|\^/| Maple 2019 (X86 64 WINDOWS) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019 \ 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 > 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 7 # Begin Function number 8 > 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 8 # Begin Function number 9 > 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 9 # Begin Function number 10 > 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 10 # Begin Function number 11 > 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 11 # Begin Function number 12 > 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 12 # Begin Function number 13 > 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 13 # Begin Function number 14 > 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 14 # Begin Function number 15 > 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 15 # Begin Function number 16 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 16 # Begin Function number 17 > 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 17 # Begin Function number 18 > 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 18 # Begin Function number 19 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 20 # Begin Function number 21 > 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 21 # Begin Function number 22 > 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 22 # Begin Function number 23 > 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 23 # Begin Function number 24 > 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 24 # Begin Function number 25 > 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 25 # Begin Function number 26 > 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 26 # Begin Function number 27 > 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 27 # Begin Function number 28 > 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 28 # Begin Function number 29 > 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 29 # Begin Function number 30 > 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 30 # Begin Function number 31 > 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 31 # Begin Function number 32 > 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 32 # Begin Function number 33 > 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 33 # Begin Function number 34 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 34 # Begin Function number 35 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 35 # Begin Function number 36 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 36 # Begin Function number 37 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 37 # Begin Function number 38 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 38 # Begin Function number 39 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 39 # Begin Function number 40 > 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 40 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_x1 := proc(t) > local c1,c2,c3; > c1 := c(1.0); > c2 := c(0.0002); > c3 := c(0.0003); > return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t)))); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := c(1.0); c2 := c(0.0002); c3 := c(0.0003); return c(2.0)*c1 + c(6.0)*c3*exp(neg(c(t))) end proc > exact_soln_x1p := proc(t) > local c1,c2,c3; > c1 := c(1.0); > c2 := c(0.0002); > c3 := c(0.0003); > return( c(-6.0) * c3 * exp(neg( c(t)))); > end; exact_soln_x1p := proc(t) local c1, c2, c3; c1 := c(1.0); c2 := c(0.0002); c3 := c(0.0003); return c(-6.0)*c3*exp(neg(c(t))) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := c(1.0); > c2 := c(0.0002); > c3 := c(0.0003); > return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t)))); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := c(1.0); c2 := c(0.0002); c3 := c(0.0003); return c1 + c2*exp(c(2.0)*c(t)) + c3*exp(neg(c(t))) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := c(1.0); > c2 := c(0.0002); > c3 := c(0.0003); > return( c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t)))); > end; exact_soln_x2p := proc(t) local c1, c2, c3; c1 := c(1.0); c2 := c(0.0002); c3 := c(0.0003); return c(2.0)*c2*exp(c(2.0)*c(t)) - c3*exp(neg(c(t))) 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_t ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := sqrt((array_t[1] - array_given_rad_poles[1,1]) * (array_t[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_t[1] - array_given_rad_poles[2,1]) * (array_t[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_t; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_t[1] - array_given_rad_poles[1, 1])* (array_t[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_t[1] - array_given_rad_poles[2, 1])* (array_t[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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_x1[1]) < min_size) then # if number 5 > min_size := float_abs(array_x1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > if (float_abs(array_x2[1]) < min_size) then # if number 5 > min_size := float_abs(array_x2[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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_x1[1]) < min_size then min_size := float_abs(array_x1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if float_abs(array_x2[1]) < min_size then min_size := float_abs(array_x2[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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_x1[no_terms-3] + array_x1[no_terms - 2] * hn_div_ho + array_x1[no_terms - 1] * hn_div_ho_2 + array_x1[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_x2[no_terms-3] + array_x2[no_terms - 2] * hn_div_ho + array_x2[no_terms - 1] * hn_div_ho_2 + array_x2[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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_x1[no_terms - 3] + array_x1[no_terms - 2]*hn_div_ho + array_x1[no_terms - 1]*hn_div_ho_2 + array_x1[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_x2[no_terms - 3] + array_x2[no_terms - 2]*hn_div_ho + array_x2[no_terms - 1]*hn_div_ho_2 + array_x2[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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_x1[no_terms-3])) + c(float_abs(array_x1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_x1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_x1[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_x1[1])) > c(est_tmp)) then # if number 5 > est_tmp := c(glob_prec) * c(float_abs(array_x1[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_x2[no_terms-3])) + c(float_abs(array_x2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_x2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_x2[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_x2[1])) > c(est_tmp)) then # if number 5 > est_tmp := c(glob_prec) * c(float_abs(array_x2[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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_x1[no_terms - 3])) + c(float_abs(array_x1[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_x1[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_x1[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_x1[1])) then est_tmp := c(glob_prec)*c(float_abs(array_x1[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_x2[no_terms - 3])) + c(float_abs(array_x2[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_x2[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_x2[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_x2[1])) then est_tmp := c(glob_prec)*c(float_abs(array_x2[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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_t[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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_t[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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > closed_form_val_y := evalf(exact_soln_x1(ind_var)); > omniout_float(ALWAYS,"x1[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7 > relerr := abserr/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 8 > glob_good_digits := round(-log10(relerr)); > 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)*76*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 * c(100.0),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_x2(ind_var)); > omniout_float(ALWAYS,"x2[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7 > relerr := abserr/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 8 > glob_good_digits := round(-log10(relerr)); > 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)*76*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 * c(100.0),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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); closed_form_val_y := evalf(exact_soln_x1(ind_var)); omniout_float(ALWAYS, "x1[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "x1[1] (numeric) ", 33, numeric_val, 20, " "); if c(glob_prec) < c(float_abs(closed_form_val_y)) then relerr := abserr/float_abs(closed_form_val_y); if c(glob_prec) < c(relerr) then glob_good_digits := round(-log10(relerr)) 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)*76*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*c(100.0), 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_x2(ind_var)); omniout_float(ALWAYS, "x2[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "x2[1] (numeric) ", 33, numeric_val, 20, " "); if c(glob_prec) < c(float_abs(closed_form_val_y)) then relerr := abserr/float_abs(closed_form_val_y); if c(glob_prec) < c(relerr) then glob_good_digits := round(-log10(relerr)) 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)*76*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*c(100.0), 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(t_start,t_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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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((t_end),(t_start),(array_t[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((t_end),(t_start),(array_t[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((t_end),(t_start),(array_t[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(t_start, t_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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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(t_end, t_start, array_t[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(t_end, t_start, array_t[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(t_end, t_start, array_t[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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_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_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-1],array_x1_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_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-1],array_x2_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_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x1_higher[1,last_no-5],array_x1_higher[1,last_no-4],array_x1_higher[1,last_no-3],array_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-5],array_x1_higher[1,last_no-4],array_x1_higher[1,last_no-3],array_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x2_higher[1,last_no-5],array_x2_higher[1,last_no-4],array_x2_higher[1,last_no-3],array_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-5],array_x2_higher[1,last_no-4],array_x2_higher[1,last_no-3],array_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x1[term] := array_x1[term]* ratio; > array_x1_higher[1,term] := array_x1_higher[1,term]* ratio; > array_t[term] := array_t[term]* ratio; > array_x2[term] := array_x2[term]* ratio; > array_x2_higher[1,term] := array_x2_higher[1,term]* ratio; > array_t[term] := array_t[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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_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_x1_higher[1, last_no - 1], array_x1_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_x1_higher[1, last_no - 1], array_x1_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_x2_higher[1, last_no - 1], array_x2_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_x2_higher[1, last_no - 1], array_x2_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_x1_higher[1, last_no - 2], array_x1_higher[1, last_no - 1], array_x1_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_x1_higher[1, last_no - 2], array_x1_higher[1, last_no - 1], array_x1_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_x2_higher[1, last_no - 2], array_x2_higher[1, last_no - 1], array_x2_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_x2_higher[1, last_no - 2], array_x2_higher[1, last_no - 1], array_x2_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_x1_higher[1, last_no - 5], array_x1_higher[1, last_no - 4], array_x1_higher[1, last_no - 3], array_x1_higher[1, last_no - 2], array_x1_higher[1, last_no - 1], array_x1_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_x1_higher[1, last_no - 5], array_x1_higher[1, last_no - 4], array_x1_higher[1, last_no - 3], array_x1_higher[1, last_no - 2], array_x1_higher[1, last_no - 1], array_x1_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_x2_higher[1, last_no - 5], array_x2_higher[1, last_no - 4], array_x2_higher[1, last_no - 3], array_x2_higher[1, last_no - 2], array_x2_higher[1, last_no - 1], array_x2_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_x2_higher[1, last_no - 5], array_x2_higher[1, last_no - 4], array_x2_higher[1, last_no - 3], array_x2_higher[1, last_no - 2], array_x2_higher[1, last_no - 1], array_x2_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_x1[term] := array_x1[term]*ratio; array_x1_higher[1, term] := array_x1_higher[1, term]*ratio; array_t[term] := array_t[term]*ratio; array_x2[term] := array_x2[term]*ratio; array_x2_higher[1, term] := array_x2_higher[1, term]*ratio; array_t[term] := array_t[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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp1[1] := array_const_4D0[1] * array_x2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre diff $eq_no = 1 i = 1 order_d = 1 > array_tmp3[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_2D0[1] * array_tmp3[1]; > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp2[1] - array_tmp4[1]; > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp6[1] := array_const_2D0[1] * array_x1[1]; > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_x1_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp7[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_x1[2] := temporary; > array_x1_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_x1_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_tmp9[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp10[1] := array_const_3D0[1] * array_tmp9[1]; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp11[1] := array_const_2D0[1] * array_x2[1]; > #emit pre sub FULL FULL $eq_no = 2 i = 1 > array_tmp12[1] := array_tmp10[1] - array_tmp11[1]; > #emit pre diff $eq_no = 2 i = 1 order_d = 2 > array_tmp13[1] := array_x1_higher[3,1]; > #emit pre sub FULL FULL $eq_no = 2 i = 1 > array_tmp14[1] := array_tmp12[1] - array_tmp13[1]; > #emit pre diff $eq_no = 2 i = 1 order_d = 1 > array_tmp15[1] := array_x1_higher[2,1]; > #emit pre sub FULL FULL $eq_no = 2 i = 1 > array_tmp16[1] := array_tmp14[1] - array_tmp15[1]; > #emit pre add FULL FULL $eq_no = 2 i = 1 > array_tmp17[1] := array_tmp16[1] + array_x1[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_x2_set_initial[2,3]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp17[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_x2[3] := temporary; > array_x2_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_x2_higher[2,2] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(1); > array_x2_higher[3,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp1[2] := array_const_4D0[1] * array_x2[2]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre diff $eq_no = 1 i = 2 order_d = 1 > array_tmp3[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_const_2D0[1] * array_tmp3[2]; > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp2[2] - array_tmp4[2]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp6[2] := array_const_2D0[1] * array_x1[2]; > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_x1_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp7[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_x1[3] := temporary; > array_x1_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_x1_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_tmp9[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp10[2] := array_const_3D0[1] * array_tmp9[2]; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp11[2] := array_const_2D0[1] * array_x2[2]; > #emit pre sub FULL FULL $eq_no = 2 i = 2 > array_tmp12[2] := array_tmp10[2] - array_tmp11[2]; > #emit pre diff $eq_no = 2 i = 2 order_d = 2 > array_tmp13[2] := array_x1_higher[3,2]; > #emit pre sub FULL FULL $eq_no = 2 i = 2 > array_tmp14[2] := array_tmp12[2] - array_tmp13[2]; > #emit pre diff $eq_no = 2 i = 2 order_d = 1 > array_tmp15[2] := array_x1_higher[2,2]; > #emit pre sub FULL FULL $eq_no = 2 i = 2 > array_tmp16[2] := array_tmp14[2] - array_tmp15[2]; > #emit pre add FULL FULL $eq_no = 2 i = 2 > array_tmp17[2] := array_tmp16[2] + array_x1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_x2_set_initial[2,4]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp17[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_x2[4] := temporary; > array_x2_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_x2_higher[2,3] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(2); > array_x2_higher[3,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp1[3] := array_const_4D0[1] * array_x2[3]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre diff $eq_no = 1 i = 3 order_d = 1 > array_tmp3[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_const_2D0[1] * array_tmp3[3]; > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp2[3] - array_tmp4[3]; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp6[3] := array_const_2D0[1] * array_x1[3]; > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_x1_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp7[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_x1[4] := temporary; > array_x1_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_x1_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_tmp9[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp10[3] := array_const_3D0[1] * array_tmp9[3]; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp11[3] := array_const_2D0[1] * array_x2[3]; > #emit pre sub FULL FULL $eq_no = 2 i = 3 > array_tmp12[3] := array_tmp10[3] - array_tmp11[3]; > #emit pre diff $eq_no = 2 i = 3 order_d = 2 > array_tmp13[3] := array_x1_higher[3,3]; > #emit pre sub FULL FULL $eq_no = 2 i = 3 > array_tmp14[3] := array_tmp12[3] - array_tmp13[3]; > #emit pre diff $eq_no = 2 i = 3 order_d = 1 > array_tmp15[3] := array_x1_higher[2,3]; > #emit pre sub FULL FULL $eq_no = 2 i = 3 > array_tmp16[3] := array_tmp14[3] - array_tmp15[3]; > #emit pre add FULL FULL $eq_no = 2 i = 3 > array_tmp17[3] := array_tmp16[3] + array_x1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_x2_set_initial[2,5]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp17[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_x2[5] := temporary; > array_x2_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_x2_higher[2,4] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(3); > array_x2_higher[3,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp1[4] := array_const_4D0[1] * array_x2[4]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre diff $eq_no = 1 i = 4 order_d = 1 > array_tmp3[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_const_2D0[1] * array_tmp3[4]; > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp2[4] - array_tmp4[4]; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp6[4] := array_const_2D0[1] * array_x1[4]; > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_x1_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp7[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_x1[5] := temporary; > array_x1_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_x1_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_tmp9[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp10[4] := array_const_3D0[1] * array_tmp9[4]; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp11[4] := array_const_2D0[1] * array_x2[4]; > #emit pre sub FULL FULL $eq_no = 2 i = 4 > array_tmp12[4] := array_tmp10[4] - array_tmp11[4]; > #emit pre diff $eq_no = 2 i = 4 order_d = 2 > array_tmp13[4] := array_x1_higher[3,4]; > #emit pre sub FULL FULL $eq_no = 2 i = 4 > array_tmp14[4] := array_tmp12[4] - array_tmp13[4]; > #emit pre diff $eq_no = 2 i = 4 order_d = 1 > array_tmp15[4] := array_x1_higher[2,4]; > #emit pre sub FULL FULL $eq_no = 2 i = 4 > array_tmp16[4] := array_tmp14[4] - array_tmp15[4]; > #emit pre add FULL FULL $eq_no = 2 i = 4 > array_tmp17[4] := array_tmp16[4] + array_x1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_x2_set_initial[2,6]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp17[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_x2[6] := temporary; > array_x2_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_x2_higher[2,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_x2_higher[3,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp1[5] := array_const_4D0[1] * array_x2[5]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre diff $eq_no = 1 i = 5 order_d = 1 > array_tmp3[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_const_2D0[1] * array_tmp3[5]; > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp2[5] - array_tmp4[5]; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp6[5] := array_const_2D0[1] * array_x1[5]; > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_x1_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp7[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_x1[6] := temporary; > array_x1_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_x1_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_tmp9[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp10[5] := array_const_3D0[1] * array_tmp9[5]; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp11[5] := array_const_2D0[1] * array_x2[5]; > #emit pre sub FULL FULL $eq_no = 2 i = 5 > array_tmp12[5] := array_tmp10[5] - array_tmp11[5]; > #emit pre diff $eq_no = 2 i = 5 order_d = 2 > array_tmp13[5] := array_x1_higher[3,5]; > #emit pre sub FULL FULL $eq_no = 2 i = 5 > array_tmp14[5] := array_tmp12[5] - array_tmp13[5]; > #emit pre diff $eq_no = 2 i = 5 order_d = 1 > array_tmp15[5] := array_x1_higher[2,5]; > #emit pre sub FULL FULL $eq_no = 2 i = 5 > array_tmp16[5] := array_tmp14[5] - array_tmp15[5]; > #emit pre add FULL FULL $eq_no = 2 i = 5 > array_tmp17[5] := array_tmp16[5] + array_x1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_x2_set_initial[2,7]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp17[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6)); > if (7 <= ATS_MAX_TERMS) then # if number 3 > array_x2[7] := temporary; > array_x2_higher[1,7] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(6); > array_x2_higher[2,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_x2_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 mult CONST FULL $eq_no = 1 i = 1 > array_tmp1[kkk] := array_const_4D0[1] * array_x2[kkk]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit diff $eq_no = 1 > if (kkk <= ATS_MAX_TERMS) then # if number 1 > array_tmp3[kkk] := array_x2_higher[2,kkk]; > fi;# end if 1; > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp4[kkk] := array_const_2D0[1] * array_tmp3[kkk]; > #emit FULL - FULL sub $eq_no = 1 > array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk]; > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp6[kkk] := array_const_2D0[1] * array_x1[kkk]; > #emit FULL - FULL sub $eq_no = 1 > array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_x1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp7[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_x1[kkk + order_d] := c(temporary); > array_x1_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_x1_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_tmp9[kkk] := array_x2_higher[2,kkk]; > fi;# end if 1; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp10[kkk] := array_const_3D0[1] * array_tmp9[kkk]; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp11[kkk] := array_const_2D0[1] * array_x2[kkk]; > #emit FULL - FULL sub $eq_no = 2 > array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk]; > #emit diff $eq_no = 2 > if (kkk <= ATS_MAX_TERMS) then # if number 1 > array_tmp13[kkk] := array_x1_higher[3,kkk]; > fi;# end if 1; > #emit FULL - FULL sub $eq_no = 2 > array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk]; > #emit diff $eq_no = 2 > if (kkk <= ATS_MAX_TERMS) then # if number 1 > array_tmp15[kkk] := array_x1_higher[2,kkk]; > fi;# end if 1; > #emit FULL - FULL sub $eq_no = 2 > array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk]; > #emit FULL - FULL add $eq_no = 2 > array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk]; > #emit assign $eq_no = 2 > order_d := 2; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_x2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := c(array_tmp17[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_x2[kkk + order_d] := c(temporary); > array_x2_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_x2_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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_4D0[1]*array_x2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_x2_higher[2, 1]; array_tmp4[1] := array_const_2D0[1]*array_tmp3[1]; array_tmp5[1] := array_tmp2[1] - array_tmp4[1]; array_tmp6[1] := array_const_2D0[1]*array_x1[1]; array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; if not array_x1_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp7[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_x1[2] := temporary; array_x1_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_x1_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp9[1] := array_x2_higher[2, 1]; array_tmp10[1] := array_const_3D0[1]*array_tmp9[1]; array_tmp11[1] := array_const_2D0[1]*array_x2[1]; array_tmp12[1] := array_tmp10[1] - array_tmp11[1]; array_tmp13[1] := array_x1_higher[3, 1]; array_tmp14[1] := array_tmp12[1] - array_tmp13[1]; array_tmp15[1] := array_x1_higher[2, 1]; array_tmp16[1] := array_tmp14[1] - array_tmp15[1]; array_tmp17[1] := array_tmp16[1] + array_x1[1]; if not array_x2_set_initial[2, 3] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp17[1])*expt(glob_h, c(2))*c(factorial_3(0, 2)); if 3 <= ATS_MAX_TERMS then array_x2[3] := temporary; array_x2_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_x2_higher[2, 2] := c(temporary); temporary := c(temporary)*c(1)/c(glob_h); array_x2_higher[3, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_4D0[1]*array_x2[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_x2_higher[2, 2]; array_tmp4[2] := array_const_2D0[1]*array_tmp3[2]; array_tmp5[2] := array_tmp2[2] - array_tmp4[2]; array_tmp6[2] := array_const_2D0[1]*array_x1[2]; array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; if not array_x1_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp7[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_x1[3] := temporary; array_x1_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_x1_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp9[2] := array_x2_higher[2, 2]; array_tmp10[2] := array_const_3D0[1]*array_tmp9[2]; array_tmp11[2] := array_const_2D0[1]*array_x2[2]; array_tmp12[2] := array_tmp10[2] - array_tmp11[2]; array_tmp13[2] := array_x1_higher[3, 2]; array_tmp14[2] := array_tmp12[2] - array_tmp13[2]; array_tmp15[2] := array_x1_higher[2, 2]; array_tmp16[2] := array_tmp14[2] - array_tmp15[2]; array_tmp17[2] := array_tmp16[2] + array_x1[2]; if not array_x2_set_initial[2, 4] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp17[2])*expt(glob_h, c(2))*c(factorial_3(1, 3)); if 4 <= ATS_MAX_TERMS then array_x2[4] := temporary; array_x2_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_x2_higher[2, 3] := c(temporary); temporary := c(temporary)*c(2)/c(glob_h); array_x2_higher[3, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := array_const_4D0[1]*array_x2[3]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_x2_higher[2, 3]; array_tmp4[3] := array_const_2D0[1]*array_tmp3[3]; array_tmp5[3] := array_tmp2[3] - array_tmp4[3]; array_tmp6[3] := array_const_2D0[1]*array_x1[3]; array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; if not array_x1_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp7[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_x1[4] := temporary; array_x1_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_x1_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp9[3] := array_x2_higher[2, 3]; array_tmp10[3] := array_const_3D0[1]*array_tmp9[3]; array_tmp11[3] := array_const_2D0[1]*array_x2[3]; array_tmp12[3] := array_tmp10[3] - array_tmp11[3]; array_tmp13[3] := array_x1_higher[3, 3]; array_tmp14[3] := array_tmp12[3] - array_tmp13[3]; array_tmp15[3] := array_x1_higher[2, 3]; array_tmp16[3] := array_tmp14[3] - array_tmp15[3]; array_tmp17[3] := array_tmp16[3] + array_x1[3]; if not array_x2_set_initial[2, 5] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp17[3])*expt(glob_h, c(2))*c(factorial_3(2, 4)); if 5 <= ATS_MAX_TERMS then array_x2[5] := temporary; array_x2_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_x2_higher[2, 4] := c(temporary); temporary := c(temporary)*c(3)/c(glob_h); array_x2_higher[3, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := array_const_4D0[1]*array_x2[4]; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_x2_higher[2, 4]; array_tmp4[4] := array_const_2D0[1]*array_tmp3[4]; array_tmp5[4] := array_tmp2[4] - array_tmp4[4]; array_tmp6[4] := array_const_2D0[1]*array_x1[4]; array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; if not array_x1_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp7[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_x1[5] := temporary; array_x1_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_x1_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp9[4] := array_x2_higher[2, 4]; array_tmp10[4] := array_const_3D0[1]*array_tmp9[4]; array_tmp11[4] := array_const_2D0[1]*array_x2[4]; array_tmp12[4] := array_tmp10[4] - array_tmp11[4]; array_tmp13[4] := array_x1_higher[3, 4]; array_tmp14[4] := array_tmp12[4] - array_tmp13[4]; array_tmp15[4] := array_x1_higher[2, 4]; array_tmp16[4] := array_tmp14[4] - array_tmp15[4]; array_tmp17[4] := array_tmp16[4] + array_x1[4]; if not array_x2_set_initial[2, 6] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp17[4])*expt(glob_h, c(2))*c(factorial_3(3, 5)); if 6 <= ATS_MAX_TERMS then array_x2[6] := temporary; array_x2_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_x2_higher[2, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_x2_higher[3, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := array_const_4D0[1]*array_x2[5]; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_x2_higher[2, 5]; array_tmp4[5] := array_const_2D0[1]*array_tmp3[5]; array_tmp5[5] := array_tmp2[5] - array_tmp4[5]; array_tmp6[5] := array_const_2D0[1]*array_x1[5]; array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; if not array_x1_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp7[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_x1[6] := temporary; array_x1_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_x1_higher[2, 5] := c(temporary) end if end if; kkk := 6; array_tmp9[5] := array_x2_higher[2, 5]; array_tmp10[5] := array_const_3D0[1]*array_tmp9[5]; array_tmp11[5] := array_const_2D0[1]*array_x2[5]; array_tmp12[5] := array_tmp10[5] - array_tmp11[5]; array_tmp13[5] := array_x1_higher[3, 5]; array_tmp14[5] := array_tmp12[5] - array_tmp13[5]; array_tmp15[5] := array_x1_higher[2, 5]; array_tmp16[5] := array_tmp14[5] - array_tmp15[5]; array_tmp17[5] := array_tmp16[5] + array_x1[5]; if not array_x2_set_initial[2, 7] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp17[5])*expt(glob_h, c(2))*c(factorial_3(4, 6)); if 7 <= ATS_MAX_TERMS then array_x2[7] := temporary; array_x2_higher[1, 7] := temporary end if; temporary := c(temporary)*c(6)/c(glob_h); array_x2_higher[2, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_x2_higher[3, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := array_const_4D0[1]*array_x2[kkk]; array_tmp2[kkk] := array_tmp1[kkk]; if kkk <= ATS_MAX_TERMS then array_tmp3[kkk] := array_x2_higher[2, kkk] end if; array_tmp4[kkk] := array_const_2D0[1]*array_tmp3[kkk]; array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk]; array_tmp6[kkk] := array_const_2D0[1]*array_x1[kkk]; array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_x1_set_initial[1, kkk + order_d] then temporary := c(array_tmp7[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_x1[kkk + order_d] := c(temporary); array_x1_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_x1_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_tmp9[kkk] := array_x2_higher[2, kkk] end if; array_tmp10[kkk] := array_const_3D0[1]*array_tmp9[kkk]; array_tmp11[kkk] := array_const_2D0[1]*array_x2[kkk]; array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk]; if kkk <= ATS_MAX_TERMS then array_tmp13[kkk] := array_x1_higher[3, kkk] end if; array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk]; if kkk <= ATS_MAX_TERMS then array_tmp15[kkk] := array_x1_higher[2, kkk] end if; array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk]; array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk]; order_d := 2; if kkk + order_d <= ATS_MAX_TERMS then if not array_x2_set_initial[2, kkk + order_d] then temporary := c(array_tmp17[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_x2[kkk + order_d] := c(temporary); array_x2_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_x2_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, > t_start,t_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_4D0, > array_const_2D0, > array_const_2, > array_const_3D0, > #END CONST > array_x1_init, > array_x2_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_x1, > array_t, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_m1, > array_x1_higher, > array_x1_higher_work, > array_x1_higher_work2, > array_x1_set_initial, > array_x2_higher, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=64; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_x1_init:= Array(0..(40),[]); > array_x2_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > 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_x1:= Array(0..(40),[]); > array_t:= Array(0..(40),[]); > array_x2:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_tmp5:= Array(0..(40),[]); > array_tmp6:= Array(0..(40),[]); > array_tmp7:= Array(0..(40),[]); > array_tmp8:= Array(0..(40),[]); > array_tmp9:= Array(0..(40),[]); > array_tmp10:= Array(0..(40),[]); > array_tmp11:= Array(0..(40),[]); > array_tmp12:= Array(0..(40),[]); > array_tmp13:= Array(0..(40),[]); > array_tmp14:= Array(0..(40),[]); > array_tmp15:= Array(0..(40),[]); > array_tmp16:= Array(0..(40),[]); > array_tmp17:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_x1_higher := Array(0..(3) ,(0..40+ 1),[]); > array_x1_higher_work := Array(0..(3) ,(0..40+ 1),[]); > array_x1_higher_work2 := Array(0..(3) ,(0..40+ 1),[]); > array_x1_set_initial := Array(0..(3) ,(0..40+ 1),[]); > array_x2_higher := Array(0..(3) ,(0..40+ 1),[]); > array_x2_higher_work := Array(0..(3) ,(0..40+ 1),[]); > array_x2_higher_work2 := Array(0..(3) ,(0..40+ 1),[]); > array_x2_set_initial := Array(0..(3) ,(0..40+ 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..(40) ,(0..40+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 40) do # do number 1 > array_x1_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x2_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 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 <= 40) do # do number 1 > array_x1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_t[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp6[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp7[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp8[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp9[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp10[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp11[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp12[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp13[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp14[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp15[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp16[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp17[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_x1_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 <= 40) do # do number 2 > array_x1_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 <= 40) do # do number 2 > array_x1_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 <= 40) do # do number 2 > array_x1_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 <= 40) do # do number 2 > array_x2_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 <= 40) do # do number 2 > array_x2_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 <= 40) do # do number 2 > array_x2_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 <= 40) do # do number 2 > array_x2_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 <=40) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_x1); > zero_ats_ar(array_t); > zero_ats_ar(array_x2); > 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_tmp5); > zero_ats_ar(array_tmp6); > zero_ats_ar(array_tmp7); > zero_ats_ar(array_tmp8); > zero_ats_ar(array_tmp9); > zero_ats_ar(array_tmp10); > zero_ats_ar(array_tmp11); > zero_ats_ar(array_tmp12); > zero_ats_ar(array_tmp13); > zero_ats_ar(array_tmp14); > zero_ats_ar(array_tmp15); > zero_ats_ar(array_tmp16); > zero_ats_ar(array_tmp17); > 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_4D0); > array_const_4D0[1] := c(4.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_const_2); > array_const_2[1] := c(2); > zero_ats_ar(array_const_3D0); > array_const_3D0[1] := c(3.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_x1_set_initial[1,1] := true; > array_x1_set_initial[1,2] := false; > array_x1_set_initial[1,3] := false; > array_x1_set_initial[1,4] := false; > array_x1_set_initial[1,5] := false; > array_x1_set_initial[1,6] := false; > array_x1_set_initial[1,7] := false; > array_x1_set_initial[1,8] := false; > array_x1_set_initial[1,9] := false; > array_x1_set_initial[1,10] := false; > array_x1_set_initial[1,11] := false; > array_x1_set_initial[1,12] := false; > array_x1_set_initial[1,13] := false; > array_x1_set_initial[1,14] := false; > array_x1_set_initial[1,15] := false; > array_x1_set_initial[1,16] := false; > array_x1_set_initial[1,17] := false; > array_x1_set_initial[1,18] := false; > array_x1_set_initial[1,19] := false; > array_x1_set_initial[1,20] := false; > array_x1_set_initial[1,21] := false; > array_x1_set_initial[1,22] := false; > array_x1_set_initial[1,23] := false; > array_x1_set_initial[1,24] := false; > array_x1_set_initial[1,25] := false; > array_x1_set_initial[1,26] := false; > array_x1_set_initial[1,27] := false; > array_x1_set_initial[1,28] := false; > array_x1_set_initial[1,29] := false; > array_x1_set_initial[1,30] := false; > array_x1_set_initial[1,31] := false; > array_x1_set_initial[1,32] := false; > array_x1_set_initial[1,33] := false; > array_x1_set_initial[1,34] := false; > array_x1_set_initial[1,35] := false; > array_x1_set_initial[1,36] := false; > array_x1_set_initial[1,37] := false; > array_x1_set_initial[1,38] := false; > array_x1_set_initial[1,39] := false; > array_x1_set_initial[1,40] := false; > array_x2_set_initial[2,1] := true; > array_x2_set_initial[2,2] := true; > array_x2_set_initial[2,3] := false; > array_x2_set_initial[2,4] := false; > array_x2_set_initial[2,5] := false; > array_x2_set_initial[2,6] := false; > array_x2_set_initial[2,7] := false; > array_x2_set_initial[2,8] := false; > array_x2_set_initial[2,9] := false; > array_x2_set_initial[2,10] := false; > array_x2_set_initial[2,11] := false; > array_x2_set_initial[2,12] := false; > array_x2_set_initial[2,13] := false; > array_x2_set_initial[2,14] := false; > array_x2_set_initial[2,15] := false; > array_x2_set_initial[2,16] := false; > array_x2_set_initial[2,17] := false; > array_x2_set_initial[2,18] := false; > array_x2_set_initial[2,19] := false; > array_x2_set_initial[2,20] := false; > array_x2_set_initial[2,21] := false; > array_x2_set_initial[2,22] := false; > array_x2_set_initial[2,23] := false; > array_x2_set_initial[2,24] := false; > array_x2_set_initial[2,25] := false; > array_x2_set_initial[2,26] := false; > array_x2_set_initial[2,27] := false; > array_x2_set_initial[2,28] := false; > array_x2_set_initial[2,29] := false; > array_x2_set_initial[2,30] := false; > array_x2_set_initial[2,31] := false; > array_x2_set_initial[2,32] := false; > array_x2_set_initial[2,33] := false; > array_x2_set_initial[2,34] := false; > array_x2_set_initial[2,35] := false; > array_x2_set_initial[2,36] := false; > array_x2_set_initial[2,37] := false; > array_x2_set_initial[2,38] := false; > array_x2_set_initial[2,39] := false; > array_x2_set_initial[2,40] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 40; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 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,"##############R:\Temp/mtest6postode.ode#################"); > omniout_str(ALWAYS,"diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; "); > omniout_str(ALWAYS,"diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=64;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"t_start := c(1.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"t_end := c(8.0);"); > omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);"); > omniout_str(ALWAYS,"array_x2_init[1 + 1] := exact_soln_x2p(t_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_h := c(0.0001);"); > 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 := 0;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=12;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=2;"); > omniout_str(ALWAYS,"glob_max_iter:=1000000;"); > 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,"glob_h_reason:=1;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_x1 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := c(1.0);"); > omniout_str(ALWAYS,"c2 := c(0.0002);"); > omniout_str(ALWAYS,"c3 := c(0.0003);"); > omniout_str(ALWAYS,"return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x1p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := c(1.0);"); > omniout_str(ALWAYS,"c2 := c(0.0002);"); > omniout_str(ALWAYS,"c3 := c(0.0003);"); > omniout_str(ALWAYS,"return( c(-6.0) * c3 * exp(neg( c(t))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := c(1.0);"); > omniout_str(ALWAYS,"c2 := c(0.0002);"); > omniout_str(ALWAYS,"c3 := c(0.0003);"); > omniout_str(ALWAYS,"return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := c(1.0);"); > omniout_str(ALWAYS,"c2 := c(0.0002);"); > omniout_str(ALWAYS,"c3 := c(0.0003);"); > omniout_str(ALWAYS,"return( c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > t_start := c(1.5); > t_end := c(8.0); > array_x1_init[0 + 1] := exact_soln_x1(t_start); > array_x2_init[0 + 1] := exact_soln_x2(t_start); > array_x2_init[1 + 1] := exact_soln_x2p(t_start); > glob_look_poles := true; > glob_max_h := c(0.0001); > glob_type_given_pole := 0; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=12; > glob_max_minutes:=(3.0); > glob_subiter_method:=2; > glob_max_iter:=1000000; > 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_h_reason:=1; > #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(t_start,t_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(t_end) - c(t_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(t_start,t_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_t[1] := c(t_start); > array_t[2] := c(glob_h); > glob_next_display := c(t_start); > order_diff := 2; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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(t_start,t_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_t[1] := c(t_start); > array_t[2] := c(glob_h); > glob_next_display := c(t_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 := 2; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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_t[1] < glob_check_sign * t_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_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > #Jump Series array_x1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x1_higher_work[2,iii] := array_x1_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_x1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x1_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_x1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x1_higher_work[1,iii] := array_x1_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_x1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x1_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_x1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x1_higher_work[1,iii] := array_x1_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_x1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x1_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_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_x1_higher[ord,term_no] := array_x1_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_x2; > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[3,iii] := array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[2,iii] := array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[2,iii] := array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[1,iii] := array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[1,iii] := array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_x2_higher_work[1,iii] := array_x2_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_x2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_x2_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_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_x2_higher[ord,term_no] := array_x2_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 ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; "); > omniout_str(INFO,"diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if (glob_html_log) then # if number 20 > logstart(html_log_file); > logitem_str(html_log_file,"2020-05-25T23:59:14-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest6") > ; > logitem_str(html_log_file,"diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; ") > ; > logitem_float(html_log_file,t_start) > ; > logitem_float(html_log_file,t_end) > ; > logitem_float(html_log_file,array_t[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," 310 ") > ; > logitem_str(html_log_file,"mtest6 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest6 maple results") > ; > logitem_str(html_log_file,"Poor Accuracy -- Possibly BAD TEST") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; ") > ; > 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, t_start, t_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_4D0, array_const_2D0, array_const_2, array_const_3D0, array_x1_init, array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1, array_x1_higher, array_x1_higher_work, array_x1_higher_work2, array_x1_set_initial, array_x2_higher, array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 64; max_terms := 40; glob_html_log := true; array_x1_init := Array(0 .. 