] (numeric) = 0.38868475336475330851574749524773 absolute error = 1.26260110768136842e-15 relative error = 3.2483937091726110713765112267252e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.92137080619139538326395099715317 y2[1] (numeric) = -0.92137080619139729179928360535458 absolute error = 1.90853533260820141e-15 relative error = 2.0714085141218848033952473707510e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.98 y1[1] (closed_form) = 0.39787887378991597815247385990719 y1[1] (numeric) = 0.39787887378991725987174201917375 absolute error = 1.28171926815926656e-15 relative error = 3.2213805572296536240932221076548e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.917437955281809840204735217402 y2[1] (numeric) = -0.91743795528181175524392319288796 absolute error = 1.91503918797548596e-15 relative error = 2.0873773282981762932026327768526e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.99 y1[1] (closed_form) = 0.40703320665926554173363571613029 y1[1] (numeric) = 0.40703320665926684263429262635246 absolute error = 1.30090065691022217e-15 relative error = 3.1960553478852361978195857519149e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.91341336134122519712879327105761 y2[1] (numeric) = -0.91341336134122711830906985831175 absolute error = 1.92118027658725414e-15 relative error = 2.1032977596980387801952542910466e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1314.5MB, alloc=40.3MB, time=15.48 TOP MAIN SOLVE Loop x[1] = 2 y1[1] (closed_form) = 0.41614683654714238699756822950076 y1[1] (numeric) = 0.41614683654714370713919148517106 absolute error = 1.32014162325567030e-15 relative error = 3.1722976298682511250119342100120e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.90929742682568169539601986591174 y2[1] (numeric) = -0.90929742682568362235002482357049 absolute error = 1.92695400495765875e-15 relative error = 2.1191679951020784336577804802999e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.01 y1[1] (closed_form) = 0.42521885209815239251738234016543 y1[1] (numeric) = 0.42521885209815373195585319297088 absolute error = 1.33943847085280545e-15 relative error = 3.1499978522674380965012695786928e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.90509056332520095536009971027372 y2[1] (numeric) = -0.90509056332520288771593357107976 absolute error = 1.93235583386080604e-15 relative error = 2.1349861684134104692365024470079e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.02 y1[1] (closed_form) = 0.4342483461183004450517028740902 y1[1] (numeric) = 0.43424834611830180383916111552769 absolute error = 1.35878745824143749e-15 relative error = 3.1290561504436190870621110400787e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.90079319152262731719701352455371 y2[1] (numeric) = -0.90079319152262925457829270541074 absolute error = 1.93738127918085703e-15 relative error = 2.1507503580328641054534435599104e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.03 y1[1] (closed_form) = 0.4432344156657090830635167316961 y1[1] (numeric) = 0.44323441566571046124831613100836 absolute error = 1.37818479939931226e-15 relative error = 3.1093812905511159194900565639443e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.89640574115155990703888883196757 y2[1] (numeric) = -0.89640574115156184906480158679328 absolute error = 1.94202591275482571e-15 relative error = 2.1664585841005646218748566709808e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.04 y1[1] (closed_form) = 0.45217616214091193201727020529136 y1[1] (numeric) = 0.45217616214091332964393451111438 absolute error = 1.39762666430582302e-15 relative error = 3.0908897490051228614199099668630e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.8919286509533796351715256485842 y2[1] (numeric) = -0.89192865095338158145688885653495 absolute error = 1.94628536320795075e-15 relative error = 2.1821088055951254094339785488599e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1356.6MB, alloc=40.3MB, time=15.97 TOP MAIN SOLVE Loop x[1] = 2.05 y1[1] (closed_form) = 0.4610726913767129021859299941674 y1[1] (numeric) = 0.4610726913767143192951095082054 absolute error = 1.41710917951403800e-15 relative error = 3.0735049071822148896966236429060e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.88736236863337542355996660468034 y2[1] (numeric) = -0.88736236863337737371528338619786 absolute error = 1.95015531678151752e-15 relative error = 2.1976989172810504371195451334325e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.06 y1[1] (closed_form) = 0.4699231137276021631231096264879 y1[1] (numeric) = 0.46992311372760359975153835745586 absolute error = 1.43662842873096796e-15 relative error = 3.0571563448648127900676868720549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.8827073508159740500427975851999 y2[1] (numeric) = -0.88270735081597600367431573820884 absolute error = 1.95363151815300894e-15 relative error = 2.2132267464942637534399498804305e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.07 y1[1] (closed_form) = 0.47872654415871995327732713901173 y1[1] (numeric) = 0.47872654415872140945778054500808 absolute error = 1.45618045340599635e-15 relative error = 3.0417792185828853779759907735727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.87796406299907808617345112044384 y2[1] (numeric) = -0.87796406299908004288322236890775 absolute error = 1.95670977124846391e-15 relative error = 2.2286900497549391952412532729841e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.08 y1[1] (closed_form) = 0.48748210233435932844156884977235 y1[1] (numeric) = 0.48748210233436080420282217716589 absolute error = 1.47576125332739354e-15 relative error = 3.0273137131815825309595753912257e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.87313297950751649487667680502462 y2[1] (numeric) = -0.87313297950751845426261685194835 absolute error = 1.95938594004692373e-15 relative error = 2.2440865091959982084845859880398e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1398.7MB, alloc=40.3MB, time=16.47 x[1] = 2.09 y1[1] (closed_form) = 0.49618891270599899883706631187045 y1[1] (numeric) = 0.49618891270600049420385353870605 absolute error = 1.49536678722683560e-15 relative error = 3.0137045567418144969542855525747e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.86821458344561254282162205872751 y2[1] (numeric) = -0.86821458344561450447757143557486 absolute error = 1.96165594937684735e-15 relative error = 2.2594137287947676099166383728851e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.1 y1[1] (closed_form) = 0.50484610459985745162093852371917 y1[1] (numeric) = 0.5048461045998589666139119155656 absolute error = 1.51499297339184643e-15 relative error = 3.0009005904732778708953449114337e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.86320936664887377068075931326902 y2[1] (numeric) = -0.8632093666488757341965450176467 absolute error = 1.96351578570437768e-15 relative error = 2.2746692303943380514971439949288e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.11 y1[1] (closed_form) = 0.51345281230395960347841015707169 y1[1] (numeric) = 0.51345281230396113811410044315309 absolute error = 1.53463569028608140e-15 relative error = 2.9888543864428001337777065142377e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.85811782963480885223737550831068 y2[1] (numeric) = -0.85811782963481081719887342165258 absolute error = 1.96496149791334190e-15 relative error = 2.2898504495001286872896157012068e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.12 y1[1] (closed_form) = 0.52200817515470727670690188298389 y1[1] (numeric) = 0.52200817515470883099767906035303 absolute error = 1.55429077717736914e-15 relative error = 2.9775219070404880812960927757875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.85294048155287626061472733365415 y2[1] (numeric) = -0.85294048155287822660392541052429 absolute error = 1.96598919807687014e-15 relative error = 2.3049547308360375353425700736085e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.13 y1[1] (closed_form) = 0.53051133762294484181652620960972 y1[1] (numeric) = 0.53051133762294641577056098303692 absolute error = 1.57395403477342720e-15 relative error = 2.9668622009584607529932972407692e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.8476778401335697467185299963159 y2[1] (numeric) = -0.8476778401335717133135922168333 absolute error = 1.96659506222051740e-15 relative error = 2.3199793236433293447292829666985e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1440.8MB, alloc=40.3MB, time=16.95 x[1] = 2.14 y1[1] (closed_form) = 0.5389614493995114201544499120086 y1[1] (numeric) = 0.53896144939951301377567577717444 absolute error = 1.59362122586516584e-15 relative error = 2.9568371311913176160255335309045e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.84233043163664572130250663706891 y2[1] (numeric) = -0.84233043163664768807783771384423 absolute error = 1.96677533107677532e-15 relative error = 2.3349213767040759043212007364455e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.15 y1[1] (closed_form) = 0.54735766548027109140415388226403 y1[1] (numeric) = 0.54735766548027270469222985975757 absolute error = 1.61328807597749354e-15 relative error = 2.9474111311877530375092236472821e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.83689879079849771787564813704379 y2[1] (numeric) = -0.8368987907984996844019589679046 absolute error = 1.96652631083086081e-15 relative error = 2.3497779330695035333118882353362e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.16 y1[1] (closed_form) = 0.55569914625061260300969874398337 y1[1] (numeric) = 0.55569914625061423595997277151963 absolute error = 1.63295027402753626e-15 relative error = 2.9385509858082422685059877571625e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.83138346077868319896103812034632 y2[1] (numeric) = -0.83138346077868516480541197801655 absolute error = 1.96584437385767023e-15 relative error = 2.3645459244720096373361220144855e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.17 y1[1] (closed_form) = 0.56398505756941013162446999441651 y1[1] (numeric) = 0.56398505756941178422794298459807 absolute error = 1.65260347299018156e-15 relative error = 2.9302256341903069179123681525473e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.82578499310560805298105642394338 y2[1] (numeric) = -0.82578499310561001770701587373187 absolute error = 1.96472595944978849e-15 relative error = 2.3792221653978682432933945803990e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.18 y1[1] (closed_form) = 0.57221457085243670057822486766249 y1[1] (numeric) = 0.57221457085243837282151543852022 absolute error = 1.67224329057085773e-15 relative error = 2.9224059920034745155589519110647e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.82010394762137421327400974608394 y2[1] (numeric) = -0.82010394762137617644158428252784 absolute error = 1.96316757453644390e-15 relative error = 2.3938033467957400632435994107209e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1483.0MB, alloc=40.3MB, time=17.45 x[1] = 2.19 y1[1] (closed_form) = 0.58038686315522191209020516379695 y1[1] (numeric) = 0.58038686315522360395551504925361 absolute error = 1.69186530988545666e-15 relative error = 2.9150647909013314956604405860851e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.814340892425795914434327645905 y2[1] (numeric) = -0.81434089242579787560012203920544 absolute error = 1.96116579439330044e-15 relative error = 2.4082860293940170793913151910544e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.2 y1[1] (closed_form) = 0.58850111725534570852414261265493 y1[1] (numeric) = 0.58850111725534741998922275996332 absolute error = 1.71146508014730839e-15 relative error = 2.9081764332568259477693087178038e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.80849640381959018430403691041612 y2[1] (numeric) = -0.80849640381959214302130025339661 absolute error = 1.95871726334298049e-15 relative error = 2.4226666365977471081013717689061e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.21 y1[1] (closed_form) = 0.59655652173415993337760917751863 y1[1] (numeric) = 0.59655652173416166441572653863276 absolute error = 1.73103811736111413e-15 relative error = 2.9017168605064831283771602310876e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.80257106624674725251897404255597 y2[1] (numeric) = -0.80257106624674920833766948876819 absolute error = 1.95581869544621222e-15 relative error = 2.4369414469333780012193659083826e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.22 y1[1] (closed_form) = 0.60455227105792951991771443750015 y1[1] (numeric) = 0.6045522710579312704976194612435 absolute error = 1.75057990502374335e-15 relative error = 2.8956634336354994148160514616384e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.79656547223608663852085674960916 y2[1] (numeric) = -0.796565472236088590987731933106 absolute error = 1.95246687518349684e-15 relative error = 2.4511065860068101538969529127784e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.23 y1[1] (closed_form) = 0.61248756565838519341190391068563 y1[1] (numeric) = 0.6124875656583869634977987424855 absolute error = 1.77008589483179987e-15 relative error = 2.8899948245138169760280264775541e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.79048022234200476337771012718854 y2[1] (numeric) = -0.79048022234200671203636825438086 absolute error = 1.94865865812719232e-15 relative error = 2.4651580179372236531260296695187e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1525.2MB, alloc=40.3MB, time=17.95 TOP MAIN SOLVE Loop x[1] = 2.24 y1[1] (closed_form) = 0.62036161201267963175076226631044 y1[1] (numeric) = 0.62036161201268142130226966217069 absolute error = 1.78955150739586025e-15 relative error = 2.8846909169474584308391046773805e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.7843159250844200106020886706045 y2[1] (numeric) = -0.78431592508442195499306027451588 absolute error = 1.94439097160391138e-15 relative error = 2.4790915362258218156519872176653e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.25 y1[1] (closed_form) = 0.6281736227227390889133890573964 y1[1] (numeric) = 0.62817362272274089788552201868382 absolute error = 1.80897213296128742e-15 relative error = 2.8797327164431492480016923684608e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.77807319688792124141096667558776 y2[1] (numeric) = -0.77807319688792318107178202272029 absolute error = 1.93966081534713253e-15 relative error = 2.4929027540149721619997924050780e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.26 y1[1] (closed_form) = 0.63592281659400254617912656874484 y1[1] (numeric) = 0.63592281659400437452225870426591 absolute error = 1.82834313213552107e-15 relative error = 2.8751022678005360361234476769525e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.77175266202012584952506163774032 y2[1] (numeric) = -0.77175266202012778399032377766488 absolute error = 1.93446526213992456e-15 relative error = 2.5065870936891920501479912528187e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.27 y1[1] (closed_form) = 0.6436084187135405172361343481243 y1[1] (numeric) = 0.6436084187135423648959709698697 absolute error = 1.84765983662174540e-15 relative error = 2.8707825797476218112088114892156e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.76535495252925351965074260193472 y2[1] (numeric) = -0.76535495252925544845220104962051 absolute error = 1.92880145844768579e-15 relative error = 2.5201397757649746593193192401125e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.28 y1[1] (closed_form) = 0.6512296605275456953713983504607 y1[1] (numeric) = 0.65122966052754756228894830929457 absolute error = 1.86691754995883387e-15 relative error = 2.8667575559234944269877538106071e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.75888070818092193221665357630092 y2[1] (numeric) = -0.75888070818092385488327861710183 absolute error = 1.92266662504080091e-15 relative error = 2.5335558070115350699055456849483e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1567.3MB, alloc=40.3MB, time=18.44 TOP MAIN SOLVE Loop x[1] = 2.29 y1[1] (closed_form) = 0.65878577991818769374203101818895 y1[1] (numeric) = 0.65878577991818957985357928565886 absolute error = 1.88611154826746991e-15 relative error = 2.8630119315898098452693451617127e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.75233057639417073474190827797365 y2[1] (numeric) = -0.75233057639417265079996588509307 absolute error = 1.91605805760711942e-15 relative error = 2.5468299677391200173068075683356e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.3 y1[1] (closed_form) = 0.66627602127982419331788057116602 y1[1] (numeric) = 0.66627602127982609855496157350688 absolute error = 1.90523708100234086e-15 relative error = 2.8595312155203238874324232614758e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.7457052121767201773854062116435 y2[1] (numeric) = -0.74570521217672208635853356580425 absolute error = 1.90897312735416075e-15 relative error = 2.5599567981855070238206685195543e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.31 y1[1] (closed_form) = 0.67369963559456087744416432347103 y1[1] (numeric) = 0.67369963559456280173353603377342 absolute error = 1.92428937171030239e-15 relative error = 2.8563016365773408541498967256961e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.73900527805947088675876419209826 y2[1] (numeric) = -0.73900527805947278816804579305133 absolute error = 1.90140928160095307e-15 relative error = 2.5729305839246504090668430748285e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.32 y1[1] (closed_form) = 0.68105588050715259709363616600823 y1[1] (numeric) = 0.68105588050715454035725496041724 absolute error = 1.94326361879440901e-15 relative error = 2.8533100945363622515708921792116e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.73223144403025132797089867772467 y2[1] (numeric) = -0.73223144403025322133494303713794 absolute error = 1.89336404435941327e-15 relative error = 2.5857453402140307971586677348707e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.33 y1[1] (closed_form) = 0.688344020399238276754180427816 y1[1] (numeric) = 0.68834402039924023890917671152176 absolute error = 1.96215499628370576e-15 relative error = 2.8505441147664207786811069349391e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.72538438746681958010284419247542 y2[1] (numeric) = -0.7253843874668214649378610976531 absolute error = 1.88483501690517768e-15 relative error = 2.5983947951890452155105925618038e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1609.5MB, alloc=40.3MB, time=18.92 TOP MAIN SOLVE Loop x[1] = 2.34 y1[1] (closed_form) = 0.69556332646290213752310557206135 y1[1] (numeric) = 0.69556332646290411848176018073634 absolute error = 1.98095865460867499e-15 relative error = 2.8479918064143788615481048728284e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.71846479306912612487942868679401 y2[1] (numeric) = -0.71846479306912800069930702458799 absolute error = 1.87581987833779398e-15 relative error = 2.6108723718036305926300999229083e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.35 y1[1] (closed_form) = 