|\^/| 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(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_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(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > glob_check_sign := c(my_check_sign(x_start,x_end)); > glob__pi := arccos(glob__m1); > glob_prec = expt(10.0,c(-Digits)); > if (glob_optimize) then # if number 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,"2015-05-01T22:16:07-05:00") > ; > 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(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_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(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; glob_check_sign := c(my_check_sign(x_start, x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0, c(-Digits)); if glob_optimize then omniout_str(ALWAYS, "START of Optimize"); found_h := false; glob_min_pole_est := glob_larger_float; last_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; glob_min_h := float_abs(glob_min_h)*glob_check_sign; glob_max_h := float_abs(glob_max_h)*glob_check_sign; glob_h := float_abs(glob_min_h)*glob_check_sign; glob_display_interval := c(float_abs(c(glob_display_interval))*glob_check_sign); display_max := c(x_end) - c(x_start)/glob__10; if display_max < glob_display_interval then glob_display_interval := c(display_max) end if; chk_data(); min_value := glob_larger_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := glob_small_float; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); order_diff := 1; term_no := 1; while term_no <= order_diff do array_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, "2015-05-01T22:16:07-05:00"); 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(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_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=0.14 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 = 0.001 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 = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=45.8MB, alloc=40.3MB, time=0.63 TOP MAIN SOLVE Loop x[1] = 0.51 y1[1] (closed_form) = -0.87274450764575126310580847357551 y1[1] (numeric) = -0.87274450764575126310580829204146 absolute error = 1.8153405e-25 relative error = 2.0800365789719186990226439353236e-23 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.48817724688290749450013023767457 y2[1] (numeric) = -0.48817724688290749450018673842341 absolute error = 5.650074884e-23 relative error = 1.1573818567081245829182316538780e-20 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=87.8MB, alloc=40.3MB, time=1.11 TOP MAIN SOLVE Loop x[1] = 0.52 y1[1] (closed_form) = -0.86781917967764990038784757198851 y1[1] (numeric) = -0.86781917967764990038784603706466 absolute error = 1.53492385e-24 relative error = 1.7687139048599330374525699087152e-22 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.49688013784373671433445894254775 y2[1] (numeric) = -0.49688013784373671433469319928928 absolute error = 2.3425674153e-22 relative error = 4.7145523374426196900849765901770e-20 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=129.8MB, alloc=40.3MB, time=1.59 TOP MAIN SOLVE Loop x[1] = 0.53 y1[1] (closed_form) = -0.8628070705147610118066950185642 y1[1] (numeric) = -0.86280707051476101180668974932709 absolute error = 5.26923711e-24 relative error = 6.1070861494636456264914944366958e-22 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.50553334120484696181366102246608 y2[1] (numeric) = -0.50553334120484696181419358947032 absolute error = 5.3256700424e-22 relative error = 1.0534755293700771725430103145241e-19 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=171.8MB, alloc=40.3MB, time=2.08 TOP MAIN SOLVE Loop x[1] = 0.54 y1[1] (closed_form) = -0.8577086813638241425379687789178 y1[1] (numeric) = -0.85770868136382414253795619250672 absolute error = 1.258641108e-23 relative error = 1.4674459234791255950566383318281e-21 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.51413599165311310467728068295824 y2[1] (numeric) = -0.51413599165311310467823138940838 absolute error = 9.5070645014e-22 relative error = 1.8491342087978941274450486348949e-19 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=213.7MB, alloc=40.3MB, time=2.56 TOP MAIN SOLVE Loop x[1] = 0.55 y1[1] (closed_form) = -0.85252452205950574280498179761777 y1[1] (numeric) = -0.85252452205950574280495711660561 absolute error = 2.468101216e-23 relative error = 2.8950501154355392165755907014611e-21 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.52268722893065916778837810775729 y2[1] (numeric) = -0.52268722893065916778986603377868 absolute error = 1.48792602139e-21 relative error = 2.8466852431693744784529787335485e-19 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=255.7MB, alloc=40.3MB, time=3.06 TOP MAIN SOLVE Loop x[1] = 0.56 y1[1] (closed_form) = -0.84725511101341612609452550386632 y1[1] (numeric) = -0.84725511101341612609448276386934 absolute error = 4.273999698e-23 relative error = 5.0445251287865314686607979484335e-21 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.53118619792088340385186944111203 y2[1] (numeric) = -0.53118619792088340385401289394696 absolute error = 2.14345283493e-21 relative error = 4.0352193700056431459950137616647e-19 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=297.6MB, alloc=40.3MB, time=3.55 TOP MAIN SOLVE Loop x[1] = 0.57 y1[1] (closed_form) = -0.84190097516226874013375636391601 y1[1] (numeric) = -0.84190097516226874013368842144124 absolute error = 6.794247477e-23 relative error = 8.0701266270542930770546015305649e-21 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.53963204873396924099446349307883 y2[1] (numeric) = -0.53963204873396924099737998341027 absolute error = 2.91649033144e-21 relative error = 5.4045906618822548026512249782746e-19 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=339.7MB, alloc=40.3MB, time=4.03 TOP MAIN SOLVE Loop x[1] = 0.58 y1[1] (closed_form) = -0.83646264991518693465788732805002 y1[1] (numeric) = -0.83646264991518693465778586857855 absolute error = 1.0145947147e-22 relative error = 1.2129587792149174290075522317684e-20 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.54802393679187355618269605957646 y2[1] (numeric) = -0.54802393679187355618650227800479 absolute error = 3.80621842833e-21 relative error = 6.9453506914525727011739579310416e-19 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=381.6MB, alloc=40.3MB, time=4.53 TOP MAIN SOLVE Loop x[1] = 0.59 y1[1] (closed_form) = -0.83094067910016349524799652249068 y1[1] (numeric) = -0.83094067910016349524785206879549 absolute error = 1.4445369519e-22 relative error = 1.7384357129612524394486386009507e-20 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.55636102291278377572254337887577 y2[1] (numeric) = -0.5563610229127837757273551725516 absolute error = 4.81179367583e-21 relative error = 8.6486893899185062673543756131147e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=423.5MB, alloc=40.3MB, time=5.02 TOP MAIN SOLVE Loop x[1] = 0.6 y1[1] (closed_form) = -0.82533561490967829724095249895538 y1[1] (numeric) = -0.82533561490967829724075441965198 absolute error = 1.9807930340e-22 relative error = 2.3999849251831580357023464394235e-20 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.56464247339503535720094544565866 y2[1] (numeric) = -0.5646424733950353572068777950756 absolute error = 5.93234941694e-21 relative error = 1.0506381819402395017993723933786e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=465.5MB, alloc=40.3MB, time=5.50 TOP MAIN SOLVE Loop x[1] = 0.61 y1[1] (closed_form) = -0.81964801784547951790074657865482 y1[1] (numeric) = -0.81964801784547951790048309698317 absolute error = 2.6348167165e-22 relative error = 3.2145709611131116706408706742149e-20 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.57286746010048126119097603216272 y2[1] (numeric) = -0.5728674601004812611981430281133 absolute error = 7.16699595058e-21 relative error = 1.2510740179452512538128791137238e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=507.4MB, alloc=40.3MB, time=5.98 TOP MAIN SOLVE Loop x[1] = 0.62 y1[1] (closed_form) = -0.8138784566625339286839996543607 y1[1] (numeric) = -0.81387845666253392868365785719681 absolute error = 3.4179716389e-22 relative error = 4.1996094268375820817880658201422e-20 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.58103516053730507584296322758221 y2[1] (numeric) = -0.58103516053730507585147804828066 absolute error = 8.51482069845e-21 relative error = 1.4654570457622607397495594928893e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=549.3MB, alloc=40.3MB, time=6.47 TOP MAIN SOLVE Loop x[1] = 0.63 y1[1] (closed_form) = -0.80802750831215187252370896577706 y1[1] (numeric) = -0.80802750831215187252327481287238 absolute error = 4.3415290468e-22 relative error = 5.3729965900156075544932130025539e-20 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.58914475794226951311811209079462 y2[1] (numeric) = -0.58914475794226951312808697916968 absolute error = 9.97488837506e-21 relative error = 1.6931133207226877445144488600830e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=591.2MB, alloc=40.3MB, time=6.97 TOP MAIN SOLVE Loop x[1] = 0.64 y1[1] (closed_form) = -0.80209575788429261358611077926032 y1[1] (numeric) = -0.80209575788429261358556911270744 absolute error = 5.4166655288e-22 relative error = 6.7531407260994244823099519940650e-20 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.59719544136239205188354623920793 y2[1] (numeric) = -0.59719544136239205189509248036934 absolute error = 1.154624116141e-20 relative error = 1.9334108001677583017473120388829e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=633.2MB, alloc=40.3MB, time=7.45 TOP MAIN SOLVE Loop x[1] = 0.65 y1[1] (closed_form) = -0.79608379854905582891760457067991 y1[1] (numeric) = -0.79608379854905582891693912460266 absolute error = 6.6544607725e-22 relative error = 8.3589953527862714744730042433820e-20 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.60518640573603956037252167860594 y2[1] (numeric) = -0.60518640573603956038574957748786 absolute error = 1.322789888192e-20 relative error = 2.1857561168830238819523201165992e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=675.2MB, alloc=40.3MB, time=7.95 TOP MAIN SOLVE Loop x[1] = 0.66 y1[1] (closed_form) = -0.78999223149736509278381709123024 y1[1] (numeric) = -0.78999223149736509278301050169653 absolute error = 8.0658953371e-22 relative error = 1.0210094499045593021978273281274e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.6131168519734337886151454793963 y2[1] (numeric) = -0.61311685197343378863016433858099 absolute error = 1.501885918469e-20 relative error = 2.4495916457603360239523195502497e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=717.3MB, alloc=40.3MB, time=8.44 TOP MAIN SOLVE Loop x[1] = 0.67 y1[1] (closed_form) = -0.78382166588084928530294214483812 y1[1] (numeric) = -0.78382166588084928530197595999353 absolute error = 9.6618484459e-22 relative error = 1.2326590175384003775642935319370e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.62098598703655968035744391412659 y2[1] (numeric) = -0.62098598703655968037436201185186 absolute error = 1.691809772527e-20 relative error = 2.7243928330823946094203839120938e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=759.2MB, alloc=40.3MB, time=8.92 TOP MAIN SOLVE Loop x[1] = 0.68 y1[1] (closed_form) = -0.77757271875092793718239408404432 y1[1] (numeric) = -0.77757271875092793718124877446474 absolute error = 1.14530957958e-21 relative error = 1.4729292218736721390509672302087e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.62879302401846851370417818742025 y2[1] (numeric) = -0.62879302401846851372310275577381 absolute error = 1.892456835356e-20 relative error = 3.0096657613370977007559007734351e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=801.2MB, alloc=40.3MB, time=9.42 TOP MAIN SOLVE Loop x[1] = 0.69 y1[1] (closed_form) = -0.77124601499710660197353931549777 y1[1] (numeric) = -0.77124601499710660197219428475914 absolute error = 1.34503073863e-21 relative error = 1.7439710708068242044070425334062e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.63653718222196794023742920700872 y2[1] (numeric) = -0.63653718222196794025846641031275 absolute error = 2.103720330403e-20 relative error = 3.3049449256986344942918520470230e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=843.2MB, alloc=40.3MB, time=9.91 TOP MAIN SOLVE Loop x[1] = 0.7 y1[1] (closed_form) = -0.76484218728448842625585999019186 y1[1] (numeric) = -0.7648421872844884262542935856551 absolute error = 1.56640453676e-21 relative error = 2.0480101160755726267510126218430e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.64421768723769105367261435139872 y2[1] (numeric) = -0.6442176872376910536958692647879 absolute error = 2.325491338918e-20 relative error = 3.6097912009981572050452194360958e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=885.2MB, alloc=40.3MB, time=10.39 TOP MAIN SOLVE Loop x[1] = 0.71 y1[1] (closed_form) = -0.75836187599050816654145794413955 y1[1] (numeric) = -0.75836187599050816653964746794872 absolute error = 1.81047619083e-21 relative error = 2.3873512740409175588624059286114e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.65183377102153668121012797285284 y2[1] (numeric) = -0.65183377102153668123570456104919 absolute error = 2.557658819635e-20 relative error = 3.9237899804220094421222568150426e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=927.2MB, alloc=40.3MB, time=10.88 TOP MAIN SOLVE Loop x[1] = 0.72 y1[1] (closed_form) = -0.75180572914089497944548696225195 y1[1] (numeric) = -0.75180572914089497944340868254367 absolute error = 2.07827970828e-21 relative error = 2.7643839727783082336367333950381e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.65938467197147315361800383264817 y2[1] (numeric) = -0.6593846719714731536460049289357 absolute error = 2.800109628753e-20 relative error = 4.2465494691907862006855278010871e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=969.3MB, alloc=40.3MB, time=11.36 TOP MAIN SOLVE Loop x[1] = 0.73 y1[1] (closed_form) = -0.74517440234487038879013215855033 y1[1] (numeric) = -0.74517440234487038878776132087246 absolute error = 2.37083767787e-21 relative error = 3.1815876530508687939638360998966e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.66686963500369787373259413076153 y2[1] (numeric) = -0.66686963500369787376312141616399 absolute error = 3.052728540246e-20 relative error = 4.5776991184027628528540501226854e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1011.5MB, alloc=40.3MB, time=11.86 TOP MAIN SOLVE Loop x[1] = 0.74 y1[1] (closed_form) = -0.73846855872958790979142456069883 y1[1] (numeric) = -0.7384685587295879097887353996363 absolute error = 2.68916106253e-21 relative error = 3.6415376534869046583913195309296e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.67428791162814506748388115760817 y2[1] (numeric) = -0.67428791162814506751703514027299 absolute error = 3.315398266482e-20 relative error = 4.9168881857552402993445875220710e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1053.5MB, alloc=40.3MB, time=12.34 TOP MAIN SOLVE Loop x[1] = 0.75 y1[1] (closed_form) = -0.73168886887382088631183875300008 y1[1] (numeric) = -0.73168886887382088630880450400587 absolute error = 3.03424899421e-21 relative error = 4.1469115129223779666979975441169e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.68163876002333416673324195277989 y2[1] (numeric) = -0.68163876002333416676912194757152 absolute error = 3.587999479163e-20 relative error = 5.2637844113209964423067667527599e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1095.5MB, alloc=40.3MB, time=12.83 TOP MAIN SOLVE Loop x[1] = 0.76 y1[1] (closed_form) = -0.72483601074090517233968836666701 y1[1] (numeric) = -0.72483601074090517233628127809615 absolute error = 3.40708857086e-21 relative error = 4.7004957264435281074368658138712e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.68892144511055133914775563876973 y2[1] (numeric) = -0.68892144511055133918645974707522 absolute error = 3.870410830549e-20 relative error = 5.6180727977308276835267900582254e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1137.5MB, alloc=40.3MB, time=13.33 TOP MAIN SOLVE Loop x[1] = 0.77 y1[1] (closed_form) = -0.71791066961094336337129056532434 y1[1] (numeric) = -0.71791066961094336336748191066874 absolute error = 3.80865465560e-21 relative error = 5.3051929952009496437475577584881e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.69613523862735674701988373445221 y2[1] (numeric) = -0.69613523862735674706150882420237 absolute error = 4.162508975016e-20 relative error = 5.9794544853434770172077730615608e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1179.4MB, alloc=40.3MB, time=13.81 TOP MAIN SOLVE Loop x[1] = 0.78 y1[1] (closed_form) = -0.71091353801227735721626502376456 y1[1] (numeric) = -0.71091353801227735721202511408656 absolute error = 4.23990967800e-21 relative error = 5.9640300139097610954072220869090e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.70327941920041018436789732511792 y2[1] (numeric) = -0.70327941920041018441253901102682 absolute error = 4.464168590890e-20 relative error = 6.3476457137982409125434698963347e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1221.4MB, alloc=40.3MB, time=14.30 TOP MAIN SOLVE Loop x[1] = 0.79 y1[1] (closed_form) = -0.70384531565223609691278086108495 y1[1] (numeric) = -0.70384531565223609690807905764735 absolute error = 4.70180343760e-21 relative error = 6.6801658447395571606482904113928e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.7103532724176078098140288749692 y2[1] (numeric) = -0.71035327241760780986178149899514 absolute error = 4.775262402594e-20 relative error = 6.7223768623489678552081675583500e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1263.4MB, alloc=40.3MB, time=14.78 TOP MAIN SOLVE Loop x[1] = 0.8 y1[1] (closed_form) = -0.69670670934716542092074998164232 y1[1] (numeric) = -0.69670670934716542091555470873273 absolute error = 5.19527290959e-21 relative error = 7.4569009310361353926800030654840e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.71735609089952276162717461058139 y2[1] (numeric) = -0.71735609089952276167813122261229 absolute error = 5.095661203090e-20 relative error = 7.1033915620627652372396137624754e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1305.4MB, alloc=40.3MB, time=15.28 TOP MAIN SOLVE Loop x[1] = 0.81 y1[1] (closed_form) = -0.6894984329517470175496392406801 y1[1] (numeric) = -0.68949843295174701754391799862726 absolute error = 5.72124205284e-21 relative error = 8.2976868103199708592187032578866e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.72428717437014251092817685251454 y2[1] (numeric) = -0.72428717437014251098242919128058 absolute error = 5.425233876604e-20 relative error = 7.4904458736576599330374893491031e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1347.4MB, alloc=40.3MB, time=15.77 TOP MAIN SOLVE Loop x[1] = 0.82 y1[1] (closed_form) = -0.68222120728761355166655797843693 y1[1] (numeric) = -0.68222120728761355166027735681676 absolute error = 6.28062162017e-21 relative error = 9.2061365918843246361889887926750e-19 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.73114582972689587938131336468772 y2[1] (numeric) = -0.73114582972689587943895183890414 absolute error = 5.763847421642e-20 relative error = 7.8833075253878747681399348270061e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1389.4MB, alloc=40.3MB, time=16.25 TOP MAIN SOLVE Loop x[1] = 0.83 y1[1] (closed_form) = -0.67487576007126710211246291786445 y1[1] (numeric) = -0.67487576007126710210558860889351 absolute error = 6.87430897094e-21 relative error = 1.0186036271645125782718015761090e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.73793137110996271872858022613808 y2[1] (numeric) = -0.73793137110996271878969389588113 absolute error = 6.111366974305e-20 relative error = 8.2817552059245841192350663005985e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1431.4MB, alloc=40.3MB, time=16.73 TOP MAIN SOLVE Loop x[1] = 0.84 y1[1] (closed_form) = -0.66746282584130811792267103687086 y1[1] (numeric) = -0.6674628258413081179151678489849 absolute error = 7.50318788596e-21 relative error = 1.1241356964715683048143001474169e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.74464311997085932125657267062965 y2[1] (numeric) = -0.74464311997085932132124922894836 absolute error = 6.467655831871e-20 relative error = 8.6855779076077458897446162682196e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1473.5MB, alloc=40.3MB, time=17.22 TOP MAIN SOLVE Loop x[1] = 0.85 y1[1] (closed_form) = -0.65998314588498217039541602946147 y1[1] (numeric) = -0.65998314588498217038724790107665 absolute error = 8.16812838482e-21 relative error = 1.2376268145252744833989019323840e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.75128040514029270271207152423547 y2[1] (numeric) = -0.75128040514029270278039727900203 absolute error = 6.832575476656e-20 relative error = 9.0945743159374662369922236999596e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1515.5MB, alloc=40.3MB, time=17.72 TOP MAIN SOLVE Loop x[1] = 0.86 y1[1] (closed_form) = -0.65243746816405184627203066422386 y1[1] (numeric) = -0.65243746816405184626316067767822 absolute error = 8.86998654564e-21 relative error = 1.3595151993033131897314697668766e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.75784256289527697229458872952865 y2[1] (numeric) = -0.75784256289527697236664858553024 absolute error = 7.205985600159e-20 relative error = 9.5085522415488352292903204363697e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1557.6MB, alloc=40.3MB, time=18.20 TOP MAIN SOLVE Loop x[1] = 0.87 y1[1] (closed_form) = -0.64482654724000119477766380548283 y1[1] (numeric) = -0.6448265472400011947680542011557 absolute error = 9.60960432713e-21 relative error = 1.4902618957394372978426845050826e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.76432893702550507814480282372285 y2[1] (numeric) = -0.76432893702550507822068026499755 absolute error = 7.587744127470e-20 relative error = 9.9273280912257319406764674822370e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1599.6MB, alloc=40.3MB, time=18.69 TOP MAIN SOLVE Loop x[1] = 0.88 y1[1] (closed_form) = -0.63715114419858020801549860572209 y1[1] (numeric) = -0.63715114419858020800511079632888 absolute error = 1.038780939321e-20 relative error = 1.6303524662544500871407210887900e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.77073887889896929120964513075599 y2[1] (numeric) = -0.77073887889896929128942220317556 absolute error = 7.977707241957e-20 relative error = 1.0350726374869615500670879809491e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1641.6MB, alloc=40.3MB, time=19.17 TOP MAIN SOLVE Loop x[1] = 0.89 y1[1] (closed_form) = -0.62941202657369688020355305738025 y1[1] (numeric) = -0.62941202657369688019234764244013 absolute error = 1.120541494012e-20 relative error = 1.7802988292293101432432857527398e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.77707174752682386549033371297318 y2[1] (numeric) = -0.77707174752682386557409100707524 absolute error = 8.375729410206e-20 relative error = 1.0778579245563006188357292311617e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1683.7MB, alloc=40.3MB, time=19.67 TOP MAIN SOLVE Loop x[1] = 0.9 y1[1] (closed_form) = -0.62160996827066445648471615140713 y1[1] (numeric) = -0.62160996827066445647265293188121 absolute error = 1.206321952592e-20 relative error = 1.9406412608665525580756779306408e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.78332690962748338846138231571355 y2[1] (numeric) = -0.78332690962748338854919894978583 absolute error = 8.781663407228e-20 relative error = 1.1210726070171879692666337896776e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1725.8MB, alloc=40.3MB, time=20.16 TOP MAIN SOLVE Loop x[1] = 0.91 y1[1] (closed_form) = -0.61374574948881154652117822617468 y1[1] (numeric) = -0.61374574948881154650821621927195 absolute error = 1.296200690273e-20 relative error = 2.1119505778290191821354695101850e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.78950373968995041187895751787155 y2[1] (numeric) = -0.78950373968995041197091112129087 absolute error = 9.195360341932e-20 relative error = 1.1647013028137335476351760712582e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1767.8MB, alloc=40.3MB, time=20.64 TOP MAIN SOLVE Loop x[1] = 0.92 y1[1] (closed_form) = -0.60582015664346284179740470667438 y1[1] (numeric) = -0.60582015664346284178350216082315 absolute error = 1.390254585123e-20 relative error = 2.2948305200435784644467043776568e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.79560162003636603026827610248162 y2[1] (numeric) = -0.79560162003636603036444279930995 absolute error = 9.616669682833e-20 relative error = 1.2087292736273504755421644130158e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1809.9MB, alloc=40.3MB, time=21.14 TOP MAIN SOLVE Loop x[1] = 0.93 y1[1] (closed_form) = -0.59783398228729823849490708443298 