40, []); array_x2_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); 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_x1 := Array(0 .. 40, []); array_t := Array(0 .. 40, []); array_x2 := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_tmp5 := Array(0 .. 40, []); array_tmp6 := Array(0 .. 40, []); array_tmp7 := Array(0 .. 40, []); array_tmp8 := Array(0 .. 40, []); array_tmp9 := Array(0 .. 40, []); array_tmp10 := Array(0 .. 40, []); array_tmp11 := Array(0 .. 40, []); array_tmp12 := Array(0 .. 40, []); array_tmp13 := Array(0 .. 40, []); array_tmp14 := Array(0 .. 40, []); array_tmp15 := Array(0 .. 40, []); array_tmp16 := Array(0 .. 40, []); array_tmp17 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_x1_higher := Array(0 .. 3, 0 .. 41, []); array_x1_higher_work := Array(0 .. 3, 0 .. 41, []); array_x1_higher_work2 := Array(0 .. 3, 0 .. 41, []); array_x1_set_initial := Array(0 .. 3, 0 .. 41, []); array_x2_higher := Array(0 .. 3, 0 .. 41, []); array_x2_higher_work := Array(0 .. 3, 0 .. 41, []); array_x2_higher_work2 := Array(0 .. 3, 0 .. 41, []); array_x2_set_initial := Array(0 .. 3, 0 .. 41, []); 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 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_x1_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x2_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 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 <= 40 do array_x1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_t[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp7[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp8[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp9[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp10[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_tmp11[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_tmp12[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_tmp13[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_tmp14[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_tmp15[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_tmp16[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_tmp17[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_x1_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 <= 40 do array_x1_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 <= 40 do array_x1_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 <= 40 do array_x1_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 <= 40 do array_x2_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 <= 40 do array_x2_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 <= 40 do array_x2_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 <= 40 do array_x2_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 <= 40 do term := 1; while term <= 40 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_x1); zero_ats_ar(array_t); zero_ats_ar(array_x2); 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_tmp5); zero_ats_ar(array_tmp6); zero_ats_ar(array_tmp7); zero_ats_ar(array_tmp8); zero_ats_ar(array_tmp9); zero_ats_ar(array_tmp10); zero_ats_ar(array_tmp11); zero_ats_ar(array_tmp12); zero_ats_ar(array_tmp13); zero_ats_ar(array_tmp14); zero_ats_ar(array_tmp15); zero_ats_ar(array_tmp16); zero_ats_ar(array_tmp17); 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_4D0); array_const_4D0[1] := c(4.0); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_const_2); array_const_2[1] := c(2); zero_ats_ar(array_const_3D0); array_const_3D0[1] := c(3.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_x1_set_initial[1, 1] := true; array_x1_set_initial[1, 2] := false; array_x1_set_initial[1, 3] := false; array_x1_set_initial[1, 4] := false; array_x1_set_initial[1, 5] := false; array_x1_set_initial[1, 6] := false; array_x1_set_initial[1, 7] := false; array_x1_set_initial[1, 8] := false; array_x1_set_initial[1, 9] := false; array_x1_set_initial[1, 10] := false; array_x1_set_initial[1, 11] := false; array_x1_set_initial[1, 12] := false; array_x1_set_initial[1, 13] := false; array_x1_set_initial[1, 14] := false; array_x1_set_initial[1, 15] := false; array_x1_set_initial[1, 16] := false; array_x1_set_initial[1, 17] := false; array_x1_set_initial[1, 18] := false; array_x1_set_initial[1, 19] := false; array_x1_set_initial[1, 20] := false; array_x1_set_initial[1, 21] := false; array_x1_set_initial[1, 22] := false; array_x1_set_initial[1, 23] := false; array_x1_set_initial[1, 24] := false; array_x1_set_initial[1, 25] := false; array_x1_set_initial[1, 26] := false; array_x1_set_initial[1, 27] := false; array_x1_set_initial[1, 28] := false; array_x1_set_initial[1, 29] := false; array_x1_set_initial[1, 30] := false; array_x1_set_initial[1, 31] := false; array_x1_set_initial[1, 32] := false; array_x1_set_initial[1, 33] := false; array_x1_set_initial[1, 34] := false; array_x1_set_initial[1, 35] := false; array_x1_set_initial[1, 36] := false; array_x1_set_initial[1, 37] := false; array_x1_set_initial[1, 38] := false; array_x1_set_initial[1, 39] := false; array_x1_set_initial[1, 40] := false; array_x2_set_initial[2, 1] := true; array_x2_set_initial[2, 2] := true; array_x2_set_initial[2, 3] := false; array_x2_set_initial[2, 4] := false; array_x2_set_initial[2, 5] := false; array_x2_set_initial[2, 6] := false; array_x2_set_initial[2, 7] := false; array_x2_set_initial[2, 8] := false; array_x2_set_initial[2, 9] := false; array_x2_set_initial[2, 10] := false; array_x2_set_initial[2, 11] := false; array_x2_set_initial[2, 12] := false; array_x2_set_initial[2, 13] := false; array_x2_set_initial[2, 14] := false; array_x2_set_initial[2, 15] := false; array_x2_set_initial[2, 16] := false; array_x2_set_initial[2, 17] := false; array_x2_set_initial[2, 18] := false; array_x2_set_initial[2, 19] := false; array_x2_set_initial[2, 20] := false; array_x2_set_initial[2, 21] := false; array_x2_set_initial[2, 22] := false; array_x2_set_initial[2, 23] := false; array_x2_set_initial[2, 24] := false; array_x2_set_initial[2, 25] := false; array_x2_set_initial[2, 26] := false; array_x2_set_initial[2, 27] := false; array_x2_set_initial[2, 28] := false; array_x2_set_initial[2, 29] := false; array_x2_set_initial[2, 30] := false; array_x2_set_initial[2, 31] := false; array_x2_set_initial[2, 32] := false; array_x2_set_initial[2, 33] := false; array_x2_set_initial[2, 34] := false; array_x2_set_initial[2, 35] := false; array_x2_set_initial[2, 36] := false; array_x2_set_initial[2, 37] := false; array_x2_set_initial[2, 38] := false; array_x2_set_initial[2, 39] := false; array_x2_set_initial[2, 40] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 40; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 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, "##############R:Temp/mtest6postode.ode#################"); omniout_str(ALWAYS, "diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 *\ diff ( x2 , t , 1 ) - 2.0 * x1 ; "); omniout_str(ALWAYS, "diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t \ , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , \ t , 1 ) + x1 ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=64;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "t_start := c(1.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "t_end := c(8.0);"); omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS, "array_x2_init[1 + 1] := exact_soln_x2p(t_start);") ; omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_h := c(0.0001);"); 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 := 0;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=12;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=2;"); omniout_str(ALWAYS, "glob_max_iter:=1000000;"); 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, "glob_h_reason:=1;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_x1 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := c(1.0);"); omniout_str(ALWAYS, "c2 := c(0.0002);"); omniout_str(ALWAYS, "c3 := c(0.0003);"); omniout_str(ALWAYS, "return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x1p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := c(1.0);"); omniout_str(ALWAYS, "c2 := c(0.0002);"); omniout_str(ALWAYS, "c3 := c(0.0003);"); omniout_str(ALWAYS, "return( c(-6.0) * c3 * exp(neg( c(t))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := c(1.0);"); omniout_str(ALWAYS, "c2 := c(0.0002);"); omniout_str(ALWAYS, "c3 := c(0.0003);"); omniout_str(ALWAYS, "return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := c(1.0);"); omniout_str(ALWAYS, "c2 := c(0.0002);"); omniout_str(ALWAYS, "c3 := c(0.0003);"); omniout_str(ALWAYS, "return( c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 \ * exp(neg(c(t))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); t_start := c(1.5); t_end := c(8.0); array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_look_poles := true; glob_max_h := c(0.0001); glob_type_given_pole := 0; glob_desired_digits_correct := 12; glob_max_minutes := 3.0; glob_subiter_method := 2; glob_max_iter := 1000000; 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_h_reason := 1; 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(t_start, t_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(t_end) - c(t_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(t_start, t_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_t[1] := c(t_start); array_t[2] := c(glob_h); glob_next_display := c(t_start); order_diff := 2; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] := array_x1_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_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] := array_x2_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(t_start, t_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_t[1] := c(t_start); array_t[2] := c(glob_h); glob_next_display := c(t_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 := 2; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] := array_x1_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_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] := array_x2_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_t[1] < glob_check_sign*t_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_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_x1_higher_work[2, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1[term_no] := array_x1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x1_higher[ord, term_no] := array_x1_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_x2_higher_work[3, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[2, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[2, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2[term_no] := array_x2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x2_higher[ord, term_no] := array_x2_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 ( x1 , t , 1 ) = 4.0 * x2 - 2.0 \ * diff ( x2 , t , 1 ) - 2.0 * x1 ; "); omniout_str(INFO, "diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , \ t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff (\ x1 , t , 1 ) + x1 ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2020-05-25T23:59:14-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest6"); logitem_str(html_log_file, "diff ( x1 , t , 1 ) = 4.0 * \ x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ;\ "); logitem_float(html_log_file, t_start); logitem_float(html_log_file, t_end); logitem_float(html_log_file, array_t[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, " 310 "); logitem_str(html_log_file, "mtest6 diffeq.mxt"); logitem_str(html_log_file, "mtest6 maple results"); logitem_str(html_log_file, "Poor Accuracy -- Possibly BAD TEST") ; logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( x2 , t , 2 ) = 3.0 * \ diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t ,\ 2 ) - diff ( x1 , t , 1 ) + x1 ; "); 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################# ##############R:Temp/mtest6postode.ode################# diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; ! #BEGIN FIRST INPUT BLOCK Digits:=64; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK t_start := c(1.5); t_end := c(8.0); array_x1_init[0 + 1] := exact_soln_x1(t_start); array_x2_init[0 + 1] := exact_soln_x2(t_start); array_x2_init[1 + 1] := exact_soln_x2p(t_start); glob_look_poles := true; glob_max_h := c(0.0001); glob_type_given_pole := 0; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=12; glob_max_minutes:=(3.0); glob_subiter_method:=2; glob_max_iter:=1000000; 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_h_reason:=1; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_x1 := proc(t) local c1,c2,c3; c1 := c(1.0); c2 := c(0.0002); c3 := c(0.0003); return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t)))); end; exact_soln_x1p := proc(t) local c1,c2,c3; c1 := c(1.0); c2 := c(0.0002); c3 := c(0.0003); return( c(-6.0) * c3 * exp(neg( c(t)))); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := c(1.0); c2 := c(0.0002); c3 := c(0.0003); return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t)))); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := c(1.0); c2 := c(0.0002); c3 := c(0.0003); return( c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t)))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# memory used=4.3MB, alloc=40.3MB, time=0.08 START of Soultion TOP MAIN SOLVE Loop t[1] = 1.5 x1[1] (closed_form) = 2.0004016342882671736920799048474 x1[1] (numeric) = 2.0004016342882671736920799048474 absolute error = 0 relative error = 0 % Desired digits = 12 Estimated correct digits = 13 Correct digits = 64 h = 0.001 x2[1] (closed_form) = 1.0040840464326820624968656900721 x2[1] (numeric) = 1.0040840464326820624968656900721 absolute error = 0 relative error = 0 % Desired digits = 12 Estimated correct digits = 13 Correct digits = 64 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.51 x1[1] (closed_form) = 2.0003976379603268807512153627942 x1[1] (numeric) = 2.0003975977965633576779707691815 absolute error = 4.0163763523073244593612711869169e-08 relative error = 2.0077889895943676930955491127694e-06 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 8 h = 0.001 x2[1] (closed_form) = 1.0041645313302264015612661796507 x2[1] (numeric) = 1.0041645516812098525218220902821 absolute error = 2.0350983450960555910631451293815e-08 relative error = 2.0266582632630344574393138003430e-06 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.52 x1[1] (closed_form) = 2.0003936813965139865699168717796 x1[1] (numeric) = 2.0003935207374434844547166802246 absolute error = 1.6065907050211520019155496336745e-07 relative error = 8.0313726241104680045932219688359e-06 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 7 h = 0.001 x2[1] (closed_form) = 1.0042466622131042155964806543355 x2[1] (numeric) = 1.0042467447063251410512563962409 absolute error = 8.2493220925454775741905370855987e-08 relative error = 8.2144381484585369485624176934887e-06 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 7 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=46.1MB, alloc=42.3MB, time=0.30 TOP MAIN SOLVE Loop t[1] = 1.53 x1[1] (closed_form) = 2.0003897642011688127112650821416 x1[1] (numeric) = 2.0003894027031982444744035693659 absolute error = 3.6149797056823686151277578688807e-07 relative error = 1.8071376740552192081864063528532e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 7 h = 0.001 x2[1] (closed_form) = 1.0043304721326001823690307320913 x2[1] (numeric) = 1.0043306602210869456859991268261 absolute error = 1.8808848676331696839473476158754e-07 relative error = 1.8727748682555550250003004154341e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 7 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.54 x1[1] (closed_form) = 2.000385885982568560317538699541 x1[1] (numeric) = 2.0003852432820207815063900364881 absolute error = 6.4270054777881114866305288347948e-07 relative error = 3.2128828356690958276373831109667e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0044159948096675089551337275755 x2[1] (numeric) = 1.0044163336460126841775630592965 absolute error = 3.3883634517522242933172096989176e-07 relative error = 3.3734662423354822487436458520861e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=88.5MB, alloc=44.3MB, time=0.52 TOP MAIN SOLVE Loop t[1] = 1.55 x1[1] (closed_form) = 2.0003820463528881375038919589956 x1[1] (numeric) = 2.0003810420579655116085107617261 absolute error = 1.0042949226258953811972695533618e-06 relative error = 5.0205155782963238114557796625660e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0045032646484363495982809213755 x2[1] (numeric) = 1.0045038011234321744818968733111 absolute error = 5.3647499582488361595193556284994e-07 relative error = 5.3406993755529823267293647831272e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.56 x1[1] (closed_form) = 2.0003782449281613765259774864397 x1[1] (numeric) = 2.0003767986109065282220598135761 absolute error = 1.4463172548483039176728636704559e-06 relative error = 7.2302188774315770207245047800034e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0045923167499953085613611752895 x2[1] (numeric) = 1.0045930995321322319025866452685 absolute error = 7.8278213692334122546997906531530e-07 relative error = 7.7920378632374691716626623608419e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.57 x1[1] (closed_form) = 2.0003744813282426368431989909583 x1[1] (numeric) = 2.0003725125164955892310286891526 absolute error = 1.9688117470476121703018057234207e-06 relative error = 9.8422158722017244193921396034876e-05 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0046831869264515426974489820757 x2[1] (numeric) = 1.0046842665022977400761135452086 absolute error = 1.0795758461973786645631329062760e-06 relative error = 0.00010745435578553278662040422373441 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=127.2MB, alloc=44.3MB, time=0.72 TOP MAIN SOLVE Loop t[1] = 1.58 x1[1] (closed_form) = 2.0003707551767687902378681154121 x1[1] (numeric) = 2.0003681833461196817842699994942 absolute error = 2.5718306491084535981159178443302e-06 relative error = 0.00012856769888545916240209313771138 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0047759117152750898876826308634 x2[1] (numeric) = 1.0047773404307551913333898719169 absolute error = 1.4287154801014457072410535403718e-06 relative error = 0.0001421924494251115198961103927321 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.59 x1[1] (closed_form) = 2.0003670661011215841887456819654 x1[1] (numeric) = 2.000363810666858160637033653522 absolute error = 3.2554342634235517120284434631313e-06 relative error = 0.00016274184466397251616050385289192 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0048705283939331631696911430512 x2[1] (numeric) = 1.004872360496524813153593652515 absolute error = 1.8321025916499839025094637903683e-06 relative error = 0.00018232225345271108223018135914189 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=165.7MB, alloc=44.3MB, time=0.94 TOP MAIN SOLVE Loop t[1] = 1.6 x1[1] (closed_form) = 2.0003634137323903797352733226818 x1[1] (numeric) = 2.0003593940414394557256739761002 absolute error = 4.0196909509240095993465815963798e-06 relative error = 0.00020094803390869084700321675510922 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0049670749948202663512576065259 x2[1] (numeric) = 1.0049693666766875210567977673337 absolute error = 2.2916818672547055401608077724313e-06 relative error = 0.00022803551721000582756174556225165 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.61 x1[1] (closed_form) = 2.0003597977053352601062508664658 x1[1] (numeric) = 2.0003549330281973446462491537708 absolute error = 4.8646771379154600017126950449201e-06 relative error = 0.00024319010727449420070580786945042 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0050655903204901052177196549322 x2[1] (numeric) = 1.0050683997625730644105159705681 absolute error = 2.8094420829591927963156358992857e-06 relative error = 0.0002795282327856167545192528612954 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=204.3MB, alloc=44.3MB, time=1.16 TOP MAIN SOLVE Loop t[1] = 1.62 x1[1] (closed_form) = 2.0003562176583505064237916071803 x1[1] (numeric) = 2.000350427181026785664224428383 absolute error = 5.7904773237207595671787973422615e-06 relative error = 0.00028947230861207242457229694549919 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 6 h = 0.001 x2[1] (closed_form) = 1.0051661139591953891453303337642 x2[1] (numeric) = 1.0051695013762758603025377798785 absolute error = 3.3874170804711572074461142549917e-06 relative error = 0.00033700072390310095963026011257578 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.63 x1[1] (closed_form) = 2.0003526732334284368300954114481 x1[1] (numeric) = 2.0003458760493393068385432029891 absolute error = 6.7971840891299915522084590087951e-06 relative error = 0.00033979928540015020601015057933311 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0052686863007417410747157107045 x2[1] (numeric) = 1.0052727139875051419097891995896 absolute error = 4.0276867634008350734888850144776e-06 relative error = 0.00040065773641295835820454560773561 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.64 x1[1] (closed_form) = 2.0003491640761236054209222092897 x1[1] (numeric) = 2.000341279178017946798941291264 absolute error = 7.8848981056586219809180256930573e-06 relative error = 0.00039417608921792020355992979157994 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0053733485526620594279258956137 x2[1] (numeric) = 1.0053780809307761817229690959371 absolute error = 4.7323781141222950432003233273632e-06 relative error = 0.00047070853041161655949572261587096 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=242.8MB, alloc=44.3MB, time=1.38 TOP MAIN SOLVE Loop t[1] = 1.65 x1[1] (closed_form) = 2.0003456898355173574056293806241 x1[1] (numeric) = 2.0003366361073717426705444923959 absolute error = 9.0537281456147350848882281716775e-06 relative error = 0.00045260817625773458055618060494798 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0054801427567178037196352378594 x2[1] (numeric) = 1.0054856464229494866229655256529 absolute error = 5.5036662316829033302877935218673e-06 relative error = 0.00054736697401040069335050704345637 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.66 x1[1] (closed_form) = 2.0003422501641827369492595039049 x1[1] (numeric) = 2.0003319463730897605945040243487 absolute error = 1.0303791092976354755479556200086e-05 relative error = 0.00051510140787810921685832051358958 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0055891118057338063690720987107 x2[1] (numeric) = 1.0055954555811250012022289313269 absolute error = 6.3437753911948331568326162577931e-06 relative error = 0.0006308516387775253301414072451749 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=281.3MB, alloc=44.3MB, time=1.58 TOP MAIN SOLVE Loop t[1] = 1.67 x1[1] (closed_form) = 2.0003388447181497441874334321061 x1[1] (numeric) = 2.0003272095061946642476835710136 absolute error = 1.1635211955079939749861092509777e-05 relative error = 0.00058166205119709884597700433727861 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0057002994607733466165511263743 x2[1] (numeric) = 1.0057075544408984979381509655155 absolute error = 7.2549801251513215998391411202142e-06 relative error = 0.00072138589687615949100787119130657 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.68 x1[1] (closed_form) = 2.0003354731568709379397212327797 x1[1] (numeric) = 2.0003224250329958167182112189248 absolute error = 1.3048123875121221510013854975284e-05 relative error = 0.00065229677972610534380634443455792 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0058137503686603585404003230836 x2[1] (numeric) = 1.005821989974987477912976819649 absolute error = 8.2396063271193725764965654280187e-06 relative error = 0.00081919801992161214927691036365054 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.69 x1[1] (closed_form) = 2.0003321351431873806817336647786 x1[1] (numeric) = 2.0003175924750419110470447568318 absolute error = 1.4542668145469634688907946858848e-05 relative error = 0.0007270126740441853814301617277507 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.005929510079855784011058223843 x2[1] (numeric) = 1.0059388101122340537939230306695 absolute error = 9.3000323782697828648068265492967e-06 relative error = 0.00092452127958066357439385788642287 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=319.9MB, alloc=44.3MB, time=1.78 TOP MAIN SOLVE Loop t[1] = 1.7 x1[1] (closed_form) = 2.000328830343294922370403021508 x1[1] (numeric) = 2.0003127113490731246985650199794 absolute error = 1.6118994221797671838001528604182e-05 relative error = 0.00080581722251292764847709743069627 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0060476250666952230646997208581 x2[1] (numeric) = 1.0060580637569924377972124492985 absolute error = 1.0438690297214732512728440420847e-05 relative error = 0.0010375940499360263234672966752566 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.71 x1[1] (closed_form) = 2.0003255584267108197508077718832 x1[1] (numeric) = 2.0003077811669727931756044670206 absolute error = 1.7777259738026575203304862564345e-05 relative error = 0.00088871832203197385563208422751881 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0061681427419951786855908768716 x2[1] (numeric) = 1.0061798008089088114211006193637 absolute error = 1.1658066913632735509742492054225e-05 relative error = 0.0011586599116388575566746021621947 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=358.4MB, alloc=44.3MB, time=2.00 TOP MAIN SOLVE Loop t[1] = 1.72 x1[1] (closed_form) = 2.0003223190662406878064438641218 x1[1] (numeric) = 2.0003028014357185979462322203 absolute error = 1.9517630522089860211643821747440e-05 relative error = 0.0009757242788352617355487738372903 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0062911114780353404122764437494 x2[1] (numeric) = 1.0063040721831015109073012611674 absolute error = 1.2960705066170495024817417997620e-05 relative error = 0.0012879677578721605113207515020162 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.73 x1[1] (closed_form) = 2.0003191119379457800480601789497 x1[1] (numeric) = 2.0002977716573332638010475711474 absolute error = 2.1340280612516247012607802290520e-05 relative error = 0.0010668438093280722809287390211973 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0064165806259245015866393892681 x2[1] (numeric) = 1.0064309298307496227404163421071 absolute error = 1.4349204825121153776952838937083e-05 relative error = 0.0014257719021478062399043381090163 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=396.9MB, alloc=44.3MB, time=2.20 TOP MAIN SOLVE Loop t[1] = 1.74 x1[1] (closed_form) = 2.0003159367211105943690597492498 x1[1] (numeric) = 2.0002926913288347607106765938597 absolute error = 2.3245392275833658383155390134989e-05 relative error = 0.00116208604096496748731961499138 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0065446005353578585070014540056 x2[1] (numeric) = 1.0065604267600982470852024288725 absolute error = 1.5826224740388578200974866956486e-05 relative error = 0.0015723321879597758778793438323863 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.75 x1[1] (closed_form) = 2.0003127930982108012280252910656 x1[1] (numeric) = 2.0002875599421860052036161194432 absolute error = 2.5233156024796024409171622401827e-05 relative error = 0.0012614605131687089066181597877952 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0066752225747735962881348650477 x2[1] (numeric) = 1.0066926170578888539572199959867 absolute error = 1.7394483115257669085130939010568e-05 relative error = 0.0017279141003160674863590223135889 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.76 x1[1] (closed_form) = 2.0003096807548814909511605719075 x1[1] (numeric) = 2.0002823769842440562345209378538 absolute error = 2.7303770637434716639634053724170e-05 relative error = 0.001364977178290251365729206637363 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0068084991519168259349449636972 x2[1] (numeric) = 1.0068275559112233271903989251387 absolute error = 1.9056759306501255453961441487427e-05 relative error = 0.0018927888791715285934504645699316 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=435.4MB, alloc=44.3MB, time=2.41 TOP MAIN SOLVE Loop t[1] = 1.77 x1[1] (closed_form) = 2.0003065993798857369793513998311 x1[1] (numeric) = 2.0002771419367088004624787205389 absolute error = 2.9457443176936516872679292193039e-05 relative error = 0.0014726464026099102637127643760911 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.006944483734819100066543734031 x2[1] (numeric) = 1.0069652996298704649734435562762 absolute error = 2.0815895051364906899822245209454e-05 relative error = 0.0020672336347836645636035546822132 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.78 x1[1] (closed_form) = 2.0003035486650834719161447420031 x1[1] (numeric) = 2.0002718542760711218077577283623 absolute error = 3.1694389012350108387013640774879e-05 relative error = 0.0015844789673798049304356358439411 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.00708323087320190094863760886 x2[1] (numeric) = 1.0071059056690238829453027660458 absolute error = 2.2674795821981996665157185735314e-05 relative error = 0.0022515314650132324328551206862787 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=473.9MB, alloc=44.3MB, time=2.61 TOP MAIN SOLVE Loop t[1] = 1.79 x1[1] (closed_form) = 2.0003005283054006732642248339551 x1[1] (numeric) = 2.000266513473560550103939787503 absolute error = 3.4014831840123160285046452142644e-05 relative error = 0.0017004860699076846106188712843479 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0072247962203126640710885972565 x2[1] (numeric) = 1.0072494326525204466390573133783 absolute error = 2.4636432207782567968716121772302e-05 relative error = 0.0024459715745911583803297061358752 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.8 x1[1] (closed_form) = 2.0002975379987988557689342484968 x1[1] (numeric) = 2.0002611189950923836102601203564 absolute error = 3.6419003706472158674128140367172e-05 relative error = 0.0018206793246822477296276494276664 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.007369236555202073512007994596 x2[1] (numeric) = 1.0073959403965285445158733758359 absolute error = 2.6703841326471003865381239982813e-05 relative error = 0.0026508493963730130280688583589311 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.81 x1[1] (closed_form) = 2.0002945774462448673180488532632 x1[1] (numeric) = 2.0002556703012142800963612007018 absolute error = 3.8907145030587221687652561392896e-05 relative error = 0.0019450707645400692017768026553992 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0075166098054515418290092603443 x2[1] (numeric) = 1.0075454899337157010099446237175 absolute error = 2.8880128264159180935363373235706e-05 relative error = 0.0028664667146019406799264681406951 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=512.5MB, alloc=44.3MB, time=2.83 TOP MAIN SOLVE Loop t[1] = 1.82 x1[1] (closed_form) = 2.0002916463516809853773714642261 x1[1] (numeric) = 2.0002501668470523111585246009433 absolute error = 4.1479504628674218846863282844752e-05 relative error = 0.0020736728418742546587157501948059 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0076669750703599672828816077678 x2[1] (numeric) = 1.0076981435379052209868932377908 absolute error = 3.1168467545253704011630022950378e-05 relative error = 0.0030931317902005647744909468133294 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.83 x1[1] (closed_form) = 2.0002887444219953109717628348128 x1[1] (numeric) = 2.0002446080822564743727674997227 absolute error = 4.4136339738836598995335090045185e-05 relative error = 0.0022064984298849446050052388698347 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0078203926445990449009751803877 x2[1] (numeric) = 1.0078539647492317528787420653408 absolute error = 3.3572104632707977766884953135021e-05 relative error = 0.0033311594881119805246396436099013 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=550.9MB, alloc=44.3MB, time=3.08 TOP MAIN SOLVE Loop t[1] = 1.84 x1[1] (closed_form) = 2.0002858713669924572509834119675 x1[1] (numeric) = 2.0002389934509456578359737528654 absolute error = 4.6877916046799415009659102120227e-05 relative error = 0.0023435608238717956507007996465728 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0079769240423465953004941506983 x2[1] (numeric) = 1.0080130183998058575766766519981 absolute error = 3.6094357459262276182501299767359e-05 relative error = 0.0035808714067094951728945451432534 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.85 x1[1] (closed_form) = 2.0002830268993645297091780170548 x1[1] (numeric) = 2.0002333223916520515914677777294 absolute error = 4.9704507712478117710239325420854e-05 relative error = 0.002484873742568570127011648893638 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0081366320219075663906418406903 x2[1] (numeric) = 1.0081753706398978740183414890049 absolute error = 3.8738617990307627699648314578312e-05 relative error = 0.003842596009294284668726135055202 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=589.4MB, alloc=44.3MB, time=3.28 TOP MAIN SOLVE Loop t[1] = 1.86 x1[1] (closed_form) = 2.0002802107346623951560012168411 x1[1] (numeric) = 2.0002275943372650003801274843818 absolute error = 5.2616397397394775873732459309629e-05 relative error = 0.0026304513295199695613080215818756 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0082995806108325581336326065058 x2[1] (numeric) = 1.0083410889646515803809290493057 absolute error = 4.1508353819022247296442799931263e-05 relative error = 0.0041166687576996009671945210594487 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.87 x1[1] (closed_form) = 2.0002774225912672365662565544882 x1[1] (numeric) = 2.0002218087149742921022645753637 absolute error = 5.5613876292944463991979124459825e-05 relative error = 0.0027803081545008516723054654376184 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0084658351315439195460043218896 x2[1] (numeric) = 1.0085102422413383619680405212846 absolute error = 4.4407109794442422036199394997172e-05 relative error = 0.0044034322480195845863833060005504 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.88 x1[1] (closed_form) = 2.0002746621903623909635109001106 x1[1] (numeric) = 2.0002159649462128763190711423021 absolute error = 5.8697244149514644439757808440168e-05 relative error = 0.0029344592149779747455640501106995 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.0086354622274796701430346141597 x2[1] (numeric) = 1.0086829007371628133421222449109 absolute error = 4.7438509683143199087630751253081e-05 relative error = 0.0047032363484801105035964807174108 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=628.0MB, alloc=44.3MB, time=3.48 TOP MAIN SOLVE Loop t[1] = 1.89 x1[1] (closed_form) = 2.0002719292559054675214488138234 x1[1] (numeric) = 2.0002100624465990070654349692868 absolute error = 6.1866809306460456013844536673493e-05 relative error = 0.0030929199376144174639081413953068 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 5 h = 0.001 x2[1] (closed_form) = 1.008808529889765705151593377472 x2[1] (numeric) = 1.0088591361476309230918255220545 absolute error = 5.0606257865217940232144582546792e-05 relative error = 0.0050164383394684198062998846332423 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.9 x1[1] (closed_form) = 2.0002692235146007430947538217244 x1[1] (numeric) = 2.0002041006258778041883566100593 absolute error = 6.5122888722938906397211665117117e-05 relative error = 0.0032557061798168264974045673197342 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0089851074844269551233038693665 x2[1] (numeric) = 1.0090390216254922149232633222884 absolute error = 5.3914141065259799959452921835906e-05 relative error = 0.0053434030557375625601357733430891 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=666.6MB, alloc=44.3MB, time=3.69 TOP MAIN SOLVE Loop t[1] = 1.91 x1[1] (closed_form) = 2.0002665446958718324190466891352 x1[1] (numeric) = 2.0001980788878622273670533816746 absolute error = 6.8465808009605051993307460581662e-05 relative error = 0.0034228342313256484035417271683919 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0091652657801483861549589201677 x2[1] (numeric) = 1.0092226318102674486159941992777 absolute error = 5.7366030119062461035279110020515e-05 relative error = 0.0056845030308008968560324146522446 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.92 x1[1] (closed_form) = 2.0002638925318346302468779100226 x1[1] (numeric) = 2.0001919966303734569121030965547 absolute error = 7.1895901461173334774813467886681e-05 relative error = 0.0035943208158485066506394245840365 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0093490769765969468529789676193 x2[1] (numeric) = 1.0094100428583737188806214459623 absolute error = 6.0965881776772027642478343017980e-05 relative error = 0.0060401186435310526190501525688333 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.93 x1[1] (closed_form) = 2.0002612667572705227139654635506 x1[1] (numeric) = 2.0001858532451806753816577644732 absolute error = 7.5413512089847332307699077412035e-05 relative error = 0.0037701830927368888567008270951326 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0095366147333157925512782662579 x2[1] (numeric) = 1.0096013324738590293889821295598 absolute error = 6.4717740543236837703863301852782e-05 relative error = 0.006410638266976874093720221190642 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=705.1MB, alloc=44.3MB, time=3.91 TOP MAIN SOLVE Loop t[1] = 1.94 x1[1] (closed_form) = 2.0002586671095998652567921376056 x1[1] (numeric) = 2.0001796481179402439928387036892 absolute error = 7.9018991659621263953433916382398e-05 relative error = 0.003950438658706313632307814418205 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.009727954199202346196975376248 x2[1] (numeric) = 1.0097965799397586633157396807076 absolute error = 6.8625740556317118764304459643353e-05 relative error = 0.0067964584194108994762500235745468 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.95 x1[1] (closed_form) = 2.000256093328855724429332077216 x1[1] (numeric) = 2.000173380628134267745903514247 absolute error = 8.2712700721456683428562968907922e-05 relative error = 0.004135105549600150730174922635166 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0099231720425819888475076435109 x2[1] (numeric) = 1.0099958661500859207294425192926 absolute error = 7.2694107503931881934875781715085e-05 relative error = 0.0071979839176189173750169087666225 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=743.6MB, alloc=44.3MB, time=4.11 TOP MAIN SOLVE Loop t[1] = 1.96 x1[1] (closed_form) = 2.00025354515765788099306634863 x1[1] (numeric) = 2.0001670501490085431176461342395 absolute error = 8.6495008649337875420214390472590e-05 relative error = 0.0043242022421972725360330011493865 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0101223464818894109693002723608 x2[1] (numeric) = 1.010199273642470047201400037825 absolute error = 7.6927160580636232099765464200371e-05 relative error = 0.0076156280324420549976247662894483 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.97 x1[1] (closed_form) = 2.0002510223411870916805748564442 x1[1] (numeric) = 2.0001606560475098821187476086125 absolute error = 9.0366293677209561827247831651965e-05 relative error = 0.004517747656063719286031525301667 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.010325557316969898787499256969 x2[1] (numeric) = 1.0104068866314544371636991435554 absolute error = 8.1329314484538376199886586396973e-05 relative error = 0.0080498126465806994528434390652942 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=782.2MB, alloc=44.3MB, time=4.31 TOP MAIN SOLVE Loop t[1] = 1.98 x1[1] (closed_form) = 2.0002485246271596070588595243716 x1[1] (numeric) = 2.0001541976842228064474310754613 absolute error = 9.4326942936800611428448910365226e-05 relative error = 0.0047157611554485647652503083616695 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0105328859610130779056295566856 x2[1] (numeric) = 1.0106187910424684599470359129778 absolute error = 8.5905081455382041406356292164843e-05 relative error = 0.0085009684146683285020226517928054 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 1.99 x1[1] (closed_form) = 2.0002460517658019429441638367841 x1[1] (numeric) = 2.0001476744133056054087835802689 absolute error = 9.8377352496337535380256515231557e-05 relative error = 0.004918262551224173630621335614278 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0107444154731318893925752262717 x2[1] (numeric) = 1.0108350745464865261705590678585 absolute error = 9.0659073354636777983841586799443e-05 relative error = 0.0089695349256220275944358466340873 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2 x1[1] (closed_form) = 2.000243603509825902845409199091 x1[1] (numeric) = 2.0001410855824257512054833650244 absolute error = 0.00010251792740015163992583406654697 relative error = 0.0051252721028710459100059857560925 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0109602305915998316231902520891 x2[1] (numeric) = 1.0110558265953882873475434930148 absolute error = 9.5596003788455724353240925689345e-05 relative error = 0.0094559608672750930849264678124492 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=820.7MB, alloc=44.3MB, time=4.53 TOP MAIN SOLVE Loop t[1] = 2.01 x1[1] (closed_form) = 2.0002411796144038489384716458907 x1[1] (numeric) = 2.0001344305326946651414078841781 absolute error = 0.00010674908170918379706376171261858 relative error = 0.0053368105205074486577806158348608 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0111804177677597644613753374967 x2[1] (numeric) = 1.0112811384580341423225418326013 absolute error = 0.00010072069027437786116649510466863 relative error = 0.0099607041932956640826000072445002 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.02 x1[1] (closed_form) = 2.0002387798371442190983757169765 x1[1] (numeric) = 2.0001277085986018282146885465578 absolute error = 0.00011107123854239088368717041874667 relative error = 0.0055528989669640391964852282584742 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.01140506520061784099592009124 x2[1] (numeric) = 1.011511103257070510580033718708 absolute error = 0.00010603805645266958411362746806153 relative error = 0.010484232292393784249402587082545 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=859.3MB, alloc=44.3MB, time=4.73 TOP MAIN SOLVE Loop t[1] = 2.03 x1[1] (closed_form) = 2.0002364039380672875410883180418 x1[1] (numeric) = 2.0001209191079482295112165806985 absolute error = 0.00011548483011905802987173734323066 relative error = 0.0057735590599036888443188707863678 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.011634262872136406087262926132 x2[1] (numeric) = 1.011745816006479624676108181656 absolute error = 0.0001115531343432185888452555240298 relative error = 0.011027022159817666800432629716684 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.04 x1[1] (closed_form) = 2.0002340516795811666509565459387 x1[1] (numeric) = 2.0001140613817791457433839143144 absolute error = 0.00011999029780202090757263162437762 relative error = 0.0059988128739867205199570364328882 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0118681025832399805671840366238 x2[1] (numeric) = 1.0119853736498888921602932720652 absolute error = 0.00011727106664891159310923544135706 relative error = 0.011589560571138217605984665948608 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.05 x1[1] (closed_form) = 2.0002317228264580475939522237301 x1[1] (numeric) = 2.0001071347343162452119569247631 absolute error = 0.00012458809214180238199529896706803 relative error = 0.0062286829430817781297584971044882 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0121066779905487351651561478966 x2[1] (numeric) = 1.0122298750996551814935678973331 absolute error = 0.00012319710910644632841174943640652 relative error = 0.012172344258319059219191524823935 