0.70271307677355388134712911225892 y1[1] (numeric) = 0.70271307677355588101685049449053 absolute error = 1.99966972138223161e-15 relative error = 2.8456418237775531763310329231308e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.71147335279084442220249118201321 y2[1] (numeric) = -0.71147335279084628851887731219945 absolute error = 1.86631638613018624e-15 relative error = 2.6231711684061302031500686025968e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.36 y1[1] (closed_form) = 0.7097925563621205484503630346451 y1[1] (numeric) = 0.709792556362122566733665220804 absolute error = 2.01828330218615890e-15 relative error = 2.8434833305809918311126191889941e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.7044107657701761194310307129327 y2[1] (numeric) = -0.70441076577017797575340738023922 absolute error = 1.85632237666730652e-15 relative error = 2.6352839378280565646447237234192e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.37 y1[1] (closed_form) = 0.71680105728654282882471660882235 y1[1] (numeric) = 0.71680105728654486561919797169881 absolute error = 2.03679448136287646e-15 relative error = 2.8415059669040963790333649770184e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.69727773825993781382969642028923 y2[1] (numeric) = -0.69727773825993965966546219417682 absolute error = 1.84583576577388759e-15 relative error = 2.6472030648507229590620186928544e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1651.5MB, alloc=40.3MB, time=19.42 x[1] = 2.38 y1[1] (closed_form) = 0.72373787870256867821114760736753 y1[1] (numeric) = 0.72373787870257073340947041979839 absolute error = 2.05519832281243086e-15 relative error = 2.8396998185264896581541203106218e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.6900749835569363594511131070202 y2[1] (numeric) = -0.69007498355693819430566233823317 absolute error = 1.83485454923121297e-15 relative error = 2.6589205419005363991352435547458e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.39 y1[1] (closed_form) = 0.73060232693383715926915829261806 y1[1] (numeric) = 0.73060232693383923275902908721667 absolute error = 2.07348987079459861e-15 relative error = 2.8380553884854686709116807285556e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.68280322193063978086250031101305 y2[1] (numeric) = -0.6828032219306416042393035938347 absolute error = 1.82337680328282165e-15 relative error = 2.6704279428078667111269960023779e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.4 y1[1] (closed_form) = 0.73739371554124549960882222733478 y1[1] (numeric) = 0.73739371554124759127297296332548 absolute error = 2.09166415073599070e-15 relative error = 2.8365635706573840719911200339647e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.67546318055115092656577152534128 y2[1] (numeric) = -0.67546318055115273796645665440781 absolute error = 1.81140068512906653e-15 relative error = 2.6817163944466018923698184917322e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.41 y1[1] (closed_form) = 0.74411136539159243003734439556795 y1[1] (numeric) = 0.74411136539159453975351443761442 absolute error = 2.10971617004204647e-15 relative error = 2.8352156251931422840864267404533e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.66805559341649106468574980065472 y2[1] (numeric) = -0.66805559341649286361018321110154 absolute error = 1.79892443341044682e-15 relative error = 2.6927765460515042037440034361327e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.42 y1[1] (closed_form) = 0.75075460472549093874353256891074 y1[1] (numeric) = 0.75075460472549306638445148271524 absolute error = 2.12764091891380450e-15 relative error = 2.8340031556539890232926947903541e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.66058120127920069250633410656023 y2[1] (numeric) = -0.66058120127920247845270278619646 absolute error = 1.78594636867963623e-15 relative error = 2.7035985359879922566749541954172e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1693.6MB, alloc=40.3MB, time=19.91 x[1] = 2.43 y1[1] (closed_form) = 0.7573227692245436502013552441779 y1[1] (numeric) = 0.75732276922454579563472641351472 absolute error = 2.14543337116933682e-15 relative error = 2.8329180877080206363960489860062e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.6530407515722648997124970471899 y2[1] (numeric) = -0.65304075157226667217739090931989 absolute error = 1.77246489386212999e-15 relative error = 2.7141719557236400519136043161885e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.44 y1[1] (closed_form) = 0.7638152020777741113106750925374 y1[1] (numeric) = 0.76381520207777627439916016226986 absolute error = 2.16308848506973246e-15 relative error = 2.8319526492606779243310200780833e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.64543499833437069274006107298253 y2[1] (numeric) = -0.64543499833437245121855577841821 absolute error = 1.75847849470543568e-15 relative error = 2.7244858107221007437659652013549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.45 y1[1] (closed_form) = 0.77023125404730734170190306733649 y1[1] (numeric) = 0.7702312540473095223031072168517 absolute error = 2.18060120414951521e-15 relative error = 2.8310993519039717201185431142557e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.63776470213450375443853285563378 y2[1] (numeric) = -0.63776470213450549842427307236739 absolute error = 1.74398574021673361e-15 relative error = 2.7345284779478580536069340088445e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.46 y1[1] (closed_form) = 0.7765702835332930802042763146862 y1[1] (numeric) = 0.77657028353329527817073436606637 absolute error = 2.19796645805138017e-15 relative error = 2.8303509735795202727846403345477e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.63003062999589217930819371861593 y2[1] (numeric) = -0.63003062999589390829347680755063 absolute error = 1.72898528308893470e-15 relative error = 2.7442876596336399416525379086481e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.47 y1[1] (closed_form) = 0.78283165663806523520721558406155 y1[1] (numeric) = 0.78283165663806745038637894919396 absolute error = 2.21517916336513241e-15 relative error = 2.8297005423597725177751706087048e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.62223355531930478987454240485577 y2[1] (numeric) = -0.62223355531930650335040251992058 absolute error = 1.71347586011506481e-15 relative error = 2.7537503329208582114793763839362e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1735.9MB, alloc=40.3MB, time=20.41 TOP MAIN SOLVE Loop x[1] = 2.48 y1[1] (closed_form) = 0.78901474722953112302319203359033 y1[1] (numeric) = 0.78901474722953335525741650430128 absolute error = 2.23223422447071095e-15 relative error = 2.8291413212601651985851120806095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.6143742578057117043045348806656 y2[1] (numeric) = -0.61437425780571340176082747157164 absolute error = 1.69745629259090604e-15 relative error = 2.7629026949363260850873513992165e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.49 y1[1] (closed_form) = 0.79511893700378415538109133257157 y1[1] (numeric) = 0.79511893700378640450762571775165 absolute error = 2.24912653438518008e-15 relative error = 2.8286667940025128156772362512460e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.6064535233783148891434102397918 y2[1] (numeric) = -0.60645352337831657006889694561911 absolute error = 1.68092548670582731e-15 relative error = 2.7717301028148871738323348689678e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.5 y1[1] (closed_form) = 0.80114361554693371483350279046735 y1[1] (numeric) = 0.80114361554693598068447840403699 absolute error = 2.26585097561356964e-15 relative error = 2.8282706516567482921708149955699e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.59847214410395649405185470218616 y2[1] (numeric) = -0.59847214410395815793428862392379 absolute error = 1.66388243392173763e-15 relative error = 2.7802170081164479680993760680935e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.51 y1[1] (closed_form) = 0.80708818039614603514191750787841 y1[1] (numeric) = 0.80708818039614831754433851132363 absolute error = 2.28240242100344522e-15 relative error = 2.8279467800942956635460733513961e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.59043091811391282764453715502405 y2[1] (numeric) = -0.5904309181139144739707484951214 absolute error = 1.64632621134009735e-15 relative error = 2.7883468850160534307825394821687e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.52 y1[1] (closed_form) = 0.81295203709988998260266426045185 y1[1] (numeric) = 0.81295203709989228137839886354035 absolute error = 2.29877573460308850e-15 relative error = 2.8276892481919332101905625824019e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.58233064952408189496642758229713 y2[1] (numeric) = -0.58233064952408352322240963922115 absolute error = 1.62825598205692402e-15 relative error = 2.7961021515656777767981679479633e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1778.0MB, alloc=40.3MB, time=20.91 TOP MAIN SOLVE Loop x[1] = 2.53 y1[1] (closed_form) = 0.81873459927738171378565517255499 y1[1] (numeric) = 0.8187345992773840287514276957223 absolute error = 2.31496577252316731e-15 relative error = 2.8274922967300575152770335036721e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.5741721483545724777866405874022 y2[1] (numeric) = -0.57417214835457408745763609313333 absolute error = 1.60967099550573113e-15 relative error = 2.8034640832346676690796765695885e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.54 y1[1] (closed_form) = 0.82443528867722226526970435580657 y1[1] (numeric) = 0.82443528867722459623708815758109 absolute error = 2.33096738380177452e-15 relative error = 2.8273503279338401223379018237361e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.56595623044870279873476574798203 y2[1] (numeric) = -0.5659562304487043893053535363214 absolute error = 1.59057058778833937e-15 relative error = 2.8104127178303158141924823447802e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.55 y1[1] (closed_form) = 0.83005353523522221166431047583229 y1[1] (numeric) = 0.83005353523522455843972174854645 absolute error = 2.34677541127271416e-15 relative error = 2.8272578956099262981263598915634e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.55768371739141686934577028176624 y2[1] (numeric) = -0.55768371739141844029995227526821 absolute error = 1.57095418199350197e-15 relative error = 2.8169267507785408768424032385121e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.56 y1[1] (closed_form) = 0.83558877713140760950028812338244 y1[1] (numeric) = 0.83558877713140997188498056029506 absolute error = 2.36238469243691262e-15 relative error = 2.8272096958351030513114136962859e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.54935543642712668031068338313728 y2[1] (numeric) = -0.54935543642712823113197188642414 absolute error = 1.55082128850328686e-15 relative error = 2.8229834196043439595859311959569e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.57 y1[1] (closed_form) = 0.84104046084620152644236372156713 y1[1] (numeric) = 0.84104046084620390423242405839933 absolute error = 2.37779006033683220e-15 relative error = 2.8272005581567987491695871452545e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.54097222037698844964557254874584 y2[1] (numeric) = -0.54097222037698997981707783590608 absolute error = 1.53017150528716024e-15 relative error = 2.8285583762893155640980842046965e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1820.0MB, alloc=40.3MB, time=21.39 TOP MAIN SOLVE Loop x[1] = 2.58 y1[1] (closed_form) = 0.84640804121577553771763249456923 y1[1] (numeric) = 0.84640804121577793070397692833309 absolute error = 2.39298634443376386e-15 relative error = 2.8272254372684034685635052765071e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.53253490755562120108505876447165 y2[1] (numeric) = -0.53253490755562271008957694818925 absolute error = 1.50900451818371760e-15 relative error = 2.8336255459950443599914625403807e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.59 y1[1] (closed_form) = 0.85169098148656565465635974540831 y1[1] (numeric) = 0.85169098148656806262473123328344 absolute error = 2.40796837148787513e-15 relative error = 2.8272794051252470352844922679991e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.52404434168727600077313024887591 y2[1] (numeric) = -0.52404434168727748809323141888579 absolute error = 1.48732010117000988e-15 relative error = 2.8381569704221130169630184962962e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.6 y1[1] (closed_form) = 0.8568887533689472337977021516452 y1[1] (numeric) = 0.85688875336894965652866859253443 absolute error = 2.42273096644088923e-15 relative error = 2.8273576434696692167753026248195e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.51550137182146423525772693520937 y2[1] (numeric) = -0.51550137182146570037584355362334 absolute error = 1.46511811661841397e-15 relative error = 2.8421226338187796480203337653240e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.61 y1[1] (closed_form) = 0.86200083709006349911416744872265 y1[1] (numeric) = 0.86200083709006593638312074999296 absolute error = 2.43726895330127031e-15 relative error = 2.8274554367359851876549635661183e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.5069068522480533678909866995555 y2[1] (numeric) = -0.50690685224805481028950224055414 absolute error = 1.44239851554099864e-15 relative error = 2.8454902693545858705132754335288e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1862.1MB, alloc=40.3MB, time=21.89 x[1] = 2.62 y1[1] (closed_form) = 0.86702672144580239454661367674835 y1[1] (numeric) = 0.86702672144580484612376970853796 absolute error = 2.45157715603178961e-15 relative error = 2.8275681653083134345080682832821e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.49826164241183866398876000999763 y2[1] (numeric) = -0.49826164241184008315009783133577 absolute error = 1.41916133782133814e-15 relative error = 2.8482251432237059546228411230050e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.63 y1[1] (closed_form) = 0.87196590385191656920784839019493 y1[1] (numeric) = 0.87196590385191903485824782954179 absolute error = 2.46565039943934686e-15 relative error = 2.8276912991062103373170010735536e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.48956660682659942750568705361163 y2[1] (numeric) = -0.4895666068266008229123994873394 absolute error = 1.39540671243372777e-15 relative error = 2.8502898134307793084907148706647e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.64 y1[1] (closed_form) = 0.87681789039428138329890731626599 y1[1] (numeric) = 0.87681789039428386278241738318662 absolute error = 2.47948351006692063e-15 relative error = 2.8278203914748633770787150041514e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.48082261498864834353055026953286 y2[1] (numeric) = -0.48082261498864971466540791929004 absolute error = 1.37113485764975718e-15 relative error = 2.8516438597259574853167519272790e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.65 y1[1] (closed_form) = 0.88158219587828590897930236605381 y1[1] (numeric) = 0.88158219587828840205061945357483 absolute error = 2.49307131708752102e-15 relative error = 2.8279510733582493019684412130240e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.47203054128988257159561077839739 y2[1] (numeric) = -0.47203054128988391794169201059605 absolute error = 1.34634608123219866e-15 relative error = 2.8522435805809077003009722269524e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.66 y1[1] (closed_form) = 0.88625834387735198713231100388259 y1[1] (numeric) = 0.88625834387735449354096420390022 absolute error = 2.50640865320001763e-15 relative error = 2.8280790477351781135247238563203e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.46319126493034528461814059379635 y2[1] (numeric) = -0.46319126493034660565892120996602 absolute error = 1.32104078061616967e-15 relative error = 2.8520416524150726796546560114102e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=1904.2MB, alloc=40.3MB, time=22.37 x[1] = 2.67 y1[1] (closed_form) = 0.89084586678057648816006285842974 y1[1] (numeric) = 0.89084586678057900765041838514513 absolute error = 2.51949035552671539e-15 relative error = 2.8282000842995312282040473476676e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.4543056698303063972473913211913 y2[1] (numeric) = -0.45430566983030769246683439872132 absolute error = 1.29521944307753002e-15 relative error = 2.8509867454688034869530371701934e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.68 y1[1] (closed_form) = 0.89534430583949201262204581862066 y1[1] (numeric) = 0.895344305839494544933312331171 absolute error = 2.53231126651255034e-15 relative error = 2.8283100143672736866514497879542e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.44537464454187127547089883192945 y2[1] (numeric) = -0.44537464454187254435354472040585 absolute error = 1.26888264588847640e-15 relative error = 2.8490230897488466463118888126032e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.69 y1[1] (closed_form) = 0.89975321121394135568593488432887 y1[1] (numeric) = 0.89975321121394390055216971010607 absolute error = 2.54486623482577720e-15 relative error = 2.8284047259939864315664457822303e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.43639908216012626653550411876099 y2[1] (numeric) = -0.43639908216012750856656057905888 absolute error = 1.24203105646029789e-15 relative error = 2.8460899833069862570172800008897e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.7 y1[1] (closed_form) = 0.90407214201706114798252728194333 y1[1] (numeric) = 0.90407214201706370513264354196349 absolute error = 2.55715011626002016e-15 relative error = 2.8284801592877341877400195667023e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.42737988023382993455605308585788 y2[1] (numeric) = -0.4273798802338311492214855591163 absolute error = 1.21466543247325842e-15 relative error = 2.8421212337105934840008918252031e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.71 y1[1] (closed_form) = 0.90830066635937017453818459371608 y1[1] (numeric) = 0.90830066635937274369595923127411 absolute error = 2.56915777463755803e-15 relative error = 2.8285323019030659644789935070896e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.41831794067565893261379068110859 y2[1] (numeric) = -0.41831794067566011940041267468204 absolute error = 1.18678662199357345e-15 relative error = 2.8370445218694158241836541157057e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1946.3MB, alloc=40.3MB, time=22.88 TOP MAIN SOLVE Loop x[1] = 2.72 y1[1] (closed_form) = 0.91243836139195796298962879998706 y1[1] (numeric) = 0.91243836139196054387371151370146 absolute error = 2.58088408271371440e-15 relative error = 2.8285571847028457933107366743663e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.40921416967201748668244467400742 y2[1] (numeric) = -0.40921416967201864507800825145718 absolute error = 1.15839556357744976e-15 relative error = 2.8307806753268009280921302036371e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.73 