y1[1] (numeric) = -0.59783398228729823848002149441488 absolute error = 1.488559001810e-20 relative error = 2.4899203556726727986878279804612e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.80161994088377715208431921591065 y2[1] (numeric) = -0.80161994088377715218477360875087 absolute error = 1.0045439284022e-19 relative error = 1.2531423897647822827580147027215e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1851.9MB, alloc=40.3MB, time=21.62 TOP MAIN SOLVE Loop x[1] = 0.94 y1[1] (closed_form) = -0.58978802503109822996098981522402 y1[1] (numeric) = -0.58978802503109822994507793746825 absolute error = 1.591187775577e-20 relative error = 2.6978977328220595117940323276191e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.80755810040511428687021979863415 y2[1] (numeric) = -0.80755810040511428697503495274804 absolute error = 1.0481515411389e-19 relative error = 1.2979270972739808932364331765446e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1894.0MB, alloc=40.3MB, time=22.11 TOP MAIN SOLVE Loop x[1] = 0.95 y1[1] (closed_form) = -0.58168308946388349416618097376046 y1[1] (numeric) = -0.58168308946388349414919884179554 absolute error = 1.698213196492e-20 relative error = 2.9194818059042809455348116473205e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.81341550478937375068542210210256 y2[1] (numeric) = -0.81341550478937375079466952979339 absolute error = 1.0924742769083e-19 relative error = 1.3430703871217525884325661005400e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1936.1MB, alloc=40.3MB, time=22.59 TOP MAIN SOLVE Loop x[1] = 0.96 y1[1] (closed_form) = -0.57351998607245666212505080035186 y1[1] (numeric) = -0.57351998607245666210695374041217 absolute error = 1.809705993969e-20 relative error = 3.1554366681484184432222628737010e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.81919156830099827163322214643043 y2[1] (numeric) = -0.8191915683009982717469717916924 absolute error = 1.1374964526197e-19 relative error = 1.3885597662813662045528743494832e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=1978.1MB, alloc=40.3MB, time=23.09 TOP MAIN SOLVE Loop x[1] = 0.97 y1[1] (closed_form) = -0.56529953116035431303652775484986 y1[1] (numeric) = -0.56529953116035431301727040163434 absolute error = 1.925735321552e-20 relative error = 3.4065751259322042244429499905884e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.82488571333845005747662003785634 y2[1] (numeric) = -0.82488571333845005759494026129349 absolute error = 1.1832022343715e-19 relative error = 1.4343832305967371181285502379502e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2020.2MB, alloc=40.3MB, time=23.58 TOP MAIN SOLVE Loop x[1] = 0.98 y1[1] (closed_form) = -0.55702254676621730087665826735994 y1[1] (numeric) = -0.55702254676621730085619457994029 absolute error = 2.046368741965e-20 relative error = 3.6737628554627649503192558558850e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.83049737049197046808453328771915 y2[1] (numeric) = -0.83049737049197046820749085173582 absolute error = 1.2295756401667e-19 relative error = 1.4805292392898527025241912254660e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2062.2MB, alloc=40.3MB, time=24.06 TOP MAIN SOLVE Loop x[1] = 0.99 y1[1] (closed_form) = -0.54868986058158757534312640865361 y1[1] (numeric) = -0.54868986058158757532140968652919 absolute error = 2.171672212442e-20 relative error = 3.9579229879336956692671881604403e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.83602597860052051678925941154711 y2[1] (numeric) = -0.83602597860052051691691946581248 absolute error = 1.2766005426537e-19 relative error = 1.5269866910005434821428867783864e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2104.3MB, alloc=40.3MB, time=24.56 TOP MAIN SOLVE Loop x[1] = 1 y1[1] (closed_form) = -0.54030230586813971740093660744298 y1[1] (numeric) = -0.54030230586813971737791950673968 absolute error = 2.301710070330e-20 relative error = 4.2600411757112327285031602609933e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.8414709848078965066525023216303 y2[1] (numeric) = -0.84147098480789650678492838881895 absolute error = 1.3242606718865e-19 relative error = 1.5737449012443630402382262605507e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2146.3MB, alloc=40.3MB, time=25.05 TOP MAIN SOLVE Loop memory used=2188.3MB, alloc=40.3MB, time=25.53 x[1] = 1.01 y1[1] (closed_form) = -0.53186072137435546620673135577918 y1[1] (numeric) = -0.53186072137435546618236590558952 absolute error = 2.436545018966e-20 relative error = 4.5811711996137679055937224635412e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.84683184461801519012309878478201 y2[1] (numeric) = -0.8468318446180151902603527465929 absolute error = 1.3725396181089e-19 relative error = 1.6207935811955896958063724948403e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=2230.4MB, alloc=40.3MB, time=26.03 x[1] = 1.02 y1[1] (closed_form) = -0.52336595125164956988961380803381 y1[1] (numeric) = -0.52336595125164956986385142689543 absolute error = 2.576238113838e-20 relative error = 4.9224411860894439285250159339416e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.85210802194936292361654998545538 y2[1] (numeric) = -0.85210802194936292375869206891141 absolute error = 1.4214208345603e-19 relative error = 1.6681228177015904945170570192116e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=2272.5MB, alloc=40.3MB, time=26.51 x[1] = 1.03 y1[1] (closed_form) = -0.51481884496995534753350229983735 y1[1] (numeric) = -0.51481884496995534750629381234707 absolute error = 2.720848749028e-20 relative error = 5.2850605132506130508587435888279e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.85729898918860337214627438529442 y2[1] (numeric) = -0.85729898918860337229336314932461 absolute error = 1.4708876403019e-19 relative error = 1.7157230544433884154071608576507e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=2314.6MB, alloc=40.3MB, time=27.00 x[1] = 1.04 y1[1] (closed_form) = -0.50622025723277840373447342099217 y1[1] (numeric) = -0.50622025723277840370576907455287 absolute error = 2.870434643930e-20 relative error = 5.6703274966139298860308481471767e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.86240422724333840328079169211617 y2[1] (numeric) = -0.86240422724333840343288401442255 absolute error = 1.5209232230638e-19 relative error = 1.7635850741657508411106959890427e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=2356.6MB, alloc=40.3MB, time=27.50 x[1] = 1.05 y1[1] (closed_form) = -0.4975710478917269902908495728121 y1[1] (numeric) = -0.49757104789172699026059905450942 absolute error = 3.025051830268e-20 relative error = 6.0796379594141110473287897896759e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.86742322559401689438140948500027 y2[1] (numeric) = -0.86742322559401689453856054921157 absolute error = 1.5715106421130e-19 relative error = 1.8116999819053952621544129711989e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2398.6MB, alloc=40.3MB, time=27.98 TOP MAIN SOLVE Loop x[1] = 1.06 y1[1] (closed_form) = -0.48887208186052756191863753995641 y1[1] (numeric) = -0.48887208186052756188678999356256 absolute error = 3.184754639385e-20 relative error = 6.5144948086718367236070558296969e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.87235548234498626228294592199742 y2[1] (numeric) = -0.87235548234498626244520920511156 absolute error = 1.6226328311414e-19 relative error = 1.8600591891502610316719535765069e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2440.6MB, alloc=40.3MB, time=28.47 TOP MAIN SOLVE Loop x[1] = 1.07 y1[1] (closed_form) = -0.48012422902853412436509306817592 y1[1] (numeric) = -0.48012422902853412433159711127754 absolute error = 3.349595689838e-20 relative error = 6.9765187576878798718835942020486e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.87720050427468161030706325777682 y2[1] (numeric) = -0.87720050427468161047449051789411 absolute error = 1.6742726011729e-19 relative error = 1.9086543988677732636133326083330e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2482.6MB, alloc=40.3MB, time=28.95 TOP MAIN SOLVE Loop x[1] = 1.08 y1[1] (closed_form) = -0.47132836417374002391352478852603 y1[1] (numeric) = -0.47132836417374002387832852977324 absolute error = 3.519625875279e-20 relative error = 7.4674603584468412317959871715545e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.88195780688494747373533498762476 y2[1] (numeric) = -0.88195780688494747390797625197372 absolute error = 1.7264126434896e-19 relative error = 1.9574775913456058811107995856314e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2524.7MB, alloc=40.3MB, time=29.45 TOP MAIN SOLVE Loop x[1] = 1.09 y1[1] (closed_form) = -0.46248536687530087702789707387514 y1[1] (numeric) = -0.46248536687530087699094813034898 absolute error = 3.694894352616e-20 relative error = 7.9892135346462711349032680758575e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.88662691444948723160860062863605 y2[1] (numeric) = -0.8866269144494872317865041818939 absolute error = 1.7790355325785e-19 relative error = 2.0065210107941686346029848592488e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2566.6MB, alloc=40.3MB, time=29.94 TOP MAIN SOLVE Loop x[1] = 1.1 y1[1] (closed_form) = -0.45359612142557738777137005178472 y1[1] (numeric) = -0.45359612142557738773261556647975 absolute error = 3.875448530497e-20 relative error = 8.5438308385819260349358893574575e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.8912073600614353399518025778717 y2[1] (numeric) = -0.891207360061435340135014950781 absolute error = 1.8321237290930e-19 relative error = 2.0557771526558113610747576021867e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2608.6MB, alloc=40.3MB, time=30.42 TOP MAIN SOLVE Loop x[1] = 1.11 y1[1] (closed_form) = -0.44466151674170684864373751193357 y1[1] (numeric) = -0.44466151674170684860312417135298 absolute error = 4.061334058059e-20 relative error = 9.1335406936466035778010554732413e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.89569868568004762924062595933937 y2[1] (numeric) = -0.89569868568004762942919191762304 absolute error = 1.8856595828367e-19 relative error = 2.1052387515842310050948088831442e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2650.7MB, alloc=40.3MB, time=30.91 TOP MAIN SOLVE Loop x[1] = 1.12 y1[1] (closed_form) = -0.43568244627671216761398879396113 y1[1] (numeric) = -0.43568244627671216757146284582102 absolute error = 4.252594814011e-20 relative error = 9.7607669309451063469360864463821e-18 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.90010044217650499711910324733915 y2[1] (numeric) = -0.90010044217650499731306578091525 absolute error = 1.9396253357610e-19 relative error = 2.1548987700426544161186648447526e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2692.8MB, alloc=40.3MB, time=31.41 TOP MAIN SOLVE Loop x[1] = 1.13 y1[1] (closed_form) = -0.42665980793015731037121583565354 y1[1] (numeric) = -0.4266598079301573103267231066937 absolute error = 4.449272895984e-20 relative error = 1.0428150984196594661645145816240e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.9044121893788259160370815224114 y2[1] (numeric) = -0.90441218937882591623648183490962 absolute error = 1.9940031249822e-19 relative error = 2.2047503874884015023227377805737e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2734.9MB, alloc=40.3MB, time=31.89 TOP MAIN SOLVE Loop x[1] = 1.14 y1[1] (closed_form) = -0.41759450395835809217518674082258 y1[1] (numeric) = -0.4175945039583580921286726547205 absolute error = 4.651408610208e-20 relative error = 1.1138577175028701057861896654935e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.9086334961158832645942155781022 y2[1] (numeric) = -0.9086334961158832647990930766836 absolute error = 2.0487749858140e-19 relative error = 2.2547869901031118520665742078300e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2776.9MB, alloc=40.3MB, time=32.45 TOP MAIN SOLVE Loop x[1] = 1.15 y1[1] (closed_form) = -0.40848744088415729815257671880992 y1[1] (numeric) = -0.40848744088415729810398631419511 absolute error = 4.859040461481e-20 relative error = 1.1895201602682742681125828127559e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.91276394026052108094403304975368 y2[1] (numeric) = -0.91276394026052108115442533523533 absolute error = 2.1039228548165e-19 relative error = 2.3050021610362897831267234842066e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2818.9MB, alloc=40.3MB, time=32.94 TOP MAIN SOLVE Loop x[1] = 1.16 y1[1] (closed_form) = -0.39933952940627315445163962339401 y1[1] (numeric) = -0.39933952940627315440091757195955 absolute error = 5.072205143446e-20 relative error = 1.2701485252379629867031640017383e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.91680310877176692661866166687433 y2[1] (numeric) = -0.91680310877176692683460452416053 absolute error = 2.1594285728620e-19 relative error = 2.3553896711312066718274349306988e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2861.0MB, alloc=40.3MB, time=33.44 TOP MAIN SOLVE Loop x[1] = 1.17 y1[1] (closed_form) = -0.3901516843082302153326619350505 y1[1] (numeric) = -0.39015168430823021527975255975873 absolute error = 5.290937529177e-20 relative error = 1.3561232059162452627599471820293e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.92075059773613563957301300896203 y2[1] (numeric) = -0.92075059773613563979454039778343 absolute error = 2.2152738882140e-19 relative error = 2.4059434701000788651797791269158e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2903.0MB, alloc=40.3MB, time=33.92 TOP MAIN SOLVE Loop x[1] = 1.18 y1[1] (closed_form) = -0.38092482436688177302959946671276 y1[1] (numeric) = -0.38092482436688177297444676009201 absolute error = 5.515270662075e-20 relative error = 1.4478632814864944380305885867278e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.92460601240802034610753802587476 y2[1] (numeric) = -0.92460601240802034633468207183713 absolute error = 2.2714404596237e-19 relative error = 2.4566576781260791584635039483007e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2944.9MB, alloc=40.3MB, time=34.41 TOP MAIN SOLVE Loop x[1] = 1.19 y1[1] (closed_form) = -0.37165987226053293806567955835047 y1[1] (numeric) = -0.37165987226053293800822720087977 absolute error = 5.745235747070e-20 relative error = 1.5458315992323754330336236756573e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.92836896724916669260202111160267 y2[1] (numeric) = -0.92836896724916669283481209754656 absolute error = 2.3279098594389e-19 relative error = 2.5075265778612652570307686331719e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=2986.7MB, alloc=40.3MB, time=34.89 TOP MAIN SOLVE Loop x[1] = 1.2 y1[1] (closed_form) = -0.36235775447667357763837335562308 y1[1] (numeric) = -0.36235775447667357757856473420177 absolute error = 5.980862142131e-20 relative error = 1.6505406792711571707505024619135e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.93203908596722634967013443549483 y2[1] (numeric) = -0.93203908596722634990860079316766 absolute error = 2.3846635767283e-19 relative error = 2.5585446068000552138825521214185e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3028.5MB, alloc=40.3MB, time=35.37 TOP MAIN SOLVE Loop x[1] = 1.21 y1[1] (closed_form) = -0.35301940121933033870301071366479 y1[1] (numeric) = -0.35301940121933033864078894016371 absolute error = 6.222177350108e-20 relative error = 1.7625596011484286828073555814313e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.93561600155338593341646488854361 y2[1] (numeric) = -0.93561600155338593366063319058551 absolute error = 2.4416830204190e-19 relative error = 2.6097063500037610147288332803635e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3070.4MB, alloc=40.3MB, time=35.86 TOP MAIN SOLVE Loop x[1] = 1.22 y1[1] (closed_form) = -0.3436457463160470204755229744352 y1[1] (numeric) = -0.34364574631604702041083090432657 absolute error = 6.469207010863e-20 relative error = 1.8825220682095523724683376229908e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.93909935631906758093524527188837 y2[1] (numeric) = -0.93909935631906758118514022413307 absolute error = 2.4989495224470e-19 relative error = 2.6610065331553257742977801195357e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3112.3MB, alloc=40.3MB, time=36.34 TOP MAIN SOLVE Loop x[1] = 1.23 y1[1] (closed_form) = -0.33423772712450259823954724549766 y1[1] (numeric) = -0.33423772712450259817232749656031 absolute error = 6.721974893735e-20 relative error = 2.0111358916796019142180227754503e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.94248880193169751002382356538924 y2[1] (numeric) = -0.9424888019316975102794679994813 absolute error = 2.5564443409206e-19 relative error = 2.7124400159248432184541609573376e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3154.1MB, alloc=40.3MB, time=36.83 TOP MAIN SOLVE Loop x[1] = 1.24 y1[1] (closed_form) = -0.32479628443877623657769341569738 y1[1] (numeric) = -0.32479628443877623650788838679418 absolute error = 6.980502890320e-20 relative error = 2.1491941948725763731311196403407e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.94578399944953898628470596308179 y2[1] (numeric) = -0.94578399944953898654612082941139 absolute error = 2.6141486632960e-19 relative error = 2.7640017856270302995473997595232e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3195.9MB, alloc=40.3MB, time=37.31 TOP MAIN SOLVE Loop x[1] = 1.25 y1[1] (closed_form) = -0.31532236239526866544753855243804 y1[1] (numeric) = -0.31532236239526866537509044236252 absolute error = 7.244811007552e-20 relative error = 2.2975887128710369603159872843841e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.94898461935558621434849084703605 y2[1] (numeric) = -0.94898461935558621461569520799256 absolute error = 2.6720436095651e-19 relative error = 2.8156869511537157339836781480276e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3237.7MB, alloc=40.3MB, time=37.80 TOP MAIN SOLVE Loop x[1] = 1.26 y1[1] (closed_form) = -0.30581690837828932688634248917648 y1[1] (numeric) = -0.30581690837828932681119331556521 absolute error = 7.514917361127e-20 relative error = 2.4573256596496617847911532262705e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.95209034159051576385681622142542 y2[1] (numeric) = -0.95209034159051576412982724497083 absolute error = 2.7301102354541e-19 relative error = 2.8674907371639867492272598638504e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3279.5MB, alloc=40.3MB, time=38.28 TOP MAIN SOLVE Loop x[1] = 1.27 y1[1] (closed_form) = -0.29628087292531873355113701608796 y1[1] (numeric) = -0.2962808729253187334732286343956 absolute error = 7.790838169236e-20 relative error = 2.6295447601167886827088341745080e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.95510085558469223509018174218289 y2[1] (numeric) = -0.95510085558469223536901469574626 absolute error = 2.7883295356337e-19 relative error = 2.9194084785179514173444145387507e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3321.4MB, alloc=40.3MB, time=38.78 TOP MAIN SOLVE Loop x[1] = 1.28 y1[1] (closed_form) = -0.28671520963195551277938689359259 y1[1] (numeric) = -0.28671520963195551269866101612642 absolute error = 8.072587746617e-20 relative error = 2.8155422089324971233111533717092e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.95801586028922496370075385916029 y2[1] (numeric) = -0.95801586028922496398542210385422 absolute error = 2.8466824469393e-19 relative error = 2.9714356149384485577621856846810e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3363.3MB, alloc=40.3MB, time=39.28 TOP MAIN SOLVE Loop x[1] = 1.29 y1[1] (closed_form) = -0.27712087505655764138660609006118 y1[1] (numeric) = -0.27712087505655764130300430507184 absolute error = 8.360178498934e-20 relative error = 3.0167985350175333789662714233328e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.96083506420607265890556129128537 y2[1] (numeric) = -0.96083506420607265919607627644554 absolute error = 2.9051498516017e-19 relative error = 3.0235676858881009442304283869563e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3405.1MB, alloc=40.3MB, time=39.76 TOP MAIN SOLVE Loop x[1] = 1.3 y1[1] (closed_form) = -0.26749882862458740699798410929287 y1[1] (numeric) = -0.26749882862458740691144790011807 absolute error = 8.653620917480e-20 relative error = 3.2350126398589374143530934143459e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.96355818541719296470134863003955 y2[1] (numeric) = -0.96355818541719296499771988808819 absolute error = 2.9637125804864e-19 relative error = 3.0758003256473792948100962564061e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3446.9MB, alloc=40.3MB, time=40.25 TOP MAIN SOLVE Loop x[1] = 1.31 y1[1] (closed_form) = -0.2578500325326696613381769786162 y1[1] (numeric) = -0.25785003253266966124864774287419 absolute error = 8.952923574201e-20 relative error = 3.4721436667131940047011004860305e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.9661849516127340291692578059375 y2[1] (numeric) = -0.96618495161273402947149294757186 absolute error = 3.0223514163436e-19 relative error = 3.1281292585842487994055188944927e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3488.7MB, alloc=40.3MB, time=40.73 TOP MAIN SOLVE Loop x[1] = 1.32 y1[1] (closed_form) = -0.24817545165237295957398272942735 y1[1] (numeric) = -0.2481754516523729594814017982569 absolute error = 9.258093117045e-20 relative error = 3.7304628863990535720591771860363e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.96871510011826526273589984597277 y2[1] (numeric) = -0.96871510011826526304400455567933 absolute error = 3.0810470970656e-19 relative error = 3.1805502946010146675366858047040e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3530.6MB, alloc=40.3MB, time=41.22 TOP MAIN SOLVE Loop x[1] = 1.33 y1[1] (closed_form) = -0.23847605343372320751578498601058 y1[1] (numeric) = -0.23847605343372320742009364335408 absolute error = 9.569134265650e-20 relative error = 4.0126185115309428097654091162737e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.9711483779210445623376830377638 y2[1] (numeric) = -0.97114837792104456265166106965904 absolute error = 3.1397803189524e-19 relative error = 3.2330593247488980658872955382290e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3572.4MB, alloc=40.3MB, time=41.72 TOP MAIN SOLVE Loop x[1] = 1.34 y1[1] (closed_form) = -0.22875280780845946523263949230014 y1[1] (numeric) = -0.2287528078084594651337789942268 absolute error = 9.886049807334e-20 relative error = 4.3217173603446391543914854826124e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.97348454169531937478787034808955 y2[1] (numeric) = -0.9734845416953193751077235220882 absolute error = 3.1985317399865e-19 relative error = 3.2856523170016341175489772607611e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3614.2MB, alloc=40.3MB, time=42.20 TOP MAIN SOLVE Loop x[1] = 1.35 y1[1] (closed_form) = -0.21900668709304158142002217301063 y1[1] (numeric) = -0.21900668709304158131793376707625 absolute error = 1.0208840593438e-19 relative error = 4.6614287120378808385668078615602e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.97572335782665906926111353926522 y2[1] (numeric) = -0.97572335782665906958684173757648 absolute error = 3.2572819831126e-19 relative error = 3.3383253121744661735580851631842e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3656.0MB, alloc=40.3MB, time=42.69 TOP MAIN SOLVE Loop x[1] = 1.36 y1[1] (closed_form) = -0.20923866589141935767597525239186 y1[1] (numeric) = -0.20923866589141935757060019703207 absolute error = 1.0537505535979e-19 relative error = 5.0361177228339091837103888465964e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.97786460243531618567849243942663 y2[1] (numeric) = -0.97786460243531618601009360337933 absolute error = 3.3160116395270e-19 relative error = 3.3910744199847929643538869129142e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3697.9MB, alloc=40.3MB, time=43.17 TOP MAIN SOLVE Loop x[1] = 1.37 y1[1] (closed_form) = -0.19944972099757296568819838964531 y1[1] (numeric) = -0.19944972099757296557947797359886 absolute error = 1.0872041604645e-19 relative error = 5.4510187080067653212641240189791e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.97990806139861422288768850489193 y2[1] (numeric) = -0.97990806139861422322515863208897 absolute error = 3.3747012719704e-19 relative error = 3.4438958152397668110437535036469e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3739.7MB, alloc=40.3MB, time=43.66 TOP MAIN SOLVE Loop x[1] = 1.38 y1[1] (closed_form) = -0.1896408312978343632091500735982 y1[1] (numeric) = -0.18964083129783436309702563535707 absolute error = 1.1212443824113e-19 relative error = 5.9124629160181510299858337865781e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.98185353037235972787813108520605 y2[1] (numeric) = -0.98185353037235972822146422700892 absolute error = 3.4333314180287e-19 relative error = 3.4967857341477784528458153897778e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3781.5MB, alloc=40.3MB, time=44.14 