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=897.8MB, alloc=44.3MB, time=4.97 TOP MAIN SOLVE Loop t[1] = 2.06 x1[1] (closed_form) = 2.0002294171458106773407646704313 x1[1] (numeric) = 2.0001001384728890094014226676586 absolute error = 0.00012927867292166793934200277274863 relative error = 0.0064631922625225501783620028243574 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0123500846438541492287285967562 x2[1] (numeric) = 1.0124794212767396967525440632167 absolute error = 0.00012933663288554752381546646049335 relative error = 0.012775880088067389321020457305092 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.07 x1[1] (closed_form) = 2.000227134407069069747424412174 x1[1] (numeric) = 2.0000930718978654653509099693921 absolute error = 0.00013406250920360439651444278190811 relative error = 0.0067023642914105746023898404929733 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0125984200243518461773128622039 x2[1] (numeric) = 1.0127341151513894224629412356737 absolute error = 0.00013569512703757628562837346977081 relative error = 0.013400685242458996861897531864953 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=936.3MB, alloc=44.3MB, time=5.17 TOP MAIN SOLVE Loop t[1] = 2.08 x1[1] (closed_form) = 2.0002248743819574483645464896661 x1[1] (numeric) = 2.000085934302582221873864752456 absolute error = 0.00013894007937522649068173721003771 relative error = 0.0069462229549643564089205978468336 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.012851783583646900497823484353 x2[1] (numeric) = 1.0129940617846414428544445811979 absolute error = 0.00014227820099454235662109684483729 relative error = 0.01404728740182864436901551300963 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.09 x1[1] (closed_form) = 2.0002226368444714186694550718867 x1[1] (numeric) = 2.0000787249732738026300432577564 absolute error = 0.00014391187119761603941181413022651 relative error = 0.0071947926469150343060153781041807 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0131102767835472200779578966481 x2[1] (numeric) = 1.0132593683706667693030603162941 absolute error = 0.00014909158711954922510241964599011 relative error = 0.014716224929914801669986497078532 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=974.8MB, alloc=44.3MB, time=5.38 TOP MAIN SOLVE Loop t[1] = 2.1 x1[1] (closed_form) = 2.0002204215708553674383935652769 x1[1] (numeric) = 2.0000714431890012689830714739357 absolute error = 0.00014897838185409845532209134119253 relative error = 0.0074480982319488371423304907997978 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0133740031366609229020699411436 x2[1] (numeric) = 1.0135301442799706458579796284734 absolute error = 0.00015614114330972295590968732982252 relative error = 0.015408047061245380753526605590807 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.11 x1[1] (closed_form) = 2.0002182283395800869987386055161 x1[1] (numeric) = 2.0000640882215801255057970484964 absolute error = 0.00015414011799996149294155701976942 relative error = 0.0077061650481965756271782511455276 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0136430682478139487316994643526 x2[1] (numeric) = 1.013806501103466645672226106554 absolute error = 0.00016343285565269694052664220143987 relative error = 0.016123314090748669650246492642538 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.12 x1[1] (closed_form) = 2.0002160569313206221236245067648 x1[1] (numeric) = 2.0000566593355075009239241369717 absolute error = 0.00015939759581312119970036979307321 relative error = 0.0079690189097704194817615564257057 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.013917579856304474486506397187 x2[1] (numeric) = 1.014088552697442221007195776104 absolute error = 0.00017097284113774652068937891696715 relative error = 0.016862597565571090983199233528527 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1013.4MB, alloc=44.3MB, time=5.59 TOP MAIN SOLVE Loop t[1] = 2.13 x1[1] (closed_form) = 2.0002139071289343373536491698366 x1[1] (numeric) = 2.0000491557878885972159648708797 absolute error = 0.00016475134104574013768429895692034 relative error = 0.0082366861093482148771656735111069 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0141976478790110367628628313787 x2[1] (numeric) = 1.0143764152294337264005809574416 absolute error = 0.00017876735042268963771812606287947 relative error = 0.017626480479080714029122081680471 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.14 x1[1] (closed_form) = 2.0002117787174392025523753425972 x1[1] (numeric) = 2.0000415768283623995143561469845 absolute error = 0.00017020188907680303801919561269804 relative error = 0.0085091934208056017455032061736697 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0144833844543716064105727682695 x2[1] (numeric) = 1.0146702072250292987179043674475 absolute error = 0.00018682277065769230733159917800949 relative error = 0.018415557467032623477565095544817 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1052.0MB, alloc=44.3MB, time=5.83 TOP MAIN SOLVE Loop t[1] = 2.15 x1[1] (closed_form) = 2.0002096714839922945241646872855 x1[1] (numeric) = 2.0000339216990266393786699409244 absolute error = 0.00017574978496565514549474636116503 relative error = 0.0087865681018961953078393360483587 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0147749039872512084697131714484 x2[1] (numeric) = 1.0149700496156183492956682563893 absolute error = 0.00019514562836714082595508494090268 relative error = 0.019230435005869289217695367664269 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.16 x1[1] (closed_form) = 2.0002075852178685125444885227851 x1[1] (numeric) = 2.0000261896343620039371819354207 absolute error = 0.00018139558350650860730658736445615 relative error = 0.0090688378969801009466407929899216 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0150723231947160361887778658907 x2[1] (numeric) = 1.0152760657871068023775782371978 absolute error = 0.0002037425923907661888003713070698 relative error = 0.020071731613125984975638287288097 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.17 x1[1] (closed_form) = 2.0002055197104395056742505358041 x1[1] (numeric) = 2.0000183798611555833176494606744 absolute error = 0.00018713984928392235660107512972245 relative error = 0.0093560310398010363619631230800434 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0153757611527323704443290268073 x2[1] (numeric) = 1.0155883816296176006960688623661 absolute error = 0.00021262047688523025173983555881907 relative error = 0.020940078049908064937677623309621 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1090.5MB, alloc=44.3MB, time=6.03 TOP MAIN SOLVE Loop t[1] = 2.18 x1[1] (closed_form) = 2.0002034747551528097508353326035 x1[1] (numeric) = 2.0000104915984235487119780307216 absolute error = 0.00019298315672926103885730188188337 relative error = 0.0096481762563123397898891106446572 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0156853393438089858062628657252 x2[1] (numeric) = 1.0159071255881963935141373328596 absolute error = 0.00022178624438740770787446713437552 relative error = 0.021836117525403522012530857380677 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.19 x1[1] (closed_form) = 2.0002014501475111919695645502313 x1[1] (numeric) = 2.0000025240573330533425185072421 absolute error = 0.00019892609017813862704604298917731 relative error = 0.0099453027675521479293320542375023 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.01600118170560210188955008355 x2[1] (numeric) = 1.0162324287145427248751076341307 absolute error = 0.00023124700894062298555755058073736 relative error = 0.02276050590339071441517650856992 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1128.9MB, alloc=44.3MB, time=6.23 TOP MAIN SOLVE Loop t[1] = 2.2 x1[1] (closed_form) = 2.0001994456850522009900014599665 x1[1] (numeric) = 1.9999944764411233485200264377914 absolute error = 0.00020496924392885246997502217511804 relative error = 0.010247440292568032119699374583104 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.016323414680502323653880405673 x2[1] (numeric) = 1.0165644247197874503714129219367 absolute error = 0.00024101003928512671753251626368501 relative error = 0.023713911910697454024313738790346 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.21 x1[1] (closed_form) = 2.0001974611673279205220976517994 x1[1] (numeric) = 1.9999863479450261069048236275535 absolute error = 0.00021111322230181361727402424598293 relative error = 0.010554619051391386237556167466246 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0166521672662234071110363657655 x2[1] (numeric) = 1.0169032500283375296020649568025 absolute error = 0.00025108276211412249102859103702223 relative error = 0.024697017347563795631107231808946 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1167.5MB, alloc=44.3MB, time=6.45 TOP MAIN SOLVE Loop t[1] = 2.22 x1[1] (closed_form) = 2.000195496395884924367523542548 x1[1] (numeric) = 1.999978137756184945003421663267 absolute error = 0.00021735863969997936410187928101118 relative error = 0.010866869768061864735819317473013 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0169875710674130876331680307776 x2[1] (numeric) = 1.0172490438328097688097601505396 absolute error = 0.00026147276539668117659211976199243 relative error = 0.025710517299856845844758749715085 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.23 x1[1] (closed_form) = 2.0001935511742444309116701364738 x1[1] (numeric) = 1.9999698450535741368527899868683 absolute error = 0.00022370612067029405888014960552197 relative error = 0.011184223673702174234638304005793 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0173297603483066168837352241901 x2[1] (numeric) = 1.0176019481500755241435222288628 absolute error = 0.00027218780176890725978700467267503 relative error = 0.026755120353081719072291177486547 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.24 x1[1] (closed_form) = 2.0001916253078826550817547005949 x1[1] (numeric) = 1.9999614690079165107635692068355 absolute error = 0.00023015629996614431818549375943042 relative error = 0.011506712509643527089469683127542 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0176788720864440714802628894828 x2[1] (numeric) = 1.0179621078784388207558254600391 absolute error = 0.00028323579199474927556257055628409 relative error = 0.027831548808128400607771268282536 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1206.0MB, alloc=44.3MB, time=6.66 TOP MAIN SOLVE Loop t[1] = 2.25 x1[1] (closed_form) = 2.0001897186042113558062097918406 x1[1] (numeric) = 1.9999530087816005209118355489572 absolute error = 0.00023670982261083489437424288345551 relative error = 0.011834368530602070409422466908235 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0180350460274729220110580566559 x2[1] (numeric) = 1.0183296708559707966922273968518 absolute error = 0.00029462482849787468116934019591568 relative error = 0.028940538898689728358145663153712 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.26 x1[1] (closed_form) = 2.0001878308725585770300853644456 x1[1] (numeric) = 1.9999444635285964854865065157322 absolute error = 0.00024336734396209154357884871333449 relative error = 0.012167224507906609078238567166782 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0183984247410577851368733188052 x2[1] (numeric) = 1.0187047879200238434482085762348 absolute error = 0.00030636317896605831133525742963294 relative error = 0.030082841010280969959378321710148 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1244.6MB, alloc=44.3MB, time=6.86 TOP MAIN SOLVE Loop t[1] = 2.27 x1[1] (closed_form) = 2.0001859619241495803605494485876 x1[1] (numeric) = 1.9999358323943719830161326931916 absolute error = 0.00025012952977759734441675539601517 relative error = 0.012505313732777946441776762472396 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0187691536779197243868201384209 x2[1] (numeric) = 1.0190876129679492873373785910926 absolute error = 0.00031845929002956295055845267166751 relative error = 0.031259219900786545817369333790944 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.28 x1[1] (closed_form) = 2.0001841115720879674357360608217 x1[1] (numeric) = 1.9999271145158063984146378810257 absolute error = 0.00025699705628156902109817979597734 relative error = 0.01284867001966017147009429133965 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0191473812280279170827919489146 x2[1] (numeric) = 1.0194783030190429376264149807436 absolute error = 0.00033092179101502054362303182897607 relative error = 0.032470454922454325729759427433231 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.29 x1[1] (closed_form) = 2.0001822796313369901291614996888 x1[1] (numeric) = 1.9999183090211046102005409081649 absolute error = 0.00026397061023237992862059152390502 relative error = 0.013197327709604226379674589336676 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0195332587799669657789869447521 x2[1] (numeric) = 1.0198770182777433189378222709781 absolute error = 0.00034375949777635315883532622601574 relative error = 0.03371734024525260196887586684567 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1283.2MB, alloc=44.3MB, time=7.08 TOP MAIN SOLVE Loop t[1] = 2.3 x1[1] (closed_form) = 2.0001804659187010467207138932488 x1[1] (numeric) = 1.9999094150297098102583091284376 absolute error = 0.00027105088899123646240476481121628 relative error = 0.013551321673704093912543753169577 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0199269407815036028672097929057 x2[1] (numeric) = 1.0202839221981079068984963388527 absolute error = 0.00035698141660430403128654594704521 relative error = 0.035000685081499309778641873790407 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.31 x1[1] (closed_form) = 2.000178670252807362183817677582 x1[1] (numeric) = 1.9999004316522154474237470812143 absolute error = 0.00027823860059191476007059636776969 relative error = 0.013910687316585948714466420142403 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0203285848013770167625912159095 x2[1] (numeric) = 1.0206991815495931976207901757568 absolute error = 0.00037059674821618085819895984728909 relative error = 0.036321313911667321899183825846147 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1321.8MB, alloc=44.3MB, time=7.28 TOP MAIN SOLVE Loop t[1] = 2.32 x1[1] (closed_form) = 2.0001768924540878507567864562299 x1[1] (numeric) = 1.9998913579902762860877054753135 absolute error = 0.00028553446381156466908098091639293 relative error = 0.014275460579950622534631844513395 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0207383515923375175401055435668 x2[1] (numeric) = 1.0211229664841649635479904184486 absolute error = 0.00038461489182744600788487488185327 relative error = 0.037680066711263681726789542471382 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.33 x1[1] (closed_form) = 2.0001751323447611589846062612862 x1[1] (numeric) = 1.9998821931365185709238967489914 absolute error = 0.00029293920824258806070951229483495 relative error = 0.014645677946169738284754588500356 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.021156405155458759235576808298 x2[1] (numeric) = 1.0215554506047655806866541862276 absolute error = 0.00039904544930682145107737792960121 relative error = 0.039077799178674454804760314601708 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=1360.3MB, alloc=44.3MB, time=7.50 t[1] = 2.34 x1[1] (closed_form) = 2.0001733897488148874354384302831 x1[1] (numeric) = 1.9998729361744492887572151245932 absolute error = 0.0003004535743655986782233056898872 relative error = 0.01502137644193587334684663747853 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0215829128057492454554868389719 x2[1] (numeric) = 1.0219968110351658554971659453987 absolute error = 0.00041389822941661004167910642680847 relative error = 0.040515382963860465312325023261692 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.35 x1[1] (closed_form) = 2.0001716644919879893139989338742 x1[1] (numeric) = 1.9998635861783645184986723745122 absolute error = 0.00030807831362347081532655936204974 relative error = 0.015402593641967117906597815836024 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0220180452390893646616122290701 x2[1] (numeric) = 1.0224472284912293339385013536039 absolute error = 0.0004291832521399692768891245338037 relative error = 0.041993705897782537906192280603153 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.36 x1[1] (closed_form) = 2.0001699564017533442116608243761 x1[1] (numeric) = 1.9998541422132568599818664167215 absolute error = 0.00031581418849648422979440765464183 relative error = 0.015789367672766399513861799127361 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0224619766005207317172157388726 x2[1] (numeric) = 1.0229068873536176405852671878057 absolute error = 0.00044491075309690886805144893316482 relative error = 0.043513672222427980561332245827075 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1398.8MB, alloc=44.3MB, time=7.70 TOP MAIN SOLVE Loop t[1] = 2.37 x1[1] (closed_form) = 2.0001682653073005052506402934904 x1[1] (numeric) = 1.9998446033347219324437892438476 absolute error = 0.00032366197257857280685104964275589 relative error = 0.016181737216435950533722275116344 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0229148845539151532132961026616 x2[1] (numeric) = 1.0233759757419659725808409416897 absolute error = 0.00046109118805081936754483902814735 relative error = 0.045076202821302915915385476101402 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.38 x1[1] (closed_form) = 2.0001665910395186178969663803834 x1[1] (numeric) = 1.9998349685888639332997443483838 absolute error = 0.00033162245065468459722203199953685 relative error = 0.016579741514547300651548246221486 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0233769503530510859526373988824 x2[1] (numeric) = 1.0238546855905584616906479356758 absolute error = 0.00047773523750737573801053679347853 relative error = 0.046682235450247692094928486303756 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1437.2MB, alloc=44.3MB, time=7.92 TOP MAIN SOLVE Loop t[1] = 2.39 x1[1] (closed_form) = 2.0001649334309795087341013927256 x1[1] (numeric) = 1.9998252370122002477681724345043 absolute error = 0.00033969641877926096592895822133982 relative error = 0.016983420372067182133883345352398 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0238483589141260209768452898533 x2[1] (numeric) = 1.0243432127255337181097376161737 absolute error = 0.00049485381140769713289232632036281 relative error = 0.048332724968424974248850716940247 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.4 x1[1] (closed_form) = 2.0001632923159209425060753099961 x1[1] (numeric) = 1.9998154076315650998062684068048 absolute error = 0.00034788468435584269980690319134881 relative error = 0.01739281416133974112449957626679 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0243292988897337999024221749256 x2[1] (numeric) = 1.0248417569436514821990604739017 absolute error = 0.00051245805391768229663829897606322 relative error = 0.050028643569322230317513531114837 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.41 x1[1] (closed_form) = 2.0001616675302300457558245299824 x1[1] (numeric) = 1.9998054794640122347214029065153 absolute error = 0.00035618806621781103442162346717244 relative error = 0.017807963826125453872033324617357 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0248199627443364563159757815122 x2[1] (numeric) = 1.0253505220926519352202616608516 absolute error = 0.00053055934831547890428587933938115 relative error = 0.051770981011602174355782406599377 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1475.9MB, alloc=44.3MB, time=8.13 TOP MAIN SOLVE Loop t[1] = 2.42 x1[1] (closed_form) = 2.0001600589114268954010849786693 x1[1] (numeric) = 1.9997954515167166237265284392425 absolute error = 0.00036460739471027167455653942682403 relative error = 0.018228910885697152442867122180731 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0253205468312607728002765309717 x2[1] (numeric) = 1.0258697161532398576594065729025 absolute error = 0.00054916932197908485913004193078666 relative error = 0.053560744849626313601195886538398 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.43 x1[1] (closed_form) = 2.0001584662986482706066834965958 x1[1] (numeric) = 1.9997853227868751806099437217133 absolute error = 0.00037314351177308999673977488249589 relative error = 0.018655697438993570170884912387341 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0258312514712503540612139473036 x2[1] (numeric) = 1.0263995513227264741308977069954 absolute error = 0.00056829985147612006968375969180266 relative error = 0.055398960663468057224446346377513 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1514.5MB, alloc=44.3MB, time=8.33 TOP MAIN SOLVE Loop t[1] = 2.44 x1[1] (closed_form) = 2.0001568895326315663284011906667 x1[1] (numeric) = 1.9997750922616064805910004875679 absolute error = 0.00038179727102508573740070309884862 relative error = 0.019088366168830822834976064795822 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0263522810326046388447180673305 x2[1] (numeric) = 1.0269402441003624873941440226484 absolute error = 0.00058796306775784854942595531791758 relative error = 0.057286672288222881322774890372955 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.45 x1[1] (closed_form) = 2.0001553284556988669197497323297 x1[1] (numeric) = 1.9997647589178494713335547549853 absolute error = 0.00039056953784939558619497734442231 relative error = 0.019526960346172247336262955143261 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0268838440129369081213033476098 x2[1] (numeric) = 1.0274920153743964809627736625853 absolute error = 0.00060817136145957284147031497549637 relative error = 0.059224942042413802464438494328363 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=1552.9MB, alloc=44.3MB, time=8.55 t[1] = 2.46 x1[1] (closed_form) = 2.0001537829117411782090080077086 x1[1] (numeric) = 1.9997543217222611659881794934978 absolute error = 0.00039946118948001222082851421078082 relative error = 0.019971523834457025470551687449021 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0274261531225839946279830379304 x2[1] (numeric) = 1.0280550905108935604101710382003 absolute error = 0.00062893738830956578218800026991164 relative error = 0.061214850955280887480139015249138 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.47 x1[1] (closed_form) = 2.0001522527462028164697136833785 x1[1] (numeric) = 1.9997437796311133080323576551781 absolute error = 0.00040847311508950843735602820046125 relative error = 0.020422101093988026258032947911264 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0279794253697010595519440746666 x2[1] (numeric) = 1.02862969944434980805217412214 absolute error = 0.000650274074648748500230047473371 relative error = 0.063257498992733717039896063187427 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.48 x1[1] (closed_form) = 2.0001507378060659527234937277056 x1[1] (numeric) = 1.9997331315901879975750534765828 absolute error = 0.00041760621587795514844025112278104 relative error = 0.020878737186379306202371906530078 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0285438821470754761818521133203 x2[1] (numeric) = 1.029216076770138844499773339882 absolute error = 0.00067219462306336831792122656170468 relative error = 0.065354005281735621995484400231836 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1591.5MB, alloc=44.3MB, time=8.75 TOP MAIN SOLVE Loop t[1] = 2.49 x1[1] (closed_form) = 2.0001492379398353108296512910108 x1[1] (numeric) = 1.9997223765346722686882055302125 absolute error = 0.00042686140516304214144576079831995 relative error = 0.021341477779063712805608834280252 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0291197493206945480105981629308 x2[1] (numeric) = 1.0298144618388275239091903727331 absolute error = 0.00069471251813297589859220980230178 relative error = 0.067505508332878122015500222389853 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.5 x1[1] (closed_form) = 2.000147752997523017831305151614 x1[1] (numeric) = 1.999711513389051607222786822277 absolute error = 0.00043623960847141060851832933702806 relative error = 0.021810369149861042664336504006744 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0297072573201024903227739746105 x2[1] (numeric) = 1.0304250988523985379071738052914 absolute error = 0.0007178415322960475843998306809662 relative error = 0.069713166260893313595036198753128 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1630.1MB, alloc=44.3MB, time=8.98 TOP MAIN SOLVE Loop t[1] = 2.51 x1[1] (closed_form) = 2.0001462828306336050431037169473 x1[1] (numeric) = 1.9997005410670023984611248073271 absolute error = 0.00044574176363120658197890962022223 relative error = 0.02228545819160721151702188204948 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0303066412305828200218012476873 x2[1] (numeric) = 1.0310482369624184664350462361891 absolute error = 0.00074159573183564641324498850183129 relative error = 0.071978157002840977420053158687892 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.52 x1[1] (closed_form) = 2.0001448272921491583806098520027 x1[1] (numeric) = 1.9996894584712832938501569244977 absolute error = 0.00045536882086586453045292750504077 relative error = 0.022766792416844899702698109943909 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0309181408872030286317372867347 x2[1] (numeric) = 1.0316841303701905924413383585147 absolute error = 0.00076598948298756380960107177995951 relative error = 0.074301678533695902113615376690189 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.53 x1[1] (closed_form) = 2.0001433862365146164463770988317 x1[1] (numeric) = 1.9996782644936254859522044528938 absolute error = 0.00046512174288913049417264593786163 relative error = 0.023254419962576142628173019653597 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0315420009707591583394179922855 x2[1] (numeric) = 1.0323330384289325917712826684633 absolute error = 0.00079103745817343343186467617775218 relative error = 0.076684949079049351903449924507242 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1668.6MB, alloc=44.3MB, time=9.19 TOP MAIN SOLVE Loop t[1] = 2.54 x1[1] (closed_form) = 2.0001419595196232149025136430807 x1[1] (numeric) = 1.9996669580146218806406683256575 absolute error = 0.00047500150500133426184531742313432 relative error = 0.023748389595077342024991861920675 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0321784711056586609217594388637 x2[1] (numeric) = 1.0329952257480200200698394885203 absolute error = 0.00081675464236135914808004965665532 relative error = 0.079129207324626739596358647184316 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.55 x1[1] (closed_form) = 2.0001405469988020756741591542312 x1[1] (numeric) = 1.9996555379036151554577741154868 absolute error = 0.00048500909518692021638503874435235 relative error = 0.024248750714777180009268796956977 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0328278059597806947347228446323 x2[1] (numeric) = 1.0336709622993373453575381939074 absolute error = 0.00084315633955665062281534927510702 relative error = 0.081635712622311403889565797853412 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1707.0MB, alloc=44.3MB, time=9.39 TOP MAIN SOLVE Loop t[1] = 2.56 x1[1] (closed_form) = 2.0001391485327979395427828381899 x1[1] (numeric) = 1.9996440030185846929401086810915 absolute error = 0.00049514551421324660267415709833422 relative error = 0.024755553361197924237783102335489 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0334902653463538059347967473061 x2[1] (numeric) = 1.0343605235257791184860346033793 absolute error = 0.00087025817942531255123785607321552 relative error = 0.084205745192351932598841462581697 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.57 x1[1] (closed_form) = 2.0001377639817630407025501424895 x1[1] (numeric) = 1.9996323522060323776051868057085 absolute error = 0.00050541177573066309736333678100381 relative error = 0.025268848217960618783046018359478 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0341661143278917470772722331457 x2[1] (numeric) = 1.0350641904519447342703918576392 absolute error = 0.00089807612405298719311962449342997 relative error = 0.086840606321417722634821489783719 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=1745.6MB, alloc=44.3MB, time=9.61 t[1] = 2.58 x1[1] (closed_form) = 2.0001363932072411218672019795289 x1[1] (numeric) = 1.9996205843008672451786513148448 absolute error = 0.00051580890637387668855066468416585 relative error = 0.025788686617854661729011682264977 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0348556233222290095108815314645 x2[1] (numeric) = 1.0357822497970711140719849068554 absolute error = 0.00092662647484210456110337539082767 relative error = 0.089541618556154426048846746526596 % Desired digits = 12 Estimated correct digits = 12 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.59 x1[1] (closed_form) = 2.0001350360721535885289455016576 x1[1] (numeric) = 1.9996086981262889725269332672958 absolute error = 0.00052633794586461600201223436179754 relative error = 0.026315120547972276918364748666969 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0355590682106984858948575712173 x2[1] (numeric) = 1.0365149940902485363208615644626 absolute error = 0.00095592587955005042600399324530046 relative error = 0.092310125891877602526307098899308 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.6 x1[1] (closed_form) = 2.0001336924407858009847707790263 x1[1] (numeric) = 1.9995966924936701966442683934117 absolute error = 0.00053699994711560434050238561463447 relative error = 0.026848202654908393762507209317183 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0362767304484945360381252899357 x2[1] (numeric) = 1.0372627217879657552777155255215 absolute error = 0.000985991339471219239590235585733 relative error = 0.095147493956029286503445728755093 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1784.0MB, alloc=44.3MB, time=9.81 TOP MAIN SOLVE Loop t[1] = 2.61 x1[1] (closed_form) = 2.000132362178773502759384588523 x1[1] (numeric) = 1.9995845662024376509258704144177 absolute error = 0.00054779597633585183351417410524043 relative error = 0.027387986250026455557131932852801 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0370088971772656034439147791413 x2[1] (numeric) = 1.0380257373940314806089276785501 absolute error = 0.0010168402167658771650128994088388 relative error = 0.098055110186008286699788678088025 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.62 x1[1] (closed_form) = 2.0001310451530893840675922974857 x1[1] (numeric) = 1.9995723180399521068407895066846 absolute error = 0.00055872711313727722680279080113515 relative error = 0.027934525314790683330260097816914 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0377558613399814217862761431891 x2[1] (numeric) = 1.0388043515819202414563859059666 absolute error = 0.0010484902419388196701097627775314 relative error = 0.10103438400097087333051025676342 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1822.5MB, alloc=44.3MB, time=10.02 TOP MAIN SOLVE Loop t[1] = 2.63 x1[1] (closed_form) = 2.0001297412320297789724628832313 x1[1] (numeric) = 1.999559946781387108998523147856 absolute error = 0.00056979445064266997393973537536569 relative error = 0.028487874506165328886488837058066 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0385179217981207604045247255734 x2[1] (numeric) = 1.039598881319591629007509578031 absolute error = 0.0010809595214708686029848524575941 relative error = 0.10408674696718408065006605648969 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.64 x1[1] (closed_form) = 2.0001284502852014949089818191613 x1[1] (numeric) = 1.9995474511896064914827849514699 absolute error = 0.00058099909559500342619686769138541 relative error = 0.029048089162081457401604254170875 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0392953834512265861415083939609 x2[1] (numeric) = 1.0404096499968329014982792823837 absolute error = 0.0011142665456063153567708884227567 relative error = 0.10721365295649916792304973068601 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.65 x1[1] (closed_form) = 2.0001271721835087732561332173007 x1[1] (numeric) = 1.9995348300150406632039627968948 absolute error = 0.00059234216846811005217042040594047 relative error = 0.029615225306971806666329141329297 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0400885573588764658430735260112 x2[1] (numeric) = 1.0412369875551759455091434448778 absolute error = 0.0011484301962994796660699188666008 relative error = 0.11041657829749784971156148006263 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1861.1MB, alloc=44.3MB, time=10.23 TOP MAIN SOLVE Loop t[1] = 2.66 x1[1] (closed_form) = 2.0001259067991403796534575692593 x1[1] (numeric) = 1.999522081995561649898698404511 absolute error = 0.00060382480357872975475916474834249 relative error = 0.030189339657374276877465339202246 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.0408977608651169999580217612353 x2[1] (numeric) = 1.0420812306204406177444805274384 absolute error = 0.0011834697553236177864587662030735 relative error = 0.11369702191884873701647773573728 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.67 x1[1] (closed_form) = 2.000124654005556822771105983281 x1[1] (numeric) = 1.9995092058563568802806841820796 absolute error = 0.00061544814919994249042180120143293 relative error = 0.0307704896276046117297344040284 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.041723317725412063316656472424 x2[1] (numeric) = 1.0429427226379575426330398928161 absolute error = 0.0012194049125454793163834203921634 relative error = 0.11705650548439603610242391863183 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1899.7MB, alloc=44.3MB, time=10.44 TOP MAIN SOLVE Loop t[1] = 2.68 x1[1] (closed_form) = 2.0001234136774777002552572717478 x1[1] (numeric) = 1.9994962003098017037211872434267 absolute error = 0.0006272133676759965340700283211129 relative error = 0.031358733335498838472899375011371 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 4 h = 0.001 x2[1] (closed_form) = 1.042565558236155634715984279575 x2[1] (numeric) = 1.0438218140105245134699948712576 absolute error = 0.0012562557743688787540105916825676 relative error = 0.12049657351948694491638238546405 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.69 x1[1] (closed_form) = 2.0001221856908691705834818857643 x1[1] (numeric) = 1.9994830640553306267109624162233 absolute error = 0.00063912163553854387251946954103244 relative error = 0.031954129608226041566952944823085 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0434248193668010228029955315253 x2[1] (numeric) = 1.0447188622391517388699421491169 absolute error = 0.0012940428723507160669466175916117 relative error = 0.12401879352802838244715686200903 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1938.2MB, alloc=44.3MB, time=10.64 TOP MAIN SOLVE Loop t[1] = 2.7 x1[1] (closed_form) = 2.0001209699229315495772277930615 x1[1] (numeric) = 1.9994697957793072552270931268557 absolute error = 0.00065117414362429435013466620587212 relative error = 0.032556737988172051593976959757018 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0443014448946593423345569015331 x2[1] (numeric) = 1.0456342320666522924520634760455 absolute error = 0.0013327871719929501175065745123646 relative error = 0.12762475609974770023668467168857 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.71 x1[1] (closed_form) = 2.0001197662520870303310692115344 x1[1] (numeric) = 1.9994563941548929299988884647537 absolute error = 0.00066337209719410033218074678070875 relative error = 0.033166618738894638169414469421665 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0451957855424211626219572516615 x2[1] (numeric) = 1.0465682956241352623802621483167 absolute error = 0.0013725100817140997583048966552274 relative error = 0.13131607500711587518904673838084 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.72 x1[1] (closed_form) = 2.0001185745579675253307008898587 x1[1] (numeric) = 1.9994428578419140415362535449051 absolute error = 0.00067571671605348379444734495363697 relative error = 0.033783832851150802738653955908483 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0461081991184563392671601334367 x2[1] (numeric) = 1.0475214325804602590879518297278 absolute error = 0.0014132334620039198207916962911176 relative error = 0.13509438729137538812569170947141 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1976.7MB, alloc=44.3MB, time=10.84 TOP MAIN SOLVE Loop t[1] = 2.73 x1[1] (closed_form) = 2.0001173947214026295438796030143 x1[1] (numeric) = 1.9994291854867280116519254344147 absolute error = 0.00068820923467461789195416859960845 relative error = 0.034408442048996774347717307203185 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0470390506599481516020662208654 x2[1] (numeric) = 1.0484940302947131246940660765367 absolute error = 0.0014549796347649730919998556713 relative error = 0.13896135333709857423278123820724 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.74 x1[1] (closed_form) = 2.0001162266244077032806119260732 x1[1] (numeric) = 1.9994153757220879280756151842648 absolute error = 0.00070085090231977520499674180847775 relative error = 0.035040508795961318740185998307352 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0479887125789190019961125230614 x2[1] (numeric) = 1.0494864839717638967379194115822 absolute error = 0.0014977713928448947418068885207522 relative error = 0.14291865693468571247496014366278 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2015.3MB, alloc=44.3MB, time=11.06 TOP MAIN SOLVE Loop t[1] = 2.75 x1[1] (closed_form) = 2.000115070150172073630864374046 x1[1] (numeric) = 1.9994014271670058186234045756133 absolute error = 0.00071364298316625500745979843274155 relative error = 0.035680096301292978457017346756906 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.04895756481120608985484851891 x2[1] (numeric) = 1.0504991968209693124095095026975 absolute error = 0.0015416320097632225546609837874198 relative error = 0.14696800533019552593494995843255 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.76 x1[1] (closed_form) = 2.0001139251830473532999298466339 x1[1] (numeric) = 1.9993873384266145512497005817356 absolute error = 0.00072658675643280205022926489827453 relative error = 0.036327268526281869002324330448811 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0499459949684466531554101441361 x2[1] (numeric) = 1.0515325802180833979222015866875 absolute error = 0.0015865852496367447667914425513525 relative error = 0.1511111292618841205759560388498 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.77 x1[1] (closed_form) = 2.0001127916085358756733241801936 x1[1] (numeric) = 1.9993731080920283461716376573799 absolute error = 0.00073968351650752950168652281368351 relative error = 0.036982090190656663587254253106884 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0509543984931335742260852950776 x2[1] (numeric) = 1.0525870538704409715699468860192 absolute error = 0.0016326553773073973438615909415368 relative error = 0.15534978298281172486096629492194 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2053.9MB, alloc=44.3MB, time=11.26 TOP MAIN SOLVE Loop t[1] = 2.78 x1[1] (closed_form) = 2.0001116693132792449547096590927 x1[1] (numeric) = 1.9993587347402018861170240554824 absolute error = 0.00075293457307735883768560361029465 relative error = 0.037644626779057406476545791752484 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0519831788168033746579891671908 x2[1] (numeric) = 1.0536630459854801988448934324416 absolute error = 0.0016798671686768241869042652507927 relative error = 0.15968574426885993787901528098632 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.79 x1[1] (closed_form) = 2.0001105581850470002318497372226 x1[1] (numeric) = 1.9993442169337880106067395573558 absolute error = 0.00076634125125898962511017986677462 relative error = 0.038314944547584802538919327027015 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0530327475214198772285324444596 x2[1] (numeric) = 1.0547609934426716742874638472044 absolute error = 0.0017282459212517970589314027447908 relative error = 0.16412081441148558221623539301809 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2092.3MB, alloc=44.3MB, time=11.47 TOP MAIN SOLVE Loop t[1] = 2.8 x1[1] (closed_form) = 2.0001094581127253923369921184987 x1[1] (numeric) = 1.9993295532209939800408942676311 absolute error = 0.00077990489173141229609785086762114 relative error = 0.038993110530426638243917071219771 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0541035245040180910200828957228 x2[1] (numeric) = 1.0558813419689228680342996229586 absolute error = 0.0017778174649047770142167272358436 relative error = 0.1686568181945207251557857458967 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.81 x1[1] (closed_form) = 2.0001083689863062723793568820079 x1[1] (numeric) = 1.9993147421354362952150373095039 absolute error = 0.00079362685086997716431957250402396 relative error = 0.039679192546561997054919039219394 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0551959381446741800443292770859 x2[1] (numeric) = 1.057024546317528165865304536918 absolute error = 0.0018286081728539858209752598320618 relative error = 0.17329560385431201565582266678134 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2131.0MB, alloc=44.3MB, time=11.69 TOP MAIN SOLVE Loop t[1] = 2.82 x1[1] (closed_form) = 2.0001072906968760908385736410284 x1[1] (numeric) = 1.9992997821959940577482460570157 absolute error = 0.00080750850088203309032758401273372 relative error = 0.040373259206543939941586637095187 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0563104254778687061550232539876 x2[1] (numeric) = 1.0581910704507361504857782384427 absolute error = 0.001880644972867444330754984455106 relative error = 0.17803904302247622515064093123563 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.83 x1[1] (closed_form) = 2.0001062231366050061189679121864 x1[1] (numeric) = 1.9992846719066608567590165132429 absolute error = 0.00082155122994414935995139894351058 relative error = 0.04107537991936132957570254418279 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0574474323673116943812063903376 x2[1] (numeric) = 1.0593813877260072193809726285258 absolute error = 0.0019339553586955249997662381882864 relative error = 0.18288903065053282028741095793748 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.84 x1[1] (closed_form) = 2.0001051661987361014755430471497 x1[1] (numeric) = 1.999269409756395166977498995249 absolute error = 0.00083575644234093449804405190075173 relative error = 0.04178562489938048468306537629435 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0586074136842994535826824233759 x2[1] (numeric) = 1.0605959810860361114274538841988 absolute error = 0.0019885674017366578447714608229549 relative error = 0.18784748491565858059269015975182 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2169.5MB, alloc=44.3MB, time=11.89 TOP MAIN SOLVE Loop t[1] = 2.85 x1[1] (closed_form) = 2.0001041197775747092333413391282 x1[1] (numeric) = 1.9992539942189692433337656807138 absolute error = 0.00085012555860546589957565841436901 relative error = 0.042504065173367359001548922476484 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0597908334896744980732958292991 x2[1] (numeric) = 1.0618353432526154211292367114514 absolute error = 0.0020445097629409230559408821523041 relative error = 0.19291634710679375177652180049868 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.86 x1[1] (closed_form) = 2.0001030837684778412325973437769 x1[1] (numeric) = 1.9992384237528164969114429213984 absolute error = 0.00086466001566134432115442237856455 relative error = 0.043230772587590947342444049609162 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0609981652194613571406419015154 x2[1] (numeric) = 1.0630999769244177164695351474574 absolute error = 0.0021018117049563593288932459419976 relative error = 0.19809758149031404668751841866867 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2208.0MB, alloc=44.3MB, time=12.09 TOP MAIN SOLVE Loop t[1] = 2.87 x1[1] (closed_form) = 2.0001020580678437244427191218434 x1[1] (numeric) = 1.9992226968008773370041764995466 absolute error = 0.00087936126696638743854262229677889 relative error = 0.043965819815008629369569172269557 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0622298918742525297896931171963 x2[1] (numeric) = 1.0643903949787754445460832850274 absolute error = 0.0021605031045229147563901678311596 relative error = 0.20339317515446802439705112443783 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.88 x1[1] (closed_form) = 2.0001010425731014406986500813311 x1[1] (numeric) = 1.9992068117904434638590070083692 absolute error = 0.00089423078265797683964307296184892 relative error = 0.044709280362534169899172073430145 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0634865062124203421406600768213 x2[1] (numeric) = 1.0657071206775394090166797541642 absolute error = 0.0022206144651190668760196773429557 relative error = 0.2088051378317650499488486384177 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.89 x1[1] (closed_form) = 2.0001000371827006695235764217836 x1[1] (numeric) = 1.9991907671330005965357999376682 absolute error = 0.00090927004970007298777648411544117 relative error = 0.045461228578389102784168578131064 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0647685109472319953182733748424 x2[1] (numeric) = 1.0670506878770982355619355081252 absolute error = 0.0022821769298662402436621332827151 relative error = 0.21433550169848522231824267528615 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2246.6MB, alloc=44.3MB, time=12.31 TOP MAIN SOLVE Loop t[1] = 2.9 x1[1] (closed_form) = 2.0000990417961015330122539037555 x1[1] (numeric) = 1.9991745612240696201553853470551 absolute error = 0.00092448057203191285686855670039979 relative error = 0.046221739659538233779596111164142 