y1[1] (closed_form) = 0.91648481334876932225826112489279 y1[1] (numeric) = 0.91648481334877191458218420711626 absolute error = 2.59232392308222347e-15 relative error = 2.8285508775754385549812755706487e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.40006947759241951035844795789445 y2[1] (numeric) = -0.40006947759242063985173432005369 absolute error = 1.12949328636215924e-15 relative error = 2.8232428356178122074039142849941e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.74 y1[1] (closed_form) = 0.92043961758798060326537325177928 y1[1] (numeric) = 0.92043961758798320673756233322094 absolute error = 2.60347218908144166e-15 relative error = 2.8285094853955345844650916646615e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.39088477889845241210831170164027 y2[1] (numeric) = -0.3908847788984535121892218457593 absolute error = 1.10008091014411903e-15 relative error = 2.8143355012293993971757878971979e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.75 y1[1] (closed_form) = 0.92430237863246354409665948952671 y1[1] (numeric) = 0.92430237863246615842044519080164 absolute error = 2.61432378570127493e-15 relative error = 2.8284291441175937440735496957016e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.38166099205233169857656137237778 y2[1] (numeric) = -0.3816609920523327687362068163298 absolute error = 1.07015964544395202e-15 relative error = 2.8039534239255353992173548425351e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.76 y1[1] (closed_form) = 0.9280727102093326532652331971401 y1[1] (numeric) = 0.92807271020933527813886368783158 absolute error = 2.62487363049069148e-15 relative error = 2.8283060169915293352577293629784e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.37239903942505551841770059244975 y2[1] (numeric) = -0.3723990394250565581484941509534 absolute error = 1.03973079355850365e-15 relative error = 2.7919803315382803733979900535256e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1988.5MB, alloc=40.3MB, time=23.36 TOP MAIN SOLVE Loop x[1] = 2.77 y1[1] (closed_form) = 0.93175023528857217636777720782907 y1[1] (numeric) = 0.93175023528857481148443167351841 absolute error = 2.63511665446568934e-15 relative error = 2.8281362908908393196948723609663e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.36309984720416833112128200917246 y2[1] (numeric) = -0.3630998472041693399170286089648 absolute error = 1.00879574659979234e-15 relative error = 2.7782874445346544832726085923049e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.78 y1[1] (closed_form) = 0.93533458612073878346935166911759 y1[1] (numeric) = 0.93533458612074142851715468670565 absolute error = 2.64504780301758806e-15 relative error = 2.8279161727439306959933082826549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.35376434530114292438633931722734 y2[1] (numeric) = -0.35376434530114390174232683810017 absolute error = 9.7735598752087283e-16 relative error = 2.7627317464367295482620352433723e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.79 y1[1] (closed_form) = 0.93882540427373620697953961962409 y1[1] (numeric) = 0.93882540427373886164157644113753 absolute error = 2.65466203682151344e-15 relative error = 2.8276418860598764489904002155872e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.34439346725839004176626159556229 y2[1] (numeric) = -0.34439346725839098717935172415571 absolute error = 9.4541309012859342e-16 relative error = 2.7451539590885240975151769736046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.8 y1[1] (closed_form) = 0.94222234066865815258678811736615 y1[1] (numeric) = 0.94222234066866081654112086231049 absolute error = 2.66395433274494434e-15 relative error = 2.8273096675402969971097680695560e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.33498815015590491954385375271242 y2[1] (numeric) = -0.33498815015590583251257283594195 absolute error = 9.1296871908322953e-16 relative error = 2.7253761622861285651210176175454e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.81 y1[1] (closed_form) = 0.94552505561469589898972047835884 y1[1] (numeric) = 0.94552505561469857190940523454882 absolute error = 2.67291968475618998e-15 relative error = 2.8269157637694714004395287975985e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.32554933451756006810510128120633 y2[1] (numeric) = -0.32554933451756094812973116618438 absolute error = 8.8002462988497805e-16 relative error = 2.7031989826952316861892747376445e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2030.6MB, alloc=40.3MB, time=23.86 TOP MAIN SOLVE Loop x[1] = 2.82 y1[1] (closed_form) = 0.94873321884310709569453606376004 y1[1] (numeric) = 0.94873321884310977724764089642668 absolute error = 2.68155310483266664e-15 relative error = 2.8264564279751625286748503691803e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.31607796421705366845541285602457 y2[1] (numeric) = -0.31607796421705451503808170332316 absolute error = 8.4658266884729859e-16 relative error = 2.6783982583042151665165801873515e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.83 y1[1] (closed_form) = 0.95184650954024236202702511272453 y1[1] (numeric) = 0.95184650954024505187664898156628 absolute error = 2.68984962386884175e-15 relative error = 2.8259279168529847255879707224877e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.3065749863835229889603130778681 y2[1] (numeric) = -0.30657498638352380160508613495731 absolute error = 8.1264477305708921e-16 relative error = 2.6507210605906273969208676264040e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.84 y1[1] (closed_form) = 0.95486461637962638472681949358624 y1[1] (numeric) = 0.95486461637962908253111207730022 absolute error = 2.69780429258371398e-15 relative error = 2.8253264874474576822075873039662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.29704135130683226089025606809731 y2[1] (numeric) = -0.29704135130683303910322638978365 absolute error = 7.7821297032168634e-16 relative error = 2.6198809253255192487294969304640e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.85 y1[1] (closed_form) = 0.95778723755309030604085410717493 y1[1] (numeric) = 0.95778723755309301145303653487234 absolute error = 2.70541218242769741e-15 relative error = 2.8246483940831754529411519095631e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.28747801234254448390307892669172 y2[1] (numeric) = -0.28747801234254522719245802937169 absolute error = 7.4328937910267997e-16 relative error = 2.5855521020404626966810555350173e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2072.8MB, alloc=40.3MB, time=24.34 x[1] = 2.86 y1[1] (closed_form) = 0.96061408080095228910317316639277 y1[1] (numeric) = 0.96061408080095500177155965517059 absolute error = 2.71266838648877782e-15 relative error = 2.8238898853397784385606832411482e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.27788592581658666420435690975324 y2[1] (numeric) = -0.27788592581658737208056534629041 absolute error = 7.0787620843653717e-16 relative error = 2.5473625782104468218033029032690e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.87 y1[1] (closed_form) = 0.96334486344124324256969375873794 y1[1] (numeric) = 0.96334486344124596213771415654727 absolute error = 2.71956802039780933e-15 relative error = 2.8230472010646501252739181898345e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.26826605092961801878239892098714 y2[1] (numeric) = -0.26826605092961869075815676301573 absolute error = 6.7197575784202859e-16 relative error = 2.5048855623491747697941091144039e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.88 y1[1] (closed_form) = 0.96597931239797478195981790476552 y1[1] (numeric) = 0.96597931239797750806604113758476 absolute error = 2.72610622323281924e-15 relative error = 2.8221165694174701058410379542285e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.25861934966111070881776692011768 y2[1] (numeric) = -0.25861934966111134440818413457195 absolute error = 6.3559041721445427e-16 relative error = 2.4576290136345885349240741113916e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.89 y1[1] (closed_form) = 0.96851716422844660093231550720928 y1[1] (numeric) = 0.9685171642284493332104739293984 absolute error = 2.73227815842218912e-15 relative error = 2.8210942039409430003656962522765e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.24894678667315269411404584058049 y2[1] (numeric) = -0.24894678667315329283671254724765 absolute error = 5.9872266670666716e-16 relative error = 2.4050226745555159214531348574193e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.9 y1[1] (closed_form) = 0.97095816514959052178110666934553 y1[1] (numeric) = 0.97095816514959325986012131592569 absolute error = 2.73807901464658016e-15 relative error = 2.8199763006521897200123797343594e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.23924932921398232818425691873958 y2[1] (numeric) = -0.23924932921398288955933351563357 absolute error = 5.6137507659689399e-16 relative error = 2.3464018830949592849199421831766e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2114.9MB, alloc=40.3MB, time=24.84 x[1] = 2.91 y1[1] (closed_form) = 0.97330207106334859076784710660275 y1[1] (numeric) = 0.97330207106335133427185384607344 absolute error = 2.74350400673947069e-15 relative error = 2.8187590351494343809005898265705e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.22952794702126434045301822382699 y2[1] (numeric) = -0.22952794702126486400332536718229 absolute error = 5.2355030714335530e-16 relative error = 2.2809871910493392414674154155738e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.92 y1[1] (closed_form) = 0.97554864758108268050293173515827 y1[1] (numeric) = 0.97554864758108542905130832133216 absolute error = 2.74854837658617389e-15 relative error = 2.8174385597287483497073617204866e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.21978361222511687789562909306458 y2[1] (numeric) = -0.21978361222511736314673751875241 absolute error = 4.8525110842568783e-16 relative error = 2.2078584636631671419828497478793e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.93 y1[1] (closed_form) = 0.97769767004701315843501960467633 y1[1] (numeric) = 0.97769767004701591164241362588015 absolute error = 2.75320739402120382e-15 relative error = 2.8160110005057230510516265934156e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.21001729925089930332910403425911 y2[1] (numeric) = -0.21001729925089974980942420743378 absolute error = 4.4648032017317467e-16 relative error = 2.1259216348639090577027910972922e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.94 y1[1] (closed_form) = 0.97974892356068427760176338132832 y1[1] (numeric) = 0.97974892356068703507812110518606 absolute error = 2.75747635772385774e-15 relative error = 2.8144724545370357962596507533527e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.20022998472177047149431709442312 y2[1] (numeric) = -0.20022998472177087873518867421279 absolute error = 4.0724087157978967e-16 relative error = 2.0338655678652282173975364601344e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.95 y1[1] (closed_form) = 0.98170220299845404312138940470197 y1[1] (numeric) = 0.98170220299845680447198551658499 absolute error = 2.76135059611188302e-15 relative error = 2.8128189869369494700636234216877e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.19042264736102722702044731405738 y2[1] (numeric) = -0.19042264736102759455622842012235 absolute error = 3.6753578110606497e-16 relative error = 1.9301054060510164392170593186675e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2157.0MB, alloc=40.3MB, time=25.34 x[1] = 2.96 y1[1] (closed_form) = 0.98355731303400640545638732297616 y1[1] (numeric) = 0.98355731303400917028185555607306 absolute error = 2.76482546823309690e-15 relative error = 2.8110466279838471483277669606521e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.18059626789423289034054450880135 y2[1] (numeric) = -0.18059626789423321770870077659321 absolute error = 3.2736815626779186e-16 relative error = 1.8127072064385996164875156150275e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.97 y1[1] (closed_form) = 0.98531406815788372924707637480614 y1[1] (numeric) = 0.98531406815788649714344102963359 absolute error = 2.76789636465482745e-15 relative error = 2.8091513702119476443437964276834e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.17075182895114551862806449866797 y2[1] (numeric) = -0.17075182895114580536925791023509 absolute error = 2.8674119341156712e-16 relative error = 1.6792862200826427303286774740494e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.98 y1[1] (closed_form) = 0.9869722926960375844844419643954 y1[1] (numeric) = 0.98697229269604035504315031543966 absolute error = 2.77055870835104426e-15 relative error = 2.8071291654833779835443670478812e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.16089031496745574884655395454133 y2[1] (numeric) = -0.16089031496745599450473143173985 absolute error = 2.4565817747719852e-16 relative error = 1.5268674035903856379450532893094e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.99 y1[1] (closed_form) = 0.98853182082739600495858418721084 y1[1] (numeric) = 0.98853182082739877776653977425842 absolute error = 2.77280795558704758e-15 relative error = 2.8049759220357941619952737596529e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.15101271208634404904629503561052 y2[1] (numeric) = -0.15101271208634425316877678259577 absolute error = 2.0412248174698525e-16 relative error = 1.3516907214425418705965842395908e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3 y1[1] (closed_form) = 0.98999249660044545727157279473126 y1[1] (numeric) = 0.98999249660044823191116959631597 absolute error = 2.77463959680158471e-15 relative error = 2.8026875015007424173163276743204e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.14112000805986722210074480280811 y2[1] (numeric) = -0.14112000805986738423831238469849 absolute error = 1.6213756758189038e-16 relative error = 1.1489339450229261348555731534831e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2199.2MB, alloc=40.3MB, time=25.83 TOP MAIN SOLVE Loop x[1] = 3.01 y1[1] (closed_form) = 0.99135417394882586223162557418242 y1[1] (numeric) = 0.99135417394882863828078306044502 absolute error = 2.77604915748626260e-15 relative error = 2.8002597158879400415860643480494e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.13121319215018402315021812468485 y2[1] (numeric) = -0.1312131921501841428572022693093 absolute error = 1.1970698414462445e-16 relative error = 9.1230906117740207734584555364356e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.02 y1[1] (closed_form) = 0.99261671670593710913946653326304 y1[1] (numeric) = 0.99261671670593988617166559538903 absolute error = 2.77703219906212599e-15 relative error = 2.7976883245306277734573341155355e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.12129325503062976810875799633911 y2[1] (numeric) = -0.12129325503062984494312610600013 absolute error = 7.683436810966102e-17 relative error = 6.3345952823393437288752248736823e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.03 y1[1] (closed_form) = 0.99377999861855560232760730870843 y1[1] (numeric) = 0.99377999861855837991192706197886 absolute error = 2.77758431975327043e-15 relative error = 2.7949690309871045296997038385045e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.11136118868664982569090503291726 y2[1] (numeric) = -0.11136118868664985921434839312381 absolute error = 3.352344336020655e-17 relative error = 3.0103345479308267382347646844039e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.04 y1[1] (closed_form) = 0.99484390335945947830924495484319 y1[1] (numeric) = 0.99484390335946225601040041220306 absolute error = 2.77770115545735987e-15 relative error = 2.7920974798935004042427395667626e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.10141798631660189952660831260879 y2[1] (numeric) = -0.10141798631660188930462898475784 absolute error = 1.022197932785095e-17 relative error = 1.0079059641295239013363486811150e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.05 y1[1] (closed_form) = 0.99580832453906123102558220156492 y1[1] (numeric) = 0.99580832453906400840396281448364 absolute error = 2.77737838061291872e-15 relative error = 2.7890692537627749480943650182583e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.091464642232437020053401588696418 y2[1] (numeric) = -0.091464642232436965655398973707628 absolute error = 5.4398002614988790e-17 relative error = 5.9474351276363581237357577978756e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2241.3MB, alloc=40.3MB, time=26.33 TOP MAIN SOLVE Loop x[1] = 3.06 y1[1] (closed_form) = 0.99667316571604658193873927179315 y1[1] (numeric) = 0.99667316571604935855044833506178 absolute error = 2.77661170906326863e-15 relative error = 2.7858798697248449260611772764344e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.081502151760269178003890088835723 y2[1] (numeric) = -0.08150215176026907900324714877169 absolute error = 9.9000642940064033e-17 relative error = 1.2146997447535495907915822995988e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.07 y1[1] (closed_form) = 0.99743834040701853109211366272677 y1[1] (numeric) = 0.99743834040702130648900857970712 absolute error = 2.77539689491698035e-15 relative error = 2.7825247762026484793662390287253e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.071531511140843542442340790318903 y2[1] (numeric) = -0.071531511140843398416509915052694 absolute error = 1.44025830875266209e-16 relative error = 2.0134599224624708536452527826981e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.08 y1[1] (closed_form) = 0.99810377209514562474111853735979 y1[1] (numeric) = 0.99810377209514839847085194207135 absolute error = 2.77372973340471156e-15 relative error = 2.7789993495188413442193341468587e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.061553717429913216445629637135705 y2[1] (numeric) = -0.061553717429913026976218143158561 absolute error = 1.89469411493977144e-16 relative error = 3.0781148467549878367624300062193e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.09 y1[1] (closed_form) = 0.99866939423781357473474351808576 y1[1] (numeric) = 0.99866939423781634634080525038738 absolute error = 2.77160606173230162e-15 relative error = 2.7752988904276943025151151862045e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.051569768398534492669958510574615 y2[1] (numeric) = -0.051569768398534257342813759069639 absolute error = 2.35327144751504976e-16 relative error = 4.5632771303699027681413396819542e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.1 y1[1] (closed_form) = 0.99913515027327946449237605454147 y1[1] (numeric) = 0.99913515027328223351413598453632 absolute error = 2.76902175992999485e-15 relative error = 2.7714186205666200948764083800907e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.041580662433290579194698271596673 y2[1] (numeric) = -0.04158066243329029759999239293888 absolute error = 2.81594705878657793e-16 relative error = 6.7722515563678373780865473625298e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2283.4MB, alloc=40.3MB, time=26.81 