TOP MAIN SOLVE Loop x[1] = 1.39 y1[1] (closed_form) = -0.17981297767299947659616321780405 y1[1] (numeric) = -0.17981297767299947648057616508703 absolute error = 1.1558705271702e-19 relative error = 6.4281818928120908129591175978668e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.98370081481127654484003822444291 y2[1] (numeric) = -0.98370081481127654518922648378679 absolute error = 3.4918825934388e-19 relative error = 3.5497404707433522727739476841513e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3823.4MB, alloc=40.3MB, time=44.63 TOP MAIN SOLVE Loop x[1] = 1.4 y1[1] (closed_form) = -0.16996714290024093861674803520365 y1[1] (numeric) = -0.16996714290024093849763986445022 absolute error = 1.1910817075343e-19 relative error = 7.0077174164972774291372055009326e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.9854497299884601806594745788061 y2[1] (numeric) = -0.98544972998846018101450810834598 absolute error = 3.5503352953988e-19 relative error = 3.6027563734178253391750061642463e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3865.2MB, alloc=40.3MB, time=45.13 TOP MAIN SOLVE Loop x[1] = 1.41 y1[1] (closed_form) = -0.16010431155483119016356254936092 y1[1] (numeric) = -0.16010431155483119004087486524186 absolute error = 1.2268768411906e-19 relative error = 7.6629843960849826668025226523224e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.98710010101385034142908886194224 y2[1] (numeric) = -0.98710010101385034178995586253057 absolute error = 3.6086700058833e-19 relative error = 3.6558298415498445060820460993233e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3907.0MB, alloc=40.3MB, time=45.61 TOP MAIN SOLVE Loop x[1] = 1.42 y1[1] (closed_form) = -0.15022546991168577348698210297591 y1[1] (numeric) = -0.15022546991168577336065663791765 absolute error = 1.2632546505826e-19 relative error = 8.4090577405099110693841647452462e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.9886517628517197927362734733357 y2[1] (numeric) = -0.98865176285171979310296019283185 absolute error = 3.6668671949615e-19 relative error = 3.7089573222269821213803196769100e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3948.7MB, alloc=40.3MB, time=46.09 TOP MAIN SOLVE Loop x[1] = 1.43 y1[1] (closed_form) = -0.14033160584673666253389762457492 y1[1] (numeric) = -0.14033160584673666240387625829392 absolute error = 1.3002136628100e-19 relative error = 9.2652945497540302168407521744264e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.99010456033717779485729149548183 y2[1] (numeric) = -0.99010456033717779522978222789396 absolute error = 3.7249073241213e-19 relative error = 3.7621353070556421972364406897508e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=3990.5MB, alloc=40.3MB, time=46.58 TOP MAIN SOLVE Loop x[1] = 1.44 y1[1] (closed_form) = -0.13042370873814549297752015612917 y1[1] (numeric) = -0.13042370873814549284374493517343 absolute error = 1.3377522095574e-19 relative error = 1.0256971086777129666446264124422e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99145834819168646252760446395798 y2[1] (numeric) = -0.99145834819168646290588154891735 absolute error = 3.7827708495937e-19 relative error = 3.8153603290476778306946018735873e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4032.3MB, alloc=40.3MB, time=47.06 TOP MAIN SOLVE Loop x[1] = 1.45 y1[1] (closed_form) = -0.12050276936736657053286662724802 y1[1] (numeric) = -0.12050276936736657039527978454206 absolute error = 1.3758684270596e-19 relative error = 1.1417732839525925279632965238565e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99271299103758849766535413432301 y2[1] (numeric) = -0.99271299103758849804939795689122 absolute error = 3.8404382256821e-19 relative error = 3.8686289595828247294334033742750e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4074.1MB, alloc=40.3MB, time=47.55 TOP MAIN SOLVE Loop x[1] = 1.46 y1[1] (closed_form) = -0.11056977982006955117464810912337 y1[1] (numeric) = -0.11056977982006955103319208351351 absolute error = 1.4145602560986e-19 relative error = 1.2793371375076599171192542648593e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99386836341164484228683230125003 y2[1] (numeric) = -0.99386836341164484267662129205929 absolute error = 3.8978899080926e-19 relative error = 3.9219378054376749797214775575184e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4115.9MB, alloc=40.3MB, time=48.03 TOP MAIN SOLVE Loop x[1] = 1.47 y1[1] (closed_form) = -0.10062573338693170090697460146241 y1[1] (numeric) = -0.10062573338693170076159205725894 absolute error = 1.4538254420347e-19 relative error = 1.4447849402939197034946508567679e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99492434977758089785992846273557 y2[1] (numeric) = -0.99492434977758089825543909846207 absolute error = 3.9551063572650e-19 relative error = 3.9752835058757773775756178845178e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4157.7MB, alloc=40.3MB, time=48.51 TOP MAIN SOLVE Loop x[1] = 1.48 y1[1] (closed_form) = -0.090671624464309655776226540647838 y1[1] (numeric) = -0.09067162446430965562686038716087 absolute error = 1.49366153486968e-19 relative error = 1.6473307318516367915100668634830e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99588084453764005648407513256269 y2[1] (numeric) = -0.99588084453764005688528193673351 absolute error = 4.0120680417082e-19 relative error = 4.0286627297976519190847114120990e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4199.5MB, alloc=40.3MB, time=49.00 TOP MAIN SOLVE Loop memory used=4241.2MB, alloc=40.3MB, time=49.48 x[1] = 1.49 y1[1] (closed_form) = -0.080708448454800614868318484563714 y1[1] (numeric) = -0.080708448454800614714911895629214 absolute error = 1.53406588934500e-19 relative error = 1.9007500685682581841266190359047e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.9967377520431433885532007170437 y2[1] (numeric) = -0.99673775204314338896007626117695 absolute error = 4.0687554413325e-19 relative error = 4.0820721729384095548341484344412e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=4283.0MB, alloc=40.3MB, time=49.97 x[1] = 1.5 y1[1] (closed_form) = -0.070737201667702910088189851434269 y1[1] (numeric) = -0.070737201667702909930686284927074 absolute error = 1.57503566507195e-19 relative error = 2.2266016013340226902991186102529e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99749498660405443094172337114149 y2[1] (numeric) = -0.99749498660405443135423827621999 absolute error = 4.1251490507850e-19 relative error = 4.1355085551146096017425152796105e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=4324.8MB, alloc=40.3MB, time=50.45 x[1] = 1.51 y1[1] (closed_form) = -0.060758881219385906581595514916193 y1[1] (numeric) = -0.060758881219385906419938732246601 absolute error = 1.61656782669592e-19 relative error = 2.6606280337172059957217264019352e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99815247249754811924273786483671 y2[1] (numeric) = -0.99815247249754811966086080311503 absolute error = 4.1812293827832e-19 relative error = 4.1889686175109593304604573730508e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=4366.6MB, alloc=40.3MB, time=50.94 x[1] = 1.52 y1[1] (closed_form) = -0.050774484933579196726129270152727 y1[1] (numeric) = -0.050774484933579196560263355743354 absolute error = 1.65865914409373e-19 relative error = 3.2667178136095525390165788964774e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99871014397558300717231239411685 y2[1] (numeric) = -0.99871014397558300759601009126173 absolute error = 4.2369769714488e-19 relative error = 4.2424491200045204004005590332705e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4408.5MB, alloc=40.3MB, time=51.42 TOP MAIN SOLVE Loop x[1] = 1.53 y1[1] (closed_form) = -0.040785011241591058688989007076121 y1[1] (numeric) = -0.04078501124159105851885838781569 absolute error = 1.70130619260431e-19 relative error = 4.1714005729373940678402577977152e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99916794527147601592426506870898 y2[1] (numeric) = -0.99916794527147601635350230627304 absolute error = 4.2923723756406e-19 relative error = 4.2959468385210791241464970596121e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4450.3MB, alloc=40.3MB, time=51.92 TOP MAIN SOLVE Loop x[1] = 1.54 y1[1] (closed_form) = -0.030791459082466157622476807076397 y1[1] (numeric) = -0.030791459082466157448026271747123 absolute error = 1.74450535329274e-19 relative error = 5.6655494909175269240750168151452e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99952583060547905600596353844003 y2[1] (numeric) = -0.99952583060547905644070315666842 absolute error = 4.3473961822839e-19 relative error = 4.3494585624169351736420246881661e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4492.1MB, alloc=40.3MB, time=52.41 TOP MAIN SOLVE Loop x[1] = 1.55 y1[1] (closed_form) = -0.020794827803092473643912774695556 y1[1] (numeric) = -0.020794827803092473465087493370795 absolute error = 1.78825281324761e-19 relative error = 8.5995076765274896462337214209917e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99978376418935696389761134763447 y2[1] (numeric) = -0.99978376418935696433781424860448 absolute error = 4.4020290097001e-19 relative error = 4.4029810918857498753519712779903e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4534.1MB, alloc=40.3MB, time=52.89 TOP MAIN SOLVE Loop x[1] = 1.56 y1[1] (closed_form) = -0.010796117058267445823920663760906 y1[1] (numeric) = -0.010796117058267445640666207169755 absolute error = 1.83254456591151e-19 relative error = 1.6974107968829263661820343440822e-15 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 17 h = 0.001 y2[1] (closed_form) = -0.99994172022996629574517002341348 y2[1] (numeric) = -0.99994172022996629619079517450676 absolute error = 4.4562515109328e-19 relative error = 4.4565112353827507259646065442982e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4575.9MB, alloc=40.3MB, time=53.38 TOP MAIN SOLVE Loop x[1] = 1.57 y1[1] (closed_form) = -0.00079632671073332548540853364535419 y1[1] (numeric) = -0.00079632671073332529767089250085802 absolute error = 1.8773764114449617e-19 relative error = 2.3575454472902378729619752932501e-14 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.99999968293183462021052992382333 y2[1] (numeric) = -0.99999968293183462066153436153037 absolute error = 4.5100443770704e-19 relative error = 4.5100458070623498240712063898226e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4617.8MB, alloc=40.3MB, time=53.86 TOP MAIN SOLVE Loop x[1] = 1.58 y1[1] (closed_form) = 0.0092035432688082648053890569827275 y1[1] (numeric) = 0.0092035432688082649976634526950694 absolute error = 1.922743957123419e-19 relative error = 2.0891344789346424276464130894318e-15 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 17 h = 0.001 y2[1] (closed_form) = -0.99995764649874005255179423225172 y2[1] (numeric) = -0.99995764649874005300813306630831 absolute error = 4.5633883405659e-19 relative error = 4.5635816242259715277072209935009e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4659.6MB, alloc=40.3MB, time=54.36 TOP MAIN SOLVE Loop x[1] = 1.59 y1[1] (closed_form) = 0.019202492901692568095027346243403 y1[1] (numeric) = 0.019202492901692568291891608020156 absolute error = 1.96864261776753e-19 relative error = 1.0252015859847070431459891485622e-15 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 17 h = 0.001 y2[1] (closed_form) = -0.99981561513429087198158434374551 y2[1] (numeric) = -0.99981561513429087244321076160073 absolute error = 4.6162641785522e-19 relative error = 4.6171155047745113811051429870703e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4701.4MB, alloc=40.3MB, time=54.84 TOP MAIN SOLVE Loop x[1] = 1.6 y1[1] (closed_form) = 0.029199522301288726205770462946499 y1[1] (numeric) = 0.02919952230128872640727722456714 absolute error = 2.01506761620641e-19 relative error = 6.9010293915578017033623617785620e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99957360304150516434211382554623 y2[1] (numeric) = -0.99957360304150516480897909716158 absolute error = 4.6686527161535e-19 relative error = 4.6706442646621632946539961106911e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4743.3MB, alloc=40.3MB, time=55.33 TOP MAIN SOLVE Loop x[1] = 1.61 y1[1] (closed_form) = 0.039193631772987609585327609601018 y1[1] (numeric) = 0.039193631772987609791529007978446 absolute error = 2.06201398377428e-19 relative error = 5.2610944444179510085891459802533e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.9992316344213905321324131478443 y2[1] (numeric) = -0.99923163442139053260446663082347 absolute error = 4.7205348297917e-19 relative error = 4.7241647153466537636846908363663e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4785.2MB, alloc=40.3MB, time=55.81 TOP MAIN SOLVE Loop x[1] = 1.62 y1[1] (closed_form) = 0.049183821914170445143744274712327 y1[1] (numeric) = 0.049183821914170445354691930796295 absolute error = 2.10947656083968e-19 relative error = 4.2889642950498620509504995521792e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.9987897434705240139155188912468 y2[1] (numeric) = -0.99878974347052401439270803629543 absolute error = 4.7718914504863e-19 relative error = 4.7776736612305096646746076781379e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4827.1MB, alloc=40.3MB, time=56.30 TOP MAIN SOLVE Loop x[1] = 1.63 y1[1] (closed_form) = 0.059169093714148245297971697419802 y1[1] (numeric) = 0.059169093714148245513716697156619 absolute error = 2.15744999736817e-19 relative error = 3.6462447908886769763393465812656e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.9982479743776324551116699849331 y2[1] (numeric) = -0.99824797437763245559394034164815 absolute error = 4.8227035671505e-19 relative error = 4.8311678970921650034467306839791e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4868.9MB, alloc=40.3MB, time=56.78 TOP MAIN SOLVE Loop x[1] = 1.64 y1[1] (closed_form) = 0.069148448654062044364492707456605 y1[1] (numeric) = 0.069148448654062044585085582808364 absolute error = 2.20592875351759e-19 relative error = 3.1901348424365631916647305323939e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99760638131917367213758197436794 y2[1] (numeric) = -0.99760638131917367262487719735585 absolute error = 4.8729522298791e-19 relative error = 4.8846442054985714569576909747643e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4910.7MB, alloc=40.3MB, time=57.26 TOP MAIN SOLVE Loop x[1] = 1.65 y1[1] (closed_form) = 0.079120888806733952359614597341276 y1[1] (numeric) = 0.079120888806733952585105307367907 absolute error = 2.25490710026631e-19 relative error = 2.8499516806166055247286886130949e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99686502845391885177170304020219 y2[1] (numeric) = -0.99686502845391885226396489552525 absolute error = 4.9226185532306e-19 relative error = 4.9380993541977315821816324857118e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4952.5MB, alloc=40.3MB, time=57.75 TOP MAIN SOLVE Loop x[1] = 1.66 y1[1] (closed_form) = 0.089085416936459041185257931650621 y1[1] (numeric) = 0.089085416936459041415695843658047 absolute error = 2.30437912007426e-19 relative error = 2.5867074537214982311044695885466e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99602398991653672750100059061296 y2[1] (numeric) = -0.99602398991653672799816896256308 absolute error = 4.9716837195012e-19 relative error = 4.9915300934848059597233981846865e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=4994.3MB, alloc=40.3MB, time=58.23 TOP MAIN SOLVE Loop x[1] = 1.67 y1[1] (closed_form) = 0.099041036598728084094782342448611 y1[1] (numeric) = 0.099041036598728084330216213206277 absolute error = 2.35433870757666e-19 relative error = 2.3771345579867397637187682703614e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99508334981018017442629724653424 y2[1] (numeric) = -0.99508334981018017492831014473352 absolute error = 5.0201289819928e-19 relative error = 5.0449331535397796890440495787105e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5036.2MB, alloc=40.3MB, time=58.73 TOP MAIN SOLVE Loop x[1] = 1.68 y1[1] (closed_form) = 0.10898675223987117624800473417282 y1[1] (numeric) = 0.10898675223987117648848269120384 absolute error = 2.4047795703102e-19 relative error = 2.2064879638008400942715275695268e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99404320219807596406048786919357 y2[1] (numeric) = -0.99404320219807596456728143602065 absolute error = 5.0679356682708e-19 relative error = 5.0983052417282647179856025204901e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5078.0MB, alloc=40.3MB, time=59.22 TOP MAIN SOLVE Loop x[1] = 1.69 y1[1] (closed_form) = 0.11892156929661227207639046983309 y1[1] (numeric) = 0.11892156929661227232195999278033 absolute error = 2.4556952294724e-19 relative error = 2.0649704204183887939551356628875e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99290365109411852003714929394559 y2[1] (numeric) = -0.99290365109411852054865781228699 absolute error = 5.1150851834140e-19 relative error = 5.1516430398634267700244093157094e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5119.8MB, alloc=40.3MB, time=59.70 TOP MAIN SOLVE Loop x[1] = 1.7 y1[1] (closed_form) = 0.12884449429552468408764285733487 y1[1] (numeric) = 0.12884449429552468433835075940614 absolute error = 2.5070790207127e-19 relative error = 1.9458177351081283189333464770177e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99166481045246861534613339864788 y2[1] (numeric) = -0.99166481045246861586228929997351 absolute error = 5.1615590132563e-19 relative error = 5.2049432014243064213363317451228e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5161.7MB, alloc=40.3MB, time=60.19 TOP MAIN SOLVE Loop x[1] = 1.71 y1[1] (closed_form) = 0.13875453495237759764268978305111 y1[1] (numeric) = 0.13875453495237759789858219254665 absolute error = 2.5589240949554e-19 relative error = 1.8442093412180414807962534764067e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.99032680415615805121775222386113 y2[1] (numeric) = -0.99032680415615805173848609662287 absolute error = 5.2073387276174e-19 relative error = 5.2582023487231487357730706235558e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5203.6MB, alloc=40.3MB, time=60.67 TOP MAIN SOLVE Loop x[1] = 1.72 y1[1] (closed_form) = 0.14865070027136366713637828033119 y1[1] (numeric) = 0.14865070027136366739750062225691 absolute error = 2.6112234192572e-19 relative error = 1.7566169647975958315604977407045e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.98888976600470145717817065708548 y2[1] (numeric) = -0.98888976600470145770341125543786 absolute error = 5.2524059835238e-19 relative error = 5.3114170700183265928246082980413e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5245.5MB, alloc=40.3MB, time=61.16 TOP MAIN SOLVE Loop x[1] = 1.73 y1[1] (closed_form) = 0.15853200064419777090494835134257 y1[1] (numeric) = 0.158532000644197771171345329112 absolute error = 2.6639697776943e-19 relative error = 1.6803987629432598004221186253490e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.98735383970071645108567767622206 y2[1] (numeric) = -0.98735383970071645161535192906413 absolute error = 5.2967425284207e-19 relative error = 5.3645839165685846859109200839657e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5287.4MB, alloc=40.3MB, time=61.64 TOP MAIN SOLVE Loop x[1] = 1.74 y1[1] (closed_form) = 0.16839744794907701506737731534509 y1[1] (numeric) = 0.16839744794907701533909289257331 absolute error = 2.7171557722822e-19 relative error = 1.6135373815782893560853409620905e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.98571917883555349712068269566555 y2[1] (numeric) = -0.98571917883555349765471571600258 absolute error = 5.3403302033703e-19 relative error = 5.4176993996189879551067551398072e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5329.2MB, alloc=40.3MB, time=62.14 TOP MAIN SOLVE Loop x[1] = 1.75 y1[1] (closed_form) = 0.17824605564949209038267694394263 y1[1] (numeric) = 0.17824605564949209065975432633552 absolute error = 2.7707738239289e-19 relative error = 1.5544657152904551696686870596358e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.98398594687393689873166293696799 y2[1] (numeric) = -0.98398594687393689926997803159215 absolute error = 5.3831509462416e-19 relative error = 5.4707599873184580859629829331344e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5371.1MB, alloc=40.3MB, time=62.62 TOP MAIN SOLVE Loop x[1] = 1.76 y1[1] (closed_form) = 0.1880768388928801010698001765041 y1[1] (numeric) = 0.18807683889288010135228179384595 absolute error = 2.8248161734185e-19 relative error = 1.5019479219487440960105306783123e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.98215431713761846242496809945596 y2[1] (numeric) = -0.98215431713761846296748677894458 absolute error = 5.4251867948862e-19 relative error = 5.5237621015578434328485460402336e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5412.9MB, alloc=40.3MB, time=63.11 TOP MAIN SOLVE Loop x[1] = 1.77 y1[1] (closed_form) = 0.19788881460910900038948584173039 y1[1] (numeric) = 0.19788881460910900067741332997306 absolute error = 2.8792748824267e-19 relative error = 1.4549962756177753078455058651772e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.98022447278804546701848144889842 y2[1] (numeric) = -0.98022447278804546756512343792868 absolute error = 5.4664198903026e-19 relative error = 5.5767021147253148537780396735264e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5454.8MB, alloc=40.3MB, time=63.59 TOP MAIN SOLVE Loop x[1] = 1.78 y1[1] (closed_form) = 0.20768100160878378462655329031263 y1[1] (numeric) = 0.20768100160878378491996747376937 absolute error = 2.9341418345674e-19 relative error = 1.4128118661978282988475314228977e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.9781966068080446715477686473056 y2[1] (numeric) = -0.97819660680804467209845189528435 absolute error = 5.5068324797875e-19 relative error = 5.6295763463715706556470067384888e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5496.6MB, alloc=40.3MB, time=64.08 TOP MAIN SOLVE Loop x[1] = 1.79 y1[1] (closed_form) = 0.21745242068136461493517026446461 y1[1] (numeric) = 0.21745242068136461523411113811191 absolute error = 2.9894087364730e-19 relative error = 1.3747415306327690735518911386493e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.97607092198252419340866043310862 y2[1] (numeric) = -0.97607092198252419396330112511605 absolute error = 5.5464069200743e-19 relative error = 5.6823810597787731170409612885822e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5538.4MB, alloc=40.3MB, time=64.58 TOP MAIN SOLVE Loop x[1] = 1.8 y1[1] (closed_form) = 0.22720209469308705531667430653058 y1[1] (numeric) = 0.22720209469308705562118101842085 absolute error = 3.0450671189027e-19 relative error = 1.3402460584776247965829212612478e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.97384763087819518653237317884336 y2[1] (numeric) = -0.9738476308781951870908857468891 absolute error = 5.5851256804574e-19 relative error = 5.7351124584251972198044437505600e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5580.3MB, alloc=40.3MB, time=65.06 TOP MAIN SOLVE Loop x[1] = 1.81 y1[1] (closed_form) = 0.23692904868467463478774985084198 y1[1] (numeric) = 0.23692904868467463509786068463047 absolute error = 3.1011083378849e-19 relative error = 1.3088763725262406307321226966202e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.97152695582231534740845126909038 y2[1] (numeric) = -0.97152695582231534797074840368063 absolute error = 5.6229713459025e-19 relative error = 5.7877666823388658628555047140192e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5622.2MB, alloc=40.3MB, time=65.55 TOP MAIN SOLVE Loop x[1] = 1.82 y1[1] (closed_form) = 0.24663230996883396256417104483087 y1[1] (numeric) = 0.24663230996883396287992340241973 absolute error = 3.1575235758886e-19 relative error = 1.2802554443445000742435754776762e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.96910912888045637458721531849805 y2[1] (numeric) = -0.96910912888045637515320798051232 absolute error = 5.6599266201427e-19 relative error = 5.8403398043326814991261136477960e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5664.0MB, alloc=40.3MB, time=66.03 TOP MAIN SOLVE Loop x[1] = 1.83 y1[1] (closed_form) = 0.25631090822752264682983758361853 y1[1] (numeric) = 0.25631090822752264715126796792121 absolute error = 3.2143038430268e-19 relative error = 1.2540643959536515290935793598705e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.96659439183329760489723892974281 y2[1] (numeric) = -0.96659439183329760546683636261869 absolute error = 5.6959743287588e-19 relative error = 5.8928278261117290990252528515097e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5705.8MB, alloc=40.3MB, time=66.52 TOP MAIN SOLVE Loop x[1] = 1.84 y1[1] (closed_form) = 0.2659638756089802903802829832816 y1[1] (numeric) = 0.26596387560898029070742698111069 absolute error = 3.2714399782909e-19 relative error = 1.2300316991547251996979009609187e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.96398299615244814699489367172712 