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0660764189479466529927580297122 x2[1] (numeric) = 1.0684216412426429067271190400517 absolute error = 0.0023452222946962537343610103394391 relative error = 0.2199863211504694184102321769813 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.91 x1[1] (closed_form) = 2.0000980563137645417594338135226 x1[1] (numeric) = 1.9991581924430461366509995629979 absolute error = 0.0009398638707184051084342505246734 relative error = 0.046990889659210006193133816993635 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0674107534449750105966241048928 x2[1] (numeric) = 1.0698205364667621463006511924988 absolute error = 0.0024097830217871357040270876059811 relative error = 0.22575967255433500182806679581734 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2285.2MB, alloc=44.3MB, time=12.52 TOP MAIN SOLVE Loop t[1] = 2.92 x1[1] (closed_form) = 2.0000970806371406408279725872075 x1[1] (numeric) = 1.999141659153038402977970335712 absolute error = 0.00095542148410223785000225149550569 relative error = 0.047768755494502481605994395964055 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0687720482391834132831821580363 x2[1] (numeric) = 1.0712479404924561665028152612796 absolute error = 0.0024758922532727532196331032433579 relative error = 0.23165765397325085505306353197334 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.93 x1[1] (closed_form) = 2.0000961146686613547612136102276 x1[1] (numeric) = 1.9991249597007036405753313724691 absolute error = 0.00097115496795771418588223775848922 relative error = 0.048555414954075696506272313117076 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.070160847915426247562448039557 x2[1] (numeric) = 1.0727044317406580593879584968093 absolute error = 0.0025435838252318118255104572522515 relative error = 0.23768238486639428405579560316727 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=2323.8MB, alloc=44.3MB, time=12.72 t[1] = 2.94 x1[1] (closed_form) = 2.0000951583117290306541342177288 x1[1] (numeric) = 1.9991080924160826997101759995411 absolute error = 0.00098706589564633094395821818772395 relative error = 0.049350946705931164309792333769388 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0715777080603920229109978316692 x2[1] (numeric) = 1.0741906003423539177142163981392 absolute error = 0.0026128922819618948032185664699654 relative error = 0.24383600576120208976519688025617 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.95 x1[1] (closed_form) = 2.0000942114707071783075568799046 x1[1] (numeric) = 1.9990910556124330621710466079725 absolute error = 0.0010031558582741161365102719320878 relative error = 0.050155430305279300953502858421195 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0730231954848502851809367896674 x2[1] (numeric) = 1.075707048375394610828229028219 absolute error = 0.002683852890544325647292238551613 relative error = 0.25012067789751877891228869654083 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.96 x1[1] (closed_form) = 2.0000932740509109064994319434195 x1[1] (numeric) = 1.9990738475860601656104900572402 absolute error = 0.0010194264648507408889418861793081 relative error = 0.05096894620249556103436943491347 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0744978884503882640196899770592 x2[1] (numeric) = 1.0772543901060940185846549002992 absolute error = 0.0027565016557057545649649232400616 relative error = 0.25653858284273657829272603715777 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2362.4MB, alloc=44.3MB, time=12.94 TOP MAIN SOLVE Loop t[1] = 2.97 x1[1] (closed_form) = 2.0000923459585974544168110874113 x1[1] (numeric) = 1.9990564666161470326690727288238 absolute error = 0.001035879342450421747738358587527 relative error = 0.051791575751166080333422111870708 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0760023769007279524609844793366 x2[1] (numeric) = 1.0788332522357104417226115406498 absolute error = 0.0028308753349824892616270613132282 relative error = 0.26309192207701470529211154533253 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 2.98 x1[1] (closed_form) = 2.0000914271009568173016468009179 x1[1] (numeric) = 1.9990389109645821878436256549897 absolute error = 0.0010525161363746294580211459281899 relative error = 0.052623401216223629510980872672416 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0775372626977161490765765682679 x2[1] (numeric) = 1.0804442741519098612197446199425 absolute error = 0.0029070114541937121431680516745687 relative error = 0.2697829165476593204778888486202 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2400.8MB, alloc=44.3MB, time=13.14 TOP MAIN SOLVE Loop t[1] = 2.99 x1[1] (closed_form) = 2.0000905173861024653729746496884 x1[1] (numeric) = 1.9990211788757858448912631442134 absolute error = 0.0010693385103166204817115054750492 relative error = 0.053464505782174692786019164074037 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0791031598620818623208975972216 x2[1] (numeric) = 1.0820881081853117127211913374874 absolute error = 0.0029849483232298504002937402657721 relative error = 0.27661380619174083507981487864861 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3 x1[1] (closed_form) = 2.0000896167230621550973628163482 x1[1] (numeric) = 1.9990032685765343473877704607892 absolute error = 0.0010863481465278077095923555589284 relative error = 0.054314973561418494521027509595249 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0807006948190573837045712388334 x2[1] (numeric) = 1.0837654198712198759927928012794 absolute error = 0.0030647250521624922882215624460572 relative error = 0.28358684942602186010834243986119 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.01 x1[1] (closed_form) = 2.0000887250217688318887483015712 x1[1] (numeric) = 1.9989851782757828448842700973747 absolute error = 0.0011035467459859870044782041964924 relative error = 0.055174889602658805824516556649678 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0823305066489612819605184014837 x2[1] (numeric) = 1.0854768882166436542891702562951 absolute error = 0.0031463815676823723286518548113943 relative error = 0.29070432260326716042604560817287 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2439.4MB, alloc=44.3MB, time=13.34 TOP MAIN SOLVE Loop t[1] = 3.02 x1[1] (closed_form) = 2.0000878421930516233279221887721 x1[1] (numeric) = 1.9989669061644861869296345367329 absolute error = 0.0011209360285654363982876520391597 relative error = 0.05604433989940937255736910038887 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0839932473428435551963513650032 x2[1] (numeric) = 1.087223205972715635387793955961 absolute error = 0.0032299586298720801914425909577721 relative error = 0.29796851943400661480773150475555 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.03 x1[1] (closed_form) = 2.0000869681486269220009784151675 x1[1] (numeric) = 1.9989484504154180170478984884717 absolute error = 0.0011385177332089049530799266958436 relative error = 0.05692341139859381548753947029923 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0856895820632952029529233604365 x2[1] (numeric) = 1.0890050799126154856667930800049 absolute error = 0.0033154978493202827138697195684532 relative error = 0.30538175037282348309298330854883 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2478.0MB, alloc=44.3MB, time=13.55 TOP MAIN SOLVE Loop t[1] = 3.04 x1[1] (closed_form) = 2.0000861028010895570650024630924 x1[1] (numeric) = 1.9989298091829880485799175864808 absolute error = 0.0011562936181015084850848766115661 relative error = 0.057812192009240862781040425232491 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0874201894105265459212409961951 x2[1] (numeric) = 1.0908232311151109318609400192928 absolute error = 0.003403041704584385939699023097745 relative error = 0.31294634196824334768994423065441 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.05 x1[1] (closed_form) = 2.0000852460639040536581491833864 x1[1] (numeric) = 1.9989109806030575041167054422987 absolute error = 0.0011742654608465495414437410877343 relative error = 0.058710770611275784546695192663973 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0891857616938207286348246366744 x2[1] (numeric) = 1.092678395253829432898405631945 absolute error = 0.003492633560008704263580995270557 relative error = 0.3206646361753040350658138420804 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=2516.5MB, alloc=44.3MB, time=13.77 t[1] = 3.06 x1[1] (closed_form) = 2.0000843978513959792800434747843 x1[1] (numeric) = 1.9988919627927527000682385871276 absolute error = 0.0011924350586432792118048876567564 relative error = 0.059619237064408908768716962510592 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0909870052084709905950696780547 x2[1] (numeric) = 1.0945713228923763373997427811649 absolute error = 0.0035843176839053468046731031101241 relative error = 0.32853898962989374181415024120669 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.07 x1[1] (closed_form) = 2.0000835580787433762771346480036 x1[1] (numeric) = 1.9988727538502767577260308362821 absolute error = 0.0012108042284666185511038117215132 relative error = 0.060537682217122107665770193355736 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.092824640518312484863304056372 x2[1] (numeric) = 1.0965027797854176619274983567191 absolute error = 0.003678139267105177064194300347146 relative error = 0.33657177288395359980270981432948 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.08 x1[1] (closed_form) = 2.0000827266619682795762458703475 x1[1] (numeric) = 1.9988533518547194219904264255363 absolute error = 0.001229374807248857585819444811194 relative error = 0.06146619791575415330873652800679 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0946994027439616610425135351807 x2[1] (numeric) = 1.0984735471858480118457965029541 absolute error = 0.0037741444418863508032829677734444 relative error = 0.3447653696006521279622106881108 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2555.0MB, alloc=44.3MB, time=13.97 TOP MAIN SOLVE Loop t[1] = 3.09 x1[1] (closed_form) = 2.0000819035179283188180849771881 x1[1] (numeric) = 1.9988337548658649687443261637605 absolute error = 0.0012481486520633500737588134275883 relative error = 0.062404877013685851212930890896398 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0966120418568785126693014730997 x2[1] (numeric) = 1.1004844221581666016390024396628 absolute error = 0.0038723803012880889697009665630535 relative error = 0.35312217570865254821537995758664 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.1 x1[1] (closed_form) = 2.0000810885643084040509230031659 x1[1] (numeric) = 1.9988139609239981816639238967414 absolute error = 0.0012671276403102223869991064244712 relative error = 0.063353813380625870594977420461067 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.0985633229793693182558329187409 x2[1] (numeric) = 1.1025362178981868157212806010023 absolute error = 0.0039728949188174974654476822613602 relative error = 0.36164459851460990488685759833337 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2593.4MB, alloc=44.3MB, time=14.19 TOP MAIN SOLVE Loop t[1] = 3.11 x1[1] (closed_form) = 2.0000802817196124941530028723464 x1[1] (numeric) = 1.9987939680497083790639726693013 absolute error = 0.0012863136699041150890302030451283 relative error = 0.064313101911998200050956365550311 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1005540266906498814940023298723 x2[1] (numeric) = 1.1046297640592072851382950518273 absolute error = 0.0040757373685574036442927219550406 relative error = 0.37033505577305343667566402239676 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.12 x1[1] (closed_form) = 2.0000794829031554471605136285329 x1[1] (numeric) = 1.9987737742436914711801018008263 absolute error = 0.0013057086594639759804118277066168 relative error = 0.065282838538432167571777257192264 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1025849493390917004104002271833 x2[1] (numeric) = 1.1067659070847750411323327156668 absolute error = 0.0041809577456833407219324884835212 relative error = 0.37919597471283082455635435857174 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.13 x1[1] (closed_form) = 2.000078692035054951686156211742 x1[1] (numeric) = 1.9987533774865500280937481530972 absolute error = 0.0013253145485049235924080586448253 relative error = 0.066263120235355974065035187518125 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1046569033607759685105791155499 x2[1] (numeric) = 1.1089455105481739443471111047202 absolute error = 0.0042886071873979758365319891703517 relative error = 0.38822979101931489472939622399987 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2632.0MB, alloc=44.3MB, time=14.39 TOP MAIN SOLVE Loop t[1] = 3.14 x1[1] (closed_form) = 2.0000779090362235386214359135791 x1[1] (numeric) = 1.9987327757385913383063274729302 absolute error = 0.0013451332976322003151084406488459 relative error = 0.06725404503269469990088993991461 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.106770717604482834163965574808 x2[1] (numeric) = 1.1111694554987742795437077781109 absolute error = 0.0043987378942914453797422033029542 relative error = 0.39743894777160020978229327804738 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.15 x1[1] (closed_form) = 2.0000771338283606723238450838225 x1[1] (numeric) = 1.9987119669396234377683349416811 absolute error = 0.0013651668887372345555101421414613 relative error = 0.06825571202467375444380559574764 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1089272376632459186658519141837 x2[1] (numeric) = 1.1134386408153821511609821477348 absolute error = 0.0045114031521362324951302335510347 relative error = 0.40682589433394684983145379956254 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2670.5MB, alloc=44.3MB, time=14.61 TOP MAIN SOLVE Loop t[1] = 3.16 x1[1] (closed_form) = 2.0000763663339449204980482157881 x1[1] (numeric) = 1.9986909490087490889661078652903 absolute error = 0.0013854173251958315319403504978064 relative error = 0.069268221379728749073344296985035 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1111273262126047195999351557694 x2[1] (numeric) = 1.115753983566730115980863306683 absolute error = 0.0046266573541253963809281509136628 relative error = 0.41639308520076168387776221835829 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.17 x1[1] (closed_form) = 2.0000756064762262019880510038612 x1[1] (numeric) = 1.9986697198441576894639874964736 absolute error = 0.0014058866320685125240635073876201 relative error = 0.070291674350522784836675004759886 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1133718633556902053643627953846 x2[1] (numeric) = 1.1181164193792533466714497549174 absolute error = 0.0047445560235631413070869595327943 relative error = 0.42614297879444367372765103111217 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=2708.9MB, alloc=44.3MB, time=14.80 t[1] = 3.18 x1[1] (closed_form) = 2.0000748541792181117051261299079 x1[1] (numeric) = 1.9986482773229150890925607951118 absolute error = 0.0014265768563030226125653347961255 relative error = 0.07132617328407215661409913050561 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1156617469752816400879249106689 x2[1] (numeric) = 1.1205269028122985352221436221959 absolute error = 0.0048651558370168951342187115269667 relative error = 0.43607803621545935039645649167015 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.19 x1[1] (closed_form) = 2.0000741093676903219239821752286 x1[1] (numeric) = 1.9986266193007512947645257980902 absolute error = 0.0014474900669390271594563771384003 relative error = 0.072371821631981486517782538836652 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1179978930929754667442822741265 x2[1] (numeric) = 1.1229864077409157194212517994583 absolute error = 0.004988514647940252676969525331786 relative error = 0.44620071994405766514134118432939 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.2 x1[1] (closed_form) = 2.0000733719671610591872989426719 x1[1] (numeric) = 1.9986047436118460416884852718816 absolute error = 0.0014686283553150174988136707903042 relative error = 0.073428723960789310184100387663872 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.120381236235609921186409479002 x2[1] (numeric) = 1.1254959277463862497474175422042 absolute error = 0.0051146915107763285610080632021922 relative error = 0.45651349249308005022138660152181 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2747.5MB, alloc=44.3MB, time=15.02 TOP MAIN SOLVE Loop t[1] = 3.21 x1[1] (closed_form) = 2.0000726419038896560663133731726 x1[1] (numeric) = 1.998582648068612209537611335986 absolute error = 0.0014899938352774465287020371866059 relative error = 0.074496985962425150662640494501932 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1228127298090919522087639648861 x2[1] (numeric) = 1.1280564765146432095657224936347 absolute error = 0.0052437467055512573569585287485977 relative error = 0.4670188150113718304132963199553 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.22 x1[1] (closed_form) = 2.0000719191048691770326259084201 x1[1] (numeric) = 1.9985603304614770619146174365636 absolute error = 0.0015115886433921151180084718564875 relative error = 0.075576714464779125751075576337632 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1252933464797759837620586915018 x2[1] (numeric) = 1.1306690882427437595756657730597 absolute error = 0.0053757417629677758136070815578481 relative error = 0.47771914583735520302687427243549 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2786.1MB, alloc=44.3MB, time=15.22 TOP MAIN SOLVE Loop t[1] = 3.23 x1[1] (closed_form) = 2.0000712034978191177038083351642 x1[1] (numeric) = 1.9985377885586612872368018664027 absolute error = 0.0015334149391578304670064687615444 relative error = 0.076668017442385145875918355864708 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.127824078563547076279364106424 x2[1] (numeric) = 1.1333348180535560993148454228495 absolute error = 0.0055107394900090230354813164254349 relative error = 0.48861693900238194431664448490397 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.24 x1[1] (closed_form) = 2.0000704950111781767327315879627 x1[1] (numeric) = 1.9985150201059558189450672023666 absolute error = 0.0015554749052223577876643855960131 relative error = 0.077771004027218770975740196652682 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1304059384227641259309674324257 x2[1] (numeric) = 1.1360547424188270254679216677012 absolute error = 0.0056488039960628995369542352755174 relative error = 0.49971464268354589054397601668823 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.25 x1[1] (closed_form) = 2.0000697935740970996177964197035 x1[1] (numeric) = 1.9984920228264964127187505784843 absolute error = 0.001577770747600686899045841219216 relative error = 0.078885784519610806306898258409949 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1330399588712218847417583687991 x2[1] (numeric) = 1.1388299595907994200802521824429 absolute error = 0.0057900007195775353384938136438164 relative error = 0.51101469760570116263331524959589 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2824.6MB, alloc=44.3MB, time=15.44 TOP MAIN SOLVE Loop t[1] = 3.26 x1[1] (closed_form) = 2.0000690991164315937184419994584 x1[1] (numeric) = 1.9984687944205359581537984247626 absolute error = 0.0016003046958956355646435746957617 relative error = 0.080012470399277728663323495686492 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1357271935872937921365781536646 x2[1] (numeric) = 1.1416615900425524228709414606507 absolute error = 0.0059343964552586307343633069860983 relative error = 0.52251953539250212707570977622428 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.27 x1[1] (closed_form) = 2.0000684115687353137674280843536 x1[1] (numeric) = 1.998445332565214502135263748297 absolute error = 0.0016230790035208116321643360566388 relative error = 0.081151174336470046182628328291214 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1384687175354208809090586474624 x2[1] (numeric) = 1.1445507769172405320495241217598 absolute error = 0.0060820593818196511404654742973792 relative error = 0.53423157686635527689368034720714 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2863.1MB, alloc=44.3MB, time=15.64 TOP MAIN SOLVE Loop t[1] = 3.28 x1[1] (closed_form) = 2.0000677308622529171784361482495 x1[1] (numeric) = 1.9984216349143269609062715585767 absolute error = 0.0016460959479259562721645896727744 relative error = 0.082302010203239706701865598136356 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1412656273961153591470049843541 x2[1] (numeric) = 1.1474986864864114387603378712063 absolute error = 0.006233059090296079613332886852167 relative error = 0.54615323029725163041714558870693 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.29 x1[1] (closed_form) = 2.0000670569289131884545144400784 x1[1] (numeric) = 1.9983976990980884976044657596089 absolute error = 0.0016693578308246908500486804695434 relative error = 0.083465093084827681528887659867115 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1441190420046508756277985708162 x2[1] (numeric) = 1.1505065086175860329332742265924 absolute error = 0.0063874666129351573054756557762028 relative error = 0.55828688960053092767195023832617 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2901.6MB, alloc=44.3MB, time=15.84 TOP MAIN SOLVE Loop t[1] = 3.3 x1[1] (closed_form) = 2.0000663897013222320098020866685 x1[1] (numeric) = 1.9983735227228975418034956341771 absolute error = 0.0016928669784246902063064524914819 relative error = 0.084640539291172863510605469562389 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1470301027986149509830540232635 x2[1] (numeric) = 1.1535754572512877243622383457817 absolute error = 0.0065453544526727733791843225182214 relative error = 0.57063493248371588881259468922907 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.31 x1[1] (closed_form) = 2.000065729112756732723808739796 x1[1] (numeric) = 1.9983491033710964273612985845107 absolute error = 0.0017166257416603053625101552852956 relative error = 0.085828466368543430408732967013284 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1499999742745026019128143173997 x2[1] (numeric) = 1.156706770887712003745874871274 absolute error = 0.0067067966132094018330605538742626 relative error = 0.58319971854264610890441467794351 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.32 x1[1] (closed_form) = 2.000065075097157283554299579207 x1[1] (numeric) = 1.9983244386007296246387644885141 absolute error = 0.0017406364964276589155350906929749 relative error = 0.087028993111291836838033934245779 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1530298444535338023239523163845 x2[1] (numeric) = 1.1599017130832310257214464573371 absolute error = 0.0068718686296972233974941409526393 relative error = 0.59598358730723680841282177583845 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2940.2MB, alloc=44.3MB, time=16.06 TOP MAIN SOLVE Loop t[1] = 3.33 x1[1] (closed_form) = 2.0000644275891217795415413997683 x1[1] (numeric) = 1.998299525945299542911802064167 absolute error = 0.001764901643822236629739335601257 relative error = 0.088242239573734610382890430181934 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1561209253568811149218495896068 x2[1] (numeric) = 1.1631615729569319311452627169395 absolute error = 0.0070406476000508162234131273327711 relative error = 0.60898885623728763524660497471269 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.34 x1[1] (closed_form) = 2.0000637865238988775433047023407 x1[1] (numeric) = 1.9982743629135198785568449500675 absolute error = 0.0017894236103789989864597522731698 relative error = 0.089468327082158139986419077250069 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1592744534904975909747556507123 x2[1] (numeric) = 1.1664876657073916405959994480488 absolute error = 0.0072132122168940496212437973365526 relative error = 0.62221781866887100375507987112623 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2978.7MB, alloc=44.3MB, time=16.27 TOP MAIN SOLVE Loop t[1] = 3.35 x1[1] (closed_form) = 2.0000631518373815210465898383458 x1[1] (numeric) = 1.9982489469890664843444105088583 absolute error = 0.0018142048483150367021793294875834 relative error = 0.090707378246951657303620916649075 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1624916903397388762022184233167 x2[1] (numeric) = 1.1698813331398949469066732272925 absolute error = 0.0073896428001560707044548039758312 relative error = 0.63567274171193802473020991462333 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.36 x1[1] (closed_form) = 2.0000625234661005294085529846314 x1[1] (numeric) = 1.9982232756303257349274330998047 absolute error = 0.0018392478357747944811198848267312 relative error = 0.091959516974868624427421163171632 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1657739228739773785487635557425 x2[1] (numeric) = 1.1733439442043069131054416209247 absolute error = 0.0075700213303295345566780651822032 relative error = 0.64935586409989287770027418571925 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.37 x1[1] (closed_form) = 2.0000619013472182508855506989161 x1[1] (numeric) = 1.9981973462701403633607109577259 absolute error = 0.0018645550770778875248397411902707 relative error = 0.093224868481417754235207913918714 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1691224640614103505587619796152 x2[1] (numeric) = 1.1768768955438148451363813913436 absolute error = 0.0077544314824044945776194117283658 relative error = 0.66326939399200343460511475135862 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3017.3MB, alloc=44.3MB, time=16.48 TOP MAIN SOLVE Loop t[1] = 3.38 x1[1] (closed_form) = 2.0000612854185222788156006711101 x1[1] (numeric) = 1.9981711563155527432349068193602 absolute error = 0.0018901291029695355806938517499116 relative error = 0.094503559303384902564896788184544 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1725386533942678167669967172467 x2[1] (numeric) = 1.1804816120547594578443220824301 absolute error = 0.0079429586604916410773253651834535 relative error = 0.67741550672963697585680680799511 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.39 x1[1] (closed_form) = 2.0000606756184192303258716800527 x1[1] (numeric) = 1.9981447031475455907531017649595 absolute error = 0.0019159724708736395727699150931418 relative error = 0.095795717311487084514926970908702 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1760238574246304365929548691315 x2[1] (numeric) = 1.1841595474577792896824972169506 absolute error = 0.0081356900331488530895423478191102 relative error = 0.69179634254743483999313813696066 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3055.8MB, alloc=44.3MB, time=16.69 TOP MAIN SOLVE Loop t[1] = 3.4 x1[1] (closed_form) = 2.0000600718859285869430683202366 x1[1] (numeric) = 1.9981179841207800608198938481736 absolute error = 0.0019420877651485261231744720630055 relative error = 0.097101471723159880373240983619981 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1795794703110716373394135141758 x2[1] (numeric) = 1.187912184880496948213184021684 absolute error = 0.0083327145694253108737705075081998 relative error = 0.70641400424066869054478757555455 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.41 x1[1] (closed_form) = 2.0000594741606765964907664041495 x1[1] (numeric) = 1.998090996563331210952432170101 absolute error = 0.0019684775973453855383342340484234 relative error = 0.098420953115479510017536041036513 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1832069143763426817451602248551 x2[1] (numeric) = 1.1917410374519803865304561382745 absolute error = 0.0085341230756377047852959134193731 relative error = 0.72127055479015362115779979879336 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3094.3MB, alloc=44.3MB, time=16.91 TOP MAIN SOLVE Loop t[1] = 3.42 x1[1] (closed_form) = 2.0000588823828902356638836920021 x1[1] (numeric) = 1.9980637377764208065595570534378 absolute error = 0.0019951446064694291043266385643535 relative error = 0.099754293438220868094232068537678 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.186907640676323751859687168719 x2[1] (numeric) = 1.1956476489092171220880746117323 absolute error = 0.0087400082328933702283874430133013 relative error = 0.73636801494622938329122243042589 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.43 x1[1] (closed_form) = 2.0000582964933912326765383647147 x1[1] (numeric) = 1.9980362050341474408693515677324 absolute error = 0.0020220914592437918071867969822311 relative error = 0.10110162602705282587802616248928 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.190683129580468637561408127737 x2[1] (numeric) = 1.1996335942158441159491134071696 absolute error = 0.0089504646353754783877052794326143 relative error = 0.7517083607734604180730253088041 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.44 x1[1] (closed_form) = 2.0000577164335901493855550448614 x1[1] (numeric) = 1.9980083955832139425168722600893 absolute error = 0.0020493208503762068686827847721138 relative error = 0.10246308561687211943895421988825 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1945348913639752156330514868414 x2[1] (numeric) = 1.2037004801933809341099539495312 absolute error = 0.0091655888294057184769024626897791 relative error = 0.76729352115784788983026468159221 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3133.0MB, alloc=44.3MB, time=17.13 TOP MAIN SOLVE Loop t[1] = 3.45 x1[1] (closed_form) = 2.0000571421454805222978257845987 x1[1] (numeric) = 1.9979803066426520435325907032926 absolute error = 0.002076835502828478765235081306133 relative error = 0.10383880835527715760092947069441 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.1984644668119185957774771658186 x2[1] (numeric) = 1.2078499461652188152514293556095 absolute error = 0.0093854793533002194739521897908675 relative error = 0.78312537527849231399856595208769 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.46 x1[1] (closed_form) = 2.0000565735716330618756218741632 x1[1] (numeric) = 1.9979519354035442801981152613983 absolute error = 0.0021046381680887816775066127648682 relative error = 0.10522893181618309716615975383422 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2024734278355885951805016754383 x2[1] (numeric) = 1.2120836646136233730354219559448 absolute error = 0.0096102367780347778549202805065166 relative error = 0.79920575004579338246872077916707 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3171.4MB, alloc=44.3MB, time=17.33 TOP MAIN SOLVE Loop t[1] = 3.47 x1[1] (closed_form) = 2.0000560106551899095597821681931 x1[1] (numeric) = 1.9979232790287430989590468949111 absolute error = 0.0021327316264468106007352732819792 relative error = 0.10663359501357954700505897632961 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2065633781012780851185458132611 x2[1] (numeric) = 1.2164033418500138679378149347161 absolute error = 0.0098399637487357828192691214550383 relative error = 0.81553641750842392567398152133027 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.48 x1[1] (closed_form) = 2.0000554533398589519364754628759 x1[1] (numeric) = 1.9978943346525871393053262119404 absolute error = 0.0021611186872718126311492509354653 relative error = 0.10805293841543227687267516587169 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2107359536717737336208652703198 x2[1] (numeric) = 1.2208107186987872956713134404204 absolute error = 0.010074765027013562050448170100511 relative error = 0.8321190922314672980057106457016 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.49 x1[1] (closed_form) = 2.0000549015699081914789488619489 x1[1] (numeric) = 1.9978650993806146652471233683198 absolute error = 0.0021898021892935262318254936291387 relative error = 0.10948710395773032121168338430908 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2149928236608057493210564942249 x2[1] (numeric) = 1.2253075711949609586293039919793 absolute error = 0.010314747534155209308247497754412 relative error = 0.84895542864826149072376588831964 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3210.1MB, alloc=44.3MB, time=17.53 TOP MAIN SOLVE Loop t[1] = 3.5 x1[1] (closed_form) = 2.0000543552901601733013316153263 x1[1] (numeric) = 1.9978355702892741167291795977801 absolute error = 0.0022187850008860565721520175461716 relative error = 0.11093623505867988274007580148052 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2193356909007184154029659835453 x2[1] (numeric) = 1.2298957112959127156425637874507 absolute error = 0.01056002039519430023959780390534 relative error = 0.86604701838864859757553187274644 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.51 x1[1] (closed_form) = 2.0000538144459864673671651663476 x1[1] (numeric) = 1.9978057444256317520385005983706 absolute error = 0.0022480700203547153286645679769907 relative error = 0.11240047663304645530027664243253 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2237662926236284910356477818614 x2[1] (numeric) = 1.2345769876075037458960099115999 absolute error = 0.010810694983875254860362129738455 relative error = 0.88339538758648448987333476362562 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3248.6MB, alloc=44.3MB, time=17.75 TOP MAIN SOLVE Loop t[1] = 3.52 x1[1] (closed_form) = 2.0000532789833022056008756624799 x1[1] (numeric) = 1.9977756188070763519693989123281 absolute error = 0.0022776601762258536314767501517455 relative error = 0.11387997510664660026698378656435 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2282864011563439530160773383676 x2[1] (numeric) = 1.2393532861248744173592194032286 absolute error = 0.01106688496853046434314206486095 relative error = 0.90100199416942028072684869996997 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.53 x1[1] (closed_form) = 2.0000527488485606733558955242995 x1[1] (numeric) = 1.9977451904210209562160557229487 absolute error = 0.0023075584275397171398398013508833 relative error = 0.11537487843099082577507299475564 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2328978246293210546551413920176 x2[1] (numeric) = 1.2442265309882097208441649393618 absolute error = 0.011328706358888666189023547344235 relative error = 0.91886822513412392750873243888698 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3287.1MB, alloc=44.3MB, time=17.95 TOP MAIN SOLVE Loop t[1] = 3.54 x1[1] (closed_form) = 2.0000522239887479546985763777881 x1[1] (numeric) = 1.9977144562246016021659927708073 absolute error = 0.00233776776414635253258360698083 relative error = 0.11688533609807903313789090797639 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2376024076999432944537829598747 x2[1] (numeric) = 1.2491986852537767201650119120541 absolute error = 0.011596277553833425711228952179402 relative error = 0.93699539381026666691940056390506 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.55 x1[1] (closed_form) = 2.0000517043513776309724172789554 x1[1] (numeric) = 1.997683413144373035968082684675 absolute error = 0.0023682912070045950043345942803833 relative error = 0.11841149915535001008171944332378 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2424020322904116160683670140284 x2[1] (numeric) = 1.2542717516805425792338688907561 absolute error = 0.011869719390130963165501876727747 relative error = 0.95538473711675440263370322973343 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.56 x1[1] (closed_form) = 2.0000511898844855321124602357358 x1[1] (numeric) = 1.9976520580760013654459509532112 absolute error = 0.0023991318084841666665092825245572 relative error = 0.11995352022078646582564201391055 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2472986183405410057490030077017 x2[1] (numeric) = 1.2594477735326879607274348686084 absolute error = 0.012149155192146954978431860906731 relative error = 0.97403741281383815150383243416786 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3325.7MB, alloc=44.3MB, time=18.17 TOP MAIN SOLVE Loop t[1] = 3.57 x1[1] (closed_form) = 2.0000506805366245401849800927894 x1[1] (numeric) = 1.9976203878839536241218047542018 absolute error = 0.0024302926526709160631753385875583 relative error = 0.12151155349817711858902093081631 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2522941245757646161896665920063 x2[1] (numeric) = 1.2647288353983369506962830781827 absolute error = 0.012434710822572334506616486176352 relative error = 0.99295449675488965717111839824848 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.58 x1[1] (closed_form) = 2.0000501762568594446328184177998 x1[1] (numeric) = 1.9975883994011842153068323267182 absolute error = 0.0024617768556752293259860910815555 relative error = 0.12308575479253736181286018568845 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2573905492906526289396859333587 x2[1] (numeric) = 1.2701170640248311517051796710847 absolute error = 0.012726514734178522765493737726004 relative error = 1.0121369801417777337088059971053 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3364.2MB, alloc=44.3MB, time=18.38 TOP MAIN SOLVE Loop t[1] = 3.59 x1[1] (closed_form) = 2.0000496769947618487118816353459 x1[1] (numeric) = 1.9975560894288182049023206286708 absolute error = 0.0024935875659436438095610066751353 relative error = 0.1246762815256900512380484580961 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2625899311482592736258631365014 x2[1] (numeric) = 1.2756146291708822063848683675567 absolute error = 0.013024698022622932759005231055363 relative error = 1.0315857667879272192879272749845 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.6 x1[1] (closed_form) = 2.0000491827004051266094428135124 x1[1] (numeric) = 1.9975234547358314312405074679782 absolute error = 0.0025257279645736953689353455341527 relative error = 0.12628329275200797099443881500686 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2678943499956177537057107719785 x2[1] (numeric) = 1.2812237444759437662911047723297 absolute error = 0.013329394480326012585394000351257 relative error = 1.0513016703932849936500317110126 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.61 x1[1] (closed_form) = 2.0000486933243594307399547309999 x1[1] (numeric) = 1.9974904920587273999758856165436 absolute error = 0.0025582012656320307640691144563072 relative error = 0.12790694917431955302152477774975 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2733059276957092878476700483593 x2[1] (numeric) = 1.286946668347150810406834419024 absolute error = 0.013640740651441522559164370664732 relative error = 1.0712854118355557179203522861265 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3402.9MB, alloc=44.3MB, time=18.59 TOP MAIN SOLVE Loop t[1] = 3.62 x1[1] (closed_form) = 2.0000482088176867487190996454436 x1[1] (numeric) = 1.9974571981012109317161787822948 absolute error = 0.0025910107164758170029208631488285 relative error = 0.12954741315997944046573342575655 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.278826828976239065897576785837 x2[1] (numeric) = 1.2927857048641812462442878923236 absolute error = 0.013958875887942180346711106486652 relative error = 1.0915376164822031490603489527859 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.63 x1[1] (closed_form) = 2.0000477291319360095217690487122 x1[1] (numeric) = 1.9974235695338585297574805756713 absolute error = 0.0026241595980774797642884730409328 relative error = 0.13120484875710550218270694310062 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2844592622955586413780870140203 x2[1] (numeric) = 1.2987432047024018971171013328359 absolute error = 0.014283942406843255739014318815613 relative error = 1.1120588115278404076265154772599 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3441.4MB, alloc=44.3MB, time=18.80 TOP MAIN SOLVE Loop t[1] = 3.64 x1[1] (closed_form) = 2.0000472542191382383345851289502 x1[1] (numeric) = 1.9973896029937854349600552899858 absolute error = 0.002657651225352803374529838964351 relative error = 0.13287942171098392211703236890025 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2902054807260811412685501036661 x2[1] (numeric) = 1.3048215660746682946268483314404 absolute error = 0.014616085348587153358298227774275 relative error = 1.132849423361753767802863243038 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.65 x1[1] (closed_form) = 2.0000467840318017596184451538712 x1[1] (numeric) = 1.9973552950843093344700106205424 absolute error = 0.0026914889474924251484345333287546 relative error = 0.13457129948064400413836924480518 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.2960677828555426711705353661781 x2[1] (numeric) = 1.3110232356921551586700245227691 absolute error = 0.014955452836612487499489156590947 relative error = 1.1539097749704187143978649260022 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=3480.0MB, alloc=44.3MB, time=19.05 t[1] = 3.66 x1[1] (closed_form) = 2.0000463185229074479013910322807 x1[1] (numeric) = 1.9973206423746106906574342461173 absolute error = 0.0027256761482967572439567861633743 relative error = 0.13628065125560434988349657029422 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3020485137064704326779141589857 x2[1] (numeric) = 1.3173507097446020613061123509642 absolute error = 0.015302196038131628628198191978526 relative error = 1.1752400833799734869125735990715 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.67 x1[1] (closed_form) = 2.0000458576459040258268793830978 x1[1] (numeric) = 1.997285641399389656303605026299 absolute error = 0.002760216246514369523274356798769 relative error = 0.13800764797279208429015060494547 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3081500656742253526956541409218 x2[1] (numeric) = 1.3238065349003665386807364457815 absolute error = 0.01565646922614118598508230485966 relative error = 1.1968404571437134157617324841108 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.68 x1[1] (closed_form) = 2.0000454013547034089872530205778 x1[1] (numeric) = 1.9972502886585195417285116308444 absolute error = 0.0027951126961838672587413897334129 relative error = 0.13975246233363682081236680856366 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3143748794839944545015623995776 x2[1] (numeric) = 1.3303933093266848399774968372483 absolute error = 0.016018429842690385475934437670724 relative error = 1.2187108938797583587376205614909 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3518.5MB, alloc=44.3MB, time=19.25 TOP MAIN SOLVE Loop t[1] = 3.69 x1[1] (closed_form) = 2.0000449496036760970768933235641 x1[1] (numeric) = 1.9972145806166967992051025745554 absolute error = 0.0028303689869792978717907490086461 relative error = 0.1415152688213410757801025553737 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3207254451671157804922385867242 x2[1] (numeric) = 1.3371136837305485872480089747798 absolute error = 0.016388238563432806755770388055582 relative error = 1.240851277864124777123517886082 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.7 x1[1] (closed_form) = 2.0000445023476466109041649632894 x1[1] (numeric) = 1.9971785137030874896584174020554 absolute error = 0.0028659886445591212457475612339742 relative error = 0.14329624371832885900994909850079 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3272043030571264098306275940663 x2[1] (numeric) = 1.3439703624206138681761995488198 absolute error = 0.016766059363487458345571954753444 relative error = 1.263261377684502765941068033557 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3557.0MB, alloc=44.3MB, time=19.47 TOP MAIN SOLVE Loop t[1] = 3.71 x1[1] (closed_form) = 2.0000440595418889748058503816955 x1[1] (numeric) = 1.9971420843109701962959743235151 absolute error = 0.0029019752309187785098760581803957 relative error = 0.14509556512387418559050560204056 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.333814044805932003711207011285 x2[1] (numeric) = 1.3509661043905676986695547552061 absolute error = 0.017152059584635694958347743921097 relative error = 1.2859408439600959958162905876609 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.72 x1[1] (closed_form) = 2.0000436211421222440123116990525 x1[1] (numeric) = 1.9971052887973753494604797671271 absolute error = 0.0029383323447468945518319319254134 relative error = 0.14691341297191127175726618809731 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3405573144205043598359120552569 x2[1] (numeric) = 1.3581037244243853770029980580393 absolute error = 0.017546410003881017167086002782387 relative error = 1.3088892071329283714362948441434 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.73 x1[1] (closed_form) = 2.0000431871045060765161128398598 x1[1] (numeric) = 1.9970681234827209266370445556581 absolute error = 0.0029750636217851498790682842017421 relative error = 0.1487499690490281959394616126598 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3474368093205216691690477632267 x2[1] (numeric) = 1.3653860942239210095045952500671 absolute error = 0.017949284903399340335547486840344 relative error = 1.3321058753360546163335077807907 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3595.7MB, alloc=44.3MB, time=19.67 TOP MAIN SOLVE Loop t[1] = 3.74 x1[1] (closed_form) = 2.00004275738563634900128504912 x1[1] (numeric) = 1.9970305846504444911846038443579 absolute error = 0.0030121727351918578166812047621312 relative error = 0.15060541701264582440701677374195 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3544552814173745453973643254512 x2[1] (numeric) = 1.372816143559282422969929370271 absolute error = 0.018360862141907877572565044819724 relative error = 1.3555901323441323287396295436037 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.75 x1[1] (closed_form) = 2.0000423319425408163948250721332 x1[1] (numeric) = 1.9969926685466315329951073268069 absolute error = 0.0030496633959092833997177453262805 relative error = 0.15247994240938381947146797519735 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3616155382149694441132311419113 x2[1] (numeric) = 1.3803968614424507946981181381062 absolute error = 0.018781323227481350584886996194905 relative error = 1.3793411356118197156793269228337 