TOP MAIN SOLVE Loop x[1] = 3.11 y1[1] (closed_form) = 0.99950099362632787616083083671683 y1[1] (numeric) = 0.9995009936263306421335825343808 absolute error = 2.76597275169766397e-15 relative error = 2.7673536788216009483822540708810e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.031587398436453773187626872703365 y2[1] (numeric) = -0.031587398436453444919941084582788 absolute error = 3.28267685788120577e-16 relative error = 1.0392362208888965105575034080109e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.12 y1[1] (closed_form) = 0.99976688771292837334358497397559 y1[1] (numeric) = 0.99976688771293113579859021988146 absolute error = 2.76245500524590587e-15 relative error = 2.7630991176006153429463385511603e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.021590975726096066090998104201892 y2[1] (numeric) = -0.021590975726095690749406610604474 absolute error = 3.75341591493597418e-16 relative error = 1.7384188480187048076881069633882e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.13 y1[1] (closed_form) = 0.99993280594389387365782723913921 y1[1] (numeric) = 0.99993280594389663212236137202161 absolute error = 2.75846453413288240e-15 relative error = 2.7586498990089735687375973524870e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.011592393936158169184681483118307 y2[1] (numeric) = -0.011592393936157746372834941439044 absolute error = 4.22811846541679263e-16 relative error = 3.6473212424473833437203029294827e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.14 y1[1] (closed_form) = 0.99999873172753954528511430634505 y1[1] (numeric) = 0.99999873172754229928251240312401 absolute error = 2.75399739809677896e-15 relative error = 2.7540008909202649819213327882564e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = -0.0015926529164869525405414363244433 y2[1] (numeric) = -0.0015926529164864818667499799286864 absolute error = 4.706737914563957569e-16 relative error = 2.9552816347117250177826419204673e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2325.5MB, alloc=40.3MB, time=27.31 x[1] = 3.15 y1[1] (closed_form) = 0.99996465847134196162819465679473 y1[1] (numeric) = 0.99996465847134471067789854054905 absolute error = 2.74904970388375432e-15 relative error = 2.7491468629363959429249764024647e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.008407247367148706459141516571067 y2[1] (numeric) = 0.0084072473671492253818257129791045 absolute error = 5.189226841964080375e-16 relative error = 6.1723256320980497040943408140752e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.16 y1[1] (closed_form) = 0.99983058958259834815991709427395 y1[1] (numeric) = 0.9998305895826010917775231655295 absolute error = 2.74361760607125555e-15 relative error = 2.7440824822299546874918260236846e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.01840630693305366670737927118737 y2[1] (numeric) = 0.018406306933054234261079895984994 absolute error = 5.67553700624797624e-16 relative error = 3.0834740651075223759899420342484e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.17 y1[1] (closed_form) = 0.99959653846808585554008835013528 y1[1] (numeric) = 0.99959653846808859323739623670747 absolute error = 2.73769730788657219e-15 relative error = 2.7388023092618769833254311178890e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.028403525883603859571285274896733 y2[1] (numeric) = 0.028403525883604476133220266301609 absolute error = 6.16561934991404876e-16 relative error = 2.1707232317496177662802135215625e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.18 y1[1] (closed_form) = 0.99926252853272089307268415386031 y1[1] (numeric) = 0.99926252853272362435774617436491 absolute error = 2.73128506202050460e-15 relative error = 2.7333007933671041853789999479789e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.03839790450523521805369524672612 y2[1] (numeric) = 0.038397904505235883996095674394908 absolute error = 6.65942400427668788e-16 relative error = 1.7343196432421810229988002184675e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.19 y1[1] (closed_form) = 0.99882859317721865656895082969948 y1[1] (numeric) = 0.99882859317722138094612226572098 absolute error = 2.72437717143602150e-15 relative error = 2.7275722682006208916515868325347e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.048388443368414200108007148451169 y2[1] (numeric) = 0.048388443368414915798036602369387 absolute error = 7.15690029453918218e-16 relative error = 1.4790515661040844433714982520869e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2367.6MB, alloc=40.3MB, time=27.80 x[1] = 3.2 y1[1] (closed_form) = 0.99829477579475308466166072228358 y1[1] (numeric) = 0.99829477579475580163165089406619 absolute error = 2.71696999017178261e-15 relative error = 2.7216109470359332638941722545941e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.058374143427579909137217414619095 y2[1] (numeric) = 0.058374143427580674936891913682042 absolute error = 7.65799674499062947e-16 relative error = 1.3118816474782689156131797880336e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.21 y1[1] (closed_form) = 0.99766112976661757757210666520424 y1[1] (numeric) = 0.99766112976662028663203080560686 absolute error = 2.70905992414040262e-15 relative error = 2.7154109179076985768789529760694e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.068354006121047817548388360676863 y2[1] (numeric) = 0.068354006121048633814496793308186 absolute error = 8.16266108432631323e-16 relative error = 1.1941744964985799914477778220986e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.22 y1[1] (closed_form) = 0.99692771845688691225434273747586 y1[1] (numeric) = 0.99692771845688961289777465880912 absolute error = 2.70064343192133326e-15 relative error = 2.7089661385898411599165884305936e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.078327033470865103073444147916042 y2[1] (numeric) = 0.078327033470865970157469257015584 absolute error = 8.67084025109099542e-16 relative error = 1.1070048062417993287982335729058e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.23 y1[1] (closed_form) = 0.99609461520608088772070849458495 y1[1] (numeric) = 0.99609461520608357943773404282573 absolute error = 2.69171702554824078e-15 relative error = 2.7022704314000879230088478837651e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.088292228182607612405875728529723 y2[1] (numeric) = 0.088292228182608530653915652985704 absolute error = 9.18248039924455981e-16 relative error = 1.0400100425887072115197165963836e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.24 y1[1] (closed_form) = 0.99516190332383033417882384374247 y1[1] (numeric) = 0.99516190332383301645609513449949 absolute error = 2.68227727129075702e-15 relative error = 2.6953174778214268723257814583843e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.098248593745108472540154959437637 y2[1] (numeric) = 0.098248593745109442292845344379967 absolute error = 9.69752690384942330e-16 relative error = 9.8703976659536020201062922602461e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2409.7MB, alloc=40.3MB, time=28.30 TOP MAIN SOLVE Loop x[1] = 3.25 y1[1] (closed_form) = 0.9941296760805462193730292251716 y1[1] (numeric) = 0.99412967608054889169381965565386 absolute error = 2.67232079043048226e-15 relative error = 2.6881008129305315116907134896176e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.10819513453010837703583084256083 y2[1] (numeric) = 0.10819513453010939862826753047245 absolute error = 1.02159243668791162e-15 relative error = 9.4421291782175697991410674427316e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.26 y1[1] (closed_form) = 0.99299803669809268521269456717166 y1[1] (numeric) = 0.99299803669809534705695459829096 absolute error = 2.66184426003111930e-15 relative error = 2.6806138196227030610575442638938e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.11813085589181758226072311033608 y2[1] (numeric) = 0.11813085589181865602238542507768 absolute error = 1.07376166231474160e-15 relative error = 9.0895952137862777062985044453801e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.27 y1[1] (closed_form) = 0.99176709833946494737596174049474 y1[1] (numeric) = 0.99176709833946759822037544311302 absolute error = 2.65084441370261828e-15 relative error = 2.6728497226223565339189622969325e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.12805476426637965749655689075362 y2[1] (numeric) = 0.12805476426638078375123152649389 absolute error = 1.12625467463574027e-15 relative error = 8.7951016979962111526001745069938e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.28 y1[1] (closed_form) = 0.99043698409747309009035841613171 y1[1] (numeric) = 0.99043698409747572940840077534453 absolute error = 2.63931804235921282e-15 relative error = 2.6648015822675159465760708747766e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.13796586727122704261491407058525 y2[1] (numeric) = 0.13796586727122822168061959756401 absolute error = 1.17906570552697876e-15 relative error = 8.5460681605331698950807131620559e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.29 y1[1] (closed_form) = 0.98900782698243288770137512553948 y1[1] (numeric) = 0.98900782698243551496337009676794 absolute error = 2.62726199497122846e-15 relative error = 2.6564622880561842422419423058378e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.14786317380431847785052978374264 y2[1] (numeric) = 0.14786317380431971003944178272781 absolute error = 1.23218891199898517e-15 relative error = 8.3333049081555557502338631573142e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2451.8MB, alloc=40.3MB, time=28.78 TOP MAIN SOLVE Loop x[1] = 3.3 y1[1] (closed_form) = 0.98747976990886488393659105110285 y1[1] (numeric) = 0.98747976990886749860977036164798 absolute error = 2.61467317931054513e-15 relative error = 2.6478245519418133779659718590022e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.15774569414324838201165427760248 y2[1] (numeric) = 0.15774569414324966763003111483365 absolute error = 1.28561837683723117e-15 relative error = 8.1499427532377844628271147556314e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.31 y1[1] (closed_form) = 0.98585296568120305894633807058553 y1[1] (numeric) = 0.98585296568120566049490076018163 absolute error = 2.60154856268959610e-15 relative error = 2.6388809013644163029884378156909e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.16761244004421826827224999431698 y2[1] (numeric) = 0.16761244004421960762035924865884 absolute error = 1.33934810925434186e-15 relative error = 7.9907440575473097078503577204865e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.32 y1[1] (closed_form) = 0.98412757697851451324228958473119 y1[1] (numeric) = 0.98412757697851710112746227851769 absolute error = 2.58788517269378650e-15 relative error = 2.6296236720031322164469588211802e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.17746242484086030048692055230841 y2[1] (numeric) = 0.17746242484086169385896610626594 absolute error = 1.39337204555395753e-15 relative error = 7.8516454782101959447787302963620e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.33 y1[1] (closed_form) = 0.98230377633823169655284671485927 y1[1] (numeric) = 0.98230377633823427023294462207447 absolute error = 2.57368009790721520e-15 relative error = 2.6200450002352764390937440311875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.18729466354290310775529282413595 y2[1] (numeric) = 0.18729466354290455543934263031036 absolute error = 1.44768404980617441e-15 relative error = 7.7294463302984451620665268845733e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.34 y1[1] (closed_form) = 0.98038174613889880835887990106991 y1[1] (numeric) = 0.98038174613890136728936853265478 absolute error = 2.55893048863158487e-15 relative error = 2.6101368152860732442718518397640e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.19710817293466999073661691059272 y2[1] (numeric) = 0.19710817293467149301453144508283 absolute error = 1.50227791453449011e-15 relative error = 7.6215911911091009560363411189113e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2493.9MB, alloc=40.3MB, time=29.28 TOP MAIN SOLVE Loop x[1] = 3.35 y1[1] (closed_form) = 0.97836167858193409545539437527153 y1[1] (numeric) = 0.97836167858193663908895197345668 absolute error = 2.54363355759818515e-15 relative error = 2.5998908310523790067631412933582e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.20690197167339966997603411602551 y2[1] (numeric) = 0.20690197167340122712339553020306 absolute error = 1.55714736141417755e-15 relative error = 7.5260150921721353282643793240649e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.36 y1[1] (closed_form) = 0.97624377567240987029416530777832 y1[1] (numeric) = 0.9762437756724123980807459806138 absolute error = 2.52778658067283548e-15 relative error = 2.5892985375827524085273778442295e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.21667508038737974424961398190553 y2[1] (numeric) = 0.21667508038738135653565596391547 absolute error = 1.61228604198200994e-15 relative error = 7.4410312394923549191354327608650e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.37 y1[1] (closed_form) = 0.97402824919885217208949176597085 y1[1] (numeric) = 0.97402824919885468347638931964497 absolute error = 2.51138689755367412e-15 relative error = 2.5783511921952105364681797184133e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.22642652177388304566410348430857 y2[1] (numeric) = 0.22642652177388471335164184156603 absolute error = 1.66768753835725746e-15 relative error = 7.3652482283973118543642059538328e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.38 y1[1] (closed_form) = 0.97171532071206209070412534999057 y1[1] (numeric) = 0.97171532071206458513603781167177 absolute error = 2.49443191246168120e-15 relative error = 2.5670398102129227167264020294683e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.23615532069689709795749177758963 y2[1] (numeric) = 0.23615532069689882130285575146477 absolute error = 1.72334536397387514e-15 relative error = 7.2975080929291066901071520429336e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2535.9MB, alloc=40.3MB, time=29.78 x[1] = 3.39 y1[1] (closed_form) = 0.96930522150296087116533607467248 y1[1] (numeric) = 0.96930522150296334808443089849679 absolute error = 2.47691909482382431e-15 relative error = 2.5553551552969306197052075108090e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.24586050428463690513600137155794 y2[1] (numeric) = 0.24586050428463868438896569535746 absolute error = 1.77925296432379952e-15 relative error = 7.2368393187054069219558920853775e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.4 y1[1] (closed_form) = 0.96679819257946101428220153976569 y1[1] (numeric) = 0.96679819257946347312818148848162 absolute error = 2.45884597994871593e-15 relative error = 2.5432877293537386370466085143394e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.25554110202683131924990242936374 y2[1] (numeric) = 0.25554110202683315465362014063406 absolute error = 1.83540371771127032e-15 relative error = 7.1824207657935062651716425140340e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.41 y1[1] (closed_form) = 0.96419448464236568623478364095296 y1[1] (numeric) = 0.96419448464236812644495333562578 absolute error = 2.44021016969467282e-15 relative error = 2.5308277619942865260412529502016e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.26519614587177325875244430757411 y2[1] (numeric) = 0.26519614587177515054338032566604 absolute error = 1.89179093601809193e-15 relative error = 7.1335536562918386787600164955478e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.42 y1[1] (closed_form) = 0.96149435806029884717415014560141 y1[1] (numeric) = 0.96149435806030126818348327566994 absolute error = 2.42100933313006853e-15 relative error = 2.5179651995193903480444050632218e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.2748246703231240725009433576662 y2[1] (numeric) = 0.27482467032312602090880883741388 absolute error = 1.94840786547974768e-15 relative error = 7.0896395989083311197527697514957e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.43 y1[1] (closed_form) = 0.95869808284366860579948964122556 y1[1] (numeric) = 0.95869808284367100704069682709639 absolute error = 2.40124120718587083e-15 relative error = 2.5046896934052098879702102186140e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.28442571253646236904429691459137 y2[1] (numeric) = 0.28442571253646437429198438687012 absolute error = 2.00524768747227875e-15 relative error = 7.0501631852823893272860050396223e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2578.1MB, alloc=40.3MB, time=30.27 x[1] = 3.44 y1[1] (closed_form) = 0.95580593861766640355516501297249 y1[1] (numeric) = 0.95580593861766878445876231322939 absolute error = 2.38090359730025690e-15 relative error = 2.4909905882606639571423868314093e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.29399831241556765639445181056032 y2[1] (numeric) = 0.29399831241556971869797112039799 absolute error = 2.06230351930983767e-15 relative error = 7.0146780856169144862255503753961e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.45 y1[1] (closed_form) = 0.95281821459430472850678513994775 y1[1] (numeric) = 0.95281821459430708850116319514776 absolute error = 2.35999437805520001e-15 relative error = 2.4768569092269600935774266338138e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.30354151270842916399808636621989 y2[1] (numeric) = 0.30354151270843128356650141904523 absolute error = 2.11956841505282534e-15 relative error = 6.9827958493730146341873919128394e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.46 y1[1] (closed_form) = 0.94973520954349615510160537578203 y1[1] (numeric) = 0.94973520954349849361309918070432 absolute error = 2.33851149380492229e-15 relative error = 2.4622773487875229632980856900822e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.31305435910297024610631577597493 y2[1] (numeric) = 0.31305435910297242314168210249342 absolute error = 2.17703536632651849e-15 relative error = 6.9541768163350991440919029599039e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.47 y1[1] (closed_form) = 0.94655723176317660188518005352668 y1[1] (numeric) = 0.94655723176317891833813934963583 absolute error = 2.31645295929610915e-15 relative error = 2.4472402529545861656974552916372e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.32253590032247879418185398715726 y2[1] (numeric) = 0.32253590032248102887915713725092 absolute error = 2.23469730315009366e-15 relative error = 6.9285226882210383961626040903207e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.48 y1[1] (closed_form) = 0.94328459904847579482359814738228 y1[1] (numeric) = 0.94328459904847808864045842716422 absolute error = 2.29381686027978194e-15 relative error = 2.4317336067965440413294423326588e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.33198518822073411538191643544275 y2[1] (numeric) = 0.33198518822073640792901121139422 absolute error = 2.29254709477595147e-15 relative error = 6.9055704173514406694505848295860e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2620.2MB, alloc=40.3MB, time=30.77 