y2[1] (numeric) = -0.96398299615244814756800341395163 absolute error = 5.7310974222451e-19 relative error = 5.9452266742459855692792584868686e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5747.6MB, alloc=40.3MB, time=66.98 TOP MAIN SOLVE Loop x[1] = 1.85 y1[1] (closed_form) = 0.2755902468245128601219498354748 y1[1] (numeric) = 0.27559024682451286045484210055617 absolute error = 3.3289226508137e-19 relative error = 1.2079246958741078020333961974450e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.96127520297529993001245916863613 y2[1] (numeric) = -0.96127520297529993058898706654198 absolute error = 5.7652789790585e-19 relative error = 5.9975321959976111700383375547264e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5789.4MB, alloc=40.3MB, time=67.48 TOP MAIN SOLVE Loop x[1] = 1.86 y1[1] (closed_form) = 0.28518905924502075207093548828912 y1[1] (numeric) = 0.28518905924502075240960972440566 absolute error = 3.3867423611654e-19 relative error = 1.1875428777426112653887693195616e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.9584712830789141819789777659032 y2[1] (numeric) = -0.95847128307891418255882798676839 absolute error = 5.7985022086519e-19 relative error = 6.0497401549948051020358121620286e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5831.2MB, alloc=40.3MB, time=67.97 TOP MAIN SOLVE Loop x[1] = 1.87 y1[1] (closed_form) = 0.29475935299726089912514806480989 y1[1] (numeric) = 0.29475935299726089946963700907774 absolute error = 3.4448894426785e-19 relative error = 1.1687125133262564240589249527071e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.95557151685294394934425049217263 y2[1] (numeric) = -0.95557151685294394992732553762163 absolute error = 5.8307504544900e-19 relative error = 6.1018462267406756618648468957959e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5873.1MB, alloc=40.3MB, time=68.45 TOP MAIN SOLVE Loop x[1] = 1.88 y1[1] (closed_form) = 0.30430017105983329547931375952224 y1[1] (numeric) = 0.30430017105983329582964916580248 absolute error = 3.5033540628024e-19 relative error = 1.1512823179167881075294419589318e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.95257619427159536533145742581513 y2[1] (numeric) = -0.95257619427159536591765814551996 absolute error = 5.8620071970483e-19 relative error = 6.1538459939478016695851009925456e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5914.9MB, alloc=40.3MB, time=68.94 TOP MAIN SOLVE Loop x[1] = 1.89 y1[1] (closed_form) = 0.31381055935888233911038241555123 y1[1] (numeric) = 0.31381055935888233946659503800014 absolute error = 3.5621262244891e-19 relative error = 1.1351199372534035789014607608487e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.94948561486463047096820167213832 y2[1] (numeric) = -0.94948561486463047155742727781787 absolute error = 5.8922560567955e-19 relative error = 6.2057349416879448103618416043672e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5956.7MB, alloc=40.3MB, time=69.42 TOP MAIN SOLVE Loop x[1] = 1.9 y1[1] (closed_form) = 0.32328956686350342227883369508031 y1[1] (numeric) = 0.32328956686350342264095327184102 absolute error = 3.6211957676071e-19 relative error = 1.1201090721050118360818158440809e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.94630008768741448848970961163496 y2[1] (numeric) = -0.9463000876874144890818576913505 absolute error = 5.9214807971554e-19 relative error = 6.2575084523413956190555703661506e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=5998.6MB, alloc=40.3MB, time=69.92 TOP MAIN SOLVE Loop x[1] = 1.91 y1[1] (closed_form) = 0.33273624568084522946633893939753 y1[1] (numeric) = 0.33273624568084522983439417643619 absolute error = 3.6805523703866e-19 relative error = 1.1061471114622484727293759144055e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.94301993129001054236188657694821 y2[1] (numeric) = -0.94301993129001054295685310969348 absolute error = 5.9496653274527e-19 relative error = 6.3091618003384241986238113215386e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6040.5MB, alloc=40.3MB, time=70.41 TOP MAIN SOLVE Loop x[1] = 1.92 y1[1] (closed_form) = 0.34214965115089823259923660315905 y1[1] (numeric) = 0.3421496511508982329732551582483 absolute error = 3.7401855508925e-19 relative error = 1.0931431723842285237616603317662e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.93964547368532491842637133968703 y2[1] (numeric) = -0.93964547368532491902405071027084 absolute error = 5.9767937058381e-19 relative error = 6.3606901466750966234841483184549e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6082.3MB, alloc=40.3MB, time=70.89 TOP MAIN SOLVE Loop x[1] = 1.93 y1[1] (closed_form) = 0.35152884194095990478728906471187 y1[1] (numeric) = 0.35152884194095990516729753156466 absolute error = 3.8000846685279e-19 relative error = 1.0810164672536693736019676380564e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.93617705231630604661512937274878 y2[1] (numeric) = -0.9361770523163060472154143869684 absolute error = 6.0028501421962e-19 relative error = 6.4120885331934173766944528767590e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6124.2MB, alloc=40.3MB, time=71.38 TOP MAIN SOLVE Loop memory used=6166.0MB, alloc=40.3MB, time=71.86 x[1] = 1.94 y1[1] (closed_form) = 0.36087288013976720613506768584073 y1[1] (numeric) = 0.36087288013976720652109157839721 absolute error = 3.8602389255648e-19 relative error = 1.0696949363636628148050965449064e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.9326150140222004873089793388657 y2[1] (numeric) = -0.93261501402220048791176123896875 absolute error = 6.0278190010305e-19 relative error = 6.4633518766051201902374265608739e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=6207.8MB, alloc=40.3MB, time=72.34 x[1] = 1.95 y1[1] (closed_form) = 0.37018083135128692845582845913069 y1[1] (numeric) = 0.37018083135128692884789219600127 absolute error = 3.9206373687058e-19 relative error = 1.0591140968575087077662780585778e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.92895971500386929571329703509148 y2[1] (numeric) = -0.92895971500386929631846551552459 absolute error = 6.0516848043311e-19 relative error = 6.5144749622494594073481295173410e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=6249.6MB, alloc=40.3MB, time=72.83 x[1] = 1.96 y1[1] (closed_form) = 0.37945176478815451993156521544745 y1[1] (numeric) = 0.3794517647881545203296921045147 absolute error = 3.9812688906725e-19 relative error = 1.0492160691083402441302977907076e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.92521152078816823258555628949003 y2[1] (numeric) = -0.92521152078816823319299951293198 absolute error = 6.0744322344195e-19 relative error = 6.5654524375624062227001950101381e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=6291.5MB, alloc=40.3MB, time=73.31 x[1] = 1.97 y1[1] (closed_form) = 0.38868475336475204591463981387931 y1[1] (numeric) = 0.38868475336475204631885203706165 absolute error = 4.0421222318234e-19 relative error = 1.0399487494252612630801209972183e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.92137080619139538326395099715317 y2[1] (numeric) = -0.92137080619139538387355561083069 absolute error = 6.0960461367752e-19 relative error = 6.6162788052445355885185994424602e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6333.3MB, alloc=40.3MB, time=73.80 TOP MAIN SOLVE Loop x[1] = 1.98 y1[1] (closed_form) = 0.39787887378991597815247385990719 y1[1] (numeric) = 0.39787887378991597856279245808707 absolute error = 4.1031859817988e-19 relative error = 1.0312651040540853663185188070197e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.917437955281809840204735217402 y2[1] (numeric) = -0.91743795528180984081638636968572 absolute error = 6.1165115228372e-19 relative error = 6.6669484161012156208485007236318e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6375.2MB, alloc=40.3MB, time=74.28 TOP MAIN SOLVE Loop x[1] = 1.99 y1[1] (closed_form) = 0.40703320665926554173363571613029 y1[1] (numeric) = 0.40703320665926554215008057424979 absolute error = 4.1644485811950e-19 relative error = 1.0231225642189756588072338126162e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.91341336134122519712879327105761 y2[1] (numeric) = -0.91341336134122519774237462833631 absolute error = 6.1358135727870e-19 relative error = 6.7174554615419457784036734338125e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6417.0MB, alloc=40.3MB, time=74.78 TOP MAIN SOLVE Loop x[1] = 2 y1[1] (closed_form) = 0.41614683654714238699756822950076 y1[1] (numeric) = 0.41614683654714238742015806182732 absolute error = 4.2258983232656e-19 relative error = 1.0154825057253264274804510408775e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.90929742682568169539601986591174 y2[1] (numeric) = -0.90929742682568169601141362974242 absolute error = 6.1539376383068e-19 relative error = 6.7677939657103531757950042321378e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6458.9MB, alloc=40.3MB, time=75.27 TOP MAIN SOLVE Loop x[1] = 2.01 y1[1] (closed_form) = 0.42521885209815239251738234016543 y1[1] (numeric) = 0.42521885209815239294613467573038 absolute error = 4.2875233556495e-19 relative error = 1.0083097996463759343529429503263e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.90509056332520095536009971027372 y2[1] (numeric) = -0.90509056332520095597718663480536 absolute error = 6.1708692453164e-19 relative error = 6.8179577772254306636069390524309e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6500.8MB, alloc=40.3MB, time=75.75 TOP MAIN SOLVE Loop x[1] = 2.02 y1[1] (closed_form) = 0.4342483461183004450517028740902 y1[1] (numeric) = 0.43424834611830044548663404230297 absolute error = 4.3493116821277e-19 relative error = 1.0015724230168594277284664990245e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 y2[1] (closed_form) = -0.90079319152262731719701352455371 y2[1] (numeric) = -0.90079319152262731781567293422251 absolute error = 6.1865940966880e-19 relative error = 6.8679405605083294309592294166159e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6542.7MB, alloc=40.3MB, time=76.23 TOP MAIN SOLVE Loop x[1] = 2.03 y1[1] (closed_form) = 0.4432344156657090830635167316961 y1[1] (numeric) = 0.44323441566570908350464184813666 absolute error = 4.4112511644056e-19 relative error = 9.9524112038551642322505754025656e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.89640574115155990703888883196757 y2[1] (numeric) = -0.896405741151559907658998639461 absolute error = 6.2010980749343e-19 relative error = 6.9177357866629823461313194453025e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6584.5MB, alloc=40.3MB, time=76.72 TOP MAIN SOLVE Loop x[1] = 2.04 y1[1] (closed_form) = 0.45217616214091193201727020529136 y1[1] (numeric) = 0.45217616214091193246460315768373 absolute error = 4.4733295239237e-19 relative error = 9.8928910863940536603957081784751e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.8919286509533796351715256485842 y2[1] (numeric) = -0.8919286509533796357929623730718 absolute error = 6.2143672448760e-19 relative error = 6.9673367238887135827084436781220e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6626.2MB, alloc=40.3MB, time=77.20 TOP MAIN SOLVE Loop x[1] = 2.05 y1[1] (closed_form) = 0.4610726913767129021859299941674 y1[1] (numeric) = 0.46107269137671290263948342853664 absolute error = 4.5355343436924e-19 relative error = 9.8369181877802994862598017127472e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.88736236863337542355996660468034 y2[1] (numeric) = -0.88736236863337542418260539030867 absolute error = 6.2263878562833e-19 relative error = 7.0167364273882207198743172790834e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6668.1MB, alloc=40.3MB, time=77.69 TOP MAIN SOLVE Loop x[1] = 2.06 y1[1] (closed_form) = 0.4699231137276021631231096264879 y1[1] (numeric) = 0.46992311372760216358289493350349 absolute error = 4.5978530701559e-19 relative error = 9.7842666935108731058054878992540e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.8827073508159740500427975851999 y2[1] (numeric) = -0.88270735081597405066651221984929 absolute error = 6.2371463464939e-19 relative error = 7.0659277287407727304748121005198e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6709.9MB, alloc=40.3MB, time=78.17 TOP MAIN SOLVE Loop x[1] = 2.07 y1[1] (closed_form) = 0.47872654415871995327732713901173 y1[1] (numeric) = 0.47872654415871995374335444051974 absolute error = 4.6602730150801e-19 relative error = 9.7347286711868734818718607241144e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.87796406299907808617345112044384 y2[1] (numeric) = -0.87796406299907808679811405474426 absolute error = 6.2466293430042e-19 relative error = 7.1149032247015323765676836733412e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6751.7MB, alloc=40.3MB, time=78.66 TOP MAIN SOLVE Loop x[1] = 2.08 y1[1] (closed_form) = 0.48748210233435932844156884977235 y1[1] (numeric) = 0.48748210233435932891384698551913 absolute error = 4.7227813574678e-19 relative error = 9.6881123119233806732022408498160e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.87313297950751649487667680502462 y2[1] (numeric) = -0.87313297950751649550215917162832 absolute error = 6.2548236660370e-19 relative error = 7.1636552653926576620616553754591e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6793.5MB, alloc=40.3MB, time=79.14 TOP MAIN SOLVE Loop x[1] = 2.09 y1[1] (closed_form) = 0.49618891270599899883706631187045 y1[1] (numeric) = 0.49618891270599899931560282642027 absolute error = 4.7853651454982e-19 relative error = 9.6442403749025652366346627953156e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.86821458344561254282162205872751 y2[1] (numeric) = -0.86821458344561254344779369183573 absolute error = 6.2617163310822e-19 relative error = 7.2121759418412854962137600541130e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6835.3MB, alloc=40.3MB, time=79.63 TOP MAIN SOLVE Loop x[1] = 2.1 y1[1] (closed_form) = 0.50484610459985745162093852371917 y1[1] (numeric) = 0.50484610459985745210573965356838 absolute error = 4.8480112984921e-19 relative error = 9.6029488082009633570753303635781e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.86320936664887377068075931326902 y2[1] (numeric) = -0.86320936664887377130748876841028 absolute error = 6.2672945514126e-19 relative error = 7.2604570728226781569603132780218e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6877.1MB, alloc=40.3MB, time=80.11 TOP MAIN SOLVE Loop x[1] = 2.11 y1[1] (closed_form) = 0.51345281230395960347841015707169 y1[1] (numeric) = 0.51345281230395960396948081796195 absolute error = 4.9107066089026e-19 relative error = 9.5640855230051877810998142859688e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.85811782963480885223737550831068 y2[1] (numeric) = -0.85811782963480885286453008236777 absolute error = 6.2715457405709e-19 relative error = 7.3084901909565215784495408506532e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6918.9MB, alloc=40.3MB, time=80.61 TOP MAIN SOLVE Loop x[1] = 2.12 y1[1] (closed_form) = 0.52200817515470727670690188298389 y1[1] (numeric) = 0.5220081751547072772042456574168 absolute error = 4.9734377443291e-19 relative error = 9.5275093016601224341754531236837e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.85294048155287626061472733365415 y2[1] (numeric) = -0.85294048155287626124217308513737 absolute error = 6.2744575148322e-19 relative error = 7.3562665280100533414693426395775e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=6960.7MB, alloc=40.3MB, time=81.09 TOP MAIN SOLVE Loop x[1] = 2.13 y1[1] (closed_form) = 0.53051133762294484181652620960972 y1[1] (numeric) = 0.53051133762294484232014533456558 absolute error = 5.0361912495586e-19 relative error = 9.4930888228029126641054356245554e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.8476778401335697467185299963159 y2[1] (numeric) = -0.84767784013356974734613176587969 absolute error = 6.2760176956379e-19 relative error = 7.4037769993479826975736583197780e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7002.5MB, alloc=40.3MB, time=81.58 TOP MAIN SOLVE Loop x[1] = 2.14 y1[1] (closed_form) = 0.5389614493995114201544499120086 y1[1] (numeric) = 0.53896144939951142066434526687135 absolute error = 5.0989535486275e-19 relative error = 9.4607017891697882691254095775327e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.84233043163664572130250663706891 y2[1] (numeric) = -0.84233043163664572193012806826917 absolute error = 6.2762143120026e-19 relative error = 7.4510121874712905528086903696528e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7044.3MB, alloc=40.3MB, time=82.06 TOP MAIN SOLVE Loop x[1] = 2.15 y1[1] (closed_form) = 0.54735766548027109140415388226403 y1[1] (numeric) = 0.54735766548027109192032497695507 absolute error = 5.1617109469104e-19 relative error = 9.4302341456775455125100450395086e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.83689879079849771787564813704379 y2[1] (numeric) = -0.83689879079849771850315169733299 absolute error = 6.2750356028920e-19 relative error = 7.4979623245779745901017464252500e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7086.2MB, alloc=40.3MB, time=82.55 TOP MAIN SOLVE Loop x[1] = 2.16 y1[1] (closed_form) = 0.55569914625061260300969874398337 y1[1] (numeric) = 0.55569914625061260353214370730651 absolute error = 5.2244496332314e-19 relative error = 9.4015793770452289302535534536182e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.83138346077868319896103812034632 y2[1] (numeric) = -0.83138346077868319958828512230367 absolute error = 6.2724700195735e-19 relative error = 7.5446172740778765145079164923749e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7128.1MB, alloc=40.3MB, time=83.03 TOP MAIN SOLVE Loop x[1] = 2.17 y1[1] (closed_form) = 0.56398505756941013162446999441651 y1[1] (numeric) = 0.56398505756941013215318556261634 absolute error = 5.2871556819983e-19 relative error = 9.3746378756632309378488691020833e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.82578499310560805298105642394338 y2[1] (numeric) = -0.82578499310560805360790704673718 absolute error = 6.2685062279380e-19 relative error = 7.5909665109842130620198303800212e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7169.9MB, alloc=40.3MB, time=83.52 TOP MAIN SOLVE Loop x[1] = 2.18 y1[1] (closed_form) = 0.57221457085243670057822486766249 y1[1] (numeric) = 0.57221457085243670111320637319855 absolute error = 5.3498150553606e-19 relative error = 9.3493163716381769158705127939925e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.82010394762137421327400974608394 y2[1] (numeric) = -0.82010394762137421390032305716313 absolute error = 6.2631331107919e-19 relative error = 7.6369991010986631573674142562118e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7211.8MB, alloc=40.3MB, time=84.00 TOP MAIN SOLVE Loop x[1] = 2.19 y1[1] (closed_form) = 0.58038686315522191209020516379695 y1[1] (numeric) = 0.5803868631552219126314465243359 absolute error = 5.4124136053895e-19 relative error = 9.3255274179801237212557157582636e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.814340892425795914434327645905 y2[1] (numeric) = -0.81434089242579591505996162291702 absolute error = 6.2563397701202e-19 relative error = 7.6827036789022454759816301449575e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7253.6MB, alloc=40.3MB, time=84.48 TOP MAIN SOLVE Loop x[1] = 2.2 y1[1] (closed_form) = 0.58850111725534570852414261265493 y1[1] (numeric) = 0.58850111725534570907163632028312 absolute error = 5.4749370762819e-19 relative error = 9.3031889247992211244404254462350e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.80849640381959018430403691041612 y2[1] (numeric) = -0.80849640381959018492884846334816 absolute error = 6.2481155293204e-19 relative error = 7.7280684240552533120105258708350e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7295.5MB, alloc=40.3MB, time=84.97 TOP MAIN SOLVE Loop x[1] = 2.21 y1[1] (closed_form) = 0.59655652173415993337760917751863 y1[1] (numeric) = 0.59655652173415993393134628817706 absolute error = 5.5373711065843e-19 relative error = 9.2822237371363228121479787854722e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.80257106624674725251897404255597 y2[1] (numeric) = -0.80257106624674725314281903609646 absolute error = 6.2384499354049e-19 relative error = 7.7730810363987300915994822133709e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7337.3MB, alloc=40.3MB, time=85.45 TOP MAIN SOLVE Loop x[1] = 2.22 y1[1] (closed_form) = 0.60455227105792951991771443750015 y1[1] (numeric) = 0.60455227105792952047768456064423 absolute error = 5.5997012314408e-19 relative error = 9.2625592517280021752461708338296e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.79656547223608663852085674960916 y2[1] (numeric) = -0.79656547223608663914359002572657 absolute error = 6.2273327611741e-19 relative error = 7.8177287093463658291008884565525e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7379.2MB, alloc=40.3MB, time=85.94 TOP MAIN SOLVE Loop x[1] = 2.23 y1[1] (closed_form) = 0.61248756565838519341190391068563 y1[1] (numeric) = 0.61248756565838519397809519917177 absolute error = 5.6619128848614e-19 relative error = 9.2441270685637570650751652100710e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.79048022234200476337771012718854 y2[1] (numeric) = -0.79048022234200476399918552792444 absolute error = 6.2147540073590e-19 relative error = 7.8619981015415705108005459242427e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7421.0MB, alloc=40.3MB, time=86.42 TOP MAIN SOLVE Loop x[1] = 2.24 y1[1] (closed_form) = 0.62036161201267963175076226631044 y1[1] (numeric) = 0.62036161201267963232316140651158 absolute error = 5.7239914020114e-19 relative error = 9.2268626735956169690976201181363e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.7843159250844200106020886706045 y2[1] (numeric) = -0.78431592508442001122215906107767 absolute error = 6.2007039047317e-19 relative error = 7.9058753066429014848760277778067e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7462.8MB, alloc=40.3MB, time=86.91 TOP MAIN SOLVE Loop x[1] = 2.25 y1[1] (closed_form) = 0.6281736227227390889133890573964 y1[1] (numeric) = 0.62817362272273908949198125954876 absolute error = 5.7859220215236e-19 relative error = 9.2107051493904711460164906982990e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.77807319688792124141096667558776 y2[1] (numeric) = -0.77807319688792124202948396720624 absolute error = 6.1851729161848e-19 relative error = 7.9493458210921418119777836965470e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7504.7MB, alloc=40.3MB, time=87.39 TOP MAIN SOLVE Loop x[1] = 2.26 y1[1] (closed_form) = 0.63592281659400254617912656874484 y1[1] (numeric) = 0.63592281659400254676389555752766 absolute error = 5.8476898878282e-19 relative error = 9.1955969108772974443835248431011e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.77175266202012584952506163774032 y2[1] (numeric) = -0.77175266202012585014187681161829 absolute error = 6.1681517387797e-19 relative error = 7.9923945097047767238576144727889e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7546.5MB, alloc=40.3MB, time=87.88 TOP MAIN SOLVE Loop x[1] = 2.27 y1[1] (closed_form) = 0.6436084187135405172361343481243 y1[1] (numeric) = 0.64360841871354051782706235347486 absolute error = 5.9092800535056e-19 relative error = 9.1814834636830985954079728826042e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.76535495252925351965074260193472 y2[1] (numeric) = -0.76535495252925352026570573251102 absolute error = 6.1496313057630e-19 relative error = 8.0350055689068632592354680502902e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7588.2MB, alloc=40.3MB, time=88.36 TOP MAIN SOLVE Loop x[1] = 2.28 y1[1] (closed_form) = 0.6512296605275456953713983504607 y1[1] (numeric) = 0.65122966052754569596846609862643 absolute error = 5.9706774816573e-19 relative error = 9.1683131828187859972273146917640e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.75888070818092193221665357630092 y2[1] (numeric) = -0.75888070818092193282961385515575 absolute error = 6.1296027885483e-19 relative error = 8.0771624874234701930879417365004e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7630.0MB, alloc=40.3MB, time=88.84 TOP MAIN SOLVE Loop x[1] = 2.29 y1[1] (closed_form) = 0.65878577991818769374203101818895 y1[1] (numeric) = 0.65878577991818769434521772301882 absolute error = 6.0318670482987e-19 relative error = 9.1560371097381253616786091870097e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.75233057639417073474190827797365 y2[1] (numeric) = -0.75233057639417073535271403784059 absolute error = 6.1080575986694e-19 relative error = 8.1188480042172149027741028092938e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7671.8MB, alloc=40.3MB, time=89.33 TOP MAIN SOLVE Loop x[1] = 2.3 y1[1] (closed_form) = 0.66627602127982419331788057116602 y1[1] (numeric) = 0.6662760212798241939271639256429 absolute error = 6.0928335447688e-19 relative error = 