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3634.1MB, alloc=44.3MB, time=19.88 TOP MAIN SOLVE Loop t[1] = 3.76 x1[1] (closed_form) = 2.0000419107326748146063775305761 x1[1] (numeric) = 1.9969543713796400739142359105716 absolute error = 0.0030875393530347406921416200045009 relative error = 0.15437373269361556690218193136061 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3689204439327698079831889627602 x2[1] (numeric) = 1.3881312973246146309036307647724 absolute error = 0.019210853391844822920441802012197 relative error = 1.4033579144054556278494518934128 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.77 x1[1] (closed_form) = 2.0000414937139170060263718820426 x1[1] (numeric) = 1.9969156893197215003838741044778 absolute error = 0.0031258043941955056424977775647933 relative error = 0.15628697724621387811040230156584 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3763729206515241695489010907622 x2[1] (numeric) = 1.3960225623176972119945341990235 absolute error = 0.019649641666173042445633108261337 relative error = 1.4276393680334561442039962114734 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=3672.7MB, alloc=44.3MB, time=20.08 t[1] = 3.78 x1[1] (closed_form) = 2.0000410808445651673571602313109 x1[1] (numeric) = 1.9968766184986375853892863908892 absolute error = 0.0031644623459275819678738404217192 relative error = 0.15821986739348934173040786598464 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.383975949482139518390936373487 x2[1] (numeric) = 1.4040738304405663026149502466226 absolute error = 0.02009788095842678422401387313556 relative error = 1.4521842641808242873260714279567 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.79 x1[1] (closed_form) = 2.0000406720833320193559355969665 x1[1] (numeric) = 1.9968371550092736614128731511867 absolute error = 0.0032035170740583579430624457797262 relative error = 0.16017259642632321849130663613949 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3917325717581674977980527470868 x2[1] (numeric) = 1.412288339890424799299396273153 absolute error = 0.020555768132257301501343526066156 relative error = 1.4769912373531160243577361895951 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.8 x1[1] (closed_form) = 2.0000402673893410980724014499806 x1[1] (numeric) = 1.996797294905247905711479163095 absolute error = 0.0032429724840931923609222868856149 relative error = 0.16214535961949679272663833119203 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.3996458902523804415291985419665 x2[1] (numeric) = 1.4206693943398910630295964736368 absolute error = 0.021023504087510621500397931670242 relative error = 1.5020587874351361043642981281865 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3711.2MB, alloc=44.3MB, time=20.30 TOP MAIN SOLVE Loop t[1] = 3.81 x1[1] (closed_form) = 2.0000398667221226671683128505534 x1[1] (numeric) = 1.9967570342005166988454568040183 absolute error = 0.0032828325216059683228560465350913 relative error = 0.16413835425121911351395878874341 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.4077190704179238975106131743253 x2[1] (numeric) = 1.4292203642602879619503726760555 absolute error = 0.021501293842364064439759501730199 relative error = 1.5273852783695511317037244601023 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.82 x1[1] (closed_form) = 2.000039470041609670910117730922 x1[1] (numeric) = 1.9967163688689760169950079977183 absolute error = 0.0033231011726336539151097332036942 relative error = 0.16615177962285507827489820260676 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.415955341654542116230819569783 x2[1] (numeric) = 1.4379446882716701351018517437712 absolute error = 0.021989346617128018871032173988229 relative error = 1.5529689369605042597627821019641 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3749.7MB, alloc=44.3MB, time=20.50 TOP MAIN SOLVE Loop t[1] = 3.83 x1[1] (closed_form) = 2.0000390773081337274299942157441 x1[1] (numeric) = 1.9966752948440588182027043643488 absolute error = 0.0033637824640749092272898513952963 relative error = 0.16818583707885583169980411442646 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.4243579986003830111144567356754 x2[1] (numeric) = 1.4468458745201296854550176276276 absolute error = 0.022487875919746674340560891952203 relative error = 1.5788078518071957510901960939021 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.84 x1[1] (closed_form) = 2.0000386884824211618546067448315 x1[1] (numeric) = 1.9966338080183283822804743132836 absolute error = 0.0034048804640927795741324315478894 relative error = 0.17024073002689347309200289237132 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.4329304024498993302837431048446 x2[1] (numeric) = 1.4559275020829314240758830313595 absolute error = 0.022997099633032093792139926514876 relative error = 1.6048999723722561903403015241065 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.85 x1[1] (closed_form) = 2.000038303525589078904890568105 x1[1] (numeric) = 1.996591904243067563714708892902 absolute error = 0.0034463992825215151901816752030448 relative error = 0.17231666395820208565696280648844 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.441675982298373217946876981587 x2[1] (numeric) = 1.4651932224020399212559995907385 absolute error = 0.023517240103666703309122609151509 relative error = 1.6312431081895842220308759187015 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3788.2MB, alloc=44.3MB, time=20.70 TOP MAIN SOLVE Loop t[1] = 3.86 x1[1] (closed_form) = 2.0000379223991414745741213183792 x1[1] (numeric) = 1.9965495793278639164944346175333 absolute error = 0.0034883430712775580796867008458552 relative error = 0.17441384646812712189326049371568 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.450598236513601993361540823053 x2[1] (numeric) = 1.4746467607466119793876019548933 absolute error = 0.024048524233009986026061131840316 relative error = 1.6578349282161482504449374660527 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.87 x1[1] (closed_form) = 2.0000375450649653864954342286528 x1[1] (numeric) = 1.9965068290401906493746903583797 absolute error = 0.0035307160247747371207438702731544 relative error = 0.17653248727688520007730347619477 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.4597007341352938401689065316217 x2[1] (numeric) = 1.4842919177050397307743018068965 absolute error = 0.024591183569745890605395275274826 relative error = 1.6846729603320615897610989166228 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3826.8MB, alloc=44.3MB, time=20.92 TOP MAIN SOLVE Loop t[1] = 3.88 x1[1] (closed_form) = 2.0000371714853270826138265377906 x1[1] (numeric) = 1.9964636491049833696702854309945 absolute error = 0.0035735223803437129435411067960918 relative error = 0.17867279825053638787432768388275 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.4689871163027331832252229789379 x2[1] (numeric) = 1.4941325707071413860886180052463 absolute error = 0.02514545440440820286339502630841 relative error = 1.7117545909930331683778988983041 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.89 x1[1] (closed_form) = 2.0000368016228682877815071087181 x1[1] (numeric) = 1.9964200352042125732539655404456 absolute error = 0.0036167664186557145275415682725454 relative error = 0.18083499342217107035637442352056 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.4784610977112868383080849036263 x2[1] (numeric) = 1.5041726755771087205451020918563 absolute error = 0.025711577865821882237017188230059 relative error = 1.7390770650390712286262978432352 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=3865.3MB, alloc=44.3MB, time=21.13 t[1] = 3.9 x1[1] (closed_form) = 2.0000364354406024478992496495787 x1[1] (numeric) = 1.996375982976451838007630141234 absolute error = 0.0036604524641506098916195083447112 relative error = 0.18301928901331352116588048555019 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.4881264680983335567662847164884 x2[1] (numeric) = 1.51441626811783268987728773067 absolute error = 0.026289800019499133111003014181658 relative error = 1.7666374856630757565548554279778 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.91 x1[1] (closed_form) = 2.0000360729019110312301605599476 x1[1] (numeric) = 1.9963314880164416775455864937154 absolute error = 0.0037045848854693536845740662321923 relative error = 0.18522590345554431723333362346527 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.4979870937592113569305659651968 x2[1] (numeric) = 1.5248674657272411218105215012624 absolute error = 0.026880371968029764879955536065598 relative error = 1.7944328145426969416123387370037 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.92 x1[1] (closed_form) = 2.0000357139705398665159896966392 x1[1] (numeric) = 1.9962865458746490115948492859863 absolute error = 0.0037491680958908549211404106529087 relative error = 0.18745505741234375934132020578881 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.5080469190937890416156853663328 x2[1] (numeric) = 1.5355304690472952359327231432117 absolute error = 0.027483549953506194317037776878855 relative error = 1.822459872138562200074928468467 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3903.8MB, alloc=44.3MB, time=21.33 TOP MAIN SOLVE Loop t[1] = 3.93 x1[1] (closed_form) = 2.0000353586105955175297926386052 x1[1] (numeric) = 1.9962411520568222089791567419588 absolute error = 0.0037942065537733085506358966464165 relative error = 0.18970697380115848292741056998239 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.5183099681842805511251145577795 x2[1] (numeric) = 1.5464095636463048108045258884932 absolute error = 0.028099595462024259679411330713689 relative error = 1.8507153381616836789739071546489 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.94 x1[1] (closed_form) = 2.000035006786541693702396695932 x1[1] (numeric) = 1.9961953020235416587106308184836 absolute error = 0.0038397047630000349917658774484501 relative error = 0.19198187781569346583690027053459 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.5287803464049332987186685812407 x2[1] (numeric) = 1.5575091217352351470458091668207 absolute error = 0.028728775330301848327140585580017 relative error = 1.8791957522125522523119354860934 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3942.4MB, alloc=44.3MB, time=21.55 TOP MAIN SOLVE Loop t[1] = 3.95 x1[1] (closed_form) = 2.0000346584631956964637303183856 x1[1] (numeric) = 1.9961489911897658242458161322037 absolute error = 0.0038856672734298722179141861819893 relative error = 0.19427999694843166227568363139928 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.539462242064234385519521609373 x2[1] (numeric) = 1.5688336039186925743196919245079 absolute error = 0.029371361854458188800170315134893 relative error = 1.9078975145941034749541176241779 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.96 x1[1] (closed_form) = 2.0000343136057249009436470750516 x1[1] (numeric) = 1.9961022149243727355111449306498 absolute error = 0.003932098681352165432502144401854 relative error = 0.19660156101338351497573348078564 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.5503599280802915994206378761936 x2[1] (numeric) = 1.5803875609812891240476612535097 absolute error = 0.030027632900997524627023377316131 relative error = 1.9368168873004065008548690754471 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.97 x1[1] (closed_form) = 2.0000339721796432726804113555428 x1[1] (numeric) = 1.9960549685496968728466485628225 absolute error = 0.0039790036299463998337627927203433 relative error = 0.19894680216906862057307365801949 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.5614777636900593729048138382209 x2[1] (numeric) = 1.5921756357101011438806212821527 absolute error = 0.030697872020041770975807443931802 relative error = 1.9659499951825794119508263903069 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3980.9MB, alloc=44.3MB, time=21.75 TOP MAIN SOLVE Loop t[1] = 3.98 x1[1] (closed_form) = 2.0000336341508079189885137385919 x1[1] (numeric) = 1.9960072473410613965559238890742 absolute error = 0.0040263868097465224325898495177183 relative error = 0.20131595494173184641305735833557 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.5728201961930934131256147180495 x2[1] (numeric) = 1.6042025647539510700823318124762 absolute error = 0.031382368560857656956717094426719 relative error = 1.9952928272930746328391067815528 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 3.99 x1[1] (closed_form) = 2.000033299485415674640949935697 x1[1] (numeric) = 1.9959590465263056752849198169256 absolute error = 0.0040742529591099993560301187713935 relative error = 0.20370925624879622044252589887057 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.5843917627305315295240483364095 x2[1] (numeric) = 1.6164731805202563058304175866066 absolute error = 0.032081417789724776306369250197194 relative error = 2.0248412384091070928570959113383 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4019.4MB, alloc=44.3MB, time=21.95 TOP MAIN SOLVE Loop t[1] = 4 x1[1] (closed_form) = 2.0000329681499997215245286924383 x1[1] (numeric) = 1.9959103612853080659819881138045 absolute error = 0.0041226068646916555425405786338007 relative error = 0.2061269454225549395253633130038 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.596197092100012275202806535297 x2[1] (numeric) = 1.628992413110204182899012696186 absolute error = 0.032795321010191907696206160889076 relative error = 2.0545909507356165851393805687556 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.01 x1[1] (closed_form) = 2.0000326401114262419301713612957 x1[1] (numeric) = 1.9958611867495038977167968170989 absolute error = 0.0041714533619223442133745441967234 relative error = 0.20856926423410486542944979841962 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.6082409066072573938828860386639 x2[1] (numeric) = 1.6417652922930273172683560267698 absolute error = 0.033524385685769923385469988105916 relative error = 2.0845375557877654773247753595321 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=4057.8MB, alloc=44.3MB, time=22.17 t[1] = 4.02 x1[1] (closed_form) = 2.0000323153368911051435293869871 x1[1] (numeric) = 1.995811518001398611156086451373 absolute error = 0.0042207973354924939874429356141694 relative error = 0.2110364569175239018814424040718 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.620528023955058730276808988428 x2[1] (numeric) = 1.6547969495201693120439233871837 absolute error = 0.034268925565110581767114398755658 relative error = 2.1146765164525747346252822416714 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.03 x1[1] (closed_form) = 2.0000319937939165870045760048956 x1[1] (numeric) = 1.9957613500740760050098109099127 absolute error = 0.0042706437198405819947650949828368 relative error = 0.21352877019429467047358908819777 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.6330633591704252239950977767798 x2[1] (numeric) = 1.6680926199801467199185294310734 absolute error = 0.035029260809721495923431654293611 relative error = 2.1450031692288963705523541432176 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.04 x1[1] (closed_form) = 2.0000316754503481221081253780429 x1[1] (numeric) = 1.9957106779507015402718978186963 absolute error = 0.0043209974996465818362275593466071 relative error = 0.21604645329797692783635099897736 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.6458519265706608716432314779239 x2[1] (numeric) = 1.6816576446949294586592287671379 absolute error = 0.035805718124268587015997289214014 relative error = 2.1755127266445102502749870878781 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4096.4MB, alloc=44.3MB, time=22.37 TOP MAIN SOLVE Loop t[1] = 4.05 x1[1] (closed_form) = 2.0000313602743510883204965180166 x1[1] (numeric) = 1.9956594965640206525856385443104 absolute error = 0.0043718637103304357348579737061895 relative error = 0.21858975799913119136443029018333 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.6588988417691601146710417576418 x2[1] (numeric) = 1.6954974726586784832597274178674 absolute error = 0.036598630889518368588685660225655 relative error = 2.2062002798487189965025968108216 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.06 x1[1] (closed_form) = 2.0000310482344076232907709766638 x1[1] (numeric) = 1.9956078007958520225645263103946 absolute error = 0.0044232474385556007262446662692594 relative error = 0.22115893863049606590436418476185 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.6722093237217229980347639779139 x2[1] (numeric) = 1.7096176630196964641128904588227 absolute error = 0.037408339297973466078126480908777 relative error = 2.2370608013783979958445543390792 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4134.9MB, alloc=44.3MB, time=22.58 TOP MAIN SOLVE Loop t[1] = 4.07 x1[1] (closed_form) = 2.0000307392993134726382927814037 x1[1] (numeric) = 1.995555585476575753395152230281 absolute error = 0.0044751538227377192431405511227079 relative error = 0.22375425211242178918166221658788 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.6857886968142086531789552939725 x2[1] (numeric) = 1.7240238873064645086055353929387 absolute error = 0.038235190492255855426580098966245 relative error = 2.2680891480950396241699224254345 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.08 x1[1] (closed_form) = 2.0000304334381748695012267376345 x1[1] (numeric) = 1.9955028453846164045394930253505 absolute error = 0.0045275880535584649617337122840813 relative error = 0.22637595797856253936706942099624 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.6996423929923621947248206165361 x2[1] (numeric) = 1.7387219316986556008347100422422 absolute error = 0.039079538706293406109889425706101 relative error = 2.2992800642899132867140075284431 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.09 x1[1] (closed_form) = 2.0000301306204054451341273536801 x1[1] (numeric) = 1.9954495752459208298395298511902 absolute error = 0.0045805553744846152945975024898604 relative error = 0.22902431840183007405749569748752 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.7137759539346669901777214371691 x2[1] (numeric) = 1.7537176993440334277464516272753 absolute error = 0.039941745409366437568730190106205 relative error = 2.3306281849540472143727493543073 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4173.5MB, alloc=44.3MB, time=22.78 TOP MAIN SOLVE Loop t[1] = 4.1 x1[1] (closed_form) = 2.0000298308157231702455755706566 x1[1] (numeric) = 1.9953957697334307678075735570734 absolute error = 0.0046340610822924024380020135831203 relative error = 0.2316995982206112960800480618241 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.7281950332690914726879769619009 x2[1] (numeric) = 1.769017212722163617102522376576 absolute error = 0.040822179453072144414545414675076 relative error = 2.3621280392093257038692927580529 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.11 x1[1] (closed_form) = 2.0000295339941473267700145120407 x1[1] (numeric) = 1.9953414234665501313608859017305 absolute error = 0.004688110527597195409128610310235 relative error = 0.23440206496525236792005116599699 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.7429053988346172253000196253081 x2[1] (numeric) = 1.7846266160558831406311368424851 absolute error = 0.041721217221265915331117217176996 relative error = 2.3937740538965881808883878724877 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4211.9MB, alloc=44.3MB, time=23.00 TOP MAIN SOLVE Loop t[1] = 4.12 x1[1] (closed_form) = 2.0000292401259955097709589129807 x1[1] (numeric) = 1.9952865310106069437291262608317 absolute error = 0.0047427091153885660418326521490275 relative error = 0.23713198888481202322858137878182 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.7579129349884529782291322066694 x2[1] (numeric) = 1.8005521777714927420059031760473 absolute error = 0.042639242783039763776770969377908 relative error = 2.4255605573162156510549741747945 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.13 x1[1] (closed_form) = 2.0000289491818806591757660518713 x1[1] (numeric) = 1.9952310868763098667277661826147 absolute error = 0.0047978623055707924479998692566462 relative error = 0.23988964297408675078453619527003 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.7732236449598574356778518000237 x2[1] (numeric) = 1.8168002930086567415661035065307 absolute error = 0.043576648048799305888251706506953 relative error = 2.4574817831162973294180408183029 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=4250.4MB, alloc=44.3MB, time=23.20 t[1] = 4.14 x1[1] (closed_form) = 2.0000286611327081210451391877239 x1[1] (numeric) = 1.9951750855191992670498462384966 absolute error = 0.004853575613508853995292949227294 relative error = 0.24267530300091055347330557870979 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.7888436532515124928559094630764 x2[1] (numeric) = 1.8333774861810144557384456759019 absolute error = 0.044533832929501962882536212825505 relative error = 2.4895318743230870386739030224556 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.15 x1[1] (closed_form) = 2.0000283759496727380834880047238 x1[1] (numeric) = 1.9951185213390927656822468980739 absolute error = 0.0049098546105799724012411066499303 relative error = 0.24548924753373201230142358858021 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.8047792080894074246561926421912 x2[1] (numeric) = 1.8502904135885277569004572048431 absolute error = 0.045511205499120332244264562651944 relative error = 2.5217048875080868532985804696352 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.16 x1[1] (closed_form) = 2.0000280936042559690991946754386 x1[1] (numeric) = 1.9950613886795252150009530119053 absolute error = 0.0049667049247307540982416635333703 relative error = 0.24833175796947141319690290170592 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.8210366839222140324732393556962 x2[1] (numeric) = 1.8675458660826099970543908388334 absolute error = 0.046509182160395964581151483137192 relative error = 2.5539947970857359260450653335079 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4288.9MB, alloc=44.3MB, time=23.41 TOP MAIN SOLVE Loop t[1] = 4.17 x1[1] (closed_form) = 2.0000278140682230371267291688236 x1[1] (numeric) = 1.995003681827183047542554741215 absolute error = 0.0050241322410399895841744276086112 relative error = 0.25120311856166072235106447984503 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.8376225839711525326924708151946 x2[1] (numeric) = 1.8851507717851026344374450636998 absolute error = 0.047528187813950101744974248505154 relative error = 2.5863954997353369129688387582769 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.18 x1[1] (closed_form) = 2.000027537313620105925423637984 x1[1] (numeric) = 1.9949453950113329398863907070156 absolute error = 0.005082142302287166039032930968397 relative error = 0.25410361644886922414237015101352 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.8545435428313681673468231729106 x2[1] (numeric) = 1.903112198862187444526107677656 absolute error = 0.048568656030819277179284504745404 relative error = 2.6189008189405223162038726955553 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4327.4MB, alloc=44.3MB, time=23.62 TOP MAIN SOLVE Loop t[1] = 4.19 x1[1] (closed_form) = 2.000027263312771484572553412207 x1[1] (numeric) = 1.994886522403244734513245457946 absolute error = 0.0051407409095267500593079542609478 relative error = 0.25703354168341766424887558830909 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.871806329125859122411705937106 x2[1] (numeric) = 1.9214373583543441744169791852238 absolute error = 0.04963102922848505200527324811783 relative error = 2.6515045096392497398556708020963 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.2 x1[1] (closed_form) = 2.0000269920382768598711815718484 x1[1] (numeric) = 1.9948270581156085619323062265176 absolute error = 0.0051999339226682979388753453308251 relative error = 0.25999318726038376940630156940786 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.8894178482130173604315585987732 x2[1] (numeric) = 1.9401336070634859210750841274209 absolute error = 0.0507157588504685606435255286477 relative error = 2.6842002629770197923225570501886 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.21 x1[1] (closed_form) = 2.0000267234630085562960055841979 x1[1] (numeric) = 1.9947669962019461047881059362637 absolute error = 0.0052597272610624515078996479342911 relative error = 0.26298284914690204440625739283152 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.9073851449488654200504672449755 x2[1] (numeric) = 1.9592084504984273884025933041555 absolute error = 0.05182330554956196835212605918002 relative error = 2.716981711155734388265416174732 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4366.0MB, alloc=44.3MB, time=23.83 TOP MAIN SOLVE Loop t[1] = 4.22 x1[1] (closed_form) = 2.0000264575601088232031983016 x1[1] (numeric) = 1.9947063306560159450733725392145 absolute error = 0.0053201269040928781298257623855548 relative error = 0.26600282631176077635675554292199 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.9257154065050941141339768832437 x2[1] (numeric) = 1.9786695458798645146464089426942 absolute error = 0.052954139374770400512432059450537 relative error = 2.7498424323703576497518449564654 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.23 x1[1] (closed_form) = 2.0000261943029871490329620452641 x1[1] (numeric) = 1.9946450554112129349820104229891 absolute error = 0.005381138891774214050951622275076 relative error = 0.26905342075529920594777377371794 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.9444159652440283792713303246495 x2[1] (numeric) = 1.9985247052060677696674092144416 absolute error = 0.054108739962039390396078889792082 relative error = 2.7827759558253075407311892079359 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4404.5MB, alloc=44.3MB, time=24.03 TOP MAIN SOLVE Loop t[1] = 4.24 x1[1] (closed_form) = 2.0000259336653176022362137920012 x1[1] (numeric) = 1.994583164339961531338798659688 absolute error = 0.0054427693253560708974151323132006 relative error = 0.27213493753960785548122166641861 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.9634943016516713014656190909487 x2[1] (numeric) = 2.0187818983805157105610935566701 absolute error = 0.055287596728844409095474465721413 relative error = 2.8157757668222947650648720441195 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.25 x1[1] (closed_form) = 2.0000256756210361986594919165025 x1[1] (numeric) = 1.9945206512531030329387435100843 absolute error = 0.005505024367933165720748406418197 relative error = 0.27524768481903503374025495110839 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 1.9829580473299995748628567213533 x2[1] (numeric) = 2.0394492564027201637650956011346 absolute error = 0.056491209072720588902238879781309 relative error = 2.8488353119111371943407125855506 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=4443.0MB, alloc=44.3MB, time=24.25 t[1] = 4.26 x1[1] (closed_form) = 2.0000254201443382951248207859828 x1[1] (numeric) = 1.9944575098992766595193084811109 absolute error = 0.005567910245061635605512304871942 relative error = 0.27839197387100256839048391772051 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.0028149880497073517329070981008 x2[1] (numeric) = 2.060535074623519682025996490149 absolute error = 0.057720086573812330293089392048193 relative error = 2.8819480040949139462868068627704 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.27 x1[1] (closed_form) = 2.000025167209676008943889021622 x1[1] (numeric) = 1.9943937339642944104729033904067 absolute error = 0.0056314332453815984709856312153189 relative error = 0.28156811912713384752830372529888 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.0230730668646196220763806460122 x2[1] (numeric) = 2.0820478160661437155387842161929 absolute error = 0.05897474920152409346240357018069 relative error = 2.9151072280806838819261461915488 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.28 x1[1] (closed_form) = 2.0000249167917556631084906942208 x1[1] (numeric) = 1.9943293170705096407849827340203 absolute error = 0.0056955997212460223235079602004323 relative error = 0.28477643820469728322242651469679 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.0437403872890209298644362372304 x2[1] (numeric) = 2.1039961148143762485341617427655 absolute error = 0.060255727525355318669725505535123 relative error = 2.9483063455668792953454480147612 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4481.6MB, alloc=44.3MB, time=24.45 TOP MAIN SOLVE Loop t[1] = 4.29 x1[1] (closed_form) = 2.0000246688655352569017463691738 x1[1] (numeric) = 1.9942642527761792910548209786342 absolute error = 0.0057604160893559658469253905395805 relative error = 0.28801725193836834143684092007179 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.0648252165391703998906782681047 x2[1] (numeric) = 2.1263887794691744960971235513811 absolute error = 0.061563562930004096206445283276391 relative error = 2.9815387005583973879438151723349 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.3 x1[1] (closed_form) = 2.0000244234062219616771630150341 x1[1] (numeric) = 1.9941985345748197078214353790846 absolute error = 0.0058258888314022538557276359495262 relative error = 0.29129088441231331458001797321898 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.0863359888402997245931410071143 x2[1] (numeric) = 2.1492347966751256417928408562645 absolute error = 0.062898807834825917199699849150218 relative error = 3.0147976247003500886886992879848 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4520.0MB, alloc=44.3MB, time=24.66 TOP MAIN SOLVE Loop t[1] = 4.31 x1[1] (closed_form) = 2.0000241803892696415551085948027 x1[1] (numeric) = 1.9941321558945559897761520952758 absolute error = 0.005892024494713651778956499526886 relative error = 0.29459766299259804509940906378416 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.1082813088004169542601996776864 x2[1] (numeric) = 2.1725433347181525357078878120178 absolute error = 0.064262025917735581447688134331414 relative error = 3.0480764426213971262954110781094 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.32 x1[1] (closed_form) = 2.000023939790376398788768921307 x1[1] (numeric) = 1.9940651100974647947958946518012 absolute error = 0.0059588296929116039928742695058183 relative error = 0.297937918359924841035358885618 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.1306699548522656572451113096039 x2[1] (numeric) = 2.1963237471959077759624783832086 absolute error = 0.065653792343642118717367073604779 relative error = 3.0813684772775780838909621384768 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.33 x1[1] (closed_form) = 2.0000237015854821435541213268221 x1[1] (numeric) = 1.9939973904789105420773504064886 absolute error = 0.0060263111065716014767709203335334 relative error = 0.30131198454270085726773358060824 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.1535108827648162798694087024757 x2[1] (numeric) = 2.2205855767623246760147166041239 absolute error = 0.067074693997508396145307901648256 relative error = 3.114667055287576459190578642824 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4558.5MB, alloc=44.3MB, time=24.87 TOP MAIN SOLVE Loop t[1] = 4.34 x1[1] (closed_form) = 2.0000234657507661879209021191163 x1[1] (numeric) = 1.9939289902668749429916752777822 absolute error = 0.0060944754838912449292268413340376 relative error = 0.3047201989504412493351234145255 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.1768132292256943495011334914806 x2[1] (numeric) = 2.2453385589478232867932798715408 absolute error = 0.068525329722128937292146380060109 relative error = 3.1479655122503923834226584552905 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.35 x1[1] (closed_form) = 2.000023232262644863763962915638 x1[1] (numeric) = 1.9938599026212797936122634752857 absolute error = 0.0061633296413650701516994403522658 relative error = 0.30816290240751044018373485377532 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.2005863154959785399757923279206 x2[1] (numeric) = 2.2705926260566999087278346468702 absolute error = 0.07000631056072136875204231894967 relative error = 3.181257198036470373503446640953 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4597.1MB, alloc=44.3MB, time=25.08 TOP MAIN SOLVE Loop t[1] = 4.36 x1[1] (closed_form) = 2.0000230010977691643768050063965 x1[1] (numeric) = 1.9937901206333029611942706689967 absolute error = 0.0062328804644662031825343373998074 relative error = 0.31164043918720487401438649868322 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.2248396511388305674366045707903 x2[1] (numeric) = 2.2963579111432594062039434233828 absolute error = 0.071518260004428838767338852592478 relative error = 3.2145354820434239427876402541792 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.37 x1[1] (closed_form) = 2.0000227722330224095514511336435 x1[1] (numeric) = 1.9937196373246874962039685363834 absolute error = 0.0063031349083349133474825972600867 relative error = 0.31515315704618066554474801617397 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 3 h = 0.001 x2[1] (closed_form) = 2.2495829378234484183860299752393 x2[1] (numeric) = 2.322644752068281138202958968021 absolute error = 0.073061814244832719816928992781637 relative error = 3.2477937584076196022854724263831 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=4635.6MB, alloc=44.3MB, time=25.28 t[1] = 4.38 x1[1] (closed_form) = 2.0000225456455179338911607297611 x1[1] (numeric) = 1.9936484456470438008085578808634 absolute error = 0.0063740999984741330826028488976759 relative error = 0.31870140725922958749352579553413 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.2748260732058645420766004970989 x2[1] (numeric) = 2.3494636956374414564986364799417 absolute error = 0.074637622431576914422035982842845 relative error = 3.2810254511630281635857837046611 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.39 x1[1] (closed_form) = 2.0000223213125967981248179584666 x1[1] (numeric) = 1.9935765384811447840427077747985 absolute error = 0.0064457828314520140821101836681006 relative error = 0.32228554465440687392715240486767 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.3005791548881413783782675496675 x2[1] (numeric) = 2.3768255018233485096267087861771 absolute error = 0.076246346935207131248441236509571 relative error = 3.3142240193389206186183205956582 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.4 x1[1] (closed_form) = 2.0000220992118255231941220908952 x1[1] (numeric) = 1.9935039086362139331667500082692 absolute error = 0.006518190575611590027372082626048 relative error = 0.32590592764851435229116236362518 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.3268524844575479522378282673268 x2[1] (numeric) = 2.4047411480728785400369514631164 absolute error = 0.077888663615330587799123195789593 relative error = 3.3473829619881784307813612131915 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4674.1MB, alloc=44.3MB, time=25.50 TOP MAIN SOLVE Loop t[1] = 4.41 x1[1] (closed_form) = 2.0000218793209938468869870473292 x1[1] (numeric) = 1.9934305488492062300230713872257 absolute error = 0.0065913304717876168639156601034942 relative error = 0.32956291828294245248135235851276 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.3536565716073332593379209147845 x2[1] (numeric) = 2.4332218337015369867597527541111 absolute error = 0.079565262094203727421831839326653 relative error = 3.3804958231382029420716329695466 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.42 x1[1] (closed_form) = 2.0000216616181125027928115750519 x1[1] (numeric) = 1.993356451784081840481740281881 absolute error = 0.0066652098340306623110712931708402 relative error = 0.33325688225987467719758303779373 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.3810021383407448073664037731665 x2[1] (numeric) = 2.4622789843766025202216401359341 absolute error = 0.081276846035857712855236362767564 relative error = 3.4135561966566448067840726678215 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4712.6MB, alloc=44.3MB, time=25.70 TOP MAIN SOLVE Loop t[1] = 4.43 x1[1] (closed_form) = 2.0000214460814110213575137384649 x1[1] (numeric) = 1.9932816100310725043437067271849 absolute error = 0.0067398360503385170138070112800685 relative error = 0.33698818897885815406927063071579 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.4089001232599739764780100549144 x2[1] (numeric) = 2.4919242566908476534531085329409 absolute error = 0.083024133430873676975098478026482 relative error = 3.4465577310244308452029576787942 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.44 x1[1] (closed_form) = 2.0000212326893355528184333924599 x1[1] (numeric) = 1.9932060161059405523399550516061 absolute error = 0.0068152165833950004784783408537811 relative error = 0.34075721157374392664986440819985 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.4373616859417438343891159630399 x2[1] (numeric) = 2.52216954282866580905528684653 absolute error = 0.084807856886921974666170883490096 relative error = 3.4794941340088413341580716651971 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.45 x1[1] (closed_form) = 2.0000210214205467118013943150625 x1[1] (numeric) = 1.9931296624492304761276914615926 absolute error = 0.0068913589713162356737028534699449 relative error = 0.34456432695000067835157118954846 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.4663982114012896996824663482177 x2[1] (numeric) = 2.5530269753264716884243305727866 absolute error = 0.086628763925181988741864224568881 relative error = 3.5123591772296843085810070941216 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4751.1MB, alloc=44.3MB, time=25.91 TOP MAIN SOLVE Loop t[1] = 4.46 x1[1] (closed_form) = 2.0000208122539174433643839093895 x1[1] (numeric) = 1.9930525414255129764399425067186 absolute error = 0.0069682708284044669244414026708789 relative error = 0.34840991582240562073496804320485 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.4960213146465181051754889376336 x2[1] (numeric) = 2.5845089319292795036616164624157 absolute error = 0.088487617282761398486127524782073 relative error = 3.5451467006119236693200750523992 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.47 x1[1] (closed_form) = 2.0000206051685309102744530645839 x1[1] (numeric) = 1.9929746453226214137927494233914 absolute error = 0.0070459598459094964817036411925089 relative error = 0.3522943627531163152846733065567 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.5262428453241658857671758687205 x2[1] (numeric) = 2.6166280405454021084102501004756 absolute error = 0.090385195221236222643074231755108 relative error = 3.5778506167184434519383082124306 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4789.5MB, alloc=44.3MB, time=26.11 TOP MAIN SOLVE Loop t[1] = 4.48 x1[1] (closed_form) = 2.0000204001436784013065621051076 x1[1] (numeric) = 1.9928959663508805853943927833522 absolute error = 0.0071244337927978159121693217554702 relative error = 0.35621805619012723589569565646629 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.5570748924598179164539256646661 x2[1] (numeric) = 2.6493971843012533169452554406743 absolute error = 0.092322291841435400491329776008152 relative error = 3.6104649149569701357450361594834 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.49 x1[1] (closed_form) = 2.0000201971588572603552009698953 x1[1] (numeric) = 1.992816496642327751133695681386 absolute error = 0.0072037005165295092215052885093028 relative error = 0.36018138850611491776926048877931 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.5885297892936795709152205866754 x2[1] (numeric) = 2.6828295066982757469081967468291 absolute error = 0.094299717404596175992976160153687 relative error = 3.642983665655526948821504733004 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=4828.1MB, alloc=44.3MB, time=26.33 t[1] = 4.5 x1[1] (closed_form) = 2.0000199961937688361516930576417 x1[1] (numeric) = 1.9927362282499258307493551453853 absolute error = 0.0072837679438430054023379122563814 relative error = 0.36418475603767557727566967670155 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.6206201182140382742339481808268 x2[1] (numeric) = 2.7169384168740573761361927178814 absolute error = 0.096318298660019101902244537054522 relative error = 3.6754010240011573084968433558232 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.51 x1[1] (closed_form) = 2.0000197972283164523821527600324 x1[1] (numeric) = 1.9926551531467686934993630306968 absolute error = 0.0073646440815477588827897293356173 relative error = 0.36822855912495912658897069954431 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.6533587157903876002553379901337 x2[1] (numeric) = 2.7517375949697416844332370366056 absolute error = 0.098378879179354084177899046471901 relative error = 3.7077112338370273592041241461656 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.52 x1[1] (closed_form) = 2.0000196002426033980031067870972 x1[1] (numeric) = 1.9925732632252784608588210800251 absolute error = 0.0074463370173249371442857070721628 relative error = 0.37231320215170354653781883811787 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.6867586779082272304341714197247 x2[1] (numeric) = 2.7872409976058787735415064281549 absolute error = 0.10048231969765154310733500843017 relative error = 3.7399086313133985469729926841194 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4866.6MB, alloc=44.3MB, time=26.53 TOP MAIN SOLVE Loop t[1] = 4.53 x1[1] (closed_form) = 2.0000194052169309375538091720763 x1[1] (numeric) = 1.992490550296394741975751013751 absolute error = 0.0075288549205361955780581583253029 relative error = 0.37643909358567362115287553490591 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.7208333650075927627192043560688 x2[1] (numeric) = 2.8234628634689082400018032778965 absolute error = 0.10262949846131547728259892182769 relative error = 3.7719876483883488105733038226392 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.54 x1[1] (closed_form) = 2.0000192121317963412662795292207 x1[1] (numeric) = 1.992407006088755720807769592301 absolute error = 0.0076122060430406204585099369196778 relative error = 0.38060664601950807782740066707411 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.7555964074274108523458402580805 x2[1] (numeric) = 2.860417719010508833398955383485 absolute error = 0.10482131158309798105311512540445 relative error = 3.8039428161745137824806024501104 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4905.1MB, alloc=44.3MB, time=26.73 TOP MAIN SOLVE Loop t[1] = 4.55 x1[1] (closed_form) = 2.0000190209678909347760739267725 x1[1] (numeric) = 1.9923226222478710130476598884127 absolute error = 0.0076963987200199217284140383598036 relative error = 0.38481627621197921784840996675255 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.7910617108578174979508880496945 x2[1] (numeric) = 2.8981203842620950843739563300088 absolute error = 0.10705867340427758642306828031436 relative error = 3.8357687681285158954484974352906 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.56 x1[1] (closed_form) = 2.0000188317060981682387578269665 x1[1] (numeric) = 1.992237390335286210122842038232 absolute error = 0.0077814413708119581159157887345033 relative error = 0.38906840512966916330496517602265 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.8272434619026204731199156978305 x2[1] (numeric) = 2.9365859787667871508115993895622 absolute error = 0.10934251686416667769168369173173 relative error = 3.8674602430801480151648325983815 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.57 x1[1] (closed_form) = 2.0000186443274917046589911312706 x1[1] (numeric) = 1.9921513018277390267224472026609 absolute error = 0.0078673424997526779365439286096569 relative error = 0.39336345798906688804196862389355 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.8641561337541309626035212595026 x2[1] (numeric) = 2.9758299276312271252069311187337 absolute error = 0.11167379387709616260340985923113 relative error = 3.8990120880987777216055453226471 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4943.8MB, alloc=44.3MB, time=26.97 TOP MAIN SOLVE Loop t[1] = 4.58 x1[1] (closed_form) = 2.000018458813333527241056646307 x1[1] (numeric) = 1.9920643481163069674660442336156 absolute error = 0.0079541106970265597750124126913974 relative error = 0.3977018642990902424064119021016 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.9018144919826344116180261173214 x2[1] (numeric) = 3.0158679676996629901748664919069 absolute error = 0.11405347571702857855684037458555 relative error = 3.9304192611948372262600613186637 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.59 x1[1] (closed_form) = 2.0000182751450720655715654460859 x1[1] (numeric) = 1.9919765205055464274799756377156 absolute error = 0.0080417546395256380915898083702271 relative error = 0.40208405790403722403258801781474 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.940233600442816453858921001294 x2[1] (numeric) = 3.0567161538527703215733669926889 absolute error = 0.11648255340995386771444599139494 relative error = 3.9616768338546607604722429235168 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4982.3MB, alloc=44.3MB, time=27.17 TOP MAIN SOLVE Loop t[1] = 4.6 x1[1] (closed_form) = 2.0000180933043403404469558395698 x1[1] (numeric) = 1.9918878102126231407906430524257 absolute error = 0.0081302830917171996563127871440678 relative error = 0.40651047702697078983756773619549 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 2.9794288272995065674453606895232 x2[1] (numeric) = 3.0983908654337317393277228471984 absolute error = 0.11896203813422517188236215767519 relative error = 3.9927799934073247650182173804672 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.61 x1[1] (closed_form) = 2.000017913272954127160267147482 x1[1] (numeric) = 1.9917982083664338895788569344405 absolute error = 0.0082197049065202375814102130415046 relative error = 0.41098156431354154775255624109264 