TOP MAIN SOLVE Loop x[1] = 3.49 y1[1] (closed_form) = 0.93991763865993801915927867276677 y1[1] (numeric) = 0.93991763865994028976063278749294 absolute error = 2.27060135411472617e-15 relative error = 2.4157450192678309832829141249220e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.3414012778768207645082874807375 y2[1] (numeric) = 0.34140127787682311508583801998214 absolute error = 2.35057755053924464e-15 relative error = 6.8850871477620666995720703917230e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.5 y1[1] (closed_form) = 0.93645668729079633769865762667176 y1[1] (numeric) = 0.9364566872907985845033279890457 absolute error = 2.24680467036237394e-15 relative error = 2.3992617073005934147772910151363e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.35078322768961984812036880004364 y2[1] (numeric) = 0.35078322768962225690178951755427 absolute error = 2.40878142071751063e-15 relative error = 6.8668660032082535685339374589183e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.51 y1[1] (closed_form) = 0.93290209103330354808266630575758 y1[1] (numeric) = 0.93290209103330577050777767879747 absolute error = 2.22242511137303989e-15 relative error = 2.3822704791147282684704435395893e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.36013009947196835175953992341737 y2[1] (numeric) = 0.36013009947197081891093732372657 absolute error = 2.46715139740030920e-15 relative error = 6.8507225611458401438811807488950e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.52 y1[1] (closed_form) = 0.92925420534412324591621651227224 y1[1] (numeric) = 0.9292542053441254433772693756834 absolute error = 2.19746105286341116e-15 relative error = 2.3647577166999670006591862522447e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.36944095854447707443057432143296 y2[1] (numeric) = 0.36944095854447960011068969019625 absolute error = 2.52568011536876329e-15 relative error = 6.8364918857926147664853042266846e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.53 y1[1] (closed_form) = 0.92551339500878445462153901468401 y1[1] (numeric) = 0.9255133950087866265324834998769 absolute error = 2.17191094448519289e-15 relative error = 2.3467093574205679952798500987991e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.37871487382899778862484425400664 y2[1] (numeric) = 0.37871487382900037298499723890712 absolute error = 2.58436015298490048e-15 relative error = 6.8240260195109844558626447102970e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2662.5MB, alloc=40.3MB, time=31.26 TOP MAIN SOLVE Loop x[1] = 3.54 y1[1] (closed_form) = 0.92168003410520337652276888612977 y1[1] (numeric) = 0.92168003410520552229607927094145 absolute error = 2.14577331038481168e-15 relative error = 2.3281108746898238169530030774900e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.38795091794173027924720110048451 y2[1] (numeric) = 0.38795091794173292243123419117534 absolute error = 2.64318403309069083e-15 relative error = 6.8131918519849812976867595214291e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.55 y1[1] (closed_form) = 0.91775450596627591295627082271047 y1[1] (numeric) = 0.91775450596627803200302057679123 absolute error = 2.11904674975408076e-15 relative error = 2.3089472576579731860195707586657e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.39714816728595995082022742343695 y2[1] (numeric) = 0.39714816728596265296445134011233 absolute error = 2.70214422391667538e-15 relative error = 6.8038693024385562602569317319896e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.56 y1[1] (closed_form) = 0.91373720314154469412352061310366 y1[1] (numeric) = 0.91373720314154678585345798483483 absolute error = 2.09172993737173117e-15 relative error = 2.2892029898532068777050538575380e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.40630570214441672928242142268591 y2[1] (numeric) = 0.40630570214441949051556142276443 absolute error = 2.76123314000007852e-15 relative error = 6.7959497625229726235266659041866e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.57 y1[1] (closed_form) = 0.90962852735794445195161343603674 y1[1] (numeric) = 0.90962852735794651577323757175177 absolute error = 2.06382162413571503e-15 relative error = 2.2688620267112494101617097868607e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.41542260677124602256709945606629 y2[1] (numeric) = 0.41542260677124884301024256836208 absolute error = 2.82044314311229579e-15 relative error = 6.7893347572809948685615561410095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.58 y1[1] (closed_form) = 0.90542888947962966139140085454902 y1[1] (numeric) = 0.90542888947963169671203844073643 absolute error = 2.03532063758618741e-15 relative error = 2.2479077719244544300295410402311e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.42449796948358254294260094834376 y2[1] (numeric) = 0.42449796948358542270914414399138 absolute error = 2.87976654319564762e-15 relative error = 6.7839347893677559229989217026392e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2704.6MB, alloc=40.3MB, time=31.75 TOP MAIN SOLVE Loop x[1] = 3.59 y1[1] (closed_form) = 0.90113870946688846735564983934783 y1[1] (numeric) = 0.90113870946689047358153225842266 absolute error = 2.00622588241907483e-15 relative error = 2.2263230525364439451271067181037e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.43353088275271783380787293204403 y2[1] (numeric) = 0.43353088275272077300347224133183 absolute error = 2.93919559930928780e-15 relative error = 6.7796683379204126333605104923280e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.6 y1[1] (closed_form) = 0.89675841633414700587029172526594 y1[1] (numeric) = 0.89675841633414898240663271540531 absolute error = 1.97653634099013937e-15 relative error = 2.2040900927030154182070298787329e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.44252044329485238426672734749269 y2[1] (numeric) = 0.44252044329485538298924793164741 absolute error = 2.99872252058415472e-15 relative error = 6.7764609884612698913476650750545e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.61 y1[1] (closed_form) = 0.89228844810706831897164969353841 y1[1] (numeric) = 0.89228844810707026522272350298694 absolute error = 1.94625107380944853e-15 relative error = 2.1811904860343010193306367138471e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.45146575216142325634494018639253 y2[1] (numeric) = 0.45146575216142631468440737324401 absolute error = 3.05833946718685148e-15 relative error = 6.7742446742523469319657664132079e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.62 y1[1] (closed_form) = 0.887729251778750153422404272068 y1[1] (numeric) = 0.88772925177875206879162429823007 absolute error = 1.91536922002616207e-15 relative error = 2.1576051664269500517112514795029e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.46036591482899819216274354079485 y2[1] (numeric) = 0.4603659148290013102012948331351 absolute error = 3.11803855129234025e-15 relative error = 6.7729570127938949250658145654308e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2746.7MB, alloc=40.3MB, time=32.25 x[1] = 3.63 y1[1] (closed_form) = 0.88308128326502602342992354439801 y1[1] (numeric) = 0.88308128326502790731992144794647 absolute error = 1.88388999790354846e-15 relative error = 2.1333143772883754279065365014785e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.46922004128872721172690481453191 y2[1] (numeric) = 0.46922004128873038953874287986648 absolute error = 3.17781183806533457e-15 relative error = 6.7725407238305018828074854029539e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.64 y1[1] (closed_form) = 0.87834500735887400722343724413409 y1[1] (numeric) = 0.87834500735887585903614252827832 absolute error = 1.85181270528414423e-15 relative error = 2.1082976390478087021848363648684e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.47802724613534275625715663887291 y2[1] (numeric) = 0.47802724613534599390850328914522 absolute error = 3.23765134665027231e-15 relative error = 6.7729431174172099816164368001419e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.65 y1[1] (closed_form) = 0.87352089768393783657240447452827 y1[1] (numeric) = 0.87352089768393965570912451949955 absolute error = 1.81913672004497128e-15 relative error = 2.0825337148409944410094147538144e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.48678664865569947710681138829532 y2[1] (numeric) = 0.4867866486557027746558625580459 absolute error = 3.29754905116975058e-15 relative error = 6.7741156423993915614087410873857e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.66 y1[1] (closed_form) = 0.86860943664716492709839092015993 y1[1] (numeric) = 0.86860943664716671295989146288798 absolute error = 1.78586150054272805e-15 relative error = 2.0560005742467626016594920027569e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.49549737291684481637245114641035 y2[1] (numeric) = 0.49549737291684817386933287771305 absolute error = 3.35749688173130270e-15 relative error = 6.7760134871487267113858139741751e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.67 y1[1] (closed_form) = 0.86361111539056608553795618647981 y1[1] (numeric) = 0.8636111153905678375245422353515 absolute error = 1.75198658604887169e-15 relative error = 2.0286753549443836162206507042503e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.50415854785361157220802405891391 y2[1] (numeric) = 0.5041585478536149896947495013101 absolute error = 3.41748672544239619e-15 relative error = 6.7785952256326795191392100876648e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2788.9MB, alloc=40.3MB, time=32.75 x[1] = 3.68 y1[1] (closed_form) = 0.85852643374210171794562486853616 y1[1] (numeric) = 0.85852643374210343545722204304576 absolute error = 1.71751159717450960e-15 relative error = 2.0005343221504627135026784697491e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.51276930735572368965980922504404 y2[1] (numeric) = 0.5127693073557271671702366585735 absolute error = 3.47751042743352946e-15 relative error = 6.7818225029234726341413800335996e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.69 y1[1] (closed_form) = 0.85335590016569945017519302837216 y1[1] (numeric) = 0.85335590016570113261142931339227 absolute error = 1.68243623628502011e-15 relative error = 1.9715528256830882528531930136929e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.52132879035440656651575454812466 y2[1] (numeric) = 0.52132879035441010407554643742832 absolute error = 3.53755979188930366e-15 relative error = 6.7856597551123568001040069196691e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.7 y1[1] (closed_form) = 0.8481000317104081588356701063544 y1[1] (numeric) = 0.84810003171040980559595801067745 absolute error = 1.64676028790432305e-15 relative error = 1.9417052544889245442758117840139e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.52983614090849321321077762570121 y2[1] (numeric) = 0.5298361409084968108373607130463 absolute error = 3.59762658308734509e-15 relative error = 6.7900739593161934570224002760926e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.71 y1[1] (closed_form) = 0.84275935395869349727638917260975 y1[1] (numeric) = 0.8427593539586951077600082813321 absolute error = 1.61048361910872235e-15 relative error = 1.9109649884558357930731148129251e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.53829050829001765624379404325037 y2[1] (numeric) = 0.53829050829002131394632048820267 absolute error = 3.65770252644495230e-15 relative error = 6.7950344100703933391585140414974e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.72 y1[1] (closed_form) = 0.83733440097388008700560008948967 y1[1] (numeric) = 0.83733440097388166061177999973382 absolute error = 1.57360617991024415e-15 relative error = 1.8793043473193351052132140258772e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.54669104706928702583745896705622 y2[1] (numeric) = 0.54669104706929074361676854039718 absolute error = 3.71777930957334096e-15 relative error = 6.8005125189148262627282156137457e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2831.1MB, alloc=40.3MB, time=33.25 x[1] = 3.73 y1[1] (closed_form) = 0.83182571524674563027960569792163 y1[1] (numeric) = 0.83182571524674716640760932731651 absolute error = 1.53612800362939488e-15 relative error = 1.8466945364555495530315159153589e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.55503691719942382070274923216573 y2[1] (numeric) = 0.55503691719942759855133257152407 absolute error = 3.77784858333935834e-15 relative error = 6.8064816344134885120121999363768e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.74 y1[1] (closed_form) = 0.82623384764127228440667735620253 y1[1] (numeric) = 0.82623384764127378245588461346804 absolute error = 1.49804920725726551e-15 relative error = 1.8131055893363457753090167375659e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.56332728410036989575236111967948 y2[1] (numeric) = 0.56332728410037373365432405421765 absolute error = 3.83790196293453817e-15 relative error = 6.8129168802175866435808202024645e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.75 y1[1] (closed_form) = 0.82055935733956072258311240229071 y1[1] (numeric) = 0.82055935733956218195310420919972 absolute error = 1.45936999180690901e-15 relative error = 1.7785063064036184325407247983131e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.57156131874234377243415557335029 y2[1] (numeric) = 0.57156131874234767036518452471597 absolute error = 3.89793102895136568e-15 relative error = 6.8197950090960027594450452105747e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.76 y1[1] (closed_form) = 0.81480281178591238980944513756309 y1[1] (numeric) = 0.81480281178591380990008779148282 absolute error = 1.42009064265391973e-15 relative error = 1.7428641900993406971023864831838e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.57973819772874292602316503775395 y2[1] (numeric) = 0.57973819772874688395049350437522 absolute error = 3.95792732846662127e-15 relative error = 6.8270942711256691865412701567281e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.77 y1[1] (closed_form) = 0.80896478663008554561462174619622 y1[1] (numeric) = 0.80896478663008692582615161234064 absolute error = 1.38021152986614442e-15 relative error = 1.7061453757656231034175738825063e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.58785710337848275971251772647441 y2[1] (numeric) = 0.58785710337848677759489385814481 absolute error = 4.01788237613167040e-15 relative error = 6.8347942944644807555616331551250e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2873.2MB, alloc=40.3MB, time=33.73 TOP MAIN SOLVE Loop x[1] = 3.78 y1[1] (closed_form) = 0.80304586566973076793658025923771 y1[1] (numeric) = 0.80304586566973210766968878169401 absolute error = 1.33973310852245630e-15 relative error = 1.6683145581045171185096447794253e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.59591722380776403167448581090021 y2[1] (numeric) = 0.59591722380776810946214108046638 absolute error = 4.07778765526956617e-15 relative error = 6.8428759773270340305398886478566e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.79 y1[1] (closed_form) = 0.79704664079201167456087725184016 y1[1] (numeric) = 0.79704664079201297321679627236455 absolute error = 1.29865591902052439e-15 relative error = 1.6293349128603968736947891223884e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.60391775301126055841709072023268 y2[1] (numeric) = 0.60391775301126469605170969906274 absolute error = 4.13763461897883006e-15 relative error = 6.8513213899537084071349746793832e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.8 y1[1] (closed_form) = 0.79096771191441669999656817435073 y1[1] (numeric) = 0.79096771191441795697715554786321 absolute error = 1.25698058737351248e-15 relative error = 1.5891680133581972595653719314826e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.61185789094271907573358608611888 y2[1] (numeric) = 0.61185789094272327314827732989403 absolute error = 4.19741469124377515e-15 relative error = 6.8601136855105604946406093723440e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.81 y1[1] (closed_form) = 0.78480968692476784656233037436496 y1[1] (numeric) = 0.7848096869247690612701558700075 absolute error = 1.21470782549564254e-15 relative error = 1.5477737414982810878673502994730e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.61973684359496319732588971051781 y2[1] (numeric) = 0.61973684359496745444515776175312 absolute error = 4.25711926805123531e-15 relative error = 6.8692370189846726443461032151775e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.82 y1[1] (closed_form) = 0.7785731816204324087577276566562 y1[1] (numeric) = 0.7785731816204335805961591332156 absolute error = 1.17183843147655940e-15 relative error = 1.5051101927729260657028535182370e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.62755382307929347077277195688991 y2[1] (numeric) = 0.62755382307929778751249047045265 absolute error = 4.31673971851356274e-15 relative error = 6.8786764732498946279433396086093e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2915.4MB, alloc=40.3MB, time=34.23 TOP MAIN SOLVE Loop x[1] = 3.83 y1[1] (closed_form) = 0.77225881964674374969652252702348 y1[1] (numeric) = 0.77225881964674487806981237145826 absolute error = 1.12837328984443478e-15 relative error = 1.4611335748299894429654524154637e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.63530804770427559090337023862228 y2[1] (numeric) = 0.63530804770427996717075623637755 absolute error = 4.37626738599775527e-15 relative error = 6.8884179915737957252648464915030e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.84 y1[1] (closed_form) = 0.76586723243463728747307694024768 y1[1] (numeric) = 0.76586723243463837178644875799754 absolute error = 1.08431337181774986e-15 relative error = 1.4157980990658067671610463672904e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.64299874205390889182034887886274 y2[1] (numeric) = 0.64299874205391332751393813943675 absolute error = 4.43569358926057401e-15 relative error = 6.8984483159201675483352528566493e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.85 y1[1] (closed_form) = 0.75939905913750792781123507395279 y1[1] (numeric) = 0.75939905913750896747097061965024 absolute error = 1.03965973554569745e-15 relative error = 1.3690558646813406375182908907499e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.650625137065167300788642218662 y2[1] (numeric) = 0.65062513706517179579826580817274 absolute error = 4.49500962358951074e-15 relative error = 6.9087549304743290749474446424791e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.86 y1[1] (closed_form) = 0.75285494656729525719980460936484 y1[1] (numeric) = 0.75285494656729625161333094651054 absolute error = 9.9441352633714570e-16 relative error = 1.3208567345824808316141918327142e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.6581864701049049999590093452957 y2[1] (numeric) = 0.6581864701049095541657712947595 absolute error = 4.55420676194946380e-15 relative error = 6.9193260098822631604945159179676e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.87 