9.1446087659965737065710630822311e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.7457052121767201773854062116435 y2[1] (numeric) = -0.74570521217672017799390495061312 absolute error = 6.0849873896962e-19 relative error = 8.1600440634363644029844795896841e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7713.6MB, alloc=40.3MB, time=89.81 TOP MAIN SOLVE Loop x[1] = 2.31 y1[1] (closed_form) = 0.67369963559456087744416432347103 y1[1] (numeric) = 0.67369963559456087805952049148706 absolute error = 6.1535616801603e-19 relative error = 9.1339839819411368229940271708913e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.73900527805947088675876419209826 y2[1] (numeric) = -0.73900527805947088736480259801033 absolute error = 6.0603840591207e-19 relative error = 8.2007317661308979308770634990408e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7755.5MB, alloc=40.3MB, time=90.30 TOP MAIN SOLVE Loop x[1] = 2.32 y1[1] (closed_form) = 0.68105588050715259709363616600823 y1[1] (numeric) = 0.68105588050715259771503977438503 absolute error = 6.2140360837680e-19 relative error = 9.1241207390217062232973229234663e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.73223144403025132797089867772467 y2[1] (numeric) = -0.73223144403025132857432265274547 absolute error = 6.0342397502080e-19 relative error = 8.2408913184540898983203372343004e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7797.3MB, alloc=40.3MB, time=90.78 TOP MAIN SOLVE Loop x[1] = 2.33 y1[1] (closed_form) = 0.688344020399238276754180427816 y1[1] (numeric) = 0.68834402039923827738160455857163 absolute error = 6.2742413075563e-19 relative error = 9.1149790244669394841569459427315e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.72538438746681958010284419247542 y2[1] (numeric) = -0.72538438746681958070349887785671 absolute error = 6.0065468538129e-19 relative error = 8.2805019760473553513370587279546e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7839.1MB, alloc=40.3MB, time=91.27 TOP MAIN SOLVE Loop x[1] = 2.34 y1[1] (closed_form) = 0.69556332646290213752310557206135 y1[1] (numeric) = 0.69556332646290213815652175492565 absolute error = 6.3341618286430e-19 relative error = 9.1065206971932446361768726103828e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.71846479306912612487942868679401 y2[1] (numeric) = -0.71846479306912612547715848781047 absolute error = 5.9772980101646e-19 relative error = 8.3195419842785564328342955776835e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7881.0MB, alloc=40.3MB, time=91.75 TOP MAIN SOLVE Loop x[1] = 2.35 y1[1] (closed_form) = 0.70271307677355388134712911225892 y1[1] (numeric) = 0.7027130767735538819865073174392 absolute error = 6.3937820518028e-19 relative error = 9.0987093639402521325425707697329e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.71147335279084442220249118201321 y2[1] (numeric) = -0.71147335279084442279713979307457 absolute error = 5.9464861106136e-19 relative error = 8.3579885139587510550967671612046e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7922.8MB, alloc=40.3MB, time=92.27 TOP MAIN SOLVE Loop x[1] = 2.36 y1[1] (closed_form) = 0.7097925563621205484503630346451 y1[1] (numeric) = 0.70979255636212054909567166584374 absolute error = 6.4530863119864e-19 relative error = 9.0915102647176498659959733544009e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.7044107657701761194310307129327 y2[1] (numeric) = -0.7044107657701761200224411428675 absolute error = 5.9141042993480e-19 relative error = 8.3958175921427631609700151762356e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=7964.7MB, alloc=40.3MB, time=92.78 TOP MAIN SOLVE Loop x[1] = 2.37 y1[1] (closed_form) = 0.71680105728654282882471660882235 y1[1] (numeric) = 0.71680105728654282947592249650812 absolute error = 6.5120588768577e-19 relative error = 9.0848901667488610749327201005579e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.69727773825993781382969642028923 y2[1] (numeric) = -0.69727773825993781441771101779635 absolute error = 5.8801459750712e-19 relative error = 8.4330040275560086346253981889760e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8006.4MB, alloc=40.3MB, time=93.28 TOP MAIN SOLVE Loop x[1] = 2.38 y1[1] (closed_form) = 0.72373787870256867821114760736753 y1[1] (numeric) = 0.72373787870256867886821600230225 absolute error = 6.5706839493472e-19 relative error = 9.0788172661714789419731868378926e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.6900749835569363594511131070202 y2[1] (numeric) = -0.69007498355693636003557358628487 absolute error = 5.8446047926467e-19 relative error = 8.4695213301620522940852612144922e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8048.3MB, alloc=40.3MB, time=93.77 TOP MAIN SOLVE Loop memory used=8090.0MB, alloc=40.3MB, time=94.25 x[1] = 2.39 y1[1] (closed_form) = 0.73060232693383715926915829261806 y1[1] (numeric) = 0.73060232693383715993205285964018 absolute error = 6.6289456702212e-19 relative error = 9.0732610968285524347348672675379e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.68280322193063978086250031101305 y2[1] (numeric) = -0.68280322193063978144324777748368 absolute error = 5.8074746647063e-19 relative error = 8.5053416243197404813976035307646e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=8131.7MB, alloc=40.3MB, time=94.73 x[1] = 2.4 y1[1] (closed_form) = 0.73739371554124549960882222733478 y1[1] (numeric) = 0.73739371554124550027750503940159 absolute error = 6.6868281206681e-19 relative error = 9.0681924455512638174013440872208e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.67546318055115092656577152534128 y2[1] (numeric) = -0.67546318055115092714264650166363 absolute error = 5.7687497632235e-19 relative error = 8.5404355549275550898665104118833e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=8173.5MB, alloc=40.3MB, time=95.22 x[1] = 2.41 y1[1] (closed_form) = 0.74411136539159243003734439556795 y1[1] (numeric) = 0.74411136539159243071177592805785 absolute error = 6.7443153248990e-19 relative error = 9.0635832733851194452987459901931e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.66805559341649106468574980065472 y2[1] (numeric) = -0.66805559341649106525859225275968 absolute error = 5.7284245210496e-19 relative error = 8.5747721858804705836283429074993e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=8215.3MB, alloc=40.3MB, time=95.70 x[1] = 2.42 y1[1] (closed_form) = 0.75075460472549093874353256891074 y1[1] (numeric) = 0.75075460472549093942367169418716 absolute error = 6.8013912527642e-19 relative error = 9.0594066422690663521269870364695e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.66058120127920069250633410656023 y2[1] (numeric) = -0.66058120127920069307498346990177 absolute error = 5.6864936334154e-19 relative error = 8.6083188900980417160997431272900e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8257.1MB, alloc=40.3MB, time=96.19 TOP MAIN SOLVE Loop x[1] = 2.43 y1[1] (closed_form) = 0.7573227692245436502013552441779 y1[1] (numeric) = 0.75732276922454365088715922641631 absolute error = 6.8580398223841e-19 relative error = 9.0556366467184803372109784995030e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.6530407515722648997124970471899 y2[1] (numeric) = -0.65304075157226490027679225312934 absolute error = 5.6429520593944e-19 relative error = 8.6410412302883000435259420334143e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8298.9MB, alloc=40.3MB, time=96.67 TOP MAIN SOLVE Loop x[1] = 2.44 y1[1] (closed_form) = 0.7638152020777741113106750925374 y1[1] (numeric) = 0.76381520207777411200209958281694 absolute error = 6.9142449027954e-19 relative error = 9.0522483501072939226560200967414e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.64543499833437069274006107298253 y2[1] (numeric) = -0.64543499833437069329984057531565 absolute error = 5.5977950233312e-19 relative error = 8.6729028295289860820704320031082e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8340.7MB, alloc=40.3MB, time=97.17 TOP MAIN SOLVE Loop x[1] = 2.45 y1[1] (closed_form) = 0.77023125404730734170190306733649 y1[1] (numeric) = 0.7702312540473073423989020989975 absolute error = 6.9699903166101e-19 relative error = 9.0492177251768669009893748013319e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.63776470213450375443853285563378 y2[1] (numeric) = -0.63776470213450375499363465725687 absolute error = 5.5510180162309e-19 relative error = 8.7038652306288933631723744835731e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8382.5MB, alloc=40.3MB, time=97.66 TOP MAIN SOLVE Loop x[1] = 2.46 y1[1] (closed_form) = 0.7765702835332930802042763146862 y1[1] (numeric) = 0.77657028353329308090680229895515 absolute error = 7.0252598426895e-19 relative error = 9.0465215984385699595900989976416e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.63003062999589217930819371861593 y2[1] (numeric) = -0.63003062999589217985845539832727 absolute error = 5.5026167971134e-19 relative error = 8.7338877431233418679836491882755e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8424.3MB, alloc=40.3MB, time=98.14 TOP MAIN SOLVE Loop x[1] = 2.47 y1[1] (closed_form) = 0.78283165663806523520721558406155 y1[1] (numeric) = 0.7828316566380652359152193059446 absolute error = 7.0800372188305e-19 relative error = 9.0441375981603766623655513523375e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.62223355531930478987454240485577 y2[1] (numeric) = -0.62223355531930479041980114428868 absolute error = 5.4525873943291e-19 relative error = 8.7629272766092714933324038371985e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8466.1MB, alloc=40.3MB, time=98.63 TOP MAIN SOLVE Loop x[1] = 2.48 y1[1] (closed_form) = 0.78901474722953112302319203359033 y1[1] (numeric) = 0.78901474722953112373662264803686 absolute error = 7.1343061444653e-19 relative error = 9.0420441056596239537747352997303e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.6143742578057117043045348806656 y2[1] (numeric) = -0.61437425780571170484462749134929 absolute error = 5.4009261068369e-19 relative error = 8.7909381589761796179808557984618e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8508.0MB, alloc=40.3MB, time=99.11 TOP MAIN SOLVE Loop x[1] = 2.49 y1[1] (closed_form) = 0.79511893700378415538109133257157 y1[1] (numeric) = 0.79511893700378415609989636090901 absolute error = 7.1880502833744e-19 relative error = 9.0402202096466863573737458062235e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.6064535233783148891434102397918 y2[1] (numeric) = -0.60645352337831488967817319033635 absolute error = 5.3476295054455e-19 relative error = 8.8178719379119968527712467255403e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8549.8MB, alloc=40.3MB, time=99.61 TOP MAIN SOLVE Loop x[1] = 2.5 y1[1] (closed_form) = 0.80114361554693371483350279046735 y1[1] (numeric) = 0.80114361554693371555762811710838 absolute error = 7.2412532664103e-19 relative error = 9.0386456633830376970079016423267e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.59847214410395649405185470218616 y2[1] (numeric) = -0.59847214410395649458112414558764 absolute error = 5.2926944340148e-19 relative error = 8.8436771638538323139051661836751e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8591.7MB, alloc=40.3MB, time=100.09 TOP MAIN SOLVE Loop x[1] = 2.51 y1[1] (closed_form) = 0.80708818039614603514191750787841 y1[1] (numeric) = 0.80708818039614603587130737730184 absolute error = 7.2938986942343e-19 relative error = 9.0373008444433037070237879587964e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.59043091811391282764453715502405 y2[1] (numeric) = -0.59043091811391282816814895608611 absolute error = 5.2361180106206e-19 relative error = 8.8682991523326476056257883183917e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8633.5MB, alloc=40.3MB, time=100.58 TOP MAIN SOLVE Loop x[1] = 2.52 y1[1] (closed_form) = 0.81295203709988998260266426045185 y1[1] (numeric) = 0.8129520370998899833372612744583 absolute error = 7.3459701400645e-19 relative error = 9.0361667168832956179132543004820e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.58233064952408189496642758229713 y2[1] (numeric) = -0.58233064952408189548421734516519 absolute error = 5.1778976286806e-19 relative error = 8.8916797233879263688425489592430e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8675.4MB, alloc=40.3MB, time=101.06 TOP MAIN SOLVE Loop x[1] = 2.53 y1[1] (closed_form) = 0.81873459927738171378565517255499 y1[1] (numeric) = 0.81873459927738171452540028779839 absolute error = 7.3974511524340e-19 relative error = 9.0352247956334307324766581257821e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.5741721483545724777866405874022 y2[1] (numeric) = -0.5741721483545724782984436832063 absolute error = 5.1180309580410e-19 relative error = 8.9137569154267425805358594218442e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8717.2MB, alloc=40.3MB, time=101.55 TOP MAIN SOLVE Loop x[1] = 2.54 y1[1] (closed_form) = 0.82443528867722226526970435580657 y1[1] (numeric) = 0.82443528867722226601453688160267 absolute error = 7.4483252579610e-19 relative error = 9.0344571129549521277680365876755e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.56595623044870279873476574798203 y2[1] (numeric) = -0.56595623044870279924041734258451 absolute error = 5.0565159460248e-19 relative error = 8.9344646705556730016467575467951e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8759.1MB, alloc=40.3MB, time=102.03 TOP MAIN SOLVE Loop x[1] = 2.55 y1[1] (closed_form) = 0.83005353523522221166431047583229 y1[1] (numeric) = 0.83005353523522221241416807224518 absolute error = 7.4985759641289e-19 relative error = 9.0338461868052145818576385446918e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.55768371739141686934577028176624 y2[1] (numeric) = -0.55768371739141686984510536361035 absolute error = 4.9933508184411e-19 relative error = 8.9537324880088942252263104410692e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8800.9MB, alloc=40.3MB, time=102.53 TOP MAIN SOLVE Loop x[1] = 2.56 y1[1] (closed_form) = 0.83558877713140760950028812338244 y1[1] (numeric) = 0.83558877713140761025510679958997 absolute error = 7.5481867620753e-19 relative error = 9.0333749909714809234647617611736e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.54935543642712668031068338313728 y2[1] (numeric) = -0.5493554364271266808035367911928 absolute error = 4.9285340805552e-19 relative error = 8.9714850418322599007197853361125e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8842.7MB, alloc=40.3MB, time=103.02 TOP MAIN SOLVE Loop x[1] = 2.57 y1[1] (closed_form) = 0.84104046084620152644236372156713 y1[1] (numeric) = 0.84104046084620152720207783450627 absolute error = 7.5971411293914e-19 relative error = 9.0330269268468235477128462253726e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.54097222037698844964557254874584 y2[1] (numeric) = -0.5409722203769884501317790005477 absolute error = 4.8620645180186e-19 relative error = 8.9876417584443853096823414188089e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8884.5MB, alloc=40.3MB, time=103.50 TOP MAIN SOLVE Loop x[1] = 2.58 y1[1] (closed_form) = 0.84640804121577553771763249456923 y1[1] (numeric) = 0.84640804121577553848217474786239 absolute error = 7.6454225329316e-19 relative error = 9.0327857967296246274939060957923e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.53253490755562120108505876447165 y2[1] (numeric) = -0.53253490755562120156445288424777 absolute error = 4.7939411977612e-19 relative error = 9.0021163490780019455472736213554e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8926.4MB, alloc=40.3MB, time=103.98 TOP MAIN SOLVE Loop x[1] = 2.59 y1[1] (closed_form) = 0.85169098148656565465635974540831 y1[1] (numeric) = 0.85169098148656565542566118857114 absolute error = 7.6930144316283e-19 relative error = 9.0326357785316616604471057144079e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.52404434168727600077313024887591 y2[1] (numeric) = -0.52404434168727600124554659576002 absolute error = 4.7241634688411e-19 relative error = 9.0148162913669038390873352340471e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=8968.2MB, alloc=40.3MB, time=104.47 TOP MAIN SOLVE Loop x[1] = 2.6 y1[1] (closed_form) = 0.8568887533689472337977021516452 y1[1] (numeric) = 0.85688875336894723457169217957714 absolute error = 7.7399002793194e-19 relative error = 9.0325614018029496259439256045224e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.51550137182146423525772693520937 y2[1] (numeric) = -0.51550137182146423572300003153507 absolute error = 4.6527309632570e-19 relative error = 9.0256422535154764670957236833459e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9010.0MB, alloc=40.3MB, time=104.95 TOP MAIN SOLVE Loop x[1] = 2.61 y1[1] (closed_form) = 0.86200083709006349911416744872265 y1[1] (numeric) = 0.86200083709006349989277380148068 absolute error = 7.7860635275803e-19 relative error = 9.0325475249704394010769962275333e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.5069068522480533678909866995555 y2[1] (numeric) = -0.50690685224805336834895105922749 absolute error = 4.5796435967199e-19 relative error = 9.0344874534835937865652100588045e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9051.8MB, alloc=40.3MB, time=105.44 TOP MAIN SOLVE Loop x[1] = 2.62 y1[1] (closed_form) = 0.86702672144580239454661367674835 y1[1] (numeric) = 0.86702672144580239532976243960489 absolute error = 7.8314876285654e-19 relative error = 9.0325793137102801160562486431872e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.49826164241183866398876000999763 y2[1] (numeric) = -0.49826164241183866443925016693593 absolute error = 4.5049015693830e-19 relative error = 9.0412369444635456324898367008496e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9093.6MB, alloc=40.3MB, time=105.94 TOP MAIN SOLVE Loop x[1] = 2.63 y1[1] (closed_form) = 0.87196590385191656920784839019493 y1[1] (numeric) = 0.87196590385191656999546399398048 absolute error = 7.8761560378555e-19 relative error = 9.0326422203695302392355446744322e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.48956660682659942750568705361163 y2[1] (numeric) = -0.48956660682659942794853759026495 absolute error = 4.4285053665332e-19 relative error = 9.0457668165707657112394299806648e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9135.4MB, alloc=40.3MB, time=106.42 TOP MAIN SOLVE Loop x[1] = 2.64 y1[1] (closed_form) = 0.87681789039428138329890731626599 y1[1] (numeric) = 0.87681789039428138409091253799727 absolute error = 7.9200522173128e-19 relative error = 9.0327219643652182882989058711466e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.48082261498864834353055026953286 y2[1] (numeric) = -0.48082261498864834396559584545704 absolute error = 4.3504557592418e-19 relative error = 9.0479433030505629277260352778144e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9177.2MB, alloc=40.3MB, time=106.89 TOP MAIN SOLVE Loop x[1] = 2.65 y1[1] (closed_form) = 0.88158219587828590897930236605381 y1[1] (numeric) = 0.88158219587828590977561832984799 absolute error = 7.9631596379418e-19 relative error = 9.0328045134899929294024551833467e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.47203054128988257159561077839739 y2[1] (numeric) = -0.47203054128988257202268615889478 absolute error = 4.2707538049739e-19 relative error = 9.0476217774034924836395805265891e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9219.1MB, alloc=40.3MB, time=107.39 TOP MAIN SOLVE Loop x[1] = 2.66 y1[1] (closed_form) = 0.88625834387735198713231100388259 y1[1] (numeric) = 0.88625834387735198793285718215816 absolute error = 8.0054617827557e-19 relative error = 9.0328760660599933375435346213175e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.46319126493034528461814059379635 y2[1] (numeric) = -0.46319126493034528503708067861208 absolute error = 4.1894008481573e-19 relative error = 9.0446456255760829530740001688453e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9261.0MB, alloc=40.3MB, time=107.88 TOP MAIN SOLVE Loop x[1] = 2.67 y1[1] (closed_form) = 0.89084586678057648816006285842974 y1[1] (numeric) = 0.89084586678057648896475707339467 absolute error = 8.0469421496493e-19 relative error = 9.0329230338465898661080931263632e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.4543056698303063972473913211913 y2[1] (numeric) = -0.45430566983030639765803117326241 absolute error = 4.1063985207111e-19 relative error = 9.0388449746729645009153579186536e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9302.8MB, alloc=40.3MB, time=108.36 TOP MAIN SOLVE Loop x[1] = 2.68 y1[1] (closed_form) = 0.89534430583949201262204581862066 y1[1] (numeric) = 0.89534430583949201343080424404825 absolute error = 8.0875842542759e-19 relative error = 9.0329320257337491121235663469908e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.44537464454187127547089883192945 y2[1] (numeric) = -0.44537464454187127587307370618264 absolute error = 4.0217487425319e-19 relative error = 9.0300352564273579931338042783723e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9344.7MB, alloc=40.3MB, time=108.84 TOP MAIN SOLVE Loop x[1] = 2.69 y1[1] (closed_form) = 0.89975321121394135568593488432887 y1[1] (numeric) = 0.89975321121394135649867204762184 absolute error = 8.1273716329297e-19 relative error = 9.0328898320510592804867463887761e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.43639908216012626653550411876099 y2[1] (numeric) = -0.43639908216012626692904949095505 absolute error = 3.9354537219406e-19 relative error = 9.0180155798232839400058319022379e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9386.6MB, alloc=40.3MB, time=109.33 TOP MAIN SOLVE Loop x[1] = 2.7 y1[1] (closed_form) = 0.90407214201706114798252728194333 y1[1] (numeric) = 0.9040721420170611487991560664865 absolute error = 8.1662878454317e-19 relative error = 9.0327834095319246608926685636304e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.42737988023382993455605308585788 y2[1] (numeric) = -0.42737988023382993494080468146657 absolute error = 3.8475159560869e-19 relative error = 9.0025668826099871032834205301877e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9428.4MB, alloc=40.3MB, time=109.81 TOP MAIN SOLVE Loop x[1] = 2.71 y1[1] (closed_form) = 0.90830066635937017453818459371608 y1[1] (numeric) = 0.90830066635937017535861624151811 absolute error = 8.2043164780203e-19 relative error = 9.0325998668531781185717973012403e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.41831794067565893261379068110859 y2[1] (numeric) = -0.41831794067565893298958450423994 absolute error = 3.7579382313135e-19 relative error = 8.9834498258519629339237015430106e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9470.2MB, alloc=40.3MB, time=110.30 TOP MAIN SOLVE Loop x[1] = 2.72 y1[1] (closed_form) = 0.91243836139195796298962879998706 y1[1] (numeric) = 0.91243836139195796381377291461153 absolute error = 8.2414411462447e-19 relative error = 9.0323264507117842706765210207692e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.40921416967201748668244467400742 y2[1] (numeric) = -0.40921416967201748704911703635514 absolute error = 3.6667236234772e-19 relative error = 8.9604023888421441902392410151302e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9512.0MB, alloc=40.3MB, time=110.78 TOP MAIN SOLVE Loop x[1] = 2.73 y1[1] (closed_form) = 0.91648481334876932225826112489279 y1[1] (numeric) = 0.91648481334876932308602567467889 absolute error = 8.2776454978610e-19 relative error = 9.0319505323989833906228251104580e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.40006947759241951035844795789445 y2[1] (numeric) = -0.40006947759241951071583550771742 absolute error = 3.5738754982297e-19 relative error = 8.9331371134257645086466554220870e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9553.9MB, alloc=40.3MB, time=111.27 TOP MAIN SOLVE Loop x[1] = 2.74 y1[1] (closed_form) = 0.92043961758798060326537325177928 y1[1] (numeric) = 0.92043961758798060409666457335251 absolute error = 8.3129132157323e-19 relative error = 9.0314595948361672257979166354936e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.39088477889845241210831170164027 y2[1] (numeric) = -0.390884778898452412456251452766 absolute error = 3.4793975112573e-19 relative error = 8.9013379366230307895228803041600e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9595.7MB, alloc=40.3MB, time=111.75 TOP MAIN SOLVE Loop x[1] = 2.75 y1[1] (closed_form) = 0.92430237863246354409665948952671 y1[1] (numeric) = 0.92430237863246354493138229159968 absolute error = 8.3472280207297e-19 relative error = 9.0308412200341890235870154892655e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.38166099205233169857656137237778 y2[1] (numeric) = -0.38166099205233169891489073322551 absolute error = 3.3832936084773e-19 relative error = 8.8646565379503008420395259522539e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9637.4MB, alloc=40.3MB, time=112.25 TOP MAIN SOLVE Loop x[1] = 2.76 y1[1] (closed_form) = 0.9280727102093326532652331971401 y1[1] (numeric) = 0.92807271020933265410329056460354 