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.0194158511751498366951676726308 x2[1] (numeric) = 3.140908812804145014732998221137 absolute error = 0.1214929616289951780378305485062 relative error = 4.0237240452225350639042890719881 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=5020.8MB, alloc=44.3MB, time=27.37 t[1] = 4.62 x1[1] (closed_form) = 2.0000177350329101370635154351373 x1[1] (numeric) = 1.9917077060067193864654439838883 absolute error = 0.0083100290261907505980714512490166 relative error = 0.41549776687625271050392113882462 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.0602106674214658904942773198963 x2[1] (numeric) = 3.1842870440323826801381376838624 absolute error = 0.12407637661091678964386036396607 relative error = 4.0545044147389881804876049893834 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.63 x1[1] (closed_form) = 2.0000175585663842172238259234998 x1[1] (numeric) = 1.9916162940831682411156015978703 absolute error = 0.0084012644832159761082243256295335 relative error = 0.42005953633917173798409599665158 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.1018295945178037645501321426678 x2[1] (numeric) = 3.228542951717078973254529928045 absolute error = 0.12671335719927520870439778537719 relative error = 4.0851166493230098735056114104727 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.64 x1[1] (closed_form) = 2.0000173838557295679932861914158 x1[1] (numeric) = 1.9915239634545119215579130917939 absolute error = 0.008493420401217646435373099621869 relative error = 0.42466732888309313942163765815827 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.1442892805987521148764831137109 x2[1] (numeric) = 3.2736942799484740050796200693962 absolute error = 0.12940499934972189020313695568523 relative error = 4.1155564199576417186304722234149 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5059.3MB, alloc=44.3MB, time=27.59 TOP MAIN SOLVE Loop t[1] = 4.65 x1[1] (closed_form) = 2.0000172108834749783142756689792 x1[1] (numeric) = 1.9914307048876106197134013886086 absolute error = 0.0085865059958643586008742803705347 relative error = 0.4293216052911569516759173941643 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.1876067101136159137200805026034 x2[1] (numeric) = 3.3197591314104001892062759474989 absolute error = 0.13215242129678427548619544489546 relative error = 4.1458195227627050877372232859301 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.66 x1[1] (closed_form) = 2.0000170396323230785838004843956 x1[1] (numeric) = 1.991336509056529929720412300048 absolute error = 0.0086805305757931488633881843476095 relative error = 0.43402283099492745554976712611268 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.2317992106204235074900698413131 x2[1] (numeric) = 3.3667559746257522331616993365681 absolute error = 0.134956764005328725671629495255 relative error = 4.1759018803467202022194502083101 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5097.9MB, alloc=44.3MB, time=27.80 TOP MAIN SOLVE Loop t[1] = 4.67 x1[1] (closed_form) = 2.0000168700851486109021186418776 x1[1] (numeric) = 1.9912413665416082467223904509116 absolute error = 0.008775503543540364179728190966036 relative error = 0.43877147612093673803743926086429 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.2768844597171817301885938060175 x2[1] (numeric) = 3.4147036513483393918920386008717 absolute error = 0.13781919163115766170344479485427 relative error = 4.2057995429918951491707614715159 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.68 x1[1] (closed_form) = 2.000016702224996716532678951625 x1[1] (numeric) = 1.9911452678285147928576494537122 absolute error = 0.0088714343964819236750294979128366 relative error = 0.44356801553769775491007448433663 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.3228804921131516668924305060304 x2[1] (numeric) = 3.4636213841040772425414728211607 absolute error = 0.14074089199092557564904231513036 relative error = 4.2355086896737250147635689836204 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.69 x1[1] (closed_form) = 2.0000165360350812404021182786619 x1[1] (numeric) = 1.9910482033072981762529503297471 absolute error = 0.008968332727783064149167948914767 relative error = 0.4484129289031915949911546407667 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.3698057068429736719616253771415 x2[1] (numeric) = 3.5135287838845359816922102187574 absolute error = 0.1437230770415623097305848416159 relative error = 4.2650256289170538479822476287082 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5136.4MB, alloc=44.3MB, time=28.01 TOP MAIN SOLVE Loop t[1] = 4.7 x1[1] (closed_form) = 2.0000163714987830524707656973337 x1[1] (numeric) = 1.9909501632714253878759946642877 absolute error = 0.0090662082273576645947710330460499 relative error = 0.45330670071283369489484258508091 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.417678874626527388256794760993 x2[1] (numeric) = 3.5644458579959231951326012498944 absolute error = 0.14676698336939580687580648890144 relative error = 4.2943467994907513370510956216854 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.71 x1[1] (closed_form) = 2.0000162085996483858057892030173 x1[1] (numeric) = 1.9908511379168111401457169065761 absolute error = 0.0091650706828372456600722964412584 relative error = 0.45824982034792380089541966416647 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.466519145377470809589498415714 x2[1] (numeric) = 3.6163930180666412303852080364944 absolute error = 0.14987387268917042079570962078036 relative error = 4.323468770943441254921448767431 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5175.0MB, alloc=44.3MB, time=28.22 TOP MAIN SOLVE Loop t[1] = 4.72 x1[1] (closed_form) = 2.0000160473213871911907909107714 x1[1] (numeric) = 1.9907511173408374502334279566729 absolute error = 0.0092649299805497409573629540985676 relative error = 0.46324278212458452297101377490458 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.516346055863461902228949938807 x2[1] (numeric) = 3.6693910882166227385285220951155 absolute error = 0.15304503235316083629957215630849 relative error = 4.3523882439829893811656556487634 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.73 x1[1] (closed_form) = 2.0000158876478715081073103292844 x1[1] (numeric) = 1.990650091541363370012323136874 absolute error = 0.0093657961065081380949871924104117 relative error = 0.46828608534319337492430424762715 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.5671795375211269763335908482988 x2[1] (numeric) = 3.723461313391712669660882834654 absolute error = 0.1562817758705856933272919863552 relative error = 4.3811020507027142850639196508642 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=5213.6MB, alloc=44.3MB, time=28.42 t[1] = 4.74 x1[1] (closed_form) = 2.0000157295631338519253325029262 x1[1] (numeric) = 1.9905480504157247636275242707015 absolute error = 0.0094676791474090882978082322246912 relative error = 0.47338023433831324383178005074068 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.6190399244289018989385228938518 x2[1] (numeric) = 3.7786253678664310315714478863563 absolute error = 0.15958544343752913263292499250458 relative error = 4.409607154657524684739286149321 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.75 x1[1] (closed_form) = 2.0000155730513656171415187287071 x1[1] (numeric) = 1.9904449837597240326635793522066 absolute error = 0.0095705892916415844779393765004792 relative error = 0.47852573852912628191634988430967 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.6719479614409353913706043160341 x2[1] (numeric) = 3.8349053639185180802122132971369 absolute error = 0.16295740247758268884160898110281 relative error = 4.4379006507934117816435594880162 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.76 x1[1] (closed_form) = 2.0000154180969154965054823405752 x1[1] (numeric) = 1.9903408812666096878810946570514 absolute error = 0.0096745368303058086243876835238218 relative error = 0.48372311247037626428064094070947 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.7259248124853080809435075104688 x2[1] (numeric) = 3.8923238606787323303520346297467 absolute error = 0.16639904819342424940852711927786 relative error = 4.46597976523393378434457128867 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5252.3MB, alloc=44.3MB, time=28.64 TOP MAIN SOLVE Loop t[1] = 4.77 x1[1] (closed_form) = 2.0000152646842879158760208712314 x1[1] (numeric) = 1.990235732526045665478822598859 absolute error = 0.0097795321582422503971982723724604 relative error = 0.48897287590382450678521170537141 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.7809920690298867052768590384168 x2[1] (numeric) = 3.9509038731594418828276425089664 absolute error = 0.16991180412955517755078347054959 relative error = 4.4938418549275226284531290443787 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.78 x1[1] (closed_form) = 2.000015112798141484650788910389 x1[1] (numeric) = 1.9901295270230702848119726336419 absolute error = 0.0098855857750711998388162767471436 relative error = 0.49427555381022448971222783291961 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.8371717587191999238790111980391 x2[1] (numeric) = 4.0106688814656210891323834621982 absolute error = 0.17349712274642116525337226415906 relative error = 4.5214844071596195887272794665794 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5290.8MB, alloc=44.3MB, time=28.84 TOP MAIN SOLVE Loop t[1] = 4.79 x1[1] (closed_form) = 2.0000149624232874616144533354484 x1[1] (numeric) = 1.9900222541370447434616495052699 absolute error = 0.0099927082862427181528038301785303 relative error = 0.49963167646182038472604449129448 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.8944863541857906025554396196341 x2[1] (numeric) = 4.0716428401919375433119945103401 absolute error = 0.17715648600614694075655489070599 relative error = 4.5489050389338070505162441598723 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.8 x1[1] (closed_form) = 2.0000148135446882360519144516482 x1[1] (numeric) = 1.9899139031405910445040495187745 absolute error = 0.010100910404097191547864932873727 relative error = 0.50504177947537473503279070486955 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 3.952958782039569229119504631582 x2[1] (numeric) = 4.1338501880096888344572683954915 absolute error = 0.18089140597011960533776376390949 relative error = 4.5761014962262482111552895054403 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.81 x1[1] (closed_form) = 2.0000146661474558239747030980614 x1[1] (numeric) = 1.9898044631985192497712566975563 absolute error = 0.010210202948936574203446400505149 relative error = 0.51050640386573059155670021032361 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.0126124320387643217074518663787 x2[1] (numeric) = 4.1973158574474244402747772388116 absolute error = 0.18470342540866011856732537243295 relative error = 4.6030716531178750298824333734521 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5329.4MB, alloc=44.3MB, time=29.08 TOP MAIN SOLVE Loop t[1] = 4.82 x1[1] (closed_form) = 2.0000145202168503793101751060006 x1[1] (numeric) = 1.989693923366743951828070945517 absolute error = 0.010320596850106427482104160483606 relative error = 0.51602609609991346139687073038481 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.0734711664461383322171391004131 x2[1] (numeric) = 4.262065284869165623659260546603 absolute error = 0.18859411842302729144212144618988 relative error = 4.6298135108088775080882687401648 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.83 x1[1] (closed_form) = 2.000014375738278719904620788596 x1[1] (numeric) = 1.9895822725911898563111629539015 absolute error = 0.010432103147088863593457834694535 relative error = 0.52160140815177847880970396493828 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.1355593295742116560575171785696 x2[1] (numeric) = 4.3281244206542152408789392547399 absolute error = 0.19256509108000358482142207617031 relative error = 4.6563251965201445862042984776198 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5367.9MB, alloc=44.3MB, time=29.30 TOP MAIN SOLVE Loop t[1] = 4.84 x1[1] (closed_form) = 2.0000142326972928681928885441622 x1[1] (numeric) = 1.989469499706686365187877750584 absolute error = 0.010544732990606503005010793578253 relative error = 0.52723289755720826348488015542401 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.1989017575233129651578181355813 x2[1] (numeric) = 4.3955197395826300135381051351443 absolute error = 0.19661798205931704838028699956298 relative error = 4.6826049622863888669334009936895 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.85 x1[1] (closed_form) = 2.0000140910795886063885883196003 x1[1] (numeric) = 1.9893555934358510503920915884651 absolute error = 0.010658497643737555996496731135203 relative error = 0.53292112746986698595180606040039 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.2635237881163512142850260766195 x2[1] (numeric) = 4.4642782514305100891588409380817 absolute error = 0.20075446331415887487381486146218 relative error = 4.7086511836457543425156274299825 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=5406.4MB, alloc=44.3MB, time=29.50 t[1] = 4.86 x1[1] (closed_form) = 2.00001395087100404605039275017 x1[1] (numeric) = 1.9892405423879619061835553169302 absolute error = 0.010773408483042139866837433239771 relative error = 0.53866666671751621557455050070042 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.3294512710342833620097942505661 x2[1] (numeric) = 4.5344275117793446499363140800637 absolute error = 0.20497624074506128792651982949761 relative error = 4.7344623582307586863016603425702 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.87 x1[1] (closed_form) = 2.0000138120575182118813914137131 x1[1] (numeric) = 1.9891243350578182674550203778725 absolute error = 0.010889476999699944426371035840632 relative error = 0.54447008985889818277190940516053 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.3967105781563321286220908345315 x2[1] (numeric) = 4.6059956330437379595452596465183 absolute error = 0.20928505488740583092316881198686 relative error = 4.7600371042654598766011676570004 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.88 x1[1] (closed_form) = 2.0000136746252496396198769545839 x1[1] (numeric) = 1.9890069598245902800780289009734 absolute error = 0.011006714800659359541848053610489 relative error = 0.55033197724119214384104038236701 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.4653286141090900160419610502842 x2[1] (numeric) = 4.6790112957219275980628029658695 absolute error = 0.21368268161283758202084191558531 relative error = 4.78537415897376140082552904314 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5445.0MB, alloc=44.3MB, time=29.72 TOP MAIN SOLVE Loop t[1] = 4.89 x1[1] (closed_form) = 2.0000135385604549878813509874685 x1[1] (numeric) = 1.9888884049506568082334436993409 absolute error = 0.011125133609798179647907288127597 relative error = 0.55625291505804959407374944843952 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.5353328270287293720600739743788 x2[1] (numeric) = 4.7535037598735957600704179169348 absolute error = 0.21817093284486638801034394255601 relative error = 4.8104723769037815204942658365505 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.9 x1[1] (closed_form) = 2.0000134038495276638129328248836 x1[1] (numeric) = 1.9887686585804316625164828047199 absolute error = 0.011244745269096001296450020163633 relative error = 0.56223349540821413273973072944802 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.6067512195406235265012085377756 x2[1] (numeric) = 4.8295028768295654164572770461237 absolute error = 0.22275165728894188995606850834818 relative error = 4.8353307281732105719647269610313 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5483.5MB, alloc=44.3MB, time=29.92 TOP MAIN SOLVE Loop t[1] = 4.91 x1[1] (closed_form) = 2.0000132704789964624227353239339 x1[1] (numeric) = 1.9886477087391780314380908992223 absolute error = 0.01136556173981843098464442471162 relative error = 0.56827431635473184197664226232305 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.6796123599607709942307646809443 x2[1] (numeric) = 4.9070391011380659027404399960998 absolute error = 0.2274267411772949085096753151555 relative error = 4.8599482966405665683673486286851 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.92 x1[1] (closed_form) = 2.0000131384355242194481396560183 x1[1] (numeric) = 1.9885255433318109977648098036768 absolute error = 0.011487595103713221683329852341545 relative error = 0.57437598198475810067869401038939 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.7539453937235034641078527201732 x2[1] (numeric) = 4.9861435027523471329509273980193 absolute error = 0.23219810902884366884307467784612 relative error = 4.8843242780072340114368552446449 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.93 x1[1] (closed_form) = 2.0000130077059064776282547043466 x1[1] (numeric) = 1.9884021501416880199477841032718 absolute error = 0.01161085756421845768047060107476 relative error = 0.58053910246996681411933308153242 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.8297800550400488095193730134044 x2[1] (numeric) = 5.0668477794645181861650244024146 absolute error = 0.23706772442446937664565138901021 relative error = 4.9084579778551343920310615020247 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5522.1MB, alloc=44.3MB, time=30.14 TOP MAIN SOLVE Loop t[1] = 4.94 x1[1] (closed_form) = 2.0000128782770701662471872237648 x1[1] (numeric) = 1.9882775168293872576880368755515 absolute error = 0.011735361447682908559150348213295 relative error = 0.58676429412756810028560029388836 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.9071466787926127012155681684807 x2[1] (numeric) = 5.1491842695905845112081870713758 absolute error = 0.24203759079797180999261890289516 relative error = 4.9323488096248299439823187677194 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.95 x1[1] (closed_form) = 2.0000127501360722938160759895201 x1[1] (numeric) = 1.9881516309314736194695539829146 absolute error = 0.011861119204598674346522006605478 relative error = 0.59305217948194053474782589045355 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 4.9860762126687366137480769584775 x2[1] (numeric) = 5.2331859649117584833259200667393 absolute error = 0.24710975224302186957784310826176 relative error = 4.9559962925388054175542325800748 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5560.5MB, alloc=44.3MB, time=30.34 TOP MAIN SOLVE Loop t[1] = 4.96 x1[1] (closed_form) = 2.0000126232700986537631570489444 x1[1] (numeric) = 1.9880244798592524086639019408961 absolute error = 0.011988143410846245099255108048302 relative error = 0.59940338732688411734461498638682 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.0666002295407861305720311080471 x2[1] (numeric) = 5.3188865238772205648991491462393 absolute error = 0.25228629433643443432711803819222 relative error = 4.9794000494746065641063726945242 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.97 x1[1] (closed_form) = 2.000012497666462543002428003988 x1[1] (numeric) = 1.9878960508975104435699511923101 absolute error = 0.012116446768952099432476811677915 relative error = 0.60581855278850018603569088737951 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.1487509400955215082609988644117 x2[1] (numeric) = 5.4063202850736129115901596518006 absolute error = 0.25756934497809140332916078738885 relative error = 5.0025598047924392853223653663757 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=5599.0MB, alloc=44.3MB, time=30.55 t[1] = 4.98 x1[1] (closed_form) = 2.0000123733126034932527671231669 x1[1] (numeric) = 1.9877663312032445254996596894504 absolute error = 0.012246042109358967753107433716536 relative error = 0.6122983173887045659703240252804 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.2325612057188024965210550294668 x2[1] (numeric) = 5.4955222809666539674767884952972 absolute error = 0.26296107524785147095573346583044 relative error = 5.0254753821217506130822466400858 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 4.99 x1[1] (closed_form) = 2.0000122501960860149806381375985 x1[1] (numeric) = 1.9876353078043771277556657492468 absolute error = 0.012376942391708887224972388351714 relative error = 0.61884332910938030514304545454797 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.3180645516405814677937746655779 x2[1] (numeric) = 5.5865282519203714504500971794103 absolute error = 0.26846370027978998265632251383232 relative error = 5.0481467021112224633385315108498 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5 x1[1] (closed_form) = 2.0000121283045983538407739448872 x1[1] (numeric) = 1.9875029675984591770685176779101 absolute error = 0.01250916070613917677225626697702 relative error = 0.62545424245717641196745905873282 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.4052951803454430290317091198714 x2[1] (numeric) = 5.6793746604995621859593249726688 absolute error = 0.2740794801541191569276158527974 relative error = 5.0705737801465120591654738564019 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5637.4MB, alloc=44.3MB, time=30.77 TOP MAIN SOLVE Loop t[1] = 5.01 x1[1] (closed_form) = 2.0000120076259512594904822529267 x1[1] (numeric) = 1.9873692973513597977706028689551 absolute error = 0.012642710274591461719879383971543 relative error = 0.63213171852895907469962176428879 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.4942879852540545103628140506596 x2[1] (numeric) = 5.7740987060612005475123037828088 absolute error = 0.27981072080714603714948973214917 relative error = 5.092756724039969648410424523716 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.02 x1[1] (closed_form) = 2.0000118881480767666544535681932 x1[1] (numeric) = 1.9872342836959428876801018840172 absolute error = 0.01277760445213387897435168417597 relative error = 0.63887642507792190789111623892963 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.585078564681000093322629201034 x2[1] (numeric) = 5.8707383396406328515019308536897 absolute error = 0.2856597749596327581793016526557 relative error = 5.1146957316964552456612544077464 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5675.9MB, alloc=44.3MB, time=30.97 TOP MAIN SOLVE Loop t[1] = 5.03 x1[1] (closed_form) = 2.0000117698590269883181769935442 x1[1] (numeric) = 1.9870979131307303933514530547648 absolute error = 0.012913856728296594966723938779471 relative error = 0.64568903658036183695512065397941 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.6777032360745818984733885441724 x2[1] (numeric) = 5.9693322791385129781675350295704 absolute error = 0.29162904306393107969414648539799 relative error = 5.1363910887592621916869040812008 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.04 x1[1] (closed_form) = 2.0000116527469729209292821714281 x1[1] (numeric) = 1.9869601720185521510187387113622 absolute error = 0.013051480728420769910543460065916 relative error = 0.65257023430312729849307545882335 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.772199050544284142771997327709 x2[1] (numeric) = 6.0699200248145547969858972292282 absolute error = 0.29772097427027065421389990151927 relative error = 5.1578431662400369188759398639256 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.05 x1[1] (closed_form) = 2.0000115368002032614873265110298 x1[1] (numeric) = 1.9868210465851821582149622398101 absolute error = 0.013190490215021103272364271219627 relative error = 0.65952070637174550126161420741077 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.868603807681711546111670407068 x2[1] (numeric) = 6.17254187509429971164509298747 absolute error = 0.30393806741258816553342258040198 relative error = 5.1790524181364619971492761568512 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5714.5MB, alloc=44.3MB, time=31.17 TOP MAIN SOLVE Loop t[1] = 5.06 x1[1] (closed_form) = 2.0000114220071232364037356923128 x1[1] (numeric) = 1.9866805229179611396932414517615 absolute error = 0.013330899089162096710494240551281 relative error = 0.6665411478392355605659875268416 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 5.9669560706809305600741434377012 x2[1] (numeric) = 6.2772389426952228560821989032264 absolute error = 0.31028287201429229600805546552527 relative error = 5.2000193790413438543445694759004 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.07 x1[1] (closed_form) = 2.0000113083562534420147824650562 x1[1] (numeric) = 1.9865385869644052699053625205936 absolute error = 0.013472721391848172109419944462622 relative error = 0.67363226075561438745405701203747 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.0672951817642617570497550501479 x2[1] (numeric) = 6.3840531710786292189520569546539 absolute error = 0.31675798931436746190230190450597 relative error = 5.2207446617466180440868171175535 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5753.0MB, alloc=44.3MB, time=31.39 TOP MAIN SOLVE Loop t[1] = 5.08 x1[1] (closed_form) = 2.0000111958362286966316540745223 x1[1] (numeric) = 1.9863952245308009129087829373292 absolute error = 0.013615971305427783722871137193086 relative error = 0.68079475423810228336092798368121 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.1696612779196939024189990450964 x2[1] (numeric) = 6.4930273512339213004393954517799 absolute error = 0.3233660733142273980203964066835 relative error = 5.2412289548456540803198115882993 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.09 x1[1] (closed_form) = 2.0000110844357969040128123638701 x1[1] (numeric) = 1.9862504212807852391749031327219 absolute error = 0.013760663155011664837909231148172 relative error = 0.68802934454203526082535428987408 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.2740953069562148853168045291196 x2[1] (numeric) = 6.6042051388019528646636416346512 absolute error = 0.33010983184573797934683710553161 relative error = 5.2614730203371091592953561956124 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=5791.5MB, alloc=44.3MB, time=31.59 t[1] = 5.1 x1[1] (closed_form) = 2.0000109741438179281449928422166 x1[1] (numeric) = 1.9861041627339125773591047693993 absolute error = 0.013906811409905350785888072817265 relative error = 0.69533675513249118157218180448354 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.3806390438834818544826118312344 x2[1] (numeric) = 6.7176310715443189962408654661487 absolute error = 0.33699202766083714175825363491427 relative error = 5.2814776912334460150037820340456 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.11 x1[1] (closed_form) = 2.0000108649492624792203198805644 x1[1] (numeric) = 1.9859564342642063576665379970508 absolute error = 0.014054430685056121553781883513522 relative error = 0.70271771675663687463736732412309 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.4893351076223826457053612984281 x2[1] (numeric) = 6.8333505871655710551210372549776 absolute error = 0.34401547954318840941567595654956 relative error = 5.3012438691770951499330282533485 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.12 x1[1] (closed_form) = 2.0000107568412110106981348187621 x1[1] (numeric) = 1.9858072210986965020067875315035 absolute error = 0.014203535742514508691347287258635 relative error = 0.71017296751680346931065445305343 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.6002269780531729483005329177854 x2[1] (numeric) = 6.9514100414954863049678719971907 absolute error = 0.35118306344231335666733907940539 relative error = 5.3207725220671061752838915111081 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5830.1MB, alloc=44.3MB, time=31.81 TOP MAIN SOLVE Loop t[1] = 5.13 x1[1] (closed_form) = 2.0000106498088526273412422471892 x1[1] (numeric) = 1.9856565083159421146752141786916 absolute error = 0.014354141492910512666028068497651 relative error = 0.71770325294429725049301768151994 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.713359013408008692852503142097 x2[1] (numeric) = 7.0718567270386660235679612310925 absolute error = 0.35849771363065733071545808899554 relative error = 5.3400646816989973869907771485105 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.14 x1[1] (closed_form) = 2.0000105438414840041173771778204 x1[1] (numeric) = 1.9855042808445393258288088424711 absolute error = 0.01450626299694467828856833534929 relative error = 0.72530932607395341761878244819847 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.8287764680148309051354401887301 x2[1] (numeric) = 7.1947388918988828466615219274436 absolute error = 0.36596242388405194152608173871349 relative error = 5.359121441420377377463333416868 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5868.6MB, alloc=44.3MB, time=32.01 TOP MAIN SOLVE Loop t[1] = 5.15 x1[1] (closed_form) = 2.000010438928508315857782350468 x1[1] (numeric) = 1.9853505234616141385396631337633 absolute error = 0.014659915466894177318119216704686 relative error = 0.73299194751944020258324784933317 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 6.9465255103997008167966492254044 x2[1] (numeric) = 7.3201057590857480079587045102634 absolute error = 0.37358024868604719116205528485902 relative error = 5.3779439538047777967755793371822 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.16 x1[1] (closed_form) = 2.0000103350594341775658606399801 x1[1] (numeric) = 1.9851952207913001287095059631148 absolute error = 0.014815114268134048856354676865381 relative error = 0.74075188554932087715310894694558 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 7.0666532417548264082678464403322 x2[1] (numeric) = 7.4480075462114220779102141708424 absolute error = 0.38135430445659566964236773051017 relative error = 5.3965334283460026674628497180935 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.17 x1[1] (closed_form) = 2.0000102322238745952699325465547 x1[1] (numeric) = 1.9850383573032008456140289826985 absolute error = 0.014971874920673749655903563856169 relative error = 0.74858991616388125612650102350987 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 7.1892077147796678408181504151059 x2[1] (numeric) = 7.578495485585248833217647220983 absolute error = 0.38928777080558099239949680587705 relative error = 5.4148911291751672380459922180086 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5907.1MB, alloc=44.3MB, time=32.23 TOP MAIN SOLVE Loop t[1] = 5.18 x1[1] (closed_form) = 2.0000101304115459273151831706267 x1[1] (numeric) = 1.9848799173108367593157739731505 absolute error = 0.015130213100709167999409197476165 relative error = 0.75650682317273037905964762464328 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 7.3142379529026584711921601925805 x2[1] (numeric) = 7.7116218447143510705119560653214 absolute error = 0.39738389181169259931979587274093 relative error = 5.4330183728024685234668713707804 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.19 x1[1] (closed_form) = 2.0000100296122668559909270014339 x1[1] (numeric) = 1.9847198849700765996390292491766 absolute error = 0.015290144642190256351897752257285 relative error = 0.76450339827318213069554288304445 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 7.441793969891230393583943585399 x2[1] (numeric) = 7.8474399472183895747732206151954 absolute error = 0.40564597732715918118927702979637 relative error = 5.4509165258856006952924359654621 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5945.6MB, alloc=44.3MB, time=32.44 TOP MAIN SOLVE Loop t[1] = 5.2 x1[1] (closed_form) = 2.0000099298159573693903523887584 x1[1] (numeric) = 1.9845582442775529298393253516918 absolute error = 0.015451685538404439551027037066618 relative error = 0.77258044112942563832456831449582 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 7.5719267898579887806856395777025 x2[1] (numeric) = 7.9860041941668521308731392734314 absolute error = 0.41407740430886335018749969572895 relative error = 5.468587003026601598584188275674 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.21 x1[1] (closed_form) = 2.0000098310126377534009308238393 x1[1] (numeric) = 1.9843949790690617965235766163851 absolute error = 0.015614851943575956877354207454208 relative error = 0.78073875945249236318524451176558 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 7.7046884676710377603505512875188 x2[1] (numeric) = 8.1273700858474084913673937664832 absolute error = 0.4226816181763707310168424789644 relative error = 5.4860312645987921121580595395692 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5984.0MB, alloc=44.3MB, time=32.64 TOP MAIN SOLVE Loop t[1] = 5.22 x1[1] (closed_form) = 2.0000097331924275937246892303732 x1[1] (numeric) = 1.9842300730179462957845270033546 absolute error = 0.015779660174481297940162227018681 relative error = 0.78897916908102788268333681034919 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 7.8401321097766222304131041904051 x2[1] (numeric) = 8.2715942439740396529611505515518 absolute error = 0.43146213419741742254804636114668 relative error = 5.5032508146053480401427121127408 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.23 x1[1] (closed_form) = 2.0000096363455447878285464611794 x1[1] (numeric) = 1.9840635096334638939047665996838 absolute error = 0.015946126712080893923779861495679 relative error = 0.79730249406287644067723810972748 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 7.9783118954424149460804246802021 x2[1] (numeric) = 8.4187344343438257168961715508697 absolute error = 0.44042253890141077081574687066765 relative error = 5.5202471985709249105343876669438 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.24 x1[1] (closed_form) = 2.0000095404623045667259082108016 x1[1] (numeric) = 1.9838952722591373393610286259953 absolute error = 0.016114268203167227364879584806288 relative error = 0.80570956673748642435498862333946 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 8.1192830984299464780275045832005 x2[1] (numeric) = 8.5688495899514560852345181227273 absolute error = 0.44956649152150960720701353952682 relative error = 5.5370220014676396263784443277734 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6022.6MB, alloc=44.3MB, time=32.86 TOP MAIN SOLVE Loop t[1] = 5.25 x1[1] (closed_form) = 2.0000094455331185264916976883528 x1[1] (numeric) = 1.9837253440710890012185931321043 absolute error = 0.016284101462029525273104556248548 relative error = 0.81420122781914500832158919222775 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 8.2631021091048473021976883283221 x2[1] (numeric) = 8.7219998345707088474354592093752 absolute error = 0.45889772546586154523777088105312 relative error = 5.5535768456765995137432651758281 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.26 x1[1] (closed_form) = 2.0000093515484936694139727465981 x1[1] (numeric) = 1.983553708076358467348248766177 absolute error = 0.016455643472135202065723980421111 relative error = 0.82277832648105028943263131084827 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 8.4098264569937464129999878361445 x2[1] (numeric) = 8.8782465068123330129830859830516 absolute error = 0.46842004981858659998309814690713 relative error = 5.5699133889860590658643090242891 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6061.1MB, alloc=44.3MB, time=33.06 TOP MAIN SOLVE Loop t[1] = 5.27 x1[1] (closed_form) = 2.0000092584990314546862438299433 x1[1] (numeric) = 1.983380347111203234224232307412 absolute error = 0.016628911387828220462011522531284 relative error = 0.83144172044022931965999496640106 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 8.5595148337968495201591067894124 x2[1] (numeric) = 9.0376521846679578208460719673518 absolute error = 0.47813735087110830068696517793936 relative error = 5.5860333226271777051277960292702 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.28 x1[1] (closed_form) = 2.0000091663754268585455611820336 x1[1] (numeric) = 1.9832052438393823183707096596417 absolute error = 0.016803922536044540174851522391958 relative error = 0.84019227604331052886582980998781 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 8.7122271168654021673828487688365 x2[1] (numeric) = 9.2002807105498477814713034965147 absolute error = 0.48805359368444561408845472767813 relative error = 5.60193836934824826741423956374 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.29 x1[1] (closed_form) = 2.0000090751684674437623843384618 x1[1] (numeric) = 1.9830283807504226178165126253915 absolute error = 0.016980694418044825945871713070317 relative error = 0.84903086835315911480069515838871 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 8.8680243931534290711783866544104 x2[1] (numeric) = 9.3661972168365204596030618880138 absolute error = 0.49817282368309138842467523360343 relative error = 5.6176302815281657340552917624114 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6099.6MB, alloc=44.3MB, time=33.28 TOP MAIN SOLVE Loop t[1] = 5.3 x1[1] (closed_form) = 2.0000089848690324383891821161067 x1[1] (numeric) = 1.9828497401578678501928322304708 absolute error = 0.017159244711164588196349885635887 relative error = 0.85795838123638406393913388933972 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 9.0269689836533306949602298800817 x2[1] (numeric) = 9.5354681519344463658235151274379 absolute error = 0.50849916828111567086328524735616 relative error = 5.6331108393298090572248481983772 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.31 x1[1] (closed_form) = 2.0000088954680918236756371913899 x1[1] (numeric) = 1.9826693041975098923662191453116 absolute error = 0.01733959127058193130941804607833 relative error = 0.86697570745172555392972423595765 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 9.1891244683251116229378956765072 x2[1] (numeric) = 9.7081613068662567722757892820563 absolute error = 0.51903683854114514933789360554903 relative error = 5.648381848893915792361700304088 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6138.1MB, alloc=44.3MB, time=33.48 TOP MAIN SOLVE Loop t[1] = 5.32 x1[1] (closed_form) = 2.0000088069567054310592460278348 x1[1] (numeric) = 1.9824870548256023447393806145452 absolute error = 0.017521752131103086319865413289591 relative error = 0.87608374873933157647550824047308 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 9.3545557115292127575725890566759 x2[1] (numeric) = 9.8843458423960958861404012368412 absolute error = 0.52979013086688312856781218016528 relative error = 5.6634451405739396998046275374912 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.33 x1[1] (closed_form) = 2.00000871932602204814101246041 x1[1] (numeric) = 1.9823029738170561415747152731318 absolute error = 0.017705745508965906566297187278199 relative error = 0.88528341591093270838344013639512 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 9.5233288879731208126359772918044 x2[1] (numeric) = 10.064092316702968687340188738021 absolute error = 0.54076342872984787470421144621642 relative error = 5.6783025672122955278361121597237 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6176.7MB, alloc=44.3MB, time=33.69 TOP MAIN SOLVE Loop t[1] = 5.34 x1[1] (closed_form) = 2.0000086325672785335568317609941 x1[1] (numeric) = 1.9821170427636170269001145394483 absolute error = 0.017891589803661506656717221545723 relative error = 0.89457562894092404833702452438302 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 9.6955115091821340916723914694997 x2[1] (numeric) = 10.247472713613154950600897816424 absolute error = 0.55196120443102085892850634692471 relative error = 5.692956002458312849227932473799 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.35 x1[1] (closed_form) = 2.0000085466717989406560515857567 x1[1] (numeric) = 1.9819292430720247137431023903326 absolute error = 0.018079303599774226912949195424045 relative error = 0.90396131705836342766360450244118 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 9.8711724505048732111683479500132 x2[1] (numeric) = 10.43456047140298361408347311263 absolute error = 0.56338802089811040291512516261657 relative error = 5.7074073391281420902297269559571 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.36 x1[1] (closed_form) = 2.0000084616309936498995769302826 x1[1] (numeric) = 1.9817395559621535426077028929772 absolute error = 0.018268905668840107291874037305402 relative error = 0.91344141883989509499588569501487 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 10.05038197866433933284075274972 x2[1] (numeric) = 10.625430512183489816790477016288 absolute error = 0.57504853351915048394972426656833 relative error = 5.721658487606780751211474755302 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6215.3MB, alloc=44.3MB, time=33.91 TOP MAIN SOLVE Loop t[1] = 5.37 x1[1] (closed_form) = 2.0000083774363585098907581799282 x1[1] (numeric) = 1.9815479624651344532583337239905 absolute error = 0.018460414971224056632424455937655 relative error = 0.92301688230360816727540627218548 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 10.233211779865540695732427133927 x2[1] (numeric) = 10.820159271878709696100799880294 absolute error = 0.58694749201316900036837274636711 relative error = 5.7357113742923162485067052627166 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.38 x1[1] (closed_form) = 2.0000082940794739869531646284069 x1[1] (numeric) = 1.9813544434214580820063390362488 absolute error = 0.018653850658015904946825592158092 relative error = 0.93268866500383923302304043438131 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 10.419734988470930873544093582741 x2[1] (numeric) = 11.018824730809605508215512777001 absolute error = 0.59908974233867463467141919426022 relative error = 5.7495679400824137749766917196084 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6253.8MB, alloc=44.3MB, time=34.11 TOP MAIN SOLVE Loop t[1] = 5.39 x1[1] (closed_form) = 2.0000082115520043231702005332674 x1[1] (numeric) = 1.9811589794790587948073095692936 absolute error = 0.018849232072945528362890963973814 relative error = 0.94245773412692858821760126115931 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 10.61002621625512931489255246397 x2[1] (numeric) = 11.221506444895855902995935075307 absolute error = 0.61148022864072658810338261133709 relative error = 5.7632301389030130416627639219541 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.4 x1[1] (closed_form) = 2.0000081298456967028023669682337 x1[1] (numeric) = 1.9809615510913794645709030908788 absolute error = 0.019046578754317238231463877354911 relative error = 0.95232506658793968048762994716642 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 10.804161582250626444821393870172 x2[1] (numeric) = 11.428285577487993347554300509694 absolute error = 0.62412399523736690273290663952168 relative error = 5.7766999362791366762308989889866 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.41 x1[1] (closed_form) = 2.0000080489523804269988105039385 x1[1] (numeric) = 1.9807621385154167991592834607608 absolute error = 0.0192459104369636278395270431777 relative error = 0.96229164912835143364305874219043 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 11.002218743196412007594570405976 x2[1] (numeric) = 11.63924493184262284888711259017 absolute error = 0.6370261886462108412925421841932 relative error = 5.7899793079476553604319842808375 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6292.3MB, alloc=44.3MB, time=34.33 TOP MAIN SOLVE Loop t[1] = 5.42 x1[1] (closed_form) = 2.0000079688639660967206291841748 x1[1] (numeric) = 1.9805607218097470246053492618735 absolute error = 0.019447247054219072115279922301318 relative error = 0.97235847841473322186224660207577 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 11.204276924601706508138338862142 x2[1] (numeric) = 11.854468984253713375687983726079 absolute error = 0.65019205965200686754964486393719 relative error = 5.8030702385118004269409678246816 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.43 x1[1] (closed_form) = 2.0000078895724448037942274473641 x1[1] (numeric) = 1.9803572808325317261174285522824 absolute error = 0.019650608739913077676798895081716 relative error = 0.98252656113841236111563859224338 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 11.410416952437221658937611456462 x2[1] (numeric) = 12.074043917853215826144696294726 absolute error = 0.66362696541599416720708483826414 relative error = 5.8159747201371635385292888522825 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6330.8MB, alloc=44.3MB, time=34.53 TOP MAIN SOLVE Loop t[1] = 5.44 x1[1] (closed_form) = 2.0000078110698873300138246546081 x1[1] (numeric) = 1.9801517952395036474528784026904 absolute error = 0.019856015830383682560946251917634 relative error = 0.99279691411614408465981910975527 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 11.620721285466626759161697533655 x2[1] (numeric) = 12.298057657094529136997458650207 absolute error = 0.67733637162790237783576111655189 relative error = 5.8286947512888751674108658563659 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.45 x1[1] (closed_form) = 2.0000077333484433542130268077615 x1[1] (numeric) = 1.9799442444819322472388480733337 absolute error = 0.020063488866511106974178734427827 relative error = 1.003170564391794069684940325224 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 11.835274048231154023703098809697 x2[1] (numeric) = 12.526599902932609286515706604079 absolute error = 0.69132585470145526281260779438252 relative error = 5.8412323355096088032319202369829 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6369.2MB, alloc=44.3MB, time=34.75 TOP MAIN SOLVE Loop t[1] = 5.46 x1[1] (closed_form) = 2.0000076564003406672261679539203 x1[1] (numeric) = 1.9797346078045688087941425311986 absolute error = 0.020273048595771858432025422721701 relative error = 1.0136485493390436834544358846172 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 12.054161064700537144101223444296 x2[1] (numeric) = 12.75976216871479461960681743402 absolute error = 0.70560110401425747550559398972397 relative error = 5.8535894802380160641706599209159 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.47 x1[1] (closed_form) = 2.0000075802178843946609167562652 x1[1] (numeric) = 