y1[1] (closed_form) = 0.74623554912980288794206080932728 y1[1] (numeric) = 0.74623554912980383651803768743445 absolute error = 9.4857597687810717e-16 relative error = 1.2711482024466090697055103374874e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.66568198504611910542431592310351 y2[1] (numeric) = 0.66568198504612371870057205808356 absolute error = 4.61327625613498005e-15 relative error = 6.9301503717505104399045379348564e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2957.6MB, alloc=40.3MB, time=34.72 TOP MAIN SOLVE Loop x[1] = 3.88 y1[1] (closed_form) = 0.73954152875925842313086807704128 y1[1] (numeric) = 0.7395415287592593252792755146995 absolute error = 9.0214840743765822e-16 relative error = 1.2198752502123959982776830229210e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.67311093234356173740418951936854 y2[1] (numeric) = 0.6731109323435664096135274472885 absolute error = 4.67220933792791996e-15 relative error = 6.9412174330028311574314155746875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.89 y1[1] (closed_form) = 0.73277355485212058549838830263169 y1[1] (numeric) = 0.73277355485212144063061436488697 absolute error = 8.5513222606225528e-16 relative error = 1.1669801951775233318809228763558e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.68047256910869392041403980815868 y2[1] (numeric) = 0.68047256910869865141126006856014 absolute error = 4.73099722026040146e-15 relative error = 6.9525171697328259415491808319451e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.9 y1[1] (closed_form) = 0.72593230420014012937233048461435 y1[1] (numeric) = 0.72593230420014093690125924301021 absolute error = 8.0752892875839586e-16 relative error = 1.1124025258087419051825680900522e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.68776615918397381809088812537869 y2[1] (numeric) = 0.68776615918397860772198650825655 absolute error = 4.78963109838287786e-15 relative error = 6.9640400802297642811212457459803e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.91 y1[1] (closed_form) = 0.71901846092268122959176361387439 y1[1] (numeric) = 0.71901846092268198893186327744806 absolute error = 7.5934009966357367e-16 relative error = 1.0560787252793894237618191820926e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.69499097321647187391443044807649 y2[1] (numeric) = 0.69499097321647672201658148528061 absolute error = 4.84810215103720412e-15 relative error = 6.9757771508884685443787865922800e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=2999.7MB, alloc=40.3MB, time=35.22 x[1] = 3.92 y1[1] (closed_form) = 0.71203271639831011518720258429259 y1[1] (numeric) = 0.71203271639831082575461378977146 absolute error = 7.1056741120547887e-16 relative error = 9.9794208165006345650528577428858e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.70214628873080549637060743782065 y2[1] (numeric) = 0.70214628873081040277214907236539 absolute error = 4.90640154163454474e-15 relative error = 6.9877198247438156149297506734691e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.93 y1[1] (closed_form) = 0.70497576919565778890458983952695 y1[1] (numeric) = 0.70497576919565845011721408892246 absolute error = 6.6121262424939551e-16 relative error = 9.3792248349727843016831525949601e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.70923139020138599514994389285155 y2[1] (numeric) = 0.70923139020139095967036333082754 absolute error = 4.96452041943797599e-15 relative error = 6.9998599723967409614352003413825e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.94 y1[1] (closed_form) = 0.69784832500356374624360614943559 y1[1] (numeric) = 0.69784832500356435752119438318583 absolute error = 6.1127758823375024e-16 relative error = 8.7594619967115144973848128372447e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.71624556912397054374724335454079 y2[1] (numeric) = 0.71624556912397556619716410417519 absolute error = 5.02244992074963440e-15 relative error = 7.0121898651219850123246186243333e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.95 y1[1] (closed_form) = 0.69065109656050767958019331164023 y1[1] (numeric) = 0.69065109656050824034443460540751 absolute error = 5.6076424129376728e-16 relative error = 8.1193564172476332027481170567404e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.72318812408651201332600433544282 y2[1] (numeric) = 0.72318812408651709350717443770527 absolute error = 5.08018117010226245e-15 relative error = 7.0247021499685762594059235753857e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.96 y1[1] (closed_form) = 0.68338480358333622414406980875151 y1[1] (numeric) = 0.68338480358333673381868018193822 absolute error = 5.0967461037318671e-16 relative error = 7.4580910740288914700278990960843e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.73005836083929959292321305873169 y2[1] (numeric) = 0.73005836083930473062849451373351 absolute error = 5.13770528145500182e-15 relative error = 7.0373898266825180979002852039402e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3041.9MB, alloc=40.3MB, time=35.70 x[1] = 3.97 y1[1] (closed_form) = 0.67605017269529187311724748931934 y1[1] (numeric) = 0.67605017269529233112805881332343 absolute error = 4.5801081132400409e-16 relative error = 6.7748050340405416210408037252933e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.73685559236438318199094255175134 y2[1] (numeric) = 0.73685559236438837700430194503536 absolute error = 5.19501335939328402e-15 relative error = 7.0502462262976120105797355432413e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.98 y1[1] (closed_form) = 0.66864793735335125890206371667484 y1[1] (numeric) = 0.66864793735335166467711271086624 absolute error = 4.0577504899419140e-16 relative error = 6.0685904543478310667324276254697e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.7435791389442746128933574013766 y2[1] (numeric) = 0.74357913894427986498985773404338 absolute error = 5.25209650033266678e-15 relative error = 7.0632649912550464327570168850601e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.99 y1[1] (closed_form) = 0.66117883777488006667005095201013 y1[1] (numeric) = 0.66117883777488041963966825537065 absolute error = 3.5296961730336052e-16 relative error = 5.3384893335551758280149088914375e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.75022832822991883329412529862008 y2[1] (numeric) = 0.75022832822992414223991902508507 absolute error = 5.30894579372646499e-15 relative error = 7.0764400569255206106211850325895e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4 y1[1] (closed_form) = 0.65364362086361191463916818309775 y1[1] (numeric) = 0.65364362086361221423606748942979 absolute error = 2.9959689930633204e-16 relative error = 4.5834899897056500517221330688597e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.75680249530792825137263909451183 y2[1] (numeric) = 0.75680249530793361692496237153505 absolute error = 5.36555232327702322e-15 relative error = 7.0897656344194320944348829458289e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.01 y1[1] (closed_form) = 0.64604304013495860312968241468503 y1[1] (numeric) = 0.64604304013495884878904965925879 absolute error = 2.4565936724457376e-16 relative error = 3.8025232373566850523119697680090e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.7633009827670735204905561792977 y2[1] (numeric) = 0.7633009827670789423977243297747 absolute error = 5.42190716815047700e-15 relative error = 7.1032361945811994322138288791653e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3084.1MB, alloc=40.3MB, time=36.20 TOP MAIN SOLVE Loop x[1] = 4.02 y1[1] (closed_form) = 0.63837785564065920131155338076535 y1[1] (numeric) = 0.6383778556406593924711359662402 absolute error = 1.9115958258547485e-16 relative error = 2.9944582334177636531858869893931e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.76972314076402411428559733354449 y2[1] (numeric) = 0.76972314076402959228700152839331 absolute error = 5.47800140419484882e-15 relative error = 7.1168464530732524322759912909578e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.03 y1[1] (closed_form) = 0.63064883389277550667185452185245 y1[1] (numeric) = 0.63064883389277564277205057127535 absolute error = 1.3610019604942290e-16 relative error = 2.1580979577703143110456102876015e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.7760683270883321181898793012325 y2[1] (numeric) = 0.77606832708833765201598446255707 absolute error = 5.53382610516132457e-15 relative error = 7.1305913564637258177102676736484e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.04 y1[1] (closed_form) = 0.62285674778704147759294657917268 y1[1] (numeric) = 0.62285674778704155807689420382579 absolute error = 8.048394762465311e-17 relative error = 1.2921742906471820509659249583207e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.78233590722665273904778223066649 y2[1] (numeric) = 0.78233590722665832842012615922198 absolute error = 5.58937234392855549e-15 relative error = 7.1444660692395430168756339626982e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.05 y1[1] (closed_form) = 0.61500237652557430403427072848237 y1[1] (numeric) = 0.6150023765255743283479372983222 absolute error = 2.431366656983983e-17 relative error = 3.9534264415690056609174569719666e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = 0.78852525442619511083590710941938 y2[1] (numeric) = 0.78852525442620075546710083924917 absolute error = 5.64463119372982979e-15 relative error = 7.1584659616734692381196803166414e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.06 y1[1] (closed_form) = 0.60708650553895484514628584778934 y1[1] (numeric) = 0.60708650553895481273855725219213 absolute error = 3.240772859559721e-17 relative error = 5.3382389988765295104140653660619e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = 0.005 y2[1] (closed_form) = 0.79463574975739705145742669274634 y2[1] (numeric) = 0.79463574975740275105115607570434 absolute error = 5.69959372938295800e-15 relative error = 7.1725865984799307827116733157580e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3126.2MB, alloc=40.3MB, time=36.69 TOP MAIN SOLVE Loop x[1] = 4.07 y1[1] (closed_form) = 0.59910992640768522570785577303961 y1[1] (numeric) = 0.59910992640768513603062565954112 absolute error = 8.967723011349849e-17 relative error = 1.4968409996344225804318721463446e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.80066678217581750318737928027569 y2[1] (numeric) = 0.80066678217582325743840780299096 absolute error = 5.75425102852271527e-15 relative error = 7.1868237282000115077336397283941e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.08 y1[1] (closed_form) = 0.59107343678303144556199101824792 y1[1] (numeric) = 0.59107343678303129807024999694112 absolute error = 1.4749174102130680e-16 relative error = 2.4953200709550309036392428130931e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.80661774858324046757643767338011 y2[1] (numeric) = 0.80661774858324627617061050906344 absolute error = 5.80859417283568333e-15 relative error = 7.2011732732611130979035217268654e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.09 y1[1] (closed_form) = 0.58297784030725891772303711364428 y1[1] (numeric) = 0.58297784030725871187496191487515 absolute error = 2.0584807519876913e-16 relative error = 3.5309759816990083900223792039040e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.81248805388798432447058271235272 y2[1] (numeric) = 0.81248805388799018708483200968713 absolute error = 5.86261424929733441e-15 relative error = 7.2156313206613598121346700172178e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.1 y1[1] (closed_form) = 0.57482394653326891153502867965979 y1[1] (numeric) = 0.57482394653326864679207125263982 absolute error = 2.6474295742701997e-16 relative error = 4.6056354997677105645695998089714e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.81827711106441050426503702435845 y2[1] (numeric) = 0.81827711106441642056738843555739 absolute error = 5.91630235141119894e-15 relative error = 7.2301941132329906894249677563834e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.11 y1[1] (closed_form) = 0.56661257084364393716992399387447 y1[1] (numeric) = 0.56661257084364361299690053380854 absolute error = 3.2417302346006593e-16 relative error = 5.7212465826057553003642467908629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.82398434121162556257482398369604 y2[1] (numeric) = 0.82398434121163153222440443365424 absolute error = 5.96964958044995820e-15 relative error = 7.2448580414427572734721897348259e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3168.4MB, alloc=40.3MB, time=37.19 TOP MAIN SOLVE Loop x[1] = 4.12 y1[1] (closed_form) = 0.5583445343691101668598082727593 y1[1] (numeric) = 0.5583445343691097827249881640689 absolute error = 3.8413482010869040e-16 relative error = 6.8798886075375588222287811838221e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.82960917361137078716340306097222 y2[1] (numeric) = 0.82960917361137680981044975927513 absolute error = 6.02264704669830291e-15 relative error = 7.2596196356907730802306771303444e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.13 y1[1] (closed_form) = 0.55002066390642504655299469207052 y1[1] (numeric) = 0.55002066390642460192818935527568 absolute error = 4.4462480533679484e-16 relative error = 8.0837836560343996081010536580717e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.83515104578509354821692987595635 y2[1] (numeric) = 0.83515104578509962350280057335445 absolute error = 6.07528587069739810e-15 relative error = 7.2744755590723762692657990331486e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.14 y1[1] (closed_form) = 0.54164179183569830916443077359731 y1[1] (numeric) = 0.54164179183569780352508240340516 absolute error = 5.0563934837019215e-16 relative error = 9.3353089808028117409713769448443e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.005 y2[1] (closed_form) = 0.84060940355019468487667282814088 y2[1] (numeric) = 0.84060940355020081243385731893503 absolute error = 6.12755718449079415e-15 relative error = 7.2894226005704013988364475335971e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.15 y1[1] (closed_form) = 0.53320875603715465725018617166272 y1[1] (numeric) = 0.53320875603715409007545635379706 absolute error = 5.6717472981786566e-16 relative error = 1.0637010802919826975705151810187e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.84598370107544630333780572921222 y2[1] (numeric) = 0.84598370107545248278993860083617 absolute error = 6.17945213287162395e-15 relative error = 7.3044576686478379575932680621457e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3210.5MB, alloc=40.3MB, time=37.67 x[1] = 4.16 y1[1] (closed_form) = 0.52472239980734643876839021070922 y1[1] (numeric) = 0.52472239980734580954124840500332 absolute error = 6.2922714180570590e-16 relative error = 1.1991619607562564934014113282365e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.85127340093557444478094790264673 y2[1] (numeric) = 0.85127340093558067574282253357174 absolute error = 6.23096187463092501e-15 relative error = 7.3195777852132054021283820389831e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.17 y1[1] (closed_form) = 0.51618357177482469458922054275779 y1[1] (numeric) = 0.51618357177482400279653242002231 absolute error = 6.9179268812273548e-16 relative error = 1.3402067131739654355999624320680e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.85647797416500116491514400141294 y2[1] (numeric) = 0.85647797416500744699272780833865 absolute error = 6.28207758380692571e-15 relative error = 7.3347800799331220774798837071177e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.18 y1[1] (closed_form) = 0.50759312581527701057891803304672 y1[1] (numeric) = 0.50759312581527625571153365321564 absolute error = 7.5486738437983108e-16 relative error = 1.4871505266494526385722239184306e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.86159690031074065096911416280091 y2[1] (numeric) = 0.86159690031074698375956509793504 absolute error = 6.33279045093513413e-15 relative error = 7.3500617848685053837899735936083e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.19 y1[1] (closed_form) = 0.49895192096614066040190125149245 y1[1] (numeric) = 0.49895192096613984195474307054292 absolute error = 8.1844715818094953e-16 relative error = 1.6403327130120220789444454497550e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.86662966748444408656315532592254 y2[1] (numeric) = 0.86662966748445046965483962499021 absolute error = 6.38309168429906767e-15 relative error = 7.3654202294126325989350319043530e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.2 y1[1] (closed_form) = 0.49026082134069957765554488137713 y1[1] (numeric) = 0.49026082134069869512769557451336 absolute error = 8.8252784930686377e-16 relative error = 1.8001190608979214478621005007723e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.87157577241358806001857709790882 y2[1] (numeric) = 0.87157577241359449299108827937027 absolute error = 6.43297251118146145e-15 relative error = 7.3808528355109311648906413669143e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3252.6MB, alloc=40.3MB, time=38.17 x[1] = 4.21 y1[1] (closed_form) = 0.48152069604167374756882294948685 y1[1] (numeric) = 0.48152069604167280046361303807413 absolute error = 9.4710520991141272e-16 relative error = 1.9669044709751051688640070859082e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.8764347204918013973064980899522 y2[1] (numeric) = 0.87643472049180787973067720574546 absolute error = 6.48242417911579326e-15 relative error = 7.3963571131438682584117493665086e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.22 y1[1] (closed_form) = 0.47273241907430965925363841315521 y1[1] (numeric) = 0.47273241907430864707873368288811 absolute error = 1.01217490473026710e-15 relative error = 2.1411159122792496829712577865549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.88120602582832538699464673122123 y2[1] (numeric) = 0.88120602582833191843260386918349 absolute error = 6.53143795713796226e-15 relative error = 7.4119306560556845159396059358036e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.23 y1[1] (closed_form) = 0.46389686925898050939118958954484 y1[1] (numeric) = 0.46389686925897943165867828733257 absolute error = 1.07773251130221227e-15 relative error = 2.3232157462579137877485713915608e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.88588921129660245121088859729926 y2[1] (numeric) = 0.88588921129660903121602563525809 absolute error = 6.58000513703795883e-15 relative error = 7.4275711377129786763043465166714e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.24 y1[1] (closed_form) = 0.45501493014330489726017186970594 y1[1] (numeric) = 0.45501493014330375348665166675892 absolute error = 1.14377352020294702e-15 relative error = 2.5137054730110080463685570916226e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.89048380858198840379687432458221 y2[1] (numeric) = 0.89048380858199503191390893594466 absolute error = 6.62811703461136245e-15 relative error = 