absolute error = 8.3805736746344e-19 relative error = 9.0300830769435174430438026321854e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.37239903942505551841770059244975 y2[1] (numeric) = -0.37239903942505551874625739506922 absolute error = 3.2855680261947e-19 relative error = 8.8227081124249604452528025891131e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9679.3MB, alloc=40.3MB, time=112.73 TOP MAIN SOLVE Loop x[1] = 2.77 y1[1] (closed_form) = 0.93175023528857217636777720782907 y1[1] (numeric) = 0.93175023528857217720907060613347 absolute error = 8.4129339830440e-19 relative error = 9.0291729096676127188272096966837e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.36309984720416833112128200917246 y2[1] (numeric) = -0.36309984720416833143990453829392 absolute error = 3.1862252912146e-19 relative error = 8.7750664610525416309761440931625e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9721.0MB, alloc=40.3MB, time=113.22 TOP MAIN SOLVE Loop x[1] = 2.78 y1[1] (closed_form) = 0.93533458612073878346935166911759 y1[1] (numeric) = 0.93533458612073878431378094894526 absolute error = 8.4442927982767e-19 relative error = 9.0280985260034620027713751535120e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.35376434530114292438633931722734 y2[1] (numeric) = -0.35376434530114292469486633931886 absolute error = 3.0852702209152e-19 relative error = 8.7212582666827398370025757712815e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9762.8MB, alloc=40.3MB, time=113.70 TOP MAIN SOLVE Loop x[1] = 2.79 y1[1] (closed_form) = 0.93882540427373620697953961962409 y1[1] (numeric) = 0.93882540427373620782700302185181 absolute error = 8.4746340222772e-19 relative error = 9.0268477862857500242936384255560e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.34439346725839004176626159556229 y2[1] (numeric) = -0.34439346725839004206453238789006 absolute error = 2.9827079232777e-19 relative error = 8.6607563930353150220360824222738e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9804.6MB, alloc=40.3MB, time=114.19 TOP MAIN SOLVE Loop x[1] = 2.8 y1[1] (closed_form) = 0.94222234066865815258678811736615 y1[1] (numeric) = 0.94222234066865815343718227831848 absolute error = 8.5039416095233e-19 relative error = 9.0254085925073554976345690445919e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.33498815015590491954385375271242 y2[1] (numeric) = -0.33498815015590491983170813239973 absolute error = 2.8785437968731e-19 relative error = 8.5929720067214717614623126718369e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=9846.3MB, alloc=40.3MB, time=114.67 TOP MAIN SOLVE Loop memory used=9888.0MB, alloc=40.3MB, time=115.16 x[1] = 2.81 y1[1] (closed_form) = 0.94552505561469589898972047835884 y1[1] (numeric) = 0.94552505561469589984294043535195 absolute error = 8.5321995699311e-19 relative error = 9.0237688776890489458827392397536e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.32554933451756006810510128120633 y2[1] (numeric) = -0.32554933451756006838237963428729 absolute error = 2.7727835308096e-19 relative error = 8.5172452738036132981993748821888e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=9929.8MB, alloc=40.3MB, time=115.64 x[1] = 2.82 y1[1] (closed_form) = 0.94873321884310709569453606376004 y1[1] (numeric) = 0.94873321884310709655047526093607 absolute error = 8.5593919717603e-19 relative error = 9.0219165954763250437697007160954e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.31607796421705366845541285602457 y2[1] (numeric) = -0.3160779642170536687219561664881 absolute error = 2.6654331046353e-19 relative error = 8.4328343206011108551585701864564e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=9971.5MB, alloc=40.3MB, time=116.12 x[1] = 2.83 y1[1] (closed_form) = 0.95184650954024236202702511272453 y1[1] (numeric) = 0.95184650954024236288557540717628 absolute error = 8.5855029445175e-19 relative error = 9.0198397099385700326160778783282e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.3065749863835229889603130778681 y2[1] (numeric) = -0.30657498638352298921596295668813 absolute error = 2.5564987882003e-19 relative error = 8.3389020688143792459342098526274e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=10013.3MB, alloc=40.3MB, time=116.61 x[1] = 2.84 y1[1] (closed_form) = 0.95486461637962638472681949358624 y1[1] (numeric) = 0.9548646163796263855878711617721 absolute error = 8.6105166818586e-19 relative error = 9.0175261855501713711005933601654e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.29704135130683226089025606809731 y2[1] (numeric) = -0.29704135130683226113485478224496 absolute error = 2.4459871414765e-19 relative error = 8.2345004515882693017287574412003e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10055.1MB, alloc=40.3MB, time=117.09 TOP MAIN SOLVE Loop x[1] = 2.85 y1[1] (closed_form) = 0.95778723755309030604085410717493 y1[1] (numeric) = 0.95778723755309030690429585162385 absolute error = 8.6344174444892e-19 relative error = 9.0149639773317534975988671375336e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.28747801234254448390307892669172 y2[1] (numeric) = -0.28747801234254448413646942812518 absolute error = 2.3339050143346e-19 relative error = 8.1185513817788436873145543410903e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10097.0MB, alloc=40.3MB, time=117.58 TOP MAIN SOLVE Loop x[1] = 2.86 y1[1] (closed_form) = 0.96061408080095228910317316639277 y1[1] (numeric) = 0.96061408080095228996889212269895 absolute error = 8.6571895630618e-19 relative error = 9.0121410211304679392216937017112e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.27788592581658666420435690975324 y2[1] (numeric) = -0.27788592581658666442638286438115 absolute error = 2.2202595462791e-19 relative error = 7.9898236650694580726242332371494e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10138.8MB, alloc=40.3MB, time=118.06 TOP MAIN SOLVE Loop x[1] = 2.87 y1[1] (closed_form) = 0.96334486344124324256969375873794 y1[1] (numeric) = 0.96334486344124324343757550284501 absolute error = 8.6788174410707e-19 relative error = 9.0090452240212129235134218975369e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.26826605092961801878239892098714 y2[1] (numeric) = -0.2682660509296180189929047376013 absolute error = 2.1050581661416e-19 relative error = 7.8469048127669375024589529850557e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10180.6MB, alloc=40.3MB, time=118.55 TOP MAIN SOLVE Loop x[1] = 2.88 y1[1] (closed_form) = 0.96597931239797478195981790476552 y1[1] (numeric) = 0.96597931239797478282974646053993 absolute error = 8.6992855577441e-19 relative error = 9.0056644548098486111199119700293e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.25861934966111070881776692011768 y2[1] (numeric) = -0.25861934966111070901659777929081 absolute error = 1.9883085917313e-19 relative error = 7.6881663894706148562308457343316e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10222.5MB, alloc=40.3MB, time=119.03 TOP MAIN SOLVE Loop x[1] = 2.89 y1[1] (closed_form) = 0.96851716422844660093231550720928 y1[1] (numeric) = 0.96851716422844660180417335430237 absolute error = 8.7185784709309e-19 relative error = 9.0019865346180140329738552299950e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.24894678667315269411404584058049 y2[1] (numeric) = -0.2489467866731526943010477235248 absolute error = 1.8700188294431e-19 relative error = 7.5117210968394052945485261011626e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10264.3MB, alloc=40.3MB, time=119.52 TOP MAIN SOLVE Loop x[1] = 2.9 y1[1] (closed_form) = 0.97095816514959052178110666934553 y1[1] (numeric) = 0.9709581651495905226547747513441 absolute error = 8.7366808199857e-19 relative error = 8.9979992275359099540266067759715e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.23924932921398232818425691873958 y2[1] (numeric) = -0.23924932921398232835927663612206 absolute error = 1.7501971738248e-19 relative error = 7.3153691990477443188998908307662e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10306.2MB, alloc=40.3MB, time=120.00 TOP MAIN SOLVE Loop x[1] = 2.91 y1[1] (closed_form) = 0.97330207106334859076784710660275 y1[1] (numeric) = 0.97330207106334859164320483946749 absolute error = 8.7535773286474e-19 relative error = 8.9936902313214767607776225400484e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.22952794702126434045301822382699 y2[1] (numeric) = -0.22952794702126434061590344453698 absolute error = 1.6288522070999e-19 relative error = 7.0965310683887960158784476445179e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10348.0MB, alloc=40.3MB, time=120.50 TOP MAIN SOLVE Loop x[1] = 2.92 y1[1] (closed_form) = 0.97554864758108268050293173515827 y1[1] (numeric) = 0.97554864758108268137985701594956 absolute error = 8.7692528079129e-19 relative error = 8.9890471681311453619135267704820e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.21978361222511687789562909306458 y2[1] (numeric) = -0.21978361222511687804622837292958 absolute error = 1.5059927986500e-19 relative error = 6.8521614664675854168420973511225e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10389.9MB, alloc=40.3MB, time=120.98 TOP MAIN SOLVE Loop x[1] = 2.93 y1[1] (closed_form) = 0.97769767004701315843501960467633 y1[1] (numeric) = 0.97769767004701315931338882056702 absolute error = 8.7836921589069e-19 relative error = 8.9840575752671386419736767338669e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.21001729925089930332910403425911 y2[1] (numeric) = -0.21001729925089930346726684470455 absolute error = 1.3816281044544e-19 relative error = 6.5786395186609076803462078813140e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10431.7MB, alloc=40.3MB, time=121.47 TOP MAIN SOLVE Loop x[1] = 2.94 y1[1] (closed_form) = 0.97974892356068427760176338132832 y1[1] (numeric) = 0.97974892356068427848145141890272 absolute error = 8.7968803757440e-19 relative error = 8.9787088959216738928669685300339e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.20022998472177047149431709442312 y2[1] (numeric) = -0.20022998472177047161989385107187 absolute error = 1.2557675664875e-19 relative error = 6.2716259417012468373482995239586e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10473.6MB, alloc=40.3MB, time=121.95 TOP MAIN SOLVE Loop x[1] = 2.95 y1[1] (closed_form) = 0.98170220299845404312138940470197 y1[1] (numeric) = 0.98170220299845404400226965954057 absolute error = 8.8088025483860e-19 relative error = 8.9729884699055441085189701224434e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.19042264736102722702044731405738 y2[1] (numeric) = -0.19042264736102722713328940526472 absolute error = 1.1284209120734e-19 relative error = 5.9258755600325079972931127737186e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10515.4MB, alloc=40.3MB, time=122.44 TOP MAIN SOLVE Loop x[1] = 2.96 y1[1] (closed_form) = 0.98355731303400640545638732297616 y1[1] (numeric) = 0.98355731303400640633833170952533 absolute error = 8.8194438654917e-19 relative error = 8.9668835243429973085777795518223e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.18059626789423289034054450880135 y2[1] (numeric) = -0.18059626789423289044050432412136 absolute error = 9.995981532001e-20 relative error = 5.5349878757490142023206292953963e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10557.3MB, alloc=40.3MB, time=122.92 TOP MAIN SOLVE Loop x[1] = 2.97 y1[1] (closed_form) = 0.98531406815788372924707637480614 y1[1] (numeric) = 0.98531406815788373012995533653222 absolute error = 8.8287896172608e-19 relative error = 8.9603811643193768002731861419597e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.17075182895114551862806449866797 y2[1] (numeric) = -0.17075182895114551871499545724694 absolute error = 8.693095857897e-20 relative error = 5.0910704214970464829998352667485e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10599.1MB, alloc=40.3MB, time=123.41 TOP MAIN SOLVE Loop x[1] = 2.98 y1[1] (closed_form) = 0.9869722926960375844844419643954 y1[1] (numeric) = 0.98697229269603758536812448422217 absolute error = 8.8368251982677e-19 relative error = 8.9534683634621725607043887847143e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.16089031496745574884655395454133 y2[1] (numeric) = -0.16089031496745574892031053343413 absolute error = 7.375657889280e-20 relative error = 4.5842771149847762171828653139993e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10640.9MB, alloc=40.3MB, time=123.91 TOP MAIN SOLVE Loop x[1] = 2.99 y1[1] (closed_form) = 0.98853182082739600495858418721084 y1[1] (numeric) = 0.98853182082739600584293779823989 absolute error = 8.8435361102905e-19 relative error = 8.9461319544458428875452678217276e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.15101271208634404904629503561052 y2[1] (numeric) = -0.1510127120863440491067327980156 absolute error = 6.043776240508e-20 relative error = 4.0021638953496641019771726938524e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10682.7MB, alloc=40.3MB, time=124.39 TOP MAIN SOLVE Loop x[1] = 3 y1[1] (closed_form) = 0.98999249660044545727157279473126 y1[1] (numeric) = 0.98999249660044545815646359124427 absolute error = 8.8489079651301e-19 relative error = 8.9383586194001850005102986365498e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.14112000805986722210074480280811 y2[1] (numeric) = -0.14112000805986722214772042621711 absolute error = 4.697562340900e-20 relative error = 3.3287713099528431763160466857245e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10724.5MB, alloc=40.3MB, time=124.88 TOP MAIN SOLVE Loop x[1] = 3.01 y1[1] (closed_form) = 0.99135417394882586223162557418242 y1[1] (numeric) = 0.99135417394882586311691822292442 absolute error = 8.8529264874200e-19 relative error = 8.9301348802077994303677787082898e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.13121319215018402315021812468485 y2[1] (numeric) = -0.1312131921501840231835894289425 absolute error = 3.337130425765e-20 relative error = 2.5432888043340844519063242228870e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10766.4MB, alloc=40.3MB, time=125.36 TOP MAIN SOLVE Loop x[1] = 3.02 y1[1] (closed_form) = 0.99261671670593710913946653326304 y1[1] (numeric) = 0.9926167167059371100250242850059 absolute error = 8.8555775174286e-19 relative error = 8.9214470886772971017329099189995e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.12129325503062976810875799633911 y2[1] (numeric) = -0.12129325503062976812838397160925 absolute error = 1.962597527014e-20 relative error = 1.6180599049125955134640272118166e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10808.2MB, alloc=40.3MB, time=125.84 TOP MAIN SOLVE Loop x[1] = 3.03 y1[1] (closed_form) = 0.99377999861855560232760730870843 y1[1] (numeric) = 0.99377999861855560321329201009346 absolute error = 8.8568470138503e-19 relative error = 8.9122814165732065783219948632333e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.11136118868664982569090503291726 y2[1] (numeric) = -0.11136118868664982569664586755088 absolute error = 5.74083463362e-21 relative error = 5.1551484869415921643258953027738e-18 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10850.1MB, alloc=40.3MB, time=126.33 TOP MAIN SOLVE Loop x[1] = 3.04 y1[1] (closed_form) = 0.99484390335945947830924495484319 y1[1] (numeric) = 0.99484390335945947919491706050189 absolute error = 8.8567210565870e-19 relative error = 8.9026238454887203313515009054846e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.10141798631660189952660831260879 y2[1] (numeric) = -0.10141798631660189951832542090987 absolute error = 8.28289169892e-21 relative error = 8.1670835714119370078836364741009e-18 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10891.9MB, alloc=40.3MB, time=126.83 TOP MAIN SOLVE Loop x[1] = 3.05 y1[1] (closed_form) = 0.99580832453906123102558220156492 y1[1] (numeric) = 0.99580832453906123191110078651696 absolute error = 8.8551858495204e-19 relative error = 8.8924601565459694642664869754305e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.091464642232437020053401588696418 y2[1] (numeric) = -0.091464642232437020030957638581427 absolute error = 2.2443950114991e-20 relative error = 2.4538389444474837398001561629002e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10933.8MB, alloc=40.3MB, time=127.31 TOP MAIN SOLVE Loop x[1] = 3.06 y1[1] (closed_form) = 0.99667316571604658193873927179315 y1[1] (numeric) = 0.99667316571604658282396204412028 absolute error = 8.8522277232713e-19 relative error = 8.8817759199040286300945190914356e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.081502151760269178003890088835723 y2[1] (numeric) = -0.081502151760269177967149029382618 absolute error = 3.6741059453105e-20 relative error = 4.5079864346619128968375363039518e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=10975.7MB, alloc=40.3MB, time=127.80 TOP MAIN SOLVE Loop x[1] = 3.07 y1[1] (closed_form) = 0.99743834040701853109211366272677 y1[1] (numeric) = 0.99743834040701853197689697652175 absolute error = 8.8478331379498e-19 relative error = 8.8705564840622821154913150547967e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.071531511140843542442340790318903 y2[1] (numeric) = -0.071531511140843542391167879201546 absolute error = 5.1172911117357e-20 relative error = 7.1538976740752716563364139518646e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11017.6MB, alloc=40.3MB, time=128.28 TOP MAIN SOLVE Loop x[1] = 3.08 y1[1] (closed_form) = 0.99810377209514562474111853735979 y1[1] (numeric) = 0.99810377209514562562531740594901 absolute error = 8.8419886858922e-19 relative error = 8.8587869649382761572936630033024e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.061553717429913216445629637135705 y2[1] (numeric) = -0.061553717429913216379891467939497 absolute error = 6.5738169196208e-20 relative error = 1.0679804882793523774145037507409e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11059.4MB, alloc=40.3MB, time=128.77 TOP MAIN SOLVE Loop x[1] = 3.09 y1[1] (closed_form) = 0.99866939423781357473474351808576 y1[1] (numeric) = 0.99866939423781357561821162752439 absolute error = 8.8346810943863e-19 relative error = 8.8464522347047050591246153857491e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.051569768398534492669958510574615 y2[1] (numeric) = -0.051569768398534492589523039989277 absolute error = 8.0435470585338e-20 relative error = 1.5597407761021438199893543315866e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11101.2MB, alloc=40.3MB, time=129.25 TOP MAIN SOLVE Loop x[1] = 3.1 y1[1] (closed_form) = 0.99913515027327946449237605454147 y1[1] (numeric) = 0.99913515027327946537496577737997 absolute error = 8.8258972283850e-19 relative error = 8.8335369103679074483176977190210e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.041580662433290579194698271596673 y2[1] (numeric) = -0.041580662433290579099434846482064 absolute error = 9.5263425114609e-20 relative error = 2.2910511651285906341929970395002e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11143.0MB, alloc=40.3MB, time=129.73 TOP MAIN SOLVE Loop x[1] = 3.11 y1[1] (closed_form) = 0.99950099362632787616083083671683 y1[1] (numeric) = 0.99950099362632787704239324603746 absolute error = 8.8156240932063e-19 relative error = 8.8200253420679415571304796704708e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.031587398436453773187626872703365 y2[1] (numeric) = -0.031587398436453773077406257024229 absolute error = 1.10220615679136e-19 relative error = 3.4893856770405860954034327959142e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11184.9MB, alloc=40.3MB, time=130.23 TOP MAIN SOLVE Loop x[1] = 3.12 y1[1] (closed_form) = 0.99976688771292837334358497397559 y1[1] (numeric) = 0.99976688771292837422396985769753 absolute error = 8.8038488372194e-19 relative error = 8.8059016010813557738058977293446e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.021590975726096066090998104201892 y2[1] (numeric) = -0.021590975726096065965692505827468 absolute error = 1.25305598374424e-19 relative error = 5.8036098027275633968527432505434e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11226.6MB, alloc=40.3MB, time=130.72 TOP MAIN SOLVE Loop x[1] = 3.13 y1[1] (closed_form) = 0.99993280594389387365782723913921 y1[1] (numeric) = 0.99993280594389387453688311459103 absolute error = 8.7905587545182e-19 relative error = 8.7911494675087571261433051911091e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.011592393936158169184681483118307 y2[1] (numeric) = -0.011592393936158169044164580482733 absolute error = 1.40516902635574e-19 relative error = 1.2121474081145887339645651708919e-15 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 17 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11268.4MB, alloc=40.3MB, time=131.20 TOP MAIN SOLVE Loop x[1] = 3.14 y1[1] (closed_form) = 0.99999873172753954528511430634505 y1[1] (numeric) = 0.9999987317275395461626884351031 absolute error = 8.7757412875805e-19 relative error = 8.7757524176256110434463345312954e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = -0.0015926529164869525405414363244433 y2[1] (numeric) = -0.0015926529164869523846884049438909 absolute error = 1.558530313805524e-19 relative error = 9.7857499124373211639763879375552e-15 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 17 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11310.3MB, alloc=40.3MB, time=131.69 TOP MAIN SOLVE Loop x[1] = 3.15 y1[1] (closed_form) = 0.99996465847134196162819465679473 y1[1] (numeric) = 0.99996465847134196250413305978588 absolute error = 8.7593840299115e-19 relative error = 8.7596936108742843491460186874842e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.008407247367148706459141516571067 y2[1] (numeric) = 0.0084072473671487066304539777285557 absolute error = 1.713124611574887e-19 relative error = 2.0376759916318344744151681559954e-15 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 17 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11352.1MB, alloc=40.3MB, time=132.17 TOP MAIN SOLVE Loop x[1] = 3.16 y1[1] (closed_form) = 0.99983058958259834815991709427395 y1[1] (numeric) = 0.99983058958259834903406456714139 absolute error = 8.7414747286744e-19 relative error = 8.7429558764787584912832019252770e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.01840630693305366670737927118737 y2[1] (numeric) = 0.018406306933053666894272913483379 absolute error = 1.86893642296009e-19 relative error = 1.0153782775424072078359415689610e-15 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 17 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11393.9MB, alloc=40.3MB, time=132.66 TOP MAIN SOLVE Loop x[1] = 3.17 y1[1] (closed_form) = 0.99959653846808585554008835013528 y1[1] (numeric) = 0.99959653846808585641228847886562 absolute error = 8.7220012873034e-19 relative error = 8.7255216996550929532964628885254e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.028403525883603859571285274896733 y2[1] (numeric) = 0.028403525883603859773880273959307 absolute error = 2.02594999062574e-19 relative error = 7.1327411918082827252994895257856e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11435.8MB, alloc=40.3MB, time=133.14 TOP MAIN SOLVE Loop x[1] = 3.18 y1[1] (closed_form) = 0.99926252853272089307268415386031 y1[1] (numeric) = 0.9992625285327208939427793306706 absolute error = 8.7009517681029e-19 relative error = 8.7073732073983068127594310572338e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.03839790450523521805369524672612 y2[1] (numeric) = 0.038397904505235218272110176545931 absolute error = 2.18414929819811e-19 relative error = 5.6881992034235106980179690669161e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11477.6MB, alloc=40.3MB, time=133.63 TOP MAIN SOLVE Loop x[1] = 3.19 y1[1] (closed_form) = 0.99882859317721865656895082969948 y1[1] (numeric) = 0.9988285931772186574367822691824 absolute error = 8.6783143948292e-19 relative error = 8.6884921538178644159924724738587e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.048388443368414200108007148451169 y2[1] (numeric) = 0.048388443368414200342358955641004 absolute error = 2.34351807189835e-19 relative error = 4.8431358993211449609409118223489e-16 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11519.4MB, alloc=40.3MB, time=134.13 TOP MAIN SOLVE Loop x[1] = 3.2 y1[1] (closed_form) = 0.99829477579475308466166072228358 y1[1] (numeric) = 0.99829477579475308552706847780925 absolute error = 8.6540775552567e-19 relative error = 8.6688599049985980844210799867337e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.058374143427579909137217414619095 y2[1] (numeric) = 0.058374143427579909387621392840611 absolute error = 2.50403978221516e-19 relative error = 4.2896385885674196890366533042442e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11561.3MB, alloc=40.3MB, time=134.61 TOP MAIN SOLVE Loop x[1] = 3.21 y1[1] (closed_form) = 0.99766112976661757757210666520424 y1[1] (numeric) = 0.99766112976661757843492964557687 absolute error = 8.6282298037263e-19 relative error = 