1.9795228642435708979614560797244 absolute error = 0.020484715974313496699460676540852 relative error = 1.0242319167651282195487015181937 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 12.277469892603743905499805239732 x2[1] (numeric) = 12.997637816796705228476608102619 absolute error = 0.72016792419296132297680286288646 relative error = 5.8657681956671590833066446834162 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.48 x1[1] (closed_form) = 2.0000075047934562274044248442268 x1[1] (numeric) = 1.9793089926244059613940297001143 absolute error = 0.020698512169050266010395144112495 relative error = 1.0349217250156184981242661298685 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 12.505289858453235610472878767015 x2[1] (numeric) = 13.240322095897864170845275622783 absolute error = 0.73503223744462856037239685576856 relative error = 5.8777704936424706053650089192757 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6407.8MB, alloc=44.3MB, time=34.94 TOP MAIN SOLVE Loop t[1] = 5.49 x1[1] (closed_form) = 2.0000074301195136597860669165589 x1[1] (numeric) = 1.9790929715597338556548137627391 absolute error = 0.020914458559779804131253153819802 relative error = 1.0457190430802563084372192437905 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 12.737712093276763480523669335646 x2[1] (numeric) = 13.487912179211984215707735655527 absolute error = 0.75020008593522073518406631988148 relative error = 5.8895983865987390683948768950745 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.5 x1[1] (closed_form) = 2.0000073561885892353205882364648 x1[1] (numeric) = 1.9788747794472680953792814599371 absolute error = 0.02113257674132113994130677652771 relative error = 1.056624950699854277264737165527 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 12.974829569070995230285395197862 x2[1] (numeric) = 13.740507203287165692382203808199 absolute error = 0.76567763421617046209680861033627 relative error = 5.901253886535585470319921064652 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6446.3MB, alloc=44.3MB, time=35.14 TOP MAIN SOLVE Loop t[1] = 5.51 x1[1] (closed_form) = 2.0000072829932897999562332049763 x1[1] (numeric) = 1.9786543944676156066249269424166 absolute error = 0.021352888525674193331306262559614 relative error = 1.0676405384742708533019994571928 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 13.216737135991553751146211735948 x2[1] (numeric) = 13.99820830769155900287461802986 absolute error = 0.78147117170000525172840629391207 relative error = 5.9127390040308709396031506498793 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.52 x1[1] (closed_form) = 2.0000072105262957627531792031471 x1[1] (numeric) = 1.978431794582094769380982897531 absolute error = 0.021575415944200993372196305616104 relative error = 1.0787669079714712051242537517257 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 13.463531560294344415682880817609 x2[1] (numeric) = 14.261118675480359563597897678949 absolute error = 0.79758711518601514791501686133972 relative error = 5.9240557472914485494838750052217 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.53 x1[1] (closed_form) = 2.000007138780360363918342930343 x1[1] (numeric) = 1.9782069575305315310407902372146 absolute error = 0.021800181249828832877552693128367 relative error = 1.0900051718376849388960218667208 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 13.71531156304334803975301563789 x2[1] (numeric) = 14.529343574480323495911636609722 absolute error = 0.81403201143697545615862097183192 relative error = 5.9352061212406499427165959261333 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6484.9MB, alloc=44.3MB, time=35.36 TOP MAIN SOLVE Loop t[1] = 5.54 x1[1] (closed_form) = 2.0000070677483089501233621092866 x1[1] (numeric) = 1.9779798608290333704463305543201 absolute error = 0.022027206919275579677031554966529 relative error = 1.1013564539086716516923029261724 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 13.972177859600363135578125325988 x2[1] (numeric) = 14.80299039940831941401625576835 absolute error = 0.83081253980795627843813044236224 relative error = 5.9461921266418766745182445413378 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.55 x1[1] (closed_form) = 2.0000069974230382570332837521271 x1[1] (numeric) = 1.9777504817677408898994707644567 absolute error = 0.022256515655297367133812987670443 relative error = 1.1128218893221054470810881264207 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 14.234233199912493879291845302051 x2[1] (numeric) = 15.082168714840765294262869979885 absolute error = 0.84793551492827141497102467783392 relative error = 5.957015759257647741586279991061 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6523.5MB, alloc=44.3MB, time=35.56 TOP MAIN SOLVE Loop t[1] = 5.56 x1[1] (closed_form) = 2.0000069277975156989742112584641 x1[1] (numeric) = 1.977518797408556810297247378224 absolute error = 0.022488130388958888676963880240154 relative error = 1.1244026246310896515136354185866 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 14.501582409613499325349916241662 x2[1] (numeric) = 15.366990299051139785385810042421 absolute error = 0.86540788943764046003589380075944 relative error = 5.9676790090434384509821099124644 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.57 x1[1] (closed_form) = 2.000006858864778665668876518091 x1[1] (numeric) = 1.9772847845828521422888114219057 absolute error = 0.022722074281926523380065096185293 relative error = 1.1360998179188130830899505204281 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 14.774332431955444955548490221285 x2[1] (numeric) = 15.657569188733104570684608390822 absolute error = 0.88323675677765961513611816953716 relative error = 5.9781838593756315013722981117807 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6562.1MB, alloc=44.3MB, time=35.77 TOP MAIN SOLVE Loop t[1] = 5.58 x1[1] (closed_form) = 2.0000067906179338259698099896122 x1[1] (numeric) = 1.9770484198891493040692381707086 absolute error = 0.022958370728784521900571818903606 relative error = 1.1479146389143593384230855000763 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 15.052592370587429782401677943033 x2[1] (numeric) = 15.954021724627128659682559388549 absolute error = 0.90142935403969887728088144551531 relative error = 5.9885322863128888084168548679338 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.59 x1[1] (closed_form) = 2.0000067230501564385204814917181 x1[1] (numeric) = 1.9768096796907819541200503339116 absolute error = 0.023197043359374484400431157806485 relative error = 1.1598482691096806786286133945252 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 15.336473533198501068145136056097 x2[1] (numeric) = 16.25646659806886690998205462013 absolute error = 0.9199930648703658418369185640332 relative error = 5.9987262578902421148911696456588 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.6 x1[1] (closed_form) = 2.0000066561546896692754772467456 x1[1] (numeric) = 1.9765685401135313048777785983611 absolute error = 0.02343811604115836439769864838451 relative error = 1.1719019018777482119264972984658 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 15.626089476042214407201052771395 x2[1] (numeric) = 16.565024898477913804497903117845 absolute error = 0.93893542243569939729685034644968 relative error = 6.0087677334451916946010985714325 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6600.6MB, alloc=44.3MB, time=35.98 TOP MAIN SOLVE Loop t[1] = 5.61 x1[1] (closed_form) = 2.0000065899248439158114646254931 x1[1] (numeric) = 1.9763249770432386809599566411898 absolute error = 0.02368161288160523485150798430328 relative error = 1.1840767425918901879731912578966 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 15.921556049360649589840359810124 x2[1] (numeric) = 16.879820161805929682474524939512 absolute error = 0.95826411244528009263416512938804 relative error = 6.0186586629750953989324750587841 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.62 x1[1] (closed_form) = 2.0000065243539961383613751266894 x1[1] (numeric) = 1.9760789661233940832023836698193 absolute error = 0.023927558230602055158991456870124 relative error = 1.1963740087463303378539512787915 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 16.222991443726052459083041717555 x2[1] (numeric) = 17.200978419963520395156617912345 absolute error = 0.9779869762374679360735761947902 relative error = 6.0284009865251248192224308730229 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6639.1MB, alloc=44.3MB, time=36.19 TOP MAIN SOLVE Loop t[1] = 5.63 x1[1] (closed_form) = 2.0000064594355891975049084519407 x1[1] (numeric) = 1.975830482752700517362048678831 absolute error = 0.02417597668288868014285977310966 relative error = 1.2087949300779383136708791182155 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 16.530516237318640035509549015317 x2[1] (numeric) = 17.528628251245642882200813237927 absolute error = 0.99811201392700284669126422260994 relative error = 6.0379966336060613620743058862543 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.64 x1[1] (closed_form) = 2.0000063951631311984491261746355 x1[1] (numeric) = 1.9755795020826138439165569832852 absolute error = 0.024426893080517354532569191350252 relative error = 1.2213407486892044028731699094054 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 16.844253444159480662445496612699 x2[1] (numeric) = 17.862900831775708599504343380218 absolute error = 1.0186473876162279370588467675194 relative error = 6.0474475226412024751810354205398 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.65 x1[1] (closed_form) = 2.0000063315301948418335625157418 x1[1] (numeric) = 1.9753259990148579029429888391406 absolute error = 0.024680332515336938890573676601173 relative error = 1.234012719172450814904508270818 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 17.164328563317742966724152090729 x2[1] (numeric) = 18.203929987988964232866097145315 absolute error = 1.0396014246712212661419450545864 relative error = 6.056755560441647037102151052375 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6677.7MB, alloc=44.3MB, time=36.39 TOP MAIN SOLVE Loop t[1] = 5.66 x1[1] (closed_form) = 2.0000062685304167809949321965753 x1[1] (numeric) = 1.9750699481989146655866073004668 absolute error = 0.024936320331502115408324896108515 relative error = 1.2468121087352919614007993030273 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 17.490869629111997190748880779318 x2[1] (numeric) = 18.551852250176144867793662910313 absolute error = 1.060982621064147677044782130995 relative error = 6.0659226417092289567889243218179 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.67 x1[1] (closed_form) = 2.0000062061574969856271613037093 x1[1] (numeric) = 1.9748113240294891611324706368199 absolute error = 0.025194882128007824494690666889447 relative error = 1.2597401973273562760717967056907 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 17.824007262325650085780119876212 x2[1] (numeric) = 18.906806907108818920128076755945 absolute error = 1.0827996447831688343479568797327 relative error = 6.0749506485663692406870864611941 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6716.3MB, alloc=44.3MB, time=36.61 TOP MAIN SOLVE Loop t[1] = 5.68 x1[1] (closed_form) = 2.000006144405198111773106638828 x1[1] (numeric) = 1.974550100643948926170543904208 absolute error = 0.025456043761249185602562734620013 relative error = 1.2727982777682822465551902832308 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 18.163874722457000223317584996634 x2[1] (numeric) = 19.268936061768276834636520109644 absolute error = 1.1050613393112766113189351130098 relative error = 6.0838414501121191024345082316689 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.69 x1[1] (closed_form) = 2.0000060832673448780849622004501 x1[1] (numeric) = 1.9742862519197377197970923813293 absolute error = 0.025719831347607158287869819120796 relative error = 1.2859876558770014579539549496971 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 18.510607961024814443410456879657 x2[1] (numeric) = 19.638384688200257002410047421526 absolute error = 1.1277767271754425589995905418693 relative error = 6.092596902003670040284721646562 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6754.8MB, alloc=44.3MB, time=36.81 TOP MAIN SOLVE Loop t[1] = 5.7 x1[1] (closed_form) = 2.0000060227378234482909783183848 x1[1] (numeric) = 1.9740197514717632462217217659083 absolute error = 0.025986271266060202069256552476547 relative error = 1.2993096506023215764699853129269 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 18.864345675950748381256556530539 x2[1] (numeric) = 20.015300689518252709383075667175 absolute error = 1.1509550135675043281265191366357 relative error = 6.1012188460626111205453136066368 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.71 x1[1] (closed_form) = 2.0000059628105808198067395982227 x1[1] (numeric) = 1.973750572649758623550148930068 absolute error = 0.026255390160822196256590668154636 relative error = 1.312765594154822331542114337544 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 19.225229367040364765440634829267 x2[1] (numeric) = 20.399834957078603387715588944727 absolute error = 1.1746055900382386222749541154601 relative error = 6.1097091099052189140190858655966 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.72 x1[1] (closed_form) = 2.0000059034796242184298622941612 x1[1] (numeric) = 1.9734786885356173348873827284687 absolute error = 0.026527214944006883542479565692549 relative error = 1.326356832140077686197541063864 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 19.593403392584942634918416636758 x2[1] (numeric) = 20.792141430851042182938868730659 absolute error = 1.1987380382660995480204520939009 relative error = 6.1180695065960715715683911588231 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6793.3MB, alloc=44.3MB, time=37.06 TOP MAIN SOLVE Loop t[1] = 5.73 x1[1] (closed_form) = 2.0000058447390204990575800754823 x1[1] (numeric) = 1.9732040719407013952542042958106 absolute error = 0.02680177279831910380337577967174 relative error = 1.3400847236932175179456010902553 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 19.969015027106718953164311718096 x2[1] (numeric) = 21.192377161008850060164948868465 absolute error = 1.2233621339021311070006371503693 relative error = 6.1263018343242853317892905937305 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.74 x1[1] (closed_form) = 2.0000057865828955523672894458521 x1[1] (numeric) = 1.9729266954031224651313952800174 absolute error = 0.027079091179773087235894165834658 relative error = 1.3539506416148422664949666041989 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 20.352214520270661486105237685763 x2[1] (numeric) = 21.600702370763254543590643421424 absolute error = 1.2484878504925930574854057356614 relative error = 6.1344078761016792680907344465203 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6831.9MB, alloc=44.3MB, time=37.27 TOP MAIN SOLVE Loop t[1] = 5.75 x1[1] (closed_form) = 2.0000057290054337174007223755524 x1[1] (numeric) = 1.9726465311849956387408026876578 absolute error = 0.027359197820438078659919687894642 relative error = 1.3679559725083041398731554921779 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 20.743155156986338438522174018869 x2[1] (numeric) = 22.017280520467208910144987765596 absolute error = 1.2741253634808704716228137467261 relative error = 6.1423893994821822463352626174967 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.76 x1[1] (closed_form) = 2.0000056720008771999930040743911 x1[1] (numeric) = 1.9723635512696656324397799306944 absolute error = 0.027642120731211567553224143696707 relative error = 1.3821021169183686071841913557945 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 21.141993318723926398172326466986 x2[1] (numeric) = 22.442278373014195439532769835031 absolute error = 1.3002850542902690413604433680456 relative error = 6.1502481563018048221098572056094 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.77 x1[1] (closed_form) = 2.0000056155635254969884383264253 x1[1] (numeric) = 1.9720777273589050958455320012912 absolute error = 0.027927888204620401142906325134119 relative error = 1.3963904894712700442700539145814 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 21.548888546068883808396303752868 x2[1] (numeric) = 22.875866060558214362237070999842 absolute error = 1.3269775144893305538407672469747 relative error = 6.1579858824385081055235082850757 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6870.5MB, alloc=44.3MB, time=37.48 TOP MAIN SOLVE Loop t[1] = 5.78 x1[1] (closed_form) = 2.0000055596877348261854414852083 x1[1] (numeric) = 1.9717890308700847655181424606812 absolute error = 0.028216528817650060667299024527149 relative error = 1.410822519016175537957995373072 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 21.964003602540312672701573733427 x2[1] (numeric) = 23.318217152581648651484258096131 absolute error = 1.3542135500413359787826843627038 relative error = 6.1656042975913114103766556836479 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.79 x1[1] (closed_form) = 2.0000055043679175619536191479135 x1[1] (numeric) = 1.9714974329333151782152923316714 absolute error = 0.028508071434602383738326816242033 relative error = 1.4253996487680709953928146241788 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 22.38750453969853668695537130435 x2[1] (numeric) = 23.769508725338233986155747203448 absolute error = 1.3820041856396972992003758990977 relative error = 6.1731051050779907351293880183893 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6909.0MB, alloc=44.3MB, time=37.69 TOP MAIN SOLVE Loop t[1] = 5.8 x1[1] (closed_form) = 2.0000054495985416764665467456803 x1[1] (numeric) = 1.9712029043885596578876144531119 absolute error = 0.028802545209982018578932292568378 relative error = 1.440123336452083847184859465476 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 22.819560763567939698580772059317 x2[1] (numeric) = 24.229921432698913284832944555791 absolute error = 1.4103606691309735862521724964736 relative error = 6.1804899916507307490928875774259 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.81 x1[1] (closed_form) = 2.0000053953741301864943768626024 x1[1] (numeric) = 1.9709054157827182877109769795747 absolute error = 0.029099979591411898783399883027743 relative error = 1.4549950544492567767650905997685 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 23.260345102401634513817204369947 x2[1] (numeric) = 24.699639578428916396622955600541 absolute error = 1.439294476027281882805751230594 relative error = 6.1877606273291039346936581356068 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6947.4MB, alloc=44.3MB, time=37.89 TOP MAIN SOLVE Loop t[1] = 5.82 x1[1] (closed_form) = 2.0000053416892606057009520830806 x1[1] (numeric) = 1.9706049373666825755504692231864 absolute error = 0.029400404322578030150482859894145 relative error = 1.4700162899437870534423562463723 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 23.710033875815068824136930181883 x2[1] (numeric) = 25.178851189924978056615899479312 absolute error = 1.4688173141099092324789692974288 relative error = 6.194918665249761823707554081568 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.83 x1[1] (closed_form) = 2.0000052885385644023906526224049 x1[1] (numeric) = 1.9703014390923605183201817825703 absolute error = 0.029703849446203884070470839834626 relative error = 1.4851885450717461932196032013279 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 24.168806965316222616009150263604 x2[1] (numeric) = 25.667748093442191301787793863728 absolute error = 1.4989411281259686857786436001233 relative error = 6.2019657415322348223603310676313 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.84 x1[1] (closed_form) = 2.000005235916726462650752973451 x1[1] (numeric) = 1.9699948906096717677427378156128 absolute error = 0.030010345307054694908015157838143 relative error = 1.5005133370712948194597454273214 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 24.636847886260610083417924258907 x2[1] (numeric) = 26.166525990840589430530276193589 absolute error = 1.5296781045799793471123519346826 relative error = 6.208903475160248909556458556208 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6986.0MB, alloc=44.3MB, time=38.11 TOP MAIN SOLVE Loop t[1] = 5.85 x1[1] (closed_form) = 2.000005183818484558835601357771 x1[1] (numeric) = 1.9696852612635125970226473723031 absolute error = 0.030319922554971961812953985467831 relative error = 1.5159921984344077450131282445943 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 25.114343861259869003338574303649 x2[1] (numeric) = 26.675384537882157514124126242266 absolute error = 1.5610406766222885107855519386164 relative error = 6.2157334678779794786707815546982 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.86 x1[1] (closed_form) = 2.0000051322386288233394699560936 x1[1] (numeric) = 1.9693725200906903649276229202069 absolute error = 0.030632612147938458411847035886649 relative error = 1.5316266770601244484419171732837 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 25.60148589507330198874358184872 x2[1] (numeric) = 27.194527424109594674557157134928 absolute error = 1.5930415290362926858135752862082 relative error = 6.2224573041006747427342994969655 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7024.4MB, alloc=44.3MB, time=38.31 TOP MAIN SOLVE Loop t[1] = 5.87 x1[1] (closed_form) = 2.0000050811720012276054527647323 x1[1] (numeric) = 1.9690566358168271707217095723485 absolute error = 0.030948445355174056883743192383798 relative error = 1.5474183364093402695174079049182 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 26.098468851012327234232690022042 x2[1] (numeric) = 27.724162454338781078210609461748 absolute error = 1.6256936033264538439779194397059 relative error = 6.2290765508390934037977979005517 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.88 x1[1] (closed_form) = 2.0000050306134950663183115335263 x1[1] (numeric) = 1.9687375768532323903131430343656 absolute error = 0.031267453760262676005168499160768 relative error = 1.5633687556611538032394519446986 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 26.605491528888401553351107263313 x2[1] (numeric) = 28.264501631797549112205574653559 absolute error = 1.6590101029091475588544673902457 relative error = 6.2355927576372136699543754387172 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.89 x1[1] (closed_form) = 2.0000049805580544467296886400677 x1[1] (numeric) = 1.9684153112937437808679438281681 absolute error = 0.031589669264310665861744811899538 relative error = 1.5794795298707861272483286096425 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 27.122756744535595916156028950345 x2[1] (numeric) = 28.815761242944016767829089770963 absolute error = 1.6930044984084208516730608206185 relative error = 6.2420074565226831599303839381344 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7063.0MB, alloc=44.3MB, time=38.51 TOP MAIN SOLVE Loop t[1] = 5.9 x1[1] (closed_form) = 2.0000049310006737830646189959375 x1[1] (numeric) = 1.9680898069115368379970767299265 absolute error = 0.031915124089136945067542266011009 relative error = 1.5957522701290876546840305288092 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 27.650471410939633577587183044222 x2[1] (numeric) = 29.378161943998413116881618846649 absolute error = 1.7276905330587795392944358024271 relative error = 6.2483221619694917390370417748599 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.91 x1[1] (closed_form) = 2.000004881936397295958781214814 x1[1] (numeric) = 1.9677610311559020864502352604592 absolute error = 0.032243850780495209508545954354763 relative error = 1.6121886037236485633117851602249 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 28.188846621005843493652960120698 x2[1] (numeric) = 29.951928849223011200758607505496 absolute error = 1.7630822282171677071056473847976 relative error = 6.2545383708723618570109481280644 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7101.6MB, alloc=44.3MB, time=38.73 TOP MAIN SOLVE Loop t[1] = 5.92 x1[1] (closed_form) = 2.0000048333603185168764313504305 x1[1] (numeric) = 1.9674289511489899820426350064291 absolute error = 0.032575882211328534833796344001416 relative error = 1.6287901743015289120915856276706 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 28.738097731999137310411058043872 x2[1] (numeric) = 30.537291620985482932782824103563 absolute error = 1.7991938889863456223717660596906 relative error = 6.2606575625323634848746478388763 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.93 x1[1] (closed_form) = 2.0000047852675797974594605847722 x1[1] (numeric) = 1.9670935336825230993022958609098 absolute error = 0.03291125158505669815716472386244 relative error = 1.6455586420336247183395864130349 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 29.298444451689787042445385187571 x2[1] (numeric) = 31.134484561641704021464330617319 absolute error = 1.8360401099519169790189454297486 relative error = 6.2666811986532732529857613993554 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7140.0MB, alloc=44.3MB, time=38.95 TOP MAIN SOLVE Loop t[1] = 5.94 x1[1] (closed_form) = 2.0000047376533718237585113634023 x1[1] (numeric) = 1.9667547452144752760538380587872 absolute error = 0.033249992438896547704673304615155 relative error = 1.6624956837806864322266302548988 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 29.870110926239462900560830495723 x2[1] (numeric) = 31.743746707274764741354993820159 absolute error = 1.8736357810353018407941633244353 relative error = 6.2726107233482098559754910305604 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.95 x1[1] (closed_form) = 2.0000046905129331352975746847229 x1[1] (numeric) = 1.9664125518657173828504829978607 absolute error = 0.033592138647215752447091686862237 relative error = 1.6796029932610064106002718741625 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 30.45332582986268685568072974468 x2[1] (numeric) = 32.365321923327684900123224530024 absolute error = 1.9119960934649980444424947853446 relative error = 6.2784475631560901937977294941065 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.96 x1[1] (closed_form) = 2.0000046438415496489239746021184 x1[1] (numeric) = 1.9660669194166293818284068442693 absolute error = 0.033937724424920267095567757849065 relative error = 1.6968822812197921590179761158784 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 31.04832245629956771589862221252 x2[1] (numeric) = 32.999459002168088872422290847759 absolute error = 1.9511365458685211565236686352395 relative error = 6.2841931270674630444847323843165 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7178.6MB, alloc=44.3MB, time=39.16 TOP MAIN SOLVE Loop t[1] = 5.97 x1[1] (closed_form) = 2.0000045976345541873961245406392 x1[1] (numeric) = 1.9657178133036783361865090639047 absolute error = 0.034286784330875851209615476734551 relative error = 1.7143352756002422794573830288363 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 31.655338812136408030391656580555 x2[1] (numeric) = 33.646411762623869396082471778109 absolute error = 1.9910729504874613656908151975539 relative error = 6.2898488065592892976146565133887 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 5.98 x1[1] (closed_form) = 2.0000045518873260126619138110115 x1[1] (numeric) = 1.96536519861596202808969218839 absolute error = 0.034639353271363984572221622621562 relative error = 1.7319637217163422314415082584125 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 32.274617712011512307272132191142 x2[1] (numeric) = 34.306439151529657263265304724252 absolute error = 2.03182143951814495599317253311 relative error = 6.2954159756382499033765725154677 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7217.0MB, alloc=44.3MB, time=39.38 TOP MAIN SOLVE Loop t[1] = 5.99 x1[1] (closed_form) = 2.0000045065952903637810517706899 x1[1] (numeric) = 1.9650090400917178393545628155892 absolute error = 0.03499546650357252442648895510075 relative error = 1.749769382427397186299511238928 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 32.906406875744280138115355167275 x2[1] (numeric) = 34.979805347324718403864122200648 absolute error = 2.0733984715804382657487670333739 relative error = 6.3008959908921746971052423024446 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6 x1[1] (closed_form) = 2.0000044617539179994451614813014 x1[1] (numeric) = 1.9646493021147965458027131389507 absolute error = 0.035355159639121453642448342350686 relative error = 1.7677540383143194279944144547564 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 33.550959027426437161508567893248 x2[1] (numeric) = 35.66677986574372047237710079783 absolute error = 2.1158208383172833108685329045826 relative error = 6.3062901915491971310295901046271 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.01 x1[1] (closed_form) = 2.0000044173587247450498744906137 x1[1] (numeric) = 1.9642859487111006726580798193405 absolute error = 0.035718468647624072391794671273204 relative error = 1.7859194878576879294052657103811 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 34.208531996515041679263275568581 x2[1] (numeric) = 36.36763766764264824097524068567 absolute error = 2.159105671127606561711965117089 relative error = 6.3115998995442516726024468290788 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7255.5MB, alloc=44.3MB, time=39.58 TOP MAIN SOLVE Loop t[1] = 6.02 x1[1] (closed_form) = 2.0000043734052710442736335710636 x1[1] (numeric) = 1.9639189435449870548209518881874 absolute error = 0.036085429860283989452681682876117 relative error = 1.8042675476175979101702476615416 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 34.879388820967705475884829205976 x2[1] (numeric) = 37.082659269003001205427396902808 absolute error = 2.2032704480352957295425676968318 relative error = 6.3168264195925422020569426600389 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.03 x1[1] (closed_form) = 2.0000043298891615151183609214338 x1[1] (numeric) = 1.9635482499156332422716572063013 absolute error = 0.036456079973528272846703715132528 relative error = 1.8228000524153183611968768574651 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 35.563797852461284304804087774842 x2[1] (numeric) = 37.81213085315827816858225326753 absolute error = 2.2483330006969938637781654926888 relative error = 6.3219710392696211516520090521972 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7294.2MB, alloc=44.3MB, time=39.78 TOP MAIN SOLVE Loop t[1] = 6.04 x1[1] (closed_form) = 2.0000042868060445103675955285323 x1[1] (numeric) = 1.9631738307533673872414398414184 absolute error = 0.036830456052677123126155687113906 relative error = 1.8415188555167757017435983370202 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 36.26203286373612692052242987512 x2[1] (numeric) = 38.556344385287642526799410190587 absolute error = 2.2943115215515156062769803154678 relative error = 6.3270350290977303672433323610057 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.05 x1[1] (closed_form) = 2.000004244151611682418145136322 x1[1] (numeric) = 1.9627956486159612461361870146604 absolute error = 0.037208595535650436281958121661636 relative error = 1.8604258288178819175918513726674 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 36.974373158108821787580688275222 x2[1] (numeric) = 39.315597729222568903666305903054 absolute error = 2.3412245711137471160856176278322 relative error = 6.3320196426380657320474230042409 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7332.7MB, alloc=44.3MB, time=40.00 TOP MAIN SOLVE Loop t[1] = 6.06 x1[1] (closed_form) = 2.0000042019215975524417356250586 x1[1] (numeric) = 1.96241366568488592551010881324 absolute error = 0.037590536236711626931626811818592 relative error = 1.8795228630317257132773188907187 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 37.70110368119724802524677940331 x2[1] (numeric) = 40.090194766613197015315820268252 absolute error = 2.389091085415948990069040864942 relative error = 6.3369261165886384662912763965832 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.07 x1[1] (closed_form) = 2.0000041601117790838335736063397 x1[1] (numeric) = 1.9620278437615299976608478152961 absolute error = 0.037976316350249086172725791043553 relative error = 1.8988118678776453976520225283627 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 38.442515134902622098008653961161 x2[1] (numeric) = 40.880445518502062582781109294386 absolute error = 2.4379303835994404847724553332245 relative error = 6.3417556708874166991836256483675 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.08 x1[1] (closed_form) = 2.0000041187179752599051667348646 x1[1] (numeric) = 1.9616381442633796076544265569771 absolute error = 0.038365974454595652250740177887409 relative error = 1.9182947722722024102238176637768 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 39.198904093694134590350980461006 x2[1] (numeric) = 41.686666269353838106676197901203 absolute error = 2.487762175659703516325217440197 relative error = 6.3465095088204413963757000667998 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7371.4MB, alloc=44.3MB, time=40.22 TOP MAIN SOLVE Loop t[1] = 6.09 x1[1] (closed_form) = 2.000004077736046665779170667012 x1[1] (numeric) = 1.9612445282201601897875520817635 absolute error = 0.038759549515886475991618585248539 relative error = 1.9379735245220745857854957179429 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 39.970573123242692471029085233229 x2[1] (numeric) = 42.509179693590698773287592832377 absolute error = 2.5386065703480063022585075991476 relative error = 6.3511888171346210125706649551245 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.1 x1[1] (closed_form) = 2.0000040371618950744444518025097 x1[1] (numeric) = 1.9608469562699394076557085554847 absolute error = 0.039157080891955666788743247025013 relative error = 1.9578500925188884468211212957375 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 40.757830901451221925571085393684 x2[1] (numeric) = 43.348314984683931061899995568921 absolute error = 2.590484083232709136328910175237 relative error = 6.3557947661549193216221192257155 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7409.9MB, alloc=44.3MB, time=40.42 TOP MAIN SOLVE Loop t[1] = 6.11 x1[1] (closed_form) = 2.0000039969914630369299709705145 x1[1] (numeric) = 1.960445388655190928117797195525 absolute error = 0.039558608336272108812173774989491 relative error = 1.9779264639360100070816170080936 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 41.560992341929945491920801485072 x2[1] (numeric) = 44.204407986853424171793483664756 absolute error = 2.643415644923478679872682179684 relative error = 6.3603285099056607523832872761116 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.12 x1[1] (closed_form) = 2.0000039572207334765565051069483 x1[1] (numeric) = 1.960039785218818635531439778912 absolute error = 0.039964172001914841025065328036361 relative error = 1.9982046464273137655743496933259 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 42.380378719966025256455178909484 x2[1] (numeric) = 45.077801329427727592875112997199 absolute error = 2.6974226094617023364199340877153 relative error = 6.3647911862356872253609276820884 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.13 x1[1] (closed_form) = 2.0000039178457292872256317571342 x1[1] (numeric) = 1.9596301054001408886770560937931 absolute error = 0.040373812445588398548575663341141 relative error = 2.0186866678279497680321536681066 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 43.216317801037961647292550756675 x2[1] (numeric) = 45.968844563918422423642655391606 absolute error = 2.7525267628804607763501046349309 relative error = 6.3691839169471099410664464447375 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7448.4MB, alloc=44.3MB, time=40.63 TOP MAIN SOLVE Loop t[1] = 6.14 x1[1] (closed_form) = 2.0000038788625129357058049674212 x1[1] (numeric) = 1.9592163082308344187930612783261 absolute error = 0.040787570631678516912743689095087 relative error = 2.0393745763571288127356318169287 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 44.069143971926155297977316132439 x2[1] (numeric) = 46.877894303863639819849990707887 absolute error = 2.8087503319374845218726745754474 relative error = 6.3735078079274088145245242998136 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.15 x1[1] (closed_form) = 2.0000038402671860678757508419584 x1[1] (numeric) = 1.9587983523308374631086064704798 absolute error = 0.041205487936348604767144371478547 relative error = 2.0602704408229460793786847770951 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 44.93919837447207795447052794312 x2[1] (numeric) = 47.805314367496667671180663913211 absolute error = 2.8661159930245897167101359700904 relative error = 6.3777639492846412808542686631232 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7487.0MB, alloc=44.3MB, time=40.84 TOP MAIN SOLVE Loop t[1] = 6.16 x1[1] (closed_form) = 2.000003802055889118885806776042 x1[1] (numeric) = 1.9583761959042117241838019760402 absolute error = 0.041627606151677394702004800001744 relative error = 2.0813763508292636635112139703689 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 45.826829042039557877308266693193 x2[1] (numeric) = 48.751475923296716694540456663497 absolute error = 2.9246468812571588172321899703036 relative error = 6.3819534154855310137786283280703 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.17 x1[1] (closed_form) = 2.0000037642248009271982201750928 x1[1] (numeric) = 1.9579497967349627412499085984288 absolute error = 0.042053967489838185948311576663946 relative error = 2.1026944169846727049852103388447 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 46.732391038732766072616221710088 x2[1] (numeric) = 49.716757638480070053304933790966 absolute error = 2.9843665997473039806887120808775 relative error = 6.386077265496215702354146802245 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7525.6MB, alloc=44.3MB, time=41.09 TOP MAIN SOLVE Loop t[1] = 6.18 x1[1] (closed_form) = 2.0000037267701383524678103675006 x1[1] (numeric) = 1.9575191121828182555831481139716 absolute error = 0.042484614587320096884662253529052 relative error = 2.124226771113556006791566756574 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 47.656246601426592402756750872451 x2[1] (numeric) = 50.701545830491016823189323303254 absolute error = 3.0452992290644244204325724308033 relative error = 6.3901365429254414215353149547436 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.19 x1[1] (closed_form) = 2.0000036896881558972247814590943 x1[1] (numeric) = 1.9570840991789641477451522330848 absolute error = 0.042919590509191749479629226009448 relative error = 2.1459755664692722507257344930316 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 48.598765284666225620835382595686 x2[1] (numeric) = 51.706234621553169597847861180946 absolute error = 3.1074693368869439770124785852603 relative error = 6.3941322761699993101382954610663 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.2 x1[1] (closed_form) = 2.0000036529751453323218540952562 x1[1] (numeric) = 1.9566447142217375202802206947965 absolute error = 0.043358938753407812041633400459693 relative error = 2.1679429779494831284817880500963 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 49.56032410849389909311963989253 x2[1] (numeric) = 52.731226096342990740864745532846 absolute error = 3.1709019878490916477451056403161 relative error = 6.3980654785622082364152850380973 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7564.1MB, alloc=44.3MB, time=41.31 TOP MAIN SOLVE Loop t[1] = 6.21 x1[1] (closed_form) = 2.0000036166274353261082605317307 x1[1] (numeric) = 1.9562009133722764951740691106964 absolute error = 0.043802703255158830934191421034311 relative error = 2.1901312023136449210677844992507 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 50.54130770926193487872743925901 x2[1] (numeric) = 53.776930462848600735172752963731 absolute error = 3.2356227535866658564453137047209 relative error = 6.4019371485192548881603235041209 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.22 x1[1] (closed_form) = 2.0000035806413910772935201046085 x1[1] (numeric) = 1.9557526522501262910501872522305 absolute error = 0.04425092839126478624333285237798 relative error = 2.2125424584026862758819326182285 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 51.542108493492413395102880946667 x2[1] (numeric) = 54.843766216478216255724704255507 absolute error = 3.3016577229858028606218233088396 relative error = 6.4057482696942102726819426033846 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7602.7MB, alloc=44.3MB, time=41.52 TOP MAIN SOLVE Loop t[1] = 6.23 x1[1] (closed_form) = 2.0000035450134139514642811710888 x1[1] (numeric) = 1.9552998860288011407078658026286 absolute error = 0.044703658984612810756415368460236 relative error = 2.2351789873608941494106685069611 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 52.563126794845014588653593745163 x2[1] (numeric) = 55.932160307483865506136179470259 absolute error = 3.3690335126388509174825857250958 relative error = 6.4094998111285489539913327347557 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.24 x1[1] (closed_form) = 2.0000035097399411212178809023075 x1[1] (numeric) = 1.9548425694313016051899469617579 absolute error = 0.045160940308639516027933940549604 relative error = 2.2580430528600301043281302891273 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 53.604771034255819839968518663471 x2[1] (numeric) = 57.042548311767354535000431577574 absolute error = 3.4377772775115346950319129141029 relative error = 6.4131927274060044922899655119625 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.25 x1[1] (closed_form) = 2.0000034748174452098766359843216 x1[1] (numeric) = 1.9543806567255868361079700949032 absolute error = 0.04562281809185837376866588941839 relative error = 2.2811369413256993728138169989132 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 54.667457883311132259608707421484 x2[1] (numeric) = 58.175374605136811213137995561333 absolute error = 3.5079167218256789535292881398492 relative error = 6.4168279588076014866298346837857 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7641.3MB, alloc=44.3MB, time=41.72 TOP MAIN SOLVE Loop t[1] = 6.26 x1[1] (closed_form) = 2.0000034402424339387472353594153 x1[1] (numeric) = 1.9539141017200013334471718127316 absolute error = 0.046089338522432605300063546683715 relative error = 2.3044629621659953231837097253638 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 55.751612430921667080953915485207 x2[1] (numeric) = 59.331092541083513850390308329756 absolute error = 3.5794801101618467694363928445483 relative error = 6.4204064314677113579836007210695 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.27 x1[1] (closed_form) = 2.0000034060114497778899606530489 x1[1] (numeric) = 1.9534428577586557415233099345835 absolute error = 0.046560548252794036366650718465424 relative error = 2.3280234480024421944723545735116 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 56.857668353363784048631935798142 x2[1] (numeric) = 60.510164632150119611838114004146 absolute error = 3.6524962787863355632061782060035 relative error = 6.4239290575309855495921317780653 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7679.8MB, alloc=44.3MB, time=41.94 TOP MAIN SOLVE Loop t[1] = 6.28 x1[1] (closed_form) = 2.0000033721210696003628109174671 x1[1] (numeric) = 1.9529668777167612211670576679527 absolute error = 0.047036494404308379195753249514381 relative error = 2.3518207549032591934321114116544 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 57.986068087755780562750168822958 x2[1] (numeric) = 61.713062734962844521814861686511 absolute error = 3.7269946472070639590646928635534 relative error = 6.4273967353100261671970205040409 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.29 x1[1] (closed_form) = 2.0000033385679043399059558163106 x1[1] (numeric) = 1.9524861139959169315692984074341 absolute error = 0.047517224571987408336657408876507 relative error = 2.375857262618969280553942767331 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 59.137263009038638409252492408855 x2[1] (numeric) = 62.940268239001612494465328065662 absolute error = 3.8030052299629740852128356568071 relative error = 6.4308103494436602365953875086957 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7718.3MB, alloc=44.3MB, time=42.14 TOP MAIN SOLVE Loop t[1] = 6.3 x1[1] (closed_form) = 2.0000033053485986520322854102853 x1[1] (numeric) = 1.9520005185193501505315785710655 absolute error = 0.048002786829248501500706839219793 relative error = 2.400135374820376206184967618868 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 60.311713610532018734885443929758 x2[1] (numeric) = 64.19227225918368608815209866537 absolute error = 3.8805586486516673532666547356122 relative error = 6.4341707710556897229737247424075 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.31 x1[1] (closed_form) = 2.0000032724598305784901653164421 x1[1] (numeric) = 1.9515100427271085571297769396685 absolute error = 0.048493229732722021360388376773628 relative error = 2.4246575193389335946449824830102 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 61.509889688137730072226012750481 x2[1] (numeric) = 65.469575832337817145862787344642 absolute error = 3.9596861442000870736367745941608 relative error = 6.4374788579139952388923155172864 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.32 x1[1] (closed_form) = 2.0000032398983112150648432369675 x1[1] (numeric) = 1.951014637571204196015250421652 absolute error = 0.048988602327107019049592815315514 relative error = 2.4494261484095301134509400149939 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 62.732270528264353258076819549979 x2[1] (numeric) = 66.772690117647511765127375108288 absolute error = 4.0404195893831585070505555583089 relative error = 6.4407354545898769688992411213939 