7.4432763074783072897734342667362e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.25 y1[1] (closed_form) = 0.44608748991379279916407772054484 y1[1] (numeric) = 0.44608748991379158887074242914913 absolute error = 1.21029333529139571e-15 relative error = 2.7131299636429774116053527212437e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.89498935822858352446575282843828 y2[1] (numeric) = 0.89498935822859020023074373894272 absolute error = 6.67576499091050444e-15 relative error = 7.4590439869850272301337034513837e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3294.8MB, alloc=40.3MB, time=38.66 x[1] = 4.26 y1[1] (closed_form) = 0.43711544130702765758652413548598 y1[1] (numeric) = 0.43711544130702638029925016695618 absolute error = 1.27728727396852980e-15 relative error = 2.9220822539448331460250728230533e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.89940540968517776589555981885312 y2[1] (numeric) = 0.89940540968518448883593331398515 absolute error = 6.72294037349513203e-15 relative error = 7.4748720667005860612774749771814e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.27 y1[1] (closed_form) = 0.42809968152039346679167732209429 y1[1] (numeric) = 0.42809968152039212204110987340152 absolute error = 1.34475056744869277e-15 relative error = 3.1412089882263381894454594493584e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.90373152135030549927585981966133 y2[1] (numeric) = 0.90373152135031226891043750207179 absolute error = 6.76963457768241046e-15 relative error = 7.4907585026663649621318972471163e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.28 y1[1] (closed_form) = 0.41904111212235578208682073683604 y1[1] (numeric) = 0.41904111212235436940845969341495 absolute error = 1.41267836104342109e-15 relative error = 3.3712166185520556848201949409672e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.90796726061640529287063252329942 y2[1] (numeric) = 0.90796726061641210870966031939865 absolute error = 6.81583902779609923e-15 relative error = 7.5067013134030061925574917184301e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.29 y1[1] (closed_form) = 0.40994063896230562457137463377925 y1[1] (numeric) = 0.40994063896230414350566017602716 absolute error = 1.48106571445775209e-15 relative error = 3.6128784845699020534906785986578e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.91211220391308030765634688524802 y2[1] (numeric) = 0.91211220391308716920152529998678 absolute error = 6.86154517841473876e-15 relative error = 7.5226985769709199131649261970902e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.3 y1[1] (closed_form) = 0.40079917207997529690676239633603 y1[1] (numeric) = 0.40079917207997374699916029732787 absolute error = 1.54990760209900816e-15 relative error = 3.8670429234063893077338482596977e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.91616593674945498403170936028464 y2[1] (numeric) = 0.91616593674946189077622497896834 absolute error = 6.90674451561868370e-15 relative error = 7.5387484281763681695561380862155e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3337.0MB, alloc=40.3MB, time=39.16 TOP MAIN SOLVE Loop x[1] = 4.31 y1[1] (closed_form) = 0.39161762561443516845006009684425 y1[1] (numeric) = 0.39161762561443354925114669879949 absolute error = 1.61919891339804476e-15 relative error = 4.1346425888200893523562322637273e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.92012805375562378396571242699099 y2[1] (numeric) = 0.92012805375563073539427066280976 absolute error = 6.95142855823581877e-15 relative error = 7.5548490559141719148088437611002e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.32 y1[1] (closed_form) = 0.38239691771268052999708015943008 y1[1] (numeric) = 0.38239691771267884106262701648179 absolute error = 1.68893445314294829e-15 relative error = 4.4167051953382994731242649563773e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.92399815872318784374430909898398 y2[1] (numeric) = 0.92399815872319483933316818477711 absolute error = 6.99558885908579313e-15 relative error = 7.5709987006386855856634110602498e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.33 y1[1] (closed_form) = 0.37313797043781765937323745066286 y1[1] (numeric) = 0.37313797043781590026429562549457 absolute error = 1.75910894182516829e-15 relative error = 4.7143659482339350913961541515498e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.92777586464487548368421918677298 y2[1] (numeric) = 0.92777586464488252290122540938249 absolute error = 7.03921700622260951e-15 relative error = 7.5871956519552367274544253310465e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.34 y1[1] (closed_form) = 0.36384170967685827918912735442367 y1[1] (numeric) = 0.36384170967685644947211135635711 absolute error = 1.82971701599806656e-15 relative error = 5.0288819762393600655536957971275e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.93146079375324261279591291098884 y2[1] (numeric) = 0.9314607937532496951005370863925 absolute error = 7.08230462417540366e-15 relative error = 7.6034382463247381890672666649691e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.35 y1[1] (closed_form) = 0.35450906504813162723820257743587 y1[1] (numeric) = 0.3545090650481297264849739295715 absolute error = 1.90075322864786437e-15 relative error = 5.3616491538511137128321780247994e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.93505257755844915838755579834142 y2[1] (numeric) = 0.9350525775584562832309309855918 absolute error = 7.12484337518725038e-15 relative error = 7.6197248648746533983040586615343e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3379.1MB, alloc=40.3MB, time=39.66 TOP MAIN SOLVE Loop x[1] = 4.36 y1[1] (closed_form) = 0.34514096980832339825235256696343 y1[1] (numeric) = 0.34514096980832142604030298999628 absolute error = 1.97221204957696715e-15 relative error = 5.7142217879037941045879468337218e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.93855085688510774299843471888496 y2[1] (numeric) = 0.93855085688511490982339517071699 absolute error = 7.16682496045183203e-15 relative error = 7.6360539313099316692157403112404e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.37 y1[1] (closed_form) = 0.33573836075915085304374269242283 y1[1] (numeric) = 0.33573836075914880895587689277834 absolute error = 2.04408786579964449e-15 relative error = 6.0883357540010596606636703576234e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.94195528190820092382487885040826 y2[1] (numeric) = 0.94195528190820813206600019821378 absolute error = 7.20824112134780552e-15 relative error = 7.6524239099179348998341037296727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.38 y1[1] (closed_form) = 0.32630217815368342744422852384408 y1[1] (numeric) = 0.32630217815368131106924657380242 absolute error = 2.11637498195004166e-15 relative error = 6.4859358093321118274564038701642e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.94526551218806340294466391093816 y2[1] (numeric) = 0.94526551218807065202830458164214 absolute error = 7.24908364067070398e-15 relative error = 7.6688333036617515908038353118130e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.39 y1[1] (closed_form) = 0.31683336560231820890338536675574 y1[1] (numeric) = 0.31683336560231601983576466425862 absolute error = 2.18906762070249712e-15 relative error = 6.9092079886881715860713685461385e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.94848121670442571014802896361413 y2[1] (numeric) = 0.94848121670443299949237282582335 absolute error = 7.28934434386220922e-15 relative error = 7.6852806523566408075041583068176e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.4 y1[1] (closed_form) = 0.30733286997841968311913974221771 y1[1] (numeric) = 0.30733286997841742095921653807887 absolute error = 2.26215992320413884e-15 relative error = 7.3606182227204767055516786475818e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.95160207388951595403539233338039 y2[1] (numeric) = 0.95160207388952328305049257001182 absolute error = 7.32901510023663143e-15 relative error = 7.7017645309246704483782643526035e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3421.2MB, alloc=40.3MB, time=40.14 TOP MAIN SOLVE Loop x[1] = 4.41 y1[1] (closed_form) = 0.29780164132363318664770646649064 y1[1] (numeric) = 0.2978016413236308510017569467597 absolute error = 2.33564594951973094e-15 relative error = 7.8429586188260435053923458626715e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.95462777166021633123424156453615 y2[1] (numeric) = 0.95462777166022369932206576896857 absolute error = 7.36808782420443242e-15 relative error = 7.7182835477229119628207137559989e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.42 y1[1] (closed_form) = 0.28824063275288153406866514349322 y1[1] (numeric) = 0.28824063275287912454898605475335 absolute error = 2.40951967908873987e-15 relative error = 8.3594032391488079148087526393351e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.95755800744927117811107273183889 y2[1] (numeric) = 0.95755800744927858466554922446793 absolute error = 7.40655447649262904e-15 relative error = 7.7348363429408303237243274111383e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.43 y1[1] (closed_form) = 0.27865080035905431996329034893364 y1[1] (numeric) = 0.27865080035905183618827915434505 absolute error = 2.48377501119458859e-15 relative error = 8.9135757298889173038923461792053e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.96039248823554344419921453430048 y2[1] (numeric) = 0.96039248823555088860627989621426 absolute error = 7.44440706536191378e-15 relative error = 7.7514215870627647411826639642215e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.44 y1[1] (closed_form) = 0.26903310311739942669651235616339 y1[1] (numeric) = 0.26903310311739686829074691009873 absolute error = 2.55840576544606466e-15 relative error = 9.5096318475337933897474209932779e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.005 y2[1] (closed_form) = 0.96313093057331656172040803307784 y2[1] (numeric) = 0.96313093057332404335805585340694 absolute error = 7.48163764782032910e-15 relative error = 7.7680379793916329468742564057373e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3463.2MB, alloc=40.3MB, time=40.64 x[1] = 4.45 y1[1] (closed_form) = 0.25938850278962629877205672974446 y1[1] (numeric) = 0.25938850278962366536637445889721 absolute error = 2.63340568227084725e-15 relative error = 1.0152360856204320588262133070411e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.96577306062063878103760801869169 y2[1] (numeric) = 0.96577306062064629927593885202471 absolute error = 7.51823833083333302e-15 relative error = 7.7846842466302136015357006561325e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.46 y1[1] (closed_form) = 0.24971796382773057335341360111266 y1[1] (numeric) = 0.2497179638277278645849901799966 absolute error = 2.70876842342111606e-15 relative error = 1.0847311030013748277227107955813e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.96831861416670713762908092824644 y2[1] (numeric) = 0.96831861416671469183035345833972 absolute error = 7.55420127253009328e-15 relative error = 7.8013591415165659801116961664179e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.47 y1[1] (closed_form) = 0.24002245327754968440743865533016 y1[1] (numeric) = 0.24002245327754689991986616412646 absolute error = 2.78448757249120370e-15 relative error = 1.1600946221774363489730927651868e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97076733665828831220992179927159 y2[1] (numeric) = 0.97076733665829590172860520511928 absolute error = 7.58951868340584769e-15 relative error = 7.8180614415103365395008431806593e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.48 y1[1] (closed_form) = 0.23030294068205908482980140684885 y1[1] (numeric) = 0.23030294068205622427316595959765 absolute error = 2.86055663544725120e-15 relative error = 1.2420842855829380592962624517346e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97311898322517374193699541853268 y2[1] (numeric) = 0.97311898322518136611982293870137 absolute error = 7.62418282752016869e-15 relative error = 7.8347899475268788587849556967434e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.49 y1[1] (closed_form) = 0.2205603979844187568494820065161 y1[1] (numeric) = 0.22056039798441581988044083769092 absolute error = 2.93696904116882518e-15 relative error = 1.3315940069061283068566865815730e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97537331870466643720739369365918 y2[1] (numeric) = 0.97537331870467409539341738462945 absolute error = 7.65818602369097027e-15 relative error = 7.8515434827162773561285681486593e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3505.4MB, alloc=40.3MB, time=41.12 x[1] = 4.5 y1[1] (closed_form) = 0.21079579943077970598048182479383 y1[1] (numeric) = 0.2107957994307766922623398223409 absolute error = 3.01371814200245293e-15 relative error = 1.4296860516862841085850415373690e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97753011766509705538913501449863 y2[1] (numeric) = 0.97753011766510474690978169859462 absolute error = 7.69152064668409599e-15 relative error = 7.8683208912845177683153192313239e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.51 y1[1] (closed_form) = 0.20101012147286015779035832174077 y1[1] (numeric) = 0.20101012147285706699314399470997 absolute error = 3.09079721432703080e-15 relative error = 1.5376326284864923426929025864847e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97958916442836687989632919704766 y2[1] (numeric) = 0.97958916442837460407545759537445 absolute error = 7.72417912839832679e-15 relative error = 7.8851210373541883050307809756054e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.52 y1[1] (closed_form) = 0.19120434267030119978472111819888 y1[1] (numeric) = 0.19120434267029803158526198713996 absolute error = 3.16819945913105892e-15 relative error = 1.6569704510289657055353575532077e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98155025309151545032968624674211 y2[1] (numeric) = 0.98155025309152320648364529239001 absolute error = 7.75615395904564790e-15 relative error = 7.9019428038622267522609713145157e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.53 y1[1] (closed_form) = 0.1813794435928116327621307913814 y1[1] (numeric) = 0.18137944359280838684412818972705 absolute error = 3.24591800260165435e-15 relative error = 1.7895732494849793701559517041110e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98341318754731068693732785543696 y2[1] (numeric) = 0.98341318754731847437501618205158 absolute error = 7.78743768832661462e-15 relative error = 7.9187850914923504191999929739000e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.54 y1[1] (closed_form) = 0.1715364067221118170727192195978 y1[1] (numeric) = 0.17153640672210849312682249430517 absolute error = 3.32394589672529263e-15 relative error = 1.9377495193251130408337596599278e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98517778150385945040061393078254 y2[1] (numeric) = 0.9851777815038672684235405314393 absolute error = 7.81802292660065676e-15 relative error = 7.9356468176399180442850141087833e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3547.5MB, alloc=40.3MB, time=41.63 TOP MAIN SOLVE Loop x[1] = 4.55 y1[1] (closed_form) = 0.16167621635368631931419242500794 y1[1] (numeric) = 0.16167621635368291703807252478154 absolute error = 3.40227611990022640e-15 relative error = 2.1043763867267496001200099526309e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98684385850323657590534765402509 y2[1] (numeric) = 0.98684385850324442380769370518747 absolute error = 7.84790234605116238e-15 relative error = 7.9525269154070774642197003162695e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.56 y1[1] (closed_form) = 0.1517998584983551841186737926099 y1[1] (numeric) = 0.15179985849835170321709623208174 absolute error = 3.48090157756052816e-15 relative error = 2.2930861807082944057373983660549e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98841125193913051861047608903809 y2[1] (numeric) = 0.98841125193913839567915793421972 absolute error = 7.87706868184518163e-15 relative error = 7.9694243326261489747791806697108e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.57 y1[1] (closed_form) = 0.14190832078367367382118531437459 y1[1] (numeric) = 0.14190832078367011400608250267219 absolute error = 3.55981510281170240e-15 relative error = 2.5085316232008105440864880559636e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98987980507350384596444412806507 y2[1] (numeric) = 0.98987980507351175147917741565706 absolute error = 7.90551473328759199e-15 relative error = 7.9863380309092834049241584486009e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.58 y1[1] (closed_form) = 0.1320025923551703359536334006823 y1[1] (numeric) = 0.13200259235516669694417632287118 absolute error = 3.63900945707781112e-15 relative error = 2.7567712058916067091786725781514e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99124937105226691083385383609731 y2[1] (numeric) = 0.99124937105227484406721880566412 absolute error = 7.93323336496956681e-15 relative error = 8.0032669847225161751249998983146e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.59 y1[1] (closed_form) = 0.1220836637774332746752485243965 y1[1] (numeric) = 0.12208366377742955619791776434166 absolute error = 3.71847733076005484e-15 relative error = 3.0458434942934617065276983345118e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99251981291996313809017767868781 y2[1] (numeric) = 0.99251981291997109830768558987722 absolute error = 7.96021750791118941e-15 relative error = 8.0202101804824140721743175235306e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3589.7MB, alloc=40.3MB, time=42.13 TOP MAIN SOLVE Loop x[1] = 4.6 y1[1] (closed_form) = 0.11215252693505451742990782122919 y1[1] (numeric) = 0.11215252693505071921856391447934 absolute error = 3.79821134390674985e-15 relative error = 3.3866480298800799699824307118221e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99369100363346445613810465990883 y2[1] (numeric) = 0.99369100363347244259826535796441 absolute error = 7.98646016069805558e-15 relative error = 8.0371666156735809762695454244817e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.61 y1[1] (closed_form) = 0.10221017493344238231112882817269 y1[1] (numeric) = 0.10221017493343850410708193353198 absolute error = 3.87820404689464071e-15 relative error = 3.7943424413665906020915786298978e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99476282607467550385377935740314 y2[1] (numeric) = 0.99476282607468351580816996911101 absolute error = 8.01195439061170787e-15 relative error = 8.0541352979853523984785841442968e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.62 y1[1] (closed_form) = 0.09225760199951176481534177561582 y1[1] (numeric) = 0.092257601999507806367420654130139 absolute error = 3.958447921121485681e-15 relative error = 4.2906468793134620263750714258321e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99573517306224534252282683445147 y2[1] (numeric) = 0.99573517306225337921616158819702 absolute error = 8.03669333475374555e-15 relative error = 8.0711152444660666989083054487766e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.63 y1[1] (closed_form) = 0.082295803382262274872007287402623 y1[1] (numeric) = 0.082295803382258235936627577551669 absolute error = 4.038935379709850954e-15 relative error = 4.9078266615237731028450329901855e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.9966079473622855016167293539807 y2[1] (numeric) = 0.99660794736229356228693051743554 absolute error = 8.06067020116345484e-15 relative error = 8.0881054806933538217089798254399e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.64 y1[1] (closed_form) = 0.072325775253254166254025200760118 y1[1] (numeric) = 0.072325775253250046595256978712032 absolute error = 4.119658768222048086e-15 relative error = 5.6959759557318973343616986518154e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99738106169809328661190893188283 y2[1] (numeric) = 0.9973810616981013704901788606872 absolute error = 8.08387826992880437e-15 relative error = 8.1051050399589299543761069223936e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3631.9MB, alloc=40.3MB, time=42.61 TOP MAIN SOLVE Loop x[1] = 4.65 y1[1] (closed_form) = 0.062348514606992010692557016177074 y1[1] (numeric) = 0.062348514606987810082191630029435 absolute error = 4.200610365386147639e-15 relative error = 6.7373062403560043534445278846874e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99805443875887937652883655089603 y2[1] (numeric) = 0.99805443875888748283973084154777 absolute error = 8.10631089429065174e-15 relative error = 8.1221129624664298311017520907683e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.66 y1[1] (closed_form) = 0.052365019161226078245837166795957 y1[1] (numeric) = 0.052365019161221796463453333795709 absolute error = 4.281782383833000248e-15 relative error = 8.1767990395455940357767436709940e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99862801120749883843868709783252 y2[1] (numeric) = 0.99862801120750696640018883784 absolute error = 8.12796150174000748e-15 relative error = 8.1391282945408466145852201751616e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.67 y1[1] (closed_form) = 0.042376287257181393700854320105276 y1[1] (numeric) = 0.042376287257177030533883475910276 absolute error = 4.363166970844195000e-15 relative error = 1.0296246446424541371948603654938e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99910172168718478584253184927338 y2[1] (numeric) = 0.9991017216871929346661269574767 absolute error = 8.14882359510820332e-15 relative error = 8.1561500878481832467812342667900e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.68 y1[1] (closed_form) = 0.032383317759724446019120367944567 y1[1] (numeric) = 0.032383317759720001262911257061192 absolute error = 4.444756209110883375e-15 relative error = 1.3725450375683508717495456283142e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99947552282728400756284194975967 y2[1] (numeric) = 0.99947552282729217645359559957237 absolute error = 8.16889075364981270e-15 relative error = 8.1731773986239492387931996645671e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3674.0MB, alloc=40.3MB, time=43.11 x[1] = 4.69 y1[1] (closed_form) = 0.022387109957477534072388396442007 y1[1] (numeric) = 0.022387109957473007530270893046502 absolute error = 4.526542117503395505e-15 relative error = 2.0219412537398477570255814187328e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99974937724799399358919340694292 y2[1] (numeric) = 0.99974937724800218174582752511456 absolute error = 8.18815663411817164e-15 relative error = 8.1902092869091619655073783382418e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.7 y1[1] (closed_form) = 0.012388663462890737150508296327111 y1[1] (numeric) = 0.012388663462886128633856444753077 absolute error = 4.608516651851574034e-15 relative error = 3.7199465992889561072577893566061e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99992325756410088417953654157497 y2[1] (numeric) = 0.99992325756410909079450837492429 absolute error = 8.20661497183334932e-15 relative error = 8.2072448157925336291418154994618e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.71 y1[1] (closed_form) = 0.0023889781122815029610961477246958 y1[1] (numeric) = 0.0023889781122768122893904119754212 absolute error = 4.6906717057357492746e-15 relative error = 1.9634636590521547819740515948700e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.005 y2[1] (closed_form) = 0.99999714638771796842523471259357 y2[1] (numeric) = 0.99999714638772619268481645501154 absolute error = 8.22425958174241797e-15 relative error = 8.2242830506575422304704917859768e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.72 y1[1] (closed_form) = -0.0076109461341481509210826531746326 y1[1] (numeric) = -0.0076109461341529239201939414525969 absolute error = 4.7729991112882779643e-15 relative error = 6.2712296568138727012336221842126e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99997103633002445843229788796164 y2[1] (numeric) = 0.99997103633003269951665735983452 absolute error = 8.24108435947187288e-15 relative error = 8.2413230584330991571589955223745e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.73 y1[1] (closed_form) = -0.017610109292306823958480184942845 y1[1] (numeric) = -0.017610109292311679449120190509171 absolute error = 4.855490640005566326e-15 relative error = 2.7572177772495384230913698639738e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99984493000200436524284191155768 y2[1] (numeric) = 0.99984493000201262232612428361145 absolute error = 8.25708328237205377e-15 relative error = 8.2583639068465356847110048015393e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3716.2MB, alloc=40.3MB, time=43.59 x[1] = 4.74 y1[1] (closed_form) = -0.027607511454211308473521317218995 y1[1] (numeric) = -0.027607511454216246611524887715737 absolute error = 4.938138003570496742e-15 relative error = 1.7886936357015339300144156263543e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99961884001418540260979704807277 y2[1] (numeric) = 0.99961884001419367486020760149246 absolute error = 8.27225041055341969e-15 relative error = 8.2754046636776371112480638956830e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.75 y1[1] (closed_form) = -0.037602152887976554715496312373334 y1[1] (numeric) = -0.037602152887981575648350997549156 absolute error = 5.020932854685175822e-15 relative error = 1.3352780277351194039230983930977e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99929278897537794473427075559708 y2[1] (numeric) = 0.99929278897538623131415867012757 absolute error = 8.28657988791453049e-15 relative error = 8.2924443960124558791413488854335e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.76 y1[1] (closed_form) = -0.047593034137788026258408716410526 y1[1] (numeric) = -0.047593034137793130125196630330737 absolute error = 5.103866787913920211e-15 relative error = 1.0723978582953046837010913933494e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.005 y2[1] (closed_form) = 0.99886680949041416406874008456944 y2[1] (numeric) = 0.99886680949042246413468324615802 absolute error = 8.30006594316158858e-15 relative error = 8.3094821694956337547128347554022e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.77 y1[1] (closed_form) = -0.057579156123846448577548772787261 y1[1] (numeric) = -0.057579156123851635508889309182265 absolute error = 5.186931340536395004e-15 relative error = 9.0083490098046499324966836353911e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99834094415688757527040933829949 y2[1] (numeric) = 0.99834094415689588797330015769518 absolute error = 8.31270289081939569e-15 relative error = 8.3265170475799584354795857569088e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.78 y1[1] (closed_form) = -0.067559520242274956413221714659554 y1[1] (numeric) = -0.067559520242280226531215125477755 absolute error = 5.270117993410818201e-15 relative error = 7.8007036972904288225627399431939e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99771524556089331134762062164767 y2[1] (numeric) = 0.99771524556090163583275285522782 absolute error = 8.32448513223358015e-15 relative error = 8.3435480907718713198361995317510e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3758.4MB, alloc=40.3MB, time=44.09 TOP MAIN SOLVE Loop x[1] = 4.79 y1[1] (closed_form) = -0.077533128464978649290150241347593 y1[1] (numeric) = -0.077533128464984002708322088490769 absolute error = 5.353418171847143176e-15 relative error = 6.9046848461238824786631627180644e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99698977627176955796815287876274 y2[1] (numeric) = 0.99698977627177789337530944271372 absolute error = 8.33540715656395098e-15 relative error = 8.3605743558716307066170881608399e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.8 y1[1] (closed_form) = -0.087498983439446569320215257649488 y1[1] (numeric) = -0.087498983439452006143461747779224 absolute error = 5.436823246490129736e-15 relative error = 6.2135844701014935800171644562489e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99616460883584067178159646650363 y2[1] (numeric) = 0.99616460883584901724513823534005 absolute error = 8.34546354176883642e-15 relative error = 8.3775948952068189466095338331854e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.81 y1[1] (closed_form) = -0.097456088588486121173922639538394 y1[1] (numeric) = -0.097456088588491641498456851751281 absolute error = 5.520324534212212887e-15 relative error = 5.6644224226175311748940211214710e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99523982576916260843875697540403 y2[1] (numeric) = 0.99523982576917096308771255566873 absolute error = 8.35464895558026470e-15 relative error = 8.3946087558578612270881935757046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.82 y1[1] (closed_form) = -0.10740344820987996086171061916977 y1[1] (numeric) = -0.10740344820988556477500963524679 absolute error = 5.60391329901607702e-15 relative error = 5.2176288493692675797842719978369e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99421551954927138575924090129834 y2[1] (numeric) = 0.99421551954927974871739737114497 absolute error = 8.36295815646984663e-15 relative error = 8.4116149788742004278456450570599e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.83 y1[1] (closed_form) = -0.11734006757595538771926678895382 y1[1] (numeric) = -0.1173400675759610753000197357957 absolute error = 5.68758075294684188e-15 relative error = 4.8470917653641323638313230094912e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.9930917926059354071940301512694 y2[1] (numeric) = 0.9930917926059437775800247564893 absolute error = 8.37038599460521990e-15 relative error = 8.4286125984797436459523612447297e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3800.5MB, alloc=40.3MB, time=44.59 TOP MAIN SOLVE Loop x[1] = 4.84 y1[1] (closed_form) = -0.12726495303305628274063040973268 y1[1] (numeric) = -0.12726495303306205405868742349781 absolute error = 5.77131805701376513e-15 relative error = 4.5348840505325146635588032840131e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99186875731091257034299275504052 y2[1] (numeric) = 0.99186875731092094727040555195688 absolute error = 8.37692741279691636e-15 relative error = 8.4456006412661639633977391992586e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.85 y1[1] (closed_form) = -0.13717711210090764614813971846528 y1[1] (numeric) = -0.13717711210091350126446183983051 absolute error = 5.85511632212136523e-15 relative error = 4.2682895363873345927010003810800e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.99054653596671318480794231629118 y2[1] (numeric) = 0.99054653596672156738538975180554 absolute error = 8.38257744743551436e-15 relative error = 8.4625781253726040329190831973956e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.86 y1[1] (closed_form) = -0.1470755535718627978282707459854 y1[1] (numeric) = -0.147075553571868736794880755852 absolute error = 5.93896661000986660e-15 relative error = 4.0380379102962339559000120103866e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98912526079436982308009669404291 y2[1] (numeric) = 0.98912526079437821041132611298214 absolute error = 8.38733122941893923e-15 relative error = 8.4795440596502866740413816614827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.87 y1[1] (closed_form) = -0.15695928761002331599602978562804 y1[1] (numeric) = -0.15695928761002933885596399049601 absolute error = 6.02285993420486797e-15 relative error = 3.8372115635291989752578828342101e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98760507392021532746665541129251 y2[1] (numeric) = 0.98760507392022371865064048106872 absolute error = 8.39118398506977621e-15 relative error = 8.4964974428104917534628166327128e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.88 y1[1] (closed_form) = -0.16682732585022180217663274703162 y1[1] (numeric) = -0.16682732585022790896389372316508 absolute error = 6.10678726097613346e-15 relative error = 3.6605437567577088236776512909736e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98598612736167029524478484231842 y2[1] (numeric) = 0.98598612736167868937582188477935 absolute error = 8.39413103704246093e-15 relative error = 8.5134372625543072795222308790075e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3842.7MB, alloc=40.3MB, time=45.08 TOP MAIN SOLVE Loop x[1] = 4.89 y1[1] (closed_form) = -0.17667868149685757431045858971384 y1[1] (numeric) = -0.17667868149686376504996889511806 absolute error = 6.19073951030540422e-15 relative error = 3.5039538770927002683022870907534e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.9842685830120414632826520572489 y2[1] (numeric) = 0.98426858301204985945045727746271 absolute error = 8.39616780522021381e-15 relative error = 8.5303624946825065564777539916176e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.9 y1[1] (closed_form) = -0.18651236942257540449432914412192 y1[1] (numeric) = -0.18651236942258167920188600724965 absolute error = 6.27470755686312773e-15 relative error = 3.3642313248654911465012395057826e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98245261262433251227637724991833 y2[1] (numeric) = 0.98245261262434090956618485150412 absolute error = 8.39728980760158579e-15 relative error = 8.5472721021838414383835645307023e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.91 y1[1] (closed_form) = -0.1963274062667774335675731995194 y1[1] (numeric) = -0.19632740626678379224980419351936 absolute error = 6.35868223099399996e-15 relative error = 3.2388153808508891565419940743678e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.98053839779406890950899010226969 y2[1] (numeric) = 0.98053839779407730700165127875344 absolute error = 8.39749266117648375e-15 relative error = 8.5641650342999740379961854775354e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.92 y1[1] (closed_form) = -0.20612281053395841143350924081177 y1[1] (numeric) = -0.20612281053396485408782895202649 absolute error = 6.44265431971121472e-15 relative error = 3.1256386923027121604975821319256e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97852612994113850763280160634113 y2[1] (numeric) = 0.97852612994114690440488439788655 absolute error = 8.39677208279154542e-15 relative error = 8.5810402255651959480527394434775e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3884.8MB, alloc=40.3MB, time=45.58 x[1] = 4.93 y1[1] (closed_form) = -0.21589760269185442967426044648577 y1[1] (numeric) = -0.21589760269186095628882814579863 absolute error = 6.52661456769931286e-15 relative error = 3.0230139132274647458412165239471e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97641601029064971540018032274914 y2[1] (numeric) = 0.97641601029065811052407032748358 absolute error = 8.39512389000473444e-15 relative error = 8.5978965948190036761847822125065e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.94 y1[1] (closed_form) = -0.22565080526939533166743080403972 y1[1] (numeric) = -0.22565080526940194222110912956284 absolute error = 6.61055367832552312e-15 relative error = 2.9295502271456339671454072084408e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97420824985280915450970852682316 y2[1] (numeric) = 0.97420824985281754705371045585056 absolute error = 8.39254400192902740e-15 relative error = 8.6147330441895120888654009856298e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.95 y1[1] (closed_form) = -0.23538144295445100504525741163474 y1[1] (numeric) = -0.23538144295445769950757207111939 absolute error = 6.69446231465948465e-15 relative error = 2.8440909489857021111310750428466e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.97190306940182081478526506337735 y2[1] (numeric) = 0.97190306940182920381370512844349 absolute error = 8.38902844006506614e-15 relative error = 8.6315484580455937481247126549236e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.96 y1[1] (closed_form) = -0.24508854269136178194844802293532 y1[1] (numeric) = -0.24508854269136856027954852417574 absolute error = 6.77833110050124042e-15 relative error = 2.7656662470090017394333348733971e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.96950069945380881775493302309673 y2[1] (numeric) = 0.96950069945381720232826214574614 absolute error = 8.38457332912264941e-15 relative error = 8.6483417019155297037212637279649e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.97 y1[1] (closed_form) = -0.25477113377824319411595351401254 y1[1] (numeric) = -0.25477113377825005626657493140172 absolute error = 6.86215062141738918e-15 relative error = 2.6934568762371301909766885133707e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.96700138024376599633497671407791 y2[1] (numeric) = 0.96700138024377437550987454501741 absolute error = 8.37917489783093950e-15 relative error = 8.6651116213698474062808407208221e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop memory used=3927.0MB, alloc=40.3MB, time=46.06 x[1] = 4.98 y1[1] (closed_form) = -0.26442824796405535241625332068078 y1[1] (numeric) = -0.26442824796406229832767910596339 absolute error = 6.94591142578528261e-15 relative error = 2.6267660430626399669026258778703e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.96440536170153059574171007792892 y2[1] (numeric) = 0.96440536170153896857118981518946 absolute error = 8.37282947973726054e-15 relative error = 8.6818570408659022354573819371369e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.99 y1[1] (closed_form) = -0.27405891954542724396309159769695 y1[1] (numeric) = -0.27405891954543427356711744284981 absolute error = 7.02960402584515286e-15 relative error = 2.5649973507539663403752708045537e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.005 y2[1] (closed_form) = 0.96171290342679349794114601441111 y2[1] (numeric) = 0.96171290342680186347466000877733 absolute error = 8.36553351399436622e-15 relative error = 8.6985767625516304593045687171124e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; Iterations = 900 Total Elapsed Time = 46 Seconds Elapsed Time(since restart) = 46 Seconds Time to Timeout = 2 Minutes 13 Seconds Percent Done = 100.1 % > quit memory used=3942.9MB, alloc=40.3MB, time=46.25