8.6484574233584683646318825800782e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.068354006121047817548388360676863 y2[1] (numeric) = 0.068354006121047817814958125238572 absolute error = 2.66569764561709e-19 relative error = 3.8998411313250863785168712955394e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11603.1MB, alloc=40.3MB, time=135.09 TOP MAIN SOLVE Loop x[1] = 3.22 y1[1] (closed_form) = 0.99692771845688691225434273747586 y1[1] (numeric) = 0.99692771845688691311441872384358 absolute error = 8.6007598636772e-19 relative error = 8.6272652514768532276414796487328e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.078327033470865103073444147916042 y2[1] (numeric) = 0.078327033470865103356291610546437 absolute error = 2.82847462630395e-19 relative error = 3.6111090909067083608383528847489e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11644.9MB, alloc=40.3MB, time=135.58 TOP MAIN SOLVE Loop x[1] = 3.23 y1[1] (closed_form) = 0.99609461520608088772070849458495 y1[1] (numeric) = 0.99609461520608088857787415760095 absolute error = 8.5716566301600e-19 relative error = 8.6052634953624557641094146768222e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.088292228182607612405875728529723 y2[1] (numeric) = 0.088292228182607612705111072329469 absolute error = 2.99235343799746e-19 relative error = 3.3891470399961132585063856881019e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11686.8MB, alloc=40.3MB, time=136.06 TOP MAIN SOLVE Loop x[1] = 3.24 y1[1] (closed_form) = 0.99516190332383033417882384374247 y1[1] (numeric) = 0.99516190332383033503291476097584 absolute error = 8.5409091723337e-19 relative error = 8.5824318071332441670338685729177e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.098248593745108472540154959437637 y2[1] (numeric) = 0.098248593745108472855886614014704 absolute error = 3.15731654577067e-19 relative error = 3.2135997324927249794497831260803e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11728.6MB, alloc=40.3MB, time=136.55 TOP MAIN SOLVE Loop memory used=11770.3MB, alloc=40.3MB, time=137.05 x[1] = 3.25 y1[1] (closed_form) = 0.9941296760805462193730292251716 y1[1] (numeric) = 0.99412967608054622022387989876572 absolute error = 8.5085067359412e-19 relative error = 8.5587493670713287266570822325247e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.10819513453010837703583084256083 y2[1] (numeric) = 0.10819513453010837736816545935245 absolute error = 3.3233461679162e-19 relative error = 3.0716225663469037940949283925849e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=11812.1MB, alloc=40.3MB, time=137.53 x[1] = 3.26 y1[1] (closed_form) = 0.99299803669809268521269456717166 y1[1] (numeric) = 0.99299803669809268606013844174859 absolute error = 8.4744387457693e-19 relative error = 8.5341948650255346431983628257588e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.11813085589181758226072311033608 y2[1] (numeric) = 0.11813085589181758260976553812137 absolute error = 3.4904242778529e-19 relative error = 2.9547100556431901038458034606905e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=11854.0MB, alloc=40.3MB, time=138.02 x[1] = 3.27 y1[1] (closed_form) = 0.99176709833946494737596174049474 y1[1] (numeric) = 0.99176709833946494821983122130335 absolute error = 8.4386948080861e-19 relative error = 8.5087464811195811857345379848972e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.12805476426637965749655689075362 y2[1] (numeric) = 0.12805476426637965786241015136072 absolute error = 3.6585326060710e-19 relative error = 2.8570062402836622013353001420977e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=11895.7MB, alloc=40.3MB, time=138.50 x[1] = 3.28 y1[1] (closed_form) = 0.99043698409747309009035841613171 y1[1] (numeric) = 0.99043698409747309093048488743786 absolute error = 8.4012647130615e-19 relative error = 8.4823818657348280405292363354021e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.13796586727122704261491407058525 y2[1] (numeric) = 0.13796586727122704299767933479674 absolute error = 3.8276526421149e-19 relative error = 2.7743475381415312096281392176885e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11937.5MB, alloc=40.3MB, time=138.98 TOP MAIN SOLVE Loop x[1] = 3.29 y1[1] (closed_form) = 0.98900782698243288770137512553948 y1[1] (numeric) = 0.98900782698243288853758896925612 absolute error = 8.3621384371664e-19 relative error = 8.4550781187244651672562330676997e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.14786317380431847785052978374264 y2[1] (numeric) = 0.14786317380431847825030634740312 absolute error = 3.9977656366048e-19 relative error = 2.7036925650570890393207487382646e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=11979.3MB, alloc=40.3MB, time=139.47 TOP MAIN SOLVE Loop x[1] = 3.3 y1[1] (closed_form) = 0.98747976990886488393659105110285 y1[1] (numeric) = 0.98747976990886488476872166565801 absolute error = 8.3213061455516e-19 relative error = 8.4268117678193837515321654457751e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.15774569414324838201165427760248 y2[1] (numeric) = 0.15774569414324838242853953793193 absolute error = 4.1688526032945e-19 relative error = 2.6427679220890667933442263784427e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12021.1MB, alloc=40.3MB, time=139.95 TOP MAIN SOLVE Loop x[1] = 3.31 y1[1] (closed_form) = 0.98585296568120305894633807058553 y1[1] (numeric) = 0.98585296568120305977421389002607 absolute error = 8.2787581944054e-19 relative error = 8.3975587461817465796427552101302e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.16761244004421826827224999431698 y2[1] (numeric) = 0.16761244004421826870633942643382 absolute error = 4.3408943211684e-19 relative error = 2.5898401813273630052746329106075e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12062.8MB, alloc=40.3MB, time=140.44 TOP MAIN SOLVE Loop x[1] = 3.32 y1[1] (closed_form) = 0.98412757697851451324228958473119 y1[1] (numeric) = 0.98412757697851451406573809806041 absolute error = 8.2344851332922e-19 relative error = 8.3672943690632656586599988331419e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.17746242484086030048692055230841 y2[1] (numeric) = 0.17746242484086030093830768596586 absolute error = 4.5138713365745e-19 relative error = 2.5435645549317389242480857283659e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12104.5MB, alloc=40.3MB, time=140.92 TOP MAIN SOLVE Loop x[1] = 3.33 y1[1] (closed_form) = 0.98230377633823169655284671485927 y1[1] (numeric) = 0.98230377633823169737169448560587 absolute error = 8.1884777074660e-19 relative error = 8.3359933095141668685490667275719e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.18729466354290310775529282413595 y2[1] (numeric) = 0.18729466354290310822406922067534 absolute error = 4.6877639653939e-19 relative error = 2.5028817568633427416715233392474e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12146.4MB, alloc=40.3MB, time=141.41 TOP MAIN SOLVE Loop x[1] = 3.34 y1[1] (closed_form) = 0.98038174613889880835887990106991 y1[1] (numeric) = 0.98038174613889880917295258708654 absolute error = 8.1407268601663e-19 relative error = 8.3036295730999215761029339569839e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.19710817293466999073661691059272 y2[1] (numeric) = 0.19710817293466999122287214011766 absolute error = 4.8625522952494e-19 relative error = 2.4669460544698245901288933560807e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12188.3MB, alloc=40.3MB, time=141.89 TOP MAIN SOLVE Loop x[1] = 3.35 y1[1] (closed_form) = 0.97836167858193409545539437527153 y1[1] (numeric) = 0.97836167858193409626451674876025 absolute error = 8.0912237348872e-19 relative error = 8.2701764715630065140025821014854e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.20690197167339966997603411602551 y2[1] (numeric) = 0.20690197167339967047985573480027 absolute error = 5.0382161877476e-19 relative error = 2.4350740338523983864638234867822e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12230.1MB, alloc=40.3MB, time=142.37 TOP MAIN SOLVE Loop x[1] = 3.36 y1[1] (closed_form) = 0.97624377567240987029416530777832 y1[1] (numeric) = 0.9762437756724098710981612755411 absolute error = 8.0399596776278e-19 relative error = 8.2356065953814628292055211616919e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.21667508038737974424961398190553 y2[1] (numeric) = 0.21667508038737974477108750998154 absolute error = 5.2147352807601e-19 relative error = 2.4067074402081692427597869796518e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12272.1MB, alloc=40.3MB, time=142.88 TOP MAIN SOLVE Loop x[1] = 3.37 y1[1] (closed_form) = 0.97402824919885217208949176597085 y1[1] (numeric) = 0.97402824919885217288818438988264 absolute error = 7.9869262391179e-19 relative error = 8.1998917851584135190954500858938e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.22642652177388304566410348430857 y2[1] (numeric) = 0.22642652177388304620331238338234 absolute error = 5.3920889907377e-19 relative error = 2.3813857795874358728131926263982e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12314.0MB, alloc=40.3MB, time=143.36 TOP MAIN SOLVE Loop x[1] = 3.38 y1[1] (closed_form) = 0.97171532071206209070412534999057 y1[1] (numeric) = 0.97171532071206209149733686769255 absolute error = 7.9321151770198e-19 relative error = 8.1630031017800922855906062597783e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.23615532069689709795749177758963 y2[1] (numeric) = 0.23615532069689709851451742909594 absolute error = 5.5702565150631e-19 relative error = 2.3587258159694256473810983856034e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12355.8MB, alloc=40.3MB, time=143.84 TOP MAIN SOLVE Loop x[1] = 3.39 y1[1] (closed_form) = 0.96930522150296087116533607467248 y1[1] (numeric) = 0.96930522150296087195288792048318 absolute error = 7.8755184581070e-19 relative error = 8.1249107952762051492831444416483e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.24586050428463690513600137155794 y2[1] (numeric) = 0.24586050428463690571092305500169 absolute error = 5.7492168344375e-19 relative error = 2.3384060205869965488589602542584e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12397.7MB, alloc=40.3MB, time=144.33 TOP MAIN SOLVE Loop x[1] = 3.4 y1[1] (closed_form) = 0.96679819257946101428220153976569 y1[1] (numeric) = 0.96679819257946101506391436580769 absolute error = 7.8171282604200e-19 relative error = 8.0855842723118364463200886882312e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.25554110202683131924990242936374 y2[1] (numeric) = 0.25554110202683131984279730089397 absolute error = 5.9289487153023e-19 relative error = 2.3201546319854924565522824171489e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12439.5MB, alloc=40.3MB, time=144.81 TOP MAIN SOLVE Loop x[1] = 3.41 y1[1] (closed_form) = 0.96419448464236568623478364095296 y1[1] (numeric) = 0.96419448464236568701047733849249 absolute error = 7.7569369753953e-19 relative error = 8.0449920622315789489532327274589e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.26519614587177325875244430757411 y2[1] (numeric) = 0.26519614587177325936338737880386 absolute error = 6.1094307122975e-19 relative error = 2.3037403851455334583467159899241e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12481.3MB, alloc=40.3MB, time=145.30 TOP MAIN SOLVE Loop x[1] = 3.42 y1[1] (closed_form) = 0.96149435806029884717415014560141 y1[1] (numeric) = 0.96149435806029884794364386659862 absolute error = 7.6949372099721e-19 relative error = 8.0031017815806280464448663470351e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.2748246703231240725009433576662 y2[1] (numeric) = 0.27482467032312407313000747474142 absolute error = 6.2906411707522e-19 relative error = 2.2889652385850230632326926741924e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12523.2MB, alloc=40.3MB, time=145.78 TOP MAIN SOLVE Loop x[1] = 3.43 y1[1] (closed_form) = 0.95869808284366860579948964122556 y1[1] (numeric) = 0.9586980828436686065626018200928 absolute error = 7.6311217886724e-19 relative error = 7.9598800970135862399914985413513e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.28442571253646236904429691459137 y2[1] (numeric) = 0.28442571253646236969155273751247 absolute error = 6.4725582292110e-19 relative error = 2.2756586145077305406380434764270e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12565.0MB, alloc=40.3MB, time=146.26 TOP MAIN SOLVE Loop x[1] = 3.44 y1[1] (closed_form) = 0.95580593861766640355516501297249 y1[1] (numeric) = 0.95580593861766640431171338853805 absolute error = 7.5654837556556e-19 relative error = 7.9152926865020058425728318000365e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.29399831241556765639445181056032 y2[1] (numeric) = 0.29399831241556765705996779275979 absolute error = 6.6551598219947e-19 relative error = 2.2636727970695314770308657478001e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12606.8MB, alloc=40.3MB, time=146.77 TOP MAIN SOLVE Loop x[1] = 3.45 y1[1] (closed_form) = 0.95281821459430472850678513994775 y1[1] (numeric) = 0.95281821459430472925658677762262 absolute error = 7.4980163767487e-19 relative error = 7.8693041987460740382392712089605e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.30354151270842916399808636621989 y2[1] (numeric) = 0.30354151270842916468192873439924 absolute error = 6.8384236817935e-19 relative error = 2.2528792259008865100677860779813e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12648.7MB, alloc=40.3MB, time=147.25 TOP MAIN SOLVE Loop x[1] = 3.46 y1[1] (closed_form) = 0.94973520954349615510160537578203 y1[1] (numeric) = 0.94973520954349615584447668992689 absolute error = 7.4287131414486e-19 relative error = 7.8218782106849734227550282949840e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.31305435910297024610631577597493 y2[1] (numeric) = 0.31305435910297024680854851020439 absolute error = 7.0223273422946e-19 relative error = 2.2431654880693761483011402292553e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12690.5MB, alloc=40.3MB, time=147.73 TOP MAIN SOLVE Loop x[1] = 3.47 y1[1] (closed_form) = 0.94655723176317660188518005352668 y1[1] (numeric) = 0.94655723176317660262093683001663 absolute error = 7.3575677648995e-19 relative error = 7.7729771830007241125248643653902e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.32253590032247879418185398715726 y2[1] (numeric) = 0.32253590032247879490253880124164 absolute error = 7.2068481408438e-19 relative error = 2.2344328596098071121779546628359e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12732.3MB, alloc=40.3MB, time=148.22 TOP MAIN SOLVE Loop x[1] = 3.48 y1[1] (closed_form) = 0.94328459904847579482359814738228 y1[1] (numeric) = 0.94328459904847579555205556636653 absolute error = 7.2845741898425e-19 relative error = 7.7225624134971620043707303847237e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.33198518822073411538191643544275 y2[1] (numeric) = 0.3319851882207341161211127575565 absolute error = 7.3919632211375e-19 relative error = 2.2265942829421193352769062112036e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12774.0MB, alloc=40.3MB, time=148.70 TOP MAIN SOLVE Loop x[1] = 3.49 y1[1] (closed_form) = 0.93991763865993801915927867276677 y1[1] (numeric) = 0.93991763865993801988025133162066 absolute error = 7.2097265885389e-19 relative error = 7.6705939882328108812769906190758e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.3414012778768207645082874807375 y2[1] (numeric) = 0.34140127787682076526605243433249 absolute error = 7.5776495359499e-19 relative error = 2.2195726926025018201398121704066e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12815.9MB, alloc=40.3MB, time=149.19 TOP MAIN SOLVE Loop x[1] = 3.5 y1[1] (closed_form) = 0.93645668729079633769865762667176 y1[1] (numeric) = 0.93645668729079633841195956313826 absolute error = 7.1330193646650e-19 relative error = 7.6170307302744428579194505766841e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.35078322768961984812036880004364 y2[1] (numeric) = 0.35078322768961984889675718503271 absolute error = 7.7638838498907e-19 relative error = 2.2132996212579304749461016775618e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12857.7MB, alloc=40.3MB, time=149.67 TOP MAIN SOLVE Loop x[1] = 3.51 y1[1] (closed_form) = 0.93290209103330354808266630575758 y1[1] (numeric) = 0.93290209103330354878811102127563 absolute error = 7.0544471551805e-19 relative error = 7.5618301459340005125381710031648e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.36013009947196835175953992341737 y2[1] (numeric) = 0.36013009947196835255460419763692 absolute error = 7.9506427421955e-19 relative error = 2.2077140327489784373925871233764e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12899.6MB, alloc=40.3MB, time=150.16 TOP MAIN SOLVE Loop x[1] = 3.52 y1[1] (closed_form) = 0.92925420534412324591621651227224 y1[1] (numeric) = 0.92925420534412324661361699548903 absolute error = 6.9740048321679e-19 relative error = 7.5049483683372439590458186149777e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.36944095854447707443057432143296 y2[1] (numeric) = 0.3694409585444770752443645823877 absolute error = 8.1379026095474e-19 relative error = 2.2027613401635531430139303448011e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12941.4MB, alloc=40.3MB, time=150.64 TOP MAIN SOLVE Loop x[1] = 3.53 y1[1] (closed_form) = 0.92551339500878445462153901468401 y1[1] (numeric) = 0.92551339500878445531070776514838 absolute error = 6.8916875046437e-19 relative error = 7.4463400981660432513903421366257e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.37871487382899778862484425400664 y2[1] (numeric) = 0.37871487382899778945740822089966 absolute error = 8.3256396689302e-19 relative error = 2.1983925755948787791668528926014e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=12983.2MB, alloc=40.3MB, time=151.13 TOP MAIN SOLVE Loop x[1] = 3.54 y1[1] (closed_form) = 0.92168003410520337652276888612977 y1[1] (numeric) = 0.92168003410520337720351793816383 absolute error = 6.8074905203406e-19 relative error = 7.3859585414037212642789476161578e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.38795091794173027924720110048451 y2[1] (numeric) = 0.38795091794173028009858409653579 absolute error = 8.5138299605128e-19 relative error = 2.1945636849328363055845887114677e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13025.1MB, alloc=40.3MB, time=151.61 TOP MAIN SOLVE Loop x[1] = 3.55 y1[1] (closed_form) = 0.91775450596627591295627082271047 y1[1] (numeric) = 0.9177545059662759136284117694567 absolute error = 6.7214094674623e-19 relative error = 7.3237553439037944235435748202455e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.39714816728595995082022742343695 y2[1] (numeric) = 0.39714816728595995169047235849326 absolute error = 8.7024493505631e-19 relative error = 2.1912349262578985244359107746748e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13066.9MB, alloc=40.3MB, time=152.09 TOP MAIN SOLVE Loop x[1] = 3.56 y1[1] (closed_form) = 0.91373720314154469412352061310366 y1[1] (numeric) = 0.91373720314154469478686463074432 absolute error = 6.6334401764066e-19 relative error = 7.2596805225835056001287028928123e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.40630570214441672928242142268591 y2[1] (numeric) = 0.40630570214441673017156877612524 absolute error = 8.8914735343933e-19 relative error = 2.1883703545053687455848738345807e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13108.7MB, alloc=40.3MB, time=152.59 TOP MAIN SOLVE Loop x[1] = 3.57 y1[1] (closed_form) = 0.90962852735794445195161343603674 y1[1] (numeric) = 0.9096285273579444526059713081828 absolute error = 6.5435787214606e-19 relative error = 7.1936823930387368978257409901765e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.41542260677124602256709945606629 y2[1] (numeric) = 0.41542260677124602347518725999968 absolute error = 9.0808780393339e-19 relative error = 2.1859373783031308878818147280727e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13150.5MB, alloc=40.3MB, time=153.16 TOP MAIN SOLVE Loop x[1] = 3.58 y1[1] (closed_form) = 0.90542888947962966139140085454902 y1[1] (numeric) = 0.90542888947962966203658299679561 absolute error = 6.4518214224659e-19 relative error = 7.1257074933558910641159652841597e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.42449796948358254294260094834376 y2[1] (numeric) = 0.42449796948358254386966477111772 absolute error = 9.2706382277396e-19 relative error = 2.1839063774598671882912912113746e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13192.3MB, alloc=40.3MB, time=153.64 TOP MAIN SOLVE Loop x[1] = 3.59 y1[1] (closed_form) = 0.90113870946688846735564983934783 y1[1] (numeric) = 0.90113870946688846799146632399305 absolute error = 6.3581648464522e-19 relative error = 7.0557005038810010830669056335143e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.43353088275271783380787293204403 y2[1] (numeric) = 0.43353088275271783475394586204612 absolute error = 9.4607293000209e-19 relative error = 2.1822503716343585125198992996409e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13234.2MB, alloc=40.3MB, time=154.13 TOP MAIN SOLVE Loop x[1] = 3.6 y1[1] (closed_form) = 0.89675841633414700587029172526594 y1[1] (numeric) = 0.89675841633414700649655230619019 absolute error = 6.2626058092425e-19 relative error = 6.9836041626945261686312609253861e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.44252044329485238426672734749269 y2[1] (numeric) = 0.44252044329485238523183997726343 absolute error = 9.6511262977074e-19 relative error = 2.1809447323717951844005918886466e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13276.0MB, alloc=40.3MB, time=154.63 TOP MAIN SOLVE Loop x[1] = 3.61 y1[1] (closed_form) = 0.89228844810706831897164969353841 y1[1] (numeric) = 0.89228844810706831958816383124098 absolute error = 6.1651413770257e-19 relative error = 6.9093591765136541673565869339386e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.45146575216142325634494018639253 y2[1] (numeric) = 0.45146575216142325732912059704639 absolute error = 9.8418041065386e-19 relative error = 2.1799669320253613370614595335521e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13317.8MB, alloc=40.3MB, time=155.11 TOP MAIN SOLVE Loop x[1] = 3.62 y1[1] (closed_form) = 0.887729251778750153422404272068 y1[1] (numeric) = 0.88772925177875015402898115885796 absolute error = 6.0657688678996e-19 relative error = 6.8329041267318506585821536885388e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.46036591482899819216274354079485 y2[1] (numeric) = 0.46036591482899819316601728675311 absolute error = 1.00327374595826e-18 relative error = 2.1792963241662311408209124634917e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13359.7MB, alloc=40.3MB, time=155.59 TOP MAIN SOLVE Loop x[1] = 3.63 y1[1] (closed_form) = 0.88308128326502602342992354439801 y1[1] (numeric) = 0.88308128326502602402637212973615 absolute error = 5.9644858533814e-19 relative error = 6.7541753702771749948493800074854e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.46922004128872721172690481453191 y2[1] (numeric) = 0.46922004128872721274929490857016 absolute error = 1.02239009403825e-18 relative error = 2.1789139509689831222359739621621e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13401.5MB, alloc=40.3MB, time=156.08 TOP MAIN SOLVE Loop x[1] = 3.64 y1[1] (closed_form) = 0.87834500735887400722343724413409 y1[1] (numeric) = 0.87834500735887400780956626012282 absolute error = 5.8612901598873e-19 relative error = 6.6731069349523784264229681863170e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.47802724613534275625715663887291 y2[1] (numeric) = 0.47802724613534275729868353748597 absolute error = 1.04152689861306e-18 relative error = 2.1788023737838886308845518589717e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13443.4MB, alloc=40.3MB, time=156.56 TOP MAIN SOLVE Loop x[1] = 3.65 y1[1] (closed_form) = 0.87352089768393783657240447452827 y1[1] (numeric) = 0.87352089768393783714802246154627 absolute error = 5.7561798701800e-19 relative error = 6.5896304088911824101802061540873e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.48678664865569947710681138829532 y2[1] (numeric) = 0.48678664865569947816749297738228 absolute error = 1.06068158908696e-18 relative error = 2.1789455237034902392462378110358e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13485.2MB, alloc=40.3MB, time=157.05 TOP MAIN SOLVE Loop x[1] = 3.66 y1[1] (closed_form) = 0.86860943664716492709839092015993 y1[1] (numeric) = 0.86860943664716492766330625263834 absolute error = 5.6491533247841e-19 relative error = 6.5036748237387899580950967004835e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.49549737291684481637245114641035 y2[1] (numeric) = 0.49549737291684481745230272728223 absolute error = 1.07985158087188e-18 relative error = 2.1793285694233185518324824781295e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13527.0MB, alloc=40.3MB, time=157.53 TOP MAIN SOLVE Loop x[1] = 3.67 y1[1] (closed_form) = 0.86361111539056608553795618647981 y1[1] (numeric) = 0.86361111539056608609197709881673 absolute error = 5.5402091233692e-19 relative error = 6.4151665311343908766861248928124e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.50415854785361157220802405891391 y2[1] (numeric) = 0.50415854785361157330705833462688 absolute error = 1.09903427571297e-18 relative error = 2.1799378001066594377011586403934e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13568.9MB, alloc=40.3MB, time=158.01 TOP MAIN SOLVE Loop x[1] = 3.68 y1[1] (closed_form) = 0.85852643374210171794562486853616 y1[1] (numeric) = 0.85852643374210171848855948114615 absolute error = 5.4293461260999e-19 relative error = 6.3240290720400302005622903582331e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.51276930735572368965980922504404 y2[1] (numeric) = 0.51276930735572369077803628706047 absolute error = 1.11822706201643e-18 relative error = 2.1807605213014082005072391832029e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13610.7MB, alloc=40.3MB, time=158.50 TOP MAIN SOLVE Loop memory used=13652.5MB, alloc=40.3MB, time=158.98 x[1] = 3.69 y1[1] (closed_form) = 0.85335590016569945017519302837216 y1[1] (numeric) = 0.85335590016569945070684937386751 absolute error = 5.3165634549535e-19 relative error = 6.2301830384264784435684091744711e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.52132879035440656651575454812466 y2[1] (numeric) = 0.52132879035440656765318186330463 absolute error = 1.13742731517997e-18 relative error = 2.1817849622437523211704586036621e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=13694.3MB, alloc=40.3MB, time=159.48 x[1] = 3.7 y1[1] (closed_form) = 0.8481000317104081588356701063544 y1[1] (numeric) = 0.84810003171040815935585615585475 absolute error = 5.2018604950035e-19 relative error = 6.1335459267848781991363125410985e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.52983614090849321321077762570121 y2[1] (numeric) = 0.52983614090849321436741002362715 absolute error = 1.15663239792594e-18 relative error = 2.1830001931214037987506623579720e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=13736.2MB, alloc=40.3MB, time=159.97 x[1] = 3.71 y1[1] (closed_form) = 0.84275935395869349727638917260975 y1[1] (numeric) = 0.84275935395869349778491286217693 absolute error = 5.0852368956718e-19 relative error = 6.0340319828963236384746930187240e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.53829050829001765624379404325037 y2[1] (numeric) = 0.53829050829001765741963370388699 absolute error = 1.17583966063662e-18 relative error = 2.1843960510689640043973801963197e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for 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=13778.0MB, alloc=40.3MB, time=160.45 x[1] = 3.72 y1[1] (closed_form) = 0.83733440097388008700560008948967 y1[1] (numeric) = 0.83733440097388008750226934668417 absolute error = 4.9666925719450e-19 relative error = 5.9315520372367116242897303891034e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.54669104706928702583745896705622 y2[1] (numeric) = 0.54669104706928702703250540874846 absolute error = 1.19504644169224e-18 relative error = 2.1859630738397314928465168375457e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13819.8MB, alloc=40.3MB, time=160.94 TOP MAIN SOLVE Loop x[1] = 3.73 y1[1] (closed_form) = 0.83182571524674563027960569792163 y1[1] (numeric) = 0.83182571524674563076422846847732 absolute error = 4.8462277055569e-19 relative error = 5.8260133303517271869684606111625e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.55503691719942382070274923216573 y2[1] (numeric) = 0.55503691719942382191699929997686 absolute error = 1.21425006781113e-18 relative error = 2.1876924402397039385487890750740e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13861.7MB, alloc=40.3MB, time=161.42 TOP MAIN SOLVE Loop x[1] = 3.74 y1[1] (closed_form) = 0.82623384764127228440667735620253 y1[1] (numeric) = 0.82623384764127228487906163081644 absolute error = 4.7238427461391e-19 relative error = 5.7173193274818013769693665840472e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.56332728410036989575236111967948 y2[1] (numeric) = 0.56332728410036989698580897407178 absolute error = 1.23344785439230e-18 relative error = 2.1895759165333317913919272120886e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13903.5MB, alloc=40.3MB, time=161.91 TOP MAIN SOLVE Loop x[1] = 3.75 y1[1] (closed_form) = 0.82055935733956072258311240229071 y1[1] (numeric) = 0.8205593573395607230430662435241 absolute error = 4.5995384123339e-19 relative error = 5.6053695216475810352425147796157e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.57156131874234377243415557335029 y2[1] (numeric) = 0.57156131874234377368679267921071 absolute error = 1.25263710586042e-18 relative error = 2.1916058081339491149770881740174e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13945.4MB, alloc=40.3MB, time=162.39 TOP MAIN SOLVE Loop x[1] = 3.76 y1[1] (closed_form) = 0.81480281178591238980944513756309 y1[1] (numeric) = 0.81480281178591239025677670685072 absolute error = 4.4733156928763e-19 relative error = 5.4900592243558109604891089138884e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.57973819772874292602316503775395 y2[1] (numeric) = 0.57973819772874292729498015376679 absolute error = 1.27181511601284e-18 relative error = 2.1937749159801213662180401733902e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=13987.2MB, alloc=40.3MB, time=162.89 TOP MAIN SOLVE Loop x[1] = 3.77 y1[1] (closed_form) = 0.80896478663008554561462174619622 y1[1] (numeric) = 0.80896478663008554604913933096 absolute error = 4.3451758476378e-19 relative error = 5.3712793429965621822745991506667e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.58785710337848275971251772647441 y2[1] (numeric) = 0.58785710337848276100349689484347 absolute error = 1.29097916836906e-18 relative error = 2.1960764970766763140507986364284e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14029.0MB, alloc=40.3MB, time=163.37 TOP MAIN SOLVE Loop x[1] = 3.78 y1[1] (closed_form) = 0.80304586566973076793658025923771 y1[1] (numeric) = 0.80304586566973076835809230010148 absolute error = 4.2151204086377e-19 relative error = 5.2489161439394739428546867268504e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.59591722380776403167448581090021 y2[1] (numeric) = 0.59591722380776403298461234742234 absolute error = 1.31012653652213e-18 relative error = 2.1985042287429530469153536723484e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14070.8MB, alloc=40.3MB, time=163.86 TOP MAIN SOLVE Loop x[1] = 3.79 y1[1] (closed_form) = 0.79704664079201167456087725184016 y1[1] (numeric) = 0.79704664079201167496919236994186 absolute error = 4.0831511810170e-19 relative error = 5.1228510002371281569875599009264e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.60391775301126055841709072023268 y2[1] (numeric) = 0.60391775301126055974634520472501 absolute error = 1.32925448449233e-18 relative error = 2.2010521761686726294850087088676e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14112.7MB, alloc=40.3MB, time=164.34 TOP MAIN SOLVE Loop x[1] = 3.8 y1[1] (closed_form) = 0.79096771191441669999656817435073 y1[1] (numeric) = 0.79096771191441670039149519874866 absolute error = 3.9492702439793e-19 relative error = 4.9929601227598706381725602035738e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.61185789094271907573358608611888 y2[1] (numeric) = 0.61185789094271907708194635320179 absolute error = 1.34836026708291e-18 relative error = 2.2037147629254663293047436231268e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14154.5MB, alloc=40.3MB, time=164.83 TOP MAIN SOLVE Loop x[1] = 3.81 y1[1] (closed_form) = 0.78480968692476784656233037436496 y1[1] (numeric) = 0.78480968692476784694367836953426 absolute error = 3.8134799516930e-19 relative error = 4.8591142734691571545201915898587e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.61973684359496319732588971051781 y2[1] (numeric) = 0.61973684359496319869333084075564 absolute error = 1.36744113023783e-18 relative error = 2.2064867441244760590399648575670e-16 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14196.4MB, alloc=40.3MB, time=165.31 TOP MAIN SOLVE Loop x[1] = 3.82 y1[1] (closed_form) = 0.7785731816204324087577276566562 y1[1] (numeric) = 0.77857318162043240912530595007228 absolute error = 3.6757829341608e-19 relative error = 4.7211784594358226118209108525189e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.62755382307929347077277195688991 y2[1] (numeric) = 0.62755382307929347215926626829145 absolute error = 1.38649431140154e-18 relative error = 2.2093631819471075473088761288877e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14238.3MB, alloc=40.3MB, time=165.80 TOP MAIN SOLVE Loop x[1] = 3.83 y1[1] (closed_form) = 0.77225881964674374969652252702348 y1[1] (numeric) = 0.77225881964674375005014073682851 absolute error = 3.5361820980503e-19 relative error = 4.5790116060673343556703575789782e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.63530804770427559090337023862228 y2[1] (numeric) = 0.63530804770427559230888727850292 absolute error = 1.40551703988064e-18 relative error = 2.2123394233074201016240950648688e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14280.1MB, alloc=40.3MB, time=166.28 TOP MAIN SOLVE Loop x[1] = 3.84 y1[1] (closed_form) = 0.76586723243463728747307694024768 y1[1] (numeric) = 0.7658672324346372878125450029967 absolute error = 3.3946806274902e-19 relative error = 4.4324662078814267778861455404253e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.64299874205390889182034887886274 y2[1] (numeric) = 0.64299874205390889324485541607024 absolute error = 1.42450653720750e-18 relative error = 2.2154110794326711820864834478531e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14321.9MB, alloc=40.3MB, time=166.76 TOP MAIN SOLVE Loop x[1] = 3.85 y1[1] (closed_form) = 0.75939905913750792781123507395279 y1[1] (numeric) = 0.75939905913750792813636327243579 absolute error = 3.2512819848300e-19 relative error = 4.2813879550004488669664086559509e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.650625137065167300788642218662 y2[1] (numeric) = 0.65062513706516730223210223616773 absolute error = 1.44346001750573e-18 relative error = 2.2185740071723535642502173356548e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14363.8MB, alloc=40.3MB, time=167.25 TOP MAIN SOLVE Loop x[1] = 3.86 y1[1] (closed_form) = 0.75285494656729525719980460936484 y1[1] (numeric) = 0.75285494656729525751040360050097 absolute error = 3.1059899113613e-19 relative error = 4.1256153333697537909893041826951e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.6581864701049049999590093452957 y2[1] (numeric) = 0.65818647010490500142138403315318 absolute error = 1.46237468785748e-18 relative error = 2.2218242918673176656954572047672e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14405.7MB, alloc=40.3MB, time=167.73 TOP MAIN SOLVE Loop x[1] = 3.87 y1[1] (closed_form) = 0.74623554912980288794206080932728 y1[1] (numeric) = 0.74623554912980288823794165212778 absolute error = 2.9588084280050e-19 relative error = 3.9649791965222153329246240174886e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.66568198504611910542431592310351 y2[1] (numeric) = 0.66568198504611910690556367177595 absolute error = 1.48124774867244e-18 relative error = 2.2251582316289026402445339556467e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14447.5MB, alloc=40.3MB, time=168.23 TOP MAIN SOLVE Loop x[1] = 3.88 y1[1] (closed_form) = 0.73954152875925842313086807704128 y1[1] (numeric) = 0.7395415287592584234118422606371 absolute error = 2.8097418359582e-19 relative error = 3.7993023064873075278863539762063e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.67311093234356173740418951936854 y2[1] (numeric) = 0.67311093234356173890426591342718 absolute error = 1.50007639405864e-18 relative error = 2.2285723228945980345709813182134e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14489.3MB, alloc=40.3MB, time=168.72 TOP MAIN SOLVE Loop x[1] = 3.89 y1[1] (closed_form) = 0.73277355485212058549838830263169 y1[1] (numeric) = 0.73277355485212058576426777436244 absolute error = 2.6587947173075e-19 relative error = 3.6283988412273768479800432079099e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.68047256910869392041403980815868 y2[1] (numeric) = 0.68047256910869392193289762035359 absolute error = 1.51885781219491e-18 relative error = 2.2320632471406768713643591425269e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14531.1MB, alloc=40.3MB, time=169.20 TOP MAIN SOLVE Loop x[1] = 3.9 y1[1] (closed_form) = 0.72593230420014012937233048461435 y1[1] (numeric) = 0.7259323042001401296229276781746 absolute error = 2.5059719356025e-19 relative error = 3.4520738657080088970863019861703e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.68776615918397381809088812537869 y2[1] (numeric) = 0.68776615918397381962847731108359 absolute error = 1.53758918570490e-18 relative error = 2.2356278586449075448254790151791e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14572.9MB, alloc=40.3MB, time=169.69 TOP MAIN SOLVE Loop x[1] = 3.91 y1[1] (closed_form) = 0.71901846092268122959176361387439 y1[1] (numeric) = 0.71901846092268122982689147751356 absolute error = 2.3512786363917e-19 relative error = 3.2701227634328319021458485742852e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.69499097321647187391443044807649 y2[1] (numeric) = 0.6949909732164718754706981401093 absolute error = 1.55626769203281e-18 relative error = 2.2392631732039381534657280650882e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14614.8MB, alloc=40.3MB, time=170.17 TOP MAIN SOLVE Loop x[1] = 3.92 y1[1] (closed_form) = 0.71203271639831011518720258429259 y1[1] (numeric) = 0.71203271639831011540667460906497 absolute error = 2.1947202477238e-19 relative error = 3.0823306249541440083624932364301e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.70214628873080549637060743782065 y2[1] (numeric) = 0.70214628873080549794549794164119 absolute error = 1.57489050382054e-18 relative error = 2.2429663577191308281964415248163e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14656.6MB, alloc=40.3MB, time=170.66 TOP MAIN SOLVE Loop x[1] = 3.93 y1[1] (closed_form) = 0.70497576919565778890458983952695 y1[1] (numeric) = 0.70497576919565778910822008758758 absolute error = 2.0363024806063e-19 relative error = 2.8884715894982030729698108321019e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.70923139020138599514994389285155 y2[1] (numeric) = 0.70923139020138599674339868213794 absolute error = 1.59345478928639e-18 relative error = 2.2467347205739569598848163733120e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14698.4MB, alloc=40.3MB, time=171.14 TOP MAIN SOLVE Loop x[1] = 3.94 y1[1] (closed_form) = 0.69784832500356374624360614943559 y1[1] (numeric) = 0.69784832500356374643120928237872 absolute error = 1.8760313294313e-19 relative error = 2.6883081354701532771903728360468e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.71624556912397054374724335454079 y2[1] (numeric) = 0.71624556912397054535920106714598 absolute error = 1.61195771260519e-18 relative error = 2.2505657027334240249844262199526e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14740.2MB, alloc=40.3MB, time=171.63 TOP MAIN SOLVE Loop x[1] = 3.95 y1[1] (closed_form) = 0.69065109656050767958019331164023 y1[1] (numeric) = 0.69065109656050767975158461887612 absolute error = 1.7139130723589e-19 relative error = 2.4815903151306221496207606018483e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.72318812408651201332600433544282 y2[1] (numeric) = 0.72318812408651201495640076973261 absolute error = 1.63039643428979e-18 relative error = 2.2544568695029516237778520711141e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14782.1MB, alloc=40.3MB, time=172.11 TOP MAIN SOLVE Loop x[1] = 3.96 y1[1] (closed_form) = 0.68338480358333622414406980875151 y1[1] (numeric) = 0.68338480358333622429906523591808 absolute error = 1.5499542716657e-19 relative error = 2.2680549282607640925211161699794e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.73005836083929959292321305873169 y2[1] (numeric) = 0.73005836083929959457198117030568 absolute error = 1.64876811157399e-18 relative error = 2.2584059028904358345388658543738e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14823.9MB, alloc=40.3MB, time=172.66 TOP MAIN SOLVE Loop x[1] = 3.97 y1[1] (closed_form) = 0.67605017269529187311724748931934 y1[1] (numeric) = 0.67605017269529187325566366672459 absolute error = 1.3841617740525e-19 relative error = 2.0474246290539251495060795095411e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.73685559236438318199094255175134 y2[1] (numeric) = 0.73685559236438318365801245054797 absolute error = 1.66706989879663e-18 relative error = 2.2624105945201887381465560367637e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14865.7MB, alloc=40.3MB, time=173.17 TOP MAIN SOLVE Loop x[1] = 3.98 y1[1] (closed_form) = 0.66864793735335125890206371667484 y1[1] (numeric) = 0.66864793735335125902371798776631 absolute error = 1.2165427109147e-19 relative error = 1.8194069598569781578184399056983e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.7435791389442746128933574013766 y2[1] (numeric) = 0.74357913894427461457865634916366 absolute error = 1.68529894778706e-18 relative error = 2.2664688390530007236006809297127e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14907.6MB, alloc=40.3MB, time=173.67 TOP MAIN SOLVE Loop x[1] = 3.99 y1[1] (closed_form) = 0.66117883777488006667005095201013 y1[1] (numeric) = 0.6611788377748800667747614018676 absolute error = 1.0471044985747e-19 relative error = 1.5836933046717096096212050157869e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.75022832822991883329412529862008 y2[1] (numeric) = 0.75022832822991883499757770687182 absolute error = 1.70345240825174e-18 relative error = 2.2705786280702682436319683551134e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14949.4MB, alloc=40.3MB, time=174.17 TOP MAIN SOLVE Loop x[1] = 4 y1[1] (closed_form) = 0.65364362086361191463916818309775 y1[1] (numeric) = 0.65364362086361191472675366694513 absolute error = 8.758548384738e-20 relative error = 1.3399577545277601242045023702880e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.75680249530792825137263909451183 y2[1] (numeric) = 0.75680249530792825309416652267381 absolute error = 1.72152742816198e-18 relative error = 2.2747380443843857724886324433395e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=14991.2MB, alloc=40.3MB, time=174.67 TOP MAIN SOLVE Loop x[1] = 4.01 y1[1] (closed_form) = 0.64604304013495860312968241468503 y1[1] (numeric) = 0.64604304013495860319996258641771 absolute error = 7.028017173268e-20 relative error = 1.0878558759490458879883601732662e-17 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.7633009827670735204905561792977 y2[1] (numeric) = 0.76330098276707352223007733344055 absolute error = 1.73952115414285e-18 relative error = 2.2789452567411100735441504897782e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15033.0MB, alloc=40.3MB, time=175.16 TOP MAIN SOLVE Loop x[1] = 4.02 y1[1] (closed_form) = 0.63837785564065920131155338076535 y1[1] (numeric) = 0.63837785564065920136434872148909 absolute error = 5.279534072374e-20 relative error = 8.2702337271326535374810626635220e-18 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.76972314076402411428559733354449 y2[1] (numeric) = 0.76972314076402411604302806540754 absolute error = 1.75743073186305e-18 relative error = 2.2831985148824176923260610310345e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15074.9MB, alloc=40.3MB, time=175.66 TOP MAIN SOLVE Loop x[1] = 4.03 y1[1] (closed_form) = 0.63064883389277550667185452185245 y1[1] (numeric) = 0.63064883389277550670698636842979 absolute error = 3.513184657734e-20 relative error = 5.5707462995663295707142162355931e-18 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.7760683270883321181898793012325 y2[1] (numeric) = 0.7760683270883321199651326076584 absolute error = 1.77525330642590e-18 relative error = 2.2874961449416819457007914686877e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15116.7MB, alloc=40.3MB, time=176.14 TOP MAIN SOLVE Loop x[1] = 4.04 y1[1] (closed_form) = 0.62285674778704147759294657917268 y1[1] (numeric) = 0.62285674778704147761023715277312 absolute error = 1.729057360044e-20 relative error = 2.7760112837939025767479634573692e-18 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.78233590722665273904778223066649 y2[1] (numeric) = 0.78233590722665274084076825342768 absolute error = 1.79298602276119e-18 relative error = 2.2918365451449730909424890226936e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15158.5MB, alloc=40.3MB, time=176.63 TOP MAIN SOLVE Loop x[1] = 4.05 y1[1] (closed_form) = 0.61500237652557430403427072848237 y1[1] (numeric) = 0.61500237652557430403354316313235 absolute error = 7.2756535002e-22 relative error = 1.1830285179227187409111283219388e-19 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.78852525442619511083590710941938 y2[1] (numeric) = 0.78852525442619511264653313543735 absolute error = 1.81062602601797e-18 relative error = 2.2962181817950158353538897888730e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15200.3MB, alloc=40.3MB, time=177.11 TOP MAIN SOLVE Loop x[1] = 4.06 y1[1] (closed_form) = 0.60708650553895484514628584778934 y1[1] (numeric) = 0.60708650553895484512736421891797 absolute error = 1.892162887137e-20 relative error = 3.1167928620933344345340667358228e-18 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.79463574975739705145742669274634 y2[1] (numeric) = 0.79463574975739705328559715470452 absolute error = 1.82817046195818e-18 relative error = 2.3006395855161587519564578406809e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15242.1MB, alloc=40.3MB, time=177.59 TOP MAIN SOLVE Loop x[1] = 4.07 y1[1] (closed_form) = 0.59910992640768522570785577303961 y1[1] (numeric) = 0.59910992640768522567056512601633 absolute error = 3.729064702328e-20 relative error = 6.2243413736904569032032045189796e-18 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.80066678217581750318737928027569 y2[1] (numeric) = 0.80066678217581750503299575762679 absolute error = 1.84561647735110e-18 relative error = 2.3050993477406724587724664965733e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15284.0MB, alloc=40.3MB, time=178.09 TOP MAIN SOLVE Loop x[1] = 4.08 y1[1] (closed_form) = 0.59107343678303144556199101824792 y1[1] (numeric) = 0.59107343678303144550615739690814 absolute error = 5.583362133978e-20 relative error = 9.4461394921854951005678083148314e-18 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.80661774858324046757643767338011 y2[1] (numeric) = 0.80661774858324046943939889374869 absolute error = 1.86296122036858e-18 relative error = 2.3095961174183463175722221363757e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15325.9MB, alloc=40.3MB, time=178.58 TOP MAIN SOLVE Loop x[1] = 4.09 y1[1] (closed_form) = 0.58297784030725891772303711364428 y1[1] (numeric) = 0.58297784030725891764848758879903 absolute error = 7.454952484525e-20 relative error = 1.2787711588824476719498380766542e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.81248805388798432447058271235272 y2[1] (numeric) = 0.81248805388798432635078455333358 absolute error = 1.88020184098086e-18 relative error = 2.3141285979326887163800360524620e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15367.7MB, alloc=40.3MB, time=179.06 TOP MAIN SOLVE Loop x[1] = 4.1 y1[1] (closed_form) = 0.57482394653326891153502867965979 y1[1] (numeric) = 0.57482394653326891144159137758531 absolute error = 9.343730207448e-20 relative error = 1.6254942515529345219169427319580e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.81827711106441050426503702435845 y2[1] (numeric) = 0.81827711106441050616237251571174 absolute error = 1.89733549135329e-18 relative error = 2.3186955442090346466508967640247e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15409.5MB, alloc=40.3MB, time=179.55 TOP MAIN SOLVE Loop x[1] = 4.11 y1[1] (closed_form) = 0.56661257084364393716992399387447 y1[1] (numeric) = 0.56661257084364393705742812477797 absolute error = 1.1249586909650e-19 relative error = 1.9854107530477487560844150806448e-17 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 0.82398434121162556257482398369604 y2[1] (numeric) = 0.82398434121162556448918330993933 absolute error = 1.91435932624329e-18 relative error = 2.3232957599999114883207659006551e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO 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=15451.2MB, alloc=40.3MB, time=180.03 Finished! Maximum Time Reached before Solution Completed! diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; Iterations = 3614 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 44 Seconds Optimized Time Remaining = 44 Seconds Expected Total Time = 3 Minutes 44 Seconds Time to Timeout 0.0 Seconds Percent Done = 80.33 % > quit memory used=15463.8MB, alloc=40.3MB, time=180.17