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7756.7MB, alloc=44.3MB, time=42.34 TOP MAIN SOLVE Loop t[1] = 6.33 x1[1] (closed_form) = 2.000003207660784382685286721306 x1[1] (numeric) = 1.9505142535107086377458396479528 absolute error = 0.04948895415007574493944707335322 relative error = 2.4744437389157150063688941914045 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 63.979345099548195600907725834599 x2[1] (numeric) = 68.102136601143591761353252470087 absolute error = 4.1227915015953961604455266354876 relative error = 6.4439413926175217619292269892143 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.34 x1[1] (closed_form) = 2.000003175744026301803562571311 x1[1] (numeric) = 1.9500088405067988446586801176551 absolute error = 0.049994335237227457144882453655939 relative error = 2.4997127926373885130513322893788 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 65.251612248447265235340768496332 x2[1] (numeric) = 69.458447304327854583036958134928 absolute error = 4.2068350558805893476961896385954 relative error = 6.4470974906534905913302384885011 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7795.3MB, alloc=44.3MB, time=42.56 TOP MAIN SOLVE Loop t[1] = 6.35 x1[1] (closed_form) = 2.000003144144845270014195556013 x1[1] (numeric) = 1.9494983480177532468672777165365 absolute error = 0.050504796127092023146917839476474 relative error = 2.5252358365009819445085213505379 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 66.549580898786505861390925669582 x2[1] (numeric) = 70.842164997011286153957835030807 absolute error = 4.2925840982247802925669093612258 relative error = 6.4502045546361256600576342525738 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.36 x1[1] (closed_form) = 2.0000031128600813428812681032263 x1[1] (numeric) = 1.9489827249938975279862783655247 absolute error = 0.051020387866183814894989737701578 relative error = 2.551015422832152432630149898573 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 67.873770255334112623013134714818 x2[1] (numeric) = 72.253843414451967017230783428389 absolute error = 4.3800731591178543942176487135711 relative error = 6.4532633779447813388242011154022 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.37 x1[1] (closed_form) = 2.0000030818866060179413434119844 x1[1] (numeric) = 1.9484619198724996151582924167591 absolute error = 0.051541162014106402783050995225294 relative error = 2.5770541296110176234430413364224 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 69.224710011490362366710010430475 x2[1] (numeric) = 73.6940474788795321133776084383 absolute error = 4.4693374673891697466675980078248 relative error = 6.4562747415587878713715421276618 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7833.8MB, alloc=44.3MB, time=42.77 TOP MAIN SOLVE Loop t[1] = 6.38 x1[1] (closed_form) = 2.0000030512213219218506120147832 x1[1] (numeric) = 1.9479358805726133628775222905397 absolute error = 0.052067170648708558973089724243441 relative error = 2.6033545607299558377872008396163 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 70.602940561172036581540833263094 x2[1] (numeric) = 75.163353525494799227377244746359 absolute error = 4.5604129643227626458364114832647 relative error = 6.459239414216061367136484342444 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.39 x1[1] (closed_form) = 2.0000030208611625006449762435771 x1[1] (numeric) = 1.9474045544898704149742787714568 absolute error = 0.05259846637129208567069747212027 relative error = 2.6299193462539974796413325448918 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 72.009013214977193614886762216495 x2[1] (numeric) = 76.662349533034971289881197618752 absolute error = 4.6533363180577776749944354022575 relative error = 6.4621581525712780310446548312463 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7872.3MB, alloc=44.3MB, time=42.97 TOP MAIN SOLVE Loop t[1] = 6.4 x1[1] (closed_form) = 2.0000029908030917130820983498575 x1[1] (numeric) = 1.9468678884912197239422442858507 absolute error = 0.053135102311871989139854064006819 relative error = 2.6567511426838337314558835069959 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 73.443490420716758955109458630421 x2[1] (numeric) = 78.191635358996644031518134287785 absolute error = 4.7481449382798850764086756573647 relative error = 6.465031701353534856600241093109 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.41 x1[1] (closed_form) = 2.0000029610441037270347462280759 x1[1] (numeric) = 1.9463258289096142015560321384235 absolute error = 0.053677132134489525478714089652473 relative error = 2.6838526332214688375825481677272 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 74.906945988401149157691927479521 x2[1] (numeric) = 79.751822979610713697012872126133 absolute error = 4.8448769912095645393209446466114 relative error = 6.4678607935234231354857929920098 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7910.8MB, alloc=44.3MB, time=43.19 TOP MAIN SOLVE Loop t[1] = 6.42 x1[1] (closed_form) = 2.0000029315812226189050758239775 x1[1] (numeric) = 1.9457783215386439694396756580141 absolute error = 0.054224610042578649465400165963414 relative error = 2.7112265280385425412501752537468 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 76.399965319771927064308863750688 x2[1] (numeric) = 81.343536734665180373020358697675 absolute error = 4.9435714148932533087114949469876 relative error = 6.4706461504294451181629998136276 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.43 x1[1] (closed_form) = 2.0000029024115020760297914055979 x1[1] (numeric) = 1.9452253116271156729066317953521 absolute error = 0.054777590784386403123159610245841 relative error = 2.7388755645473495075545944128345 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 77.923145642470304037392037456088 x2[1] (numeric) = 82.9674135772737817304912181534 absolute error = 5.0442679348034776930991806973121 relative error = 6.4733884819637079990873429198083 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.44 x1[1] (closed_form) = 2.0000028735320251020464239649531 x1[1] (numeric) = 1.9446667438735773159981659196242 absolute error = 0.055336129658447786048258045328933 relative error = 2.7668025076745828346307244903858 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 79.477096248936159733387750512059 x2[1] (numeric) = 84.624103328690370404769075005765 absolute error = 5.1470070797542106713813244937065 relative error = 6.4760884867168331007116506778901 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7949.4MB, alloc=44.3MB, time=43.39 TOP MAIN SOLVE Loop t[1] = 6.45 x1[1] (closed_form) = 2.0000028449399037251912641327335 x1[1] (numeric) = 1.9441025624207880701990589996575 absolute error = 0.055900282519115654992205133075955 relative error = 2.7950101501378290275864094465291 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 81.062438740133142207993135650175 x2[1] (numeric) = 86.314268938270966625868920110134 absolute error = 5.2518301981378244178757844599589 relative error = 6.478746852132021696028448545349 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.46 x1[1] (closed_form) = 2.0000028166322787094997791562087 x1[1] (numeric) = 1.9435327108501325038069002323391 absolute error = 0.056470105782146205692878923869579 relative error = 2.8235013127248420849259928530243 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 82.679807274197341643139308210452 x2[1] (numeric) = 88.038586748687476874885318212867 absolute error = 5.3587794744901352317460100024142 relative error = 6.4813642546582223435336447611309 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7987.8MB, alloc=44.3MB, time=43.59 TOP MAIN SOLVE Loop t[1] = 6.47 x1[1] (closed_form) = 2.0000027886063192688806337413727 x1[1] (numeric) = 1.9429571321759786733732472231584 absolute error = 0.057045656430340595507386518214231 relative error = 2.8522788445756246251052027722223 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 84.329848820109000480586458875754 x2[1] (numeric) = 89.797746766499170103924603694119 absolute error = 5.4678979463901696233381448183657 relative error = 6.4839413599023479146975981522975 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.48 x1[1] (closed_form) = 2.0000027608592227840347219231417 x1[1] (numeric) = 1.9423757688399795130210962287548 absolute error = 0.057626992019243271013625694386854 relative error = 2.8813456234673442615652671938784 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 86.013223416488732028533188242103 x2[1] (numeric) = 91.592452938190146256681460999831 absolute error = 5.5792295217014142281482727577283 relative error = 6.4864788227804936757810694889778 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.49 x1[1] (closed_form) = 2.00000273338821452219090163089 x1[1] (numeric) = 1.9417885627053169517728453504278 absolute error = 0.05821417068289757041805628046222 relative error = 2.9107045561021137181213869567012 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 87.730604435621769479359138230302 x2[1] (numeric) = 93.423423431783218322098431932278 absolute error = 5.692818996161448842739293701976 relative error = 6.4889772876681108465704223091171 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8026.4MB, alloc=44.3MB, time=43.81 TOP MAIN SOLVE Loop t[1] = 6.5 x1[1] (closed_form) = 2.000002706190547359630405289226 x1[1] (numeric) = 1.9411954550508881832956868900484 absolute error = 0.058807251139659176334718399177602 relative error = 2.9403585783976634629571111655686 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 89.482678852815858558492289404689 x2[1] (numeric) = 95.291390924142859819086766092914 absolute error = 5.8087120713270012605944766882258 relative error = 6.4914373885490930017232588499216 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.51 x1[1] (closed_form) = 2.000002679263501506972178663838 x1[1] (numeric) = 1.9405963865654335066865586162457 absolute error = 0.059406292698068000285620047592317 relative error = 2.9703106557809359287304274112928 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 91.2701475212005405529608003167 x2[1] (numeric) = 97.197102894082145338347169266833 absolute error = 5.9269553728816047853863689501332 relative error = 6.4938597491637355092611334911869 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8064.8MB, alloc=44.3MB, time=44.02 TOP MAIN SOLVE Loop t[1] = 6.52 x1[1] (closed_form) = 2.0000026526043842371916762573653 x1[1] (numeric) = 1.9399912973416051510758389536707 absolute error = 0.060011355262779086115837303694569 relative error = 3.0005637834846306784584212739464 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 93.093725452077749096893839849885 x2[1] (numeric) = 99.141321921390933468233578177214 absolute error = 6.0475964693131843713397383273287 relative error = 6.4962449831555309186202655132731 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.53 x1[1] (closed_form) = 2.0000026262105296163459149081808 x1[1] (numeric) = 1.9393801268699764909273038022172 absolute error = 0.060622499340553125418611105963616 relative error = 3.0311209868467301719443929892902 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 94.954142100935864690757010128283 x2[1] (numeric) = 101.12482599190491003406604650955 absolute error = 6.1706838909690453433090363812665 relative error = 6.4985936942167658208236290151562 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8103.3MB, alloc=44.3MB, time=44.22 TOP MAIN SOLVE Loop t[1] = 6.54 x1[1] (closed_form) = 2.0000026000792982369778578730513 x1[1] (numeric) = 1.9387628140329910529508826446582 absolute error = 0.061239786046307184026975228393116 relative error = 3.0619853216130360855738537285974 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 96.852141659241636389715092694997 x2[1] (numeric) = 103.14840880873752603179538924001 absolute error = 6.296267149495889642080296545009 relative error = 6.5009064762328872089648963348451 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.55 x1[1] (closed_form) = 2.0000025742080769541734696099162 x1[1] (numeric) = 1.9381392970988507095238627072591 absolute error = 0.061863277109226244649606902657138 relative error = 3.0931598742427464393636661855732 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 98.788483352126691320421623730435 x2[1] (numeric) = 105.21288010979932990406790106057 absolute error = 6.424396757672638583646277330131 relative error = 6.5031839134256087714382342798857 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.56 x1[1] (closed_form) = 2.0000025485942786242450467463139 x1[1] (numeric) = 1.9375095137153424474347901046597 absolute error = 0.06249303487893617681025664165411 relative error = 3.1246477622171040892318501138676 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 100.76394174208771059926159448546 x2[1] (numeric) = 107.31906599173170887567567852286 absolute error = 6.5551242496439982764140840373942 relative error = 6.5054265804947298562934468013573 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8141.9MB, alloc=44.3MB, time=44.44 TOP MAIN SOLVE Loop t[1] = 6.57 x1[1] (closed_form) = 2.0000025232353418460146933487839 x1[1] (numeric) = 1.9368734009036030946217979826095 absolute error = 0.063129122331738751392895366174433 relative error = 3.1564521343511474495946516925008 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 2 h = 0.001 x2[1] (closed_form) = 102.77930703882175577181731082545 x2[1] (numeric) = 109.46780924038461994217068075191 absolute error = 6.6885022015628641703533699264533 relative error = 6.5076350427586420557714121198347 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.58 x1[1] (closed_form) = 2.0000024981287307046720686251778 x1[1] (numeric) = 1.9362308950518213813728394129996 absolute error = 0.063771603076909323299229212178213 relative error = 3.188576171108594621623090276829 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 104.83538541532068403533890268309 x2[1] (numeric) = 111.65996966797050881645635364801 absolute error = 6.8245842526498247811174509649198 relative error = 6.5098098562935004784494971428878 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8180.4MB, alloc=44.3MB, time=44.64 TOP MAIN SOLVE Loop t[1] = 6.59 x1[1] (closed_form) = 2.0000024732719345181807926211933 x1[1] (numeric) = 1.9355819319088767061886967646546 absolute error = 0.064420541363057811992095856538708 relative error = 3.2210230849198924158343700381575 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 106.9329993303510942249696772003 x2[1] (numeric) = 113.89642445702928573057152698444 absolute error = 6.9634251266781915056018497841404 relative error = 6.5119515680710388054103878365678 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.6 x1[1] (closed_form) = 2.0000024486624675862081503403746 x1[1] (numeric) = 1.9349264465779139701800528047017 absolute error = 0.065076002084553616028097535672966 relative error = 3.2537961205034620741856117829991 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 109.07298785744879984192342923606 x2[1] (numeric) = 116.17806851134195153192276153856 absolute error = 7.1050806538931516899993323025056 relative error = 6.514060716095009169289984804416 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.61 x1[1] (closed_form) = 2.000002424297868941552987048764 x1[1] (numeric) = 1.9342643735098538374767089151116 absolute error = 0.065738050788015104076278133652398 relative error = 3.2868985551901738165099713425591 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 111.25620702055943129948899623507 x2[1] (numeric) = 118.50581481393324709475936709471 absolute error = 7.2496077933738157952703708596393 relative error = 6.5161378295362297537492504166027 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8218.9MB, alloc=44.3MB, time=44.86 TOP MAIN SOLVE Loop t[1] = 6.62 x1[1] (closed_form) = 2.0000024001757021040469373465914 x1[1] (numeric) = 1.9335956464968377726695832118807 absolute error = 0.066406753678864331377354134710723 relative error = 3.3203336992510826590203328605824 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 113.48353013645942810304058821594 x2[1] (numeric) = 120.88059479230653480059248568865 absolute error = 7.3970646558471066975518974727107 relative error = 6.5181834288662247885784709859877 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.63 x1[1] (closed_form) = 2.0000023762935548369043779248263 x1[1] (numeric) = 1.9329201986656071997837702796582 absolute error = 0.067082177627947637120607645168125 relative error = 3.3541048962284582787356868632862 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 115.75584816409439392661230680657 x2[1] (numeric) = 123.30335869105701385986981694461 absolute error = 7.5475105269626199332575101380397 relative error = 6.5201980259894433149461213824139 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8257.4MB, alloc=44.3MB, time=45.06 TOP MAIN SOLVE Loop t[1] = 6.64 x1[1] (closed_form) = 2.0000023526490389054967387988246 x1[1] (numeric) = 1.9322379624708161206930424418795 absolute error = 0.067764390178222784803696356945152 relative error = 3.3882155232701420270926374314925 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 118.0740700609745545859865055389 x2[1] (numeric) = 125.77507595201232270877970713695 absolute error = 7.701005891037768122793201598056 relative error = 6.5221821243740447188525773893227 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.65 x1[1] (closed_form) = 2.0000023292397898385270502491726 x1[1] (numeric) = 1.9315488696882765242320611799679 absolute error = 0.068453459551513314294989069204624 relative error = 3.4226689914672645287221711190462 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 120.43912314676988184350008782028 x2[1] (numeric) = 128.29673560205259280019937357172 absolute error = 7.8576124552827109566992857514346 relative error = 6.5241362191812405811838940721932 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8295.9MB, alloc=44.3MB, time=45.28 TOP MAIN SOLVE Loop t[1] = 6.66 x1[1] (closed_form) = 2.000002306063466691580842725399 x1[1] (numeric) = 1.9308528514081359105415810782446 absolute error = 0.069149454655330781039261647154444 relative error = 3.4574687461953576374331345181523 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 122.85195347425032594210223052992 x2[1] (numeric) = 130.86934664876509002099919026065 absolute error = 8.0173931745147640788969597307299 relative error = 6.5260607973931838723638600602603 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.67 x1[1] (closed_form) = 2.0000022831177518130297546055061 x1[1] (numeric) = 1.9301498380279862483933953996102 absolute error = 0.069852445089765564636359205895982 relative error = 3.492618267458894860882413971735 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 125.3135262077195379076246917993 x2[1] (numeric) = 133.49393848409171393797748247239 absolute error = 8.1804122763721760303527906730872 relative error = 6.5279563379393979308934091898685 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.68 x1[1] (closed_form) = 2.000002260400350612264437977012 x1[1] (numeric) = 1.9294397592459036763850132318522 absolute error = 0.070562501154446935879424745159785 relative error = 3.5281210702392947082615340117717 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 127.82482600909346015404755802424 x2[1] (numeric) = 136.17156129613082235526103339267 absolute error = 8.3467352870373622012134753684245 relative error = 6.5298233118217390104041736814489 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8334.5MB, alloc=44.3MB, time=45.48 TOP MAIN SOLVE Loop t[1] = 6.69 x1[1] (closed_form) = 2.0000022379089913302335855369444 x1[1] (numeric) = 1.9287225440534182519683874039535 absolute error = 0.071279693855573078265198132990833 relative error = 3.563980704846421761624575917733 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 130.38685743177822197579730333247 x2[1] (numeric) = 138.90328648925811053602343675598 absolute error = 8.5164290574798885602261334235184 relative error = 6.5316621822378874615359595001608 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.7 x1[1] (closed_form) = 2.0000022156414248122661323222573 x1[1] (numeric) = 1.9279981207284130452817374831891 absolute error = 0.072004094913011766984394839068162 relative error = 3.600200757273620621257594146785 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 133.00064532250489633706085072507 x2[1] (numeric) = 141.69020711273460220564115055948 absolute error = 8.6895617902297058685802998344144 relative error = 6.5334734047033638352146909884267 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8373.0MB, alloc=44.3MB, time=45.69 TOP MAIN SOLVE Loop t[1] = 6.71 x1[1] (closed_form) = 2.0000021935954242831539143015279 x1[1] (numeric) = 1.9272664168279518676879335937796 absolute error = 0.072735776767472415465980707748309 relative error = 3.6367848495563182287800541053772 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 135.66723523128185721871091487072 x2[1] (numeric) = 144.53343829797320444307884471065 absolute error = 8.8662030666913472243679298399312 relative error = 6.5352574271720673549369739628122 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.72 x1[1] (closed_form) = 2.0000021717687851244722919063609 x1[1] (numeric) = 1.9265273591810349177863179826751 absolute error = 0.073474812587750206685973923685821 relative error = 3.673736640134230428509559138233 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 138.3876938296287239318969552574 x2[1] (numeric) = 147.43411770463874214041570516469 absolute error = 9.0464238750100182085187499072924 relative error = 6.5370146901553353095801618715966 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.73 x1[1] (closed_form) = 2.0000021501593246541164703792872 x1[1] (numeric) = 1.9257808738812816204565285328465 absolute error = 0.074221276278043033659941846440686 relative error = 3.7110598242172089880479620763998 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 141.16310933725919155256525459577 x2[1] (numeric) = 150.39340597575992125247139999197 absolute error = 9.2302966385007296999061453962042 relative error = 6.5387456268395229671149102764079 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8411.7MB, alloc=44.3MB, time=45.91 TOP MAIN SOLVE Loop t[1] = 6.74 x1[1] (closed_form) = 2.0000021287648819080314703864714 x1[1] (numeric) = 1.9250268862795399272121309519799 absolute error = 0.074975242485341980819339434491423 relative error = 3.7487581341547656630959101930471 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 143.99459195738342629827321520984 x2[1] (numeric) = 153.41248720203527498293160609668 absolute error = 9.4178952446518486846583908868398 relative error = 6.540450663202104605405593345626 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.75 x1[1] (closed_form) = 2.0000021075833174241139217103962 x1[1] (numeric) = 1.9242653209764213387879360628905 absolute error = 0.075736786606896085325985647505666 relative error = 3.7868353398093102592103571619125 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 146.88327432080415260956883909233 x2[1] (numeric) = 156.4925693955188248022294582384 absolute error = 9.6092950747146721926606191460725 relative error = 6.5421302181262972009910494634622 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8450.1MB, alloc=44.3MB, time=46.13 TOP MAIN SOLVE Loop t[1] = 6.76 x1[1] (closed_form) = 2.0000020866125130282640700218119 x1[1] (numeric) = 1.9234961018147609034570400921392 absolute error = 0.076505984797752124807029929672672 relative error = 3.8252952489331400146223626526459 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 149.83031193898407629213886084174 x2[1] (numeric) = 159.634884972874940236862903887 absolute error = 9.8045730338908639447240430452612 relative error = 6.5437847035142092122366802377198 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.77 x1[1] (closed_form) = 2.0000020658503716225666017533363 x1[1] (numeric) = 1.9227191518720014370711363052005 absolute error = 0.077282913978370185495465448135789 relative error = 3.8641417075492180033677301171118 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 152.83688366626587672997261170357 x2[1] (numeric) = 162.84069124839570921068986830855 absolute error = 10.00380758212983248071725660498 relative error = 6.5454145243985177413769327484933 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8488.6MB, alloc=44.3MB, time=46.33 TOP MAIN SOLVE Loop t[1] = 6.78 x1[1] (closed_form) = 2.0000020452948169755791049806766 x1[1] (numeric) = 1.9219343934525012032397555148897 absolute error = 0.078067651842315772339349465786872 relative error = 3.9033786003357786368882199556797 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 155.90419217142966232945287419986 x2[1] (numeric) = 166.11127093697803588723411372372 absolute error = 10.207078765548373557781239523862 relative error = 6.54702007905267816250877636635 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.79 x1[1] (closed_form) = 2.0000020249437935147071949828012 x1[1] (numeric) = 1.9211417480797642844100430992166 absolute error = 0.078860276864029230297151883584622 relative error = 3.9430098510147987249741094362226 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 159.03346441877651846407842199297 x2[1] (numeric) = 169.44793266726166702027759059377 absolute error = 10.414468248485148556199168600797 relative error = 6.5486017590996710612831587914532 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.8 x1[1] (closed_form) = 2.0000020047952661206455418205954 x1[1] (numeric) = 1.9203411364885928668777057940164 absolute error = 0.079660868306673253767836026578953 relative error = 3.9830394227443729434780240924404 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 162.22595215893058775353934818023 x2[1] (numeric) = 172.85201150513341236168979118739 absolute error = 10.626059346202824608150443007158 relative error = 6.5501599496192920485518650554912 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8527.2MB, alloc=44.3MB, time=46.53 TOP MAIN SOLVE Loop t[1] = 6.81 x1[1] (closed_form) = 2.0000019848472199238642438654598 x1[1] (numeric) = 1.9195324786171606549510895707494 absolute error = 0.080469506230059268913154294710411 relative error = 4.0234713185150329466738940888658 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 165.48293242955601005338208190848 x2[1] (numeric) = 176.32486948780697132642546914617 absolute error = 10.841937058250961273043387237691 relative error = 6.5516950292539906861900300832301 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.82 x1[1] (closed_form) = 2.0000019650976601031201957456096 x1[1] (numeric) = 1.9187156935990066216031994970402 absolute error = 0.081286271498653481516996248569386 relative error = 4.0643095815500497565026379249186 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 168.80570806618901560758501893 x2[1] (numeric) = 179.86789616869200853362827960273 absolute error = 11.062188102502992926043260672724 relative error = 6.553207370313265400308146954654 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8565.8MB, alloc=44.3MB, time=46.75 TOP MAIN SOLVE Loop t[1] = 6.83 x1[1] (closed_form) = 2.0000019455446116859733016789598 x1[1] (numeric) = 1.9178906997549482949800548852475 absolute error = 0.082111245789663390993246793712215 relative error = 4.1055582957097594592771819623798 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 172.19560822338951101250126181423 x2[1] (numeric) = 183.4825091732704367220369806957 absolute error = 11.28690094988092570953571888147 relative error = 6.5546973388766218566212214583207 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.84 x1[1] (closed_form) = 2.0000019261861193512875856476941 x1[1] (numeric) = 1.9170574145849137720872916142057 absolute error = 0.082944511601205579200294033488402 relative error = 4.1472215858999526427535210314234 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 175.65398890642062557534448420131 x2[1] (numeric) = 187.17015476620226860381565356467 absolute error = 11.516165859781643028471169363362 relative error = 6.5561652948951028363383071840827 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.85 x1[1] (closed_form) = 2.0000019070202472336974483609522 x1[1] (numeric) = 1.9162157547596916428495736064209 absolute error = 0.083786152260555590847874754531315 relative error = 4.1893036184843684128519465440568 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 179.18223351366889697492632839581 x2[1] (numeric) = 190.93230842988789123480864341878 absolute error = 11.750074916218994259882315022967 relative error = 6.5576115922913981800077170383143 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8604.3MB, alloc=44.3MB, time=46.98 TOP MAIN SOLVE Loop t[1] = 6.86 x1[1] (closed_form) = 2.0000018880450787300195174683849 x1[1] (numeric) = 1.9153656361125979995283443156686 absolute error = 0.084636251932480730491173152716341 relative error = 4.2318086017013342397739522004916 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 182.78175339002207153128498144128 x2[1] (numeric) = 194.77047545471819923792370253005 absolute error = 11.988722064696127706638721088764 relative error = 6.5590365790585438626906372548448 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.87 x1[1] (closed_form) = 2.0000018692587163075907320482758 x1[1] (numeric) = 1.914506973631059698191915818175 absolute error = 0.085494895627656609398816230100853 relative error = 4.2747407860845932978467199932689 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 186.45398839142587758279151015691 x2[1] (numeric) = 198.6861915412486985530414065996 absolute error = 12.232203149822820970249896442688 relative error = 6.5604405973572197279827929823251 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8642.8MB, alloc=44.3MB, time=47.20 TOP MAIN SOLVE Loop t[1] = 6.88 x1[1] (closed_form) = 2.0000018506592813145134950189591 x1[1] (numeric) = 1.9136396814481130305570285441374 absolute error = 0.08636216921116828395646647482169 relative error = 4.3181044648883613821799497799231 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 190.20040746084560220761839255897 x2[1] (numeric) = 202.68102341453846217173606671753 absolute error = 12.480615953692859964117674158562 relative error = 6.5618239836116558420606344831458 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.89 x1[1] (closed_form) = 2.0000018322449137917889178306446 x1[1] (numeric) = 1.9127636728338169560619813418091 absolute error = 0.087238159411096835726936488835442 relative error = 4.3619039745166559081809998418909 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 194.02250921586286359985840473748 x2[1] (numeric) = 206.75656945089968545615439177133 absolute error = 12.734060235036821856295987033854 relative error = 6.5631870686041578333529583147871 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8681.3MB, alloc=44.3MB, time=47.41 TOP MAIN SOLVE Loop t[1] = 6.9 x1[1] (closed_form) = 2.000001814013772287319370605564 x1[1] (numeric) = 1.9118788601865800354873835233646 absolute error = 0.088122953827192251831987082199387 relative error = 4.4061436949569399271861500474415 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 197.92182254814262564398179854817 x2[1] (numeric) = 210.91446031730855308515818453608 absolute error = 12.99263776916592744117638598791 relative error = 6.5645301775682619598470421369639 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.91 x1[1] (closed_form) = 2.0000017959640336717617378264535 x1[1] (numeric) = 1.9109851550244001988106633883415 absolute error = 0.089016640939633472951074438112059 relative error = 4.4508280502181245229710050293727 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 201.89990723501024948647095358522 x2[1] (numeric) = 215.15635962373319440314392126129 absolute error = 13.25645238872294491667296767607 relative error = 6.5658536302805309956057491490273 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.92 x1[1] (closed_form) = 2.0000017780938929562129647454848 x1[1] (numeric) = 1.9100824679760164712638184577224 absolute error = 0.089919310117876484949146287762392 relative error = 4.4959615087729733897447730535675 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 205.95835456338322107973977822382 x2[1] (numeric) = 219.4839645886396709937695062698 absolute error = 13.525610025256449914029728045986 relative error = 6.567157741151002351934571929755 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8719.8MB, alloc=44.3MB, time=47.63 TOP MAIN SOLVE Loop t[1] = 6.93 x1[1] (closed_form) = 2.0000017604015631117096629163573 x1[1] (numeric) = 1.9091707087719717727596396074844 absolute error = 0.090831051629591338950023308872853 relative error = 4.54154858400495383245497152663 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 210.09878796630713570856516616966 x2[1] (numeric) = 223.89900671794221172903835441269 absolute error = 13.800218751635076020473188243029 relative error = 6.5684428193123001478926083489991 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.94 x1[1] (closed_form) = 2.000001742885274890523724659687 x1[1] (numeric) = 1.9082497862355858969589040320577 absolute error = 0.091751956649688993564820627629297 relative error = 4.5875938346595788748750449174305 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 214.32286367235056238010972960701 x2[1] (numeric) = 228.40325249766928846245877184939 absolute error = 14.080388825318726082349042242379 relative error = 6.5697091687074232205488269938607 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8758.4MB, alloc=44.3MB, time=47.83 TOP MAIN SOLVE Loop t[1] = 6.95 x1[1] (closed_form) = 2.0000017255432766492360758742168 x1[1] (numeric) = 1.9073196082738377672689212144707 absolute error = 0.092682117269438881967154659746064 relative error = 4.6341018653002856100619002118954 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 218.63227136811855468201439429785 x2[1] (numeric) = 232.99850410062261209455539510496 absolute error = 14.366232732504057412541000807109 relative error = 6.5709570881762213185679788016563 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.96 x1[1] (closed_form) = 2.0000017083738341735708744216918 x1[1] (numeric) = 1.9063800818681560579914336124521 absolute error = 0.093621626505678115579440809239672 relative error = 4.6810773267688953813983807083453 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 223.02873487414982234654419947994 x2[1] (numeric) = 237.68660010731172613456023043115 absolute error = 14.657865233161903788016030951219 relative error = 6.5721868715405719543568857688625 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.97 x1[1] (closed_form) = 2.0000016913752305049726373592649 x1[1] (numeric) = 1.9054311130651172596743123425974 absolute error = 0.094570578310113245298325016667421 relative error = 4.7285249166507018406225741711047 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 227.51401283446793140150416741615 x2[1] (numeric) = 242.46941624145258535269054615744 absolute error = 14.955403406984653951186378741284 relative error = 6.5733988076882706010647502331178 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8797.0MB, alloc=44.3MB, time=48.05 TOP MAIN SOLVE Loop t[1] = 6.98 x1[1] (closed_form) = 2.0000016745457657689089545876366 x1[1] (numeric) = 1.9044726069670502584658313941248 absolute error = 0.095529067578715510443123193511849 relative error = 4.7764493797442333920374051617297 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 232.0898994200623625821328702158 x2[1] (numeric) = 247.34886612032433294729800624278 absolute error = 15.258966700261970365165136026974 relative error = 6.5745931806556471121301275131378 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 6.99 x1[1] (closed_form) = 2.0000016578837570048816190432136 x1[1] (numeric) = 1.9035044677225464899216262563375 absolute error = 0.096497190161210514959992786876131 relative error = 4.8248555085357369995364733004776 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 236.75822504658082980721954626104 x2[1] (numeric) = 252.32690202028443317076178847021 absolute error = 15.568676973703603363542242209166 relative error = 6.5757702697089214136891707958184 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8835.6MB, alloc=44.3MB, time=48.25 TOP MAIN SOLVE Loop t[1] = 7 x1[1] (closed_form) = 2.000001641387537998129174405645 x1[1] (numeric) = 1.9025265985168747182718094241343 absolute error = 0.097475042870663279857364981510623 relative error = 4.8737481436784308052223139157425 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 241.52085710651994521620221655451 x2[1] (numeric) = 257.40551565774837994478929607045 absolute error = 15.884658551228434728587079515932 relative error = 6.5769303494243116748598344475655 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.01 x1[1] (closed_form) = 2.0000016250554591130040504352607 x1[1] (numeric) = 1.9015389015622994826181817825486 absolute error = 0.098462723493159630385868652712134 relative error = 4.9231321744765734852783894304525 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 246.37970071620711679594242411158 x2[1] (numeric) = 262.58673898594638807530126162816 absolute error = 16.207038269739271279358837516587 relative error = 6.5780736897669082985192356688565 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8874.1MB, alloc=44.3MB, time=48.45 TOP MAIN SOLVE Loop t[1] = 7.02 x1[1] (closed_form) = 2.0000016088858871280076235150929 x1[1] (numeric) = 1.9005412780883022418980916030589 absolute error = 0.099460330797584886109531912033939 relative error = 4.9730125393743987504338578219255 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 251.33669947787248131612707053744 x2[1] (numeric) = 267.8726450077757847238321364203 absolute error = 16.53594552990330340770506588286 relative error = 6.5792005561683271964907314191288 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.03 x1[1] (closed_form) = 2.000001592877205072466705766061 x1[1] (numeric) = 1.8995336283317042407212884645442 absolute error = 0.10046796454550083174541730151684 relative error = 5.0233942264499638848786767500583 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 256.39383625711571150757434534216 x2[1] (numeric) = 273.2653486050742573308788421137 absolute error = 16.871512347958545823304496771537 relative error = 6.5803112096031559188188403284418 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.04 x1[1] (closed_form) = 2.0000015770278120648351302481322 x1[1] (numeric) = 1.8985158515266901083581248117024 absolute error = 0.10148572550112195647700543642981 relative error = 5.0742822739139617088945407341213 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 261.5531339760786945726855499004 x2[1] (numeric) = 278.76700738464568279238686298311 absolute error = 17.213873408566988219701313082712 relative error = 6.5814059066642062977711334385753 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8912.7MB, alloc=44.3MB, time=48.67 TOP MAIN SOLVE Loop t[1] = 7.05 x1[1] (closed_form) = 2.0000015613361231526042622712247 x1[1] (numeric) = 1.8974878458947311932306902758672 absolute error = 0.10251371544139195937357199535745 relative error = 5.1256817706135458468136552737077 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 266.81665642264136167523180499918 x2[1] (numeric) = 284.37982254137696399110658321952 absolute error = 17.563166118735602315874778220342 relative error = 6.5824848996365873440765218996556 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.06 x1[1] (closed_form) = 2.0000015458005691538064277335791 x1[1] (numeric) = 1.896449508634407625231930622406 absolute error = 0.10355203716616152857449711117308 relative error = 5.1775978565412196832520611183156 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 272.18650907596435753070114605907 x2[1] (numeric) = 290.10603973879113646049876215065 absolute error = 17.91953066282677892979761609158 relative error = 6.5835484365706121963723891551906 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8951.1MB, alloc=44.3MB, time=48.87 TOP MAIN SOLVE Loop t[1] = 7.07 x1[1] (closed_form) = 2.0000015304195965000954086983497 x1[1] (numeric) = 1.8954007359111280880705015935878 absolute error = 0.10460079450846841202490710476189 relative error = 5.2300357233488398969372678808335 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 277.66483994870877817243242875313 x2[1] (numeric) = 295.94795000738898274498213770817 absolute error = 18.283110058680204572549708955039 relative error = 6.5845967613535529755464861512217 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.08 x1[1] (closed_form) = 2.0000015151916670813883141272069 x1[1] (numeric) = 1.8943414228467462736100252473707 absolute error = 0.1056600923449208077782888798362 relative error = 5.2830006148667859729119765889499 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 283.25384044626987601839657745941 x2[1] (numeric) = 301.90789066113850770661035675257 absolute error = 18.654050214868631688213779293159 relative error = 6.5856301137802574342562963961058 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.09 x1[1] (closed_form) = 2.0000015001152580920532898285582 x1[1] (numeric) = 1.8932714635090729798395297341808 absolute error = 0.1067300366061851122137600943774 relative error = 5.3364978276283476104978122029939 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 288.95574624336843717726181191663 x2[1] (numeric) = 307.988246232478887461113747951 absolute error = 19.032499989110450283851936034367 relative error = 6.5866487296226413189974581697691 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8989.6MB, alloc=44.3MB, time=49.09 TOP MAIN SOLVE Loop t[1] = 7.1 x1[1] (closed_form) = 2.0000014851888618786276862632058 x1[1] (numeric) = 1.8921907509012828036761296081703 absolute error = 0.1078107342875790749515566550355 relative error = 5.3905327113993824661969102431124 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 294.77283817835047923271383943649 x2[1] (numeric) = 314.19144942621291070951846139433 absolute error = 19.418611247862431476804621957843 relative error = 6.5876528406980703782592501416716 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.11 x1[1] (closed_form) = 2.0000014704109857890514558973195 x1[1] (numeric) = 1.8910991769512143692603991555623 absolute error = 0.10890229345977141979105674175722 relative error = 5.4451106697132971977470862896918 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 300.70744316555300130930731336444 x2[1] (numeric) = 320.5199820926694869277979552052 absolute error = 19.812538927116485618490641840755 relative error = 6.5886426749366459561119662630489 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9028.2MB, alloc=44.3MB, time=49.30 TOP MAIN SOLVE Loop t[1] = 7.12 x1[1] (closed_form) = 2.00000145578015202340070331682 x1[1] (numeric) = 1.8899966325005630217583517712717 absolute error = 0.11000482327958900164235154554832 relative error = 5.5002371604114053078808674757398 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 306.76193512610074488492130407539 x2[1] (numeric) = 326.97637622052550420860369744097 absolute error = 20.214441094424759323682393365586 relative error = 6.5896184564474081065592307585723 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.13 x1[1] (closed_form) = 2.0000014412948974861064613337963 x1[1] (numeric) = 1.8888830072939649059303994632231 absolute error = 0.11111843400093258017606187057317 relative error = 5.5559176961887158240231150767683 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 312.9387359375062964649401819873 x2[1] (numeric) = 333.56321494968418359950347865751 absolute error = 20.624479012177887134563296670208 relative error = 6.5905804055834701506777906354687 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9066.6MB, alloc=44.3MB, time=49.50 TOP MAIN SOLVE Loop t[1] = 7.14 x1[1] (closed_form) = 2.0000014269537736396439148394147 x1[1] (numeric) = 1.8877581899679713378660527487995 absolute error = 0.11224323698580230177786209061521 relative error = 5.6121578451452073932500858152009 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 319.24031640245338482074049563925 x2[1] (numeric) = 340.28313360461509969705674387797 absolute error = 21.042817202161714876316248238726 relative error = 6.5915287390060985764574706500024 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.15 x1[1] (closed_form) = 2.0000014127553463596774412037808 x1[1] (numeric) = 1.8866220680399123673123463592319 absolute error = 0.1133793447154339923650948445489 relative error = 5.6689632313426429203788757964712 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 325.66919723715089902866941464719 x2[1] (numeric) = 347.1388207485692222447546743681 absolute error = 21.469623511418323216085259720911 relative error = 6.5924636697477521508244004169646 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.16 x1[1] (closed_form) = 2.0000013986981957916469816060794 x1[1] (numeric) = 1.8854745278966484169429431988385 absolute error = 0.11452687080154737470403840724091 relative error = 5.7263395353669804311151201491108 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 332.22795007965298209496685445354 x2[1] (numeric) = 354.13301925909068381945793057385 absolute error = 21.905069179437701724491076120311 relative error = 6.5933854072740940750418152815763 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9105.1MB, alloc=44.3MB, time=49.72 TOP MAIN SOLVE Loop t[1] = 7.17 x1[1] (closed_form) = 2.0000013847809162087814018126152 x1[1] (numeric) = 1.8843154547832088737224698043216 absolute error = 0.11568592999770733505893200829364 relative error = 5.7842924948964364018139898054879 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 338.91919851854854164853559588551 x2[1] (numeric) = 361.26852742525549771572797588194 absolute error = 22.349328906706956067192379996427 relative error = 6.5942941575449909689766948519509 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.18 x1[1] (closed_form) = 2.0000013710021158715246436205085 x1[1] (numeric) = 1.8831447327913164962157518655788 absolute error = 0.1168566382107993753088917549297 relative error = 5.8428279052752583626608976162304 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 345.74561914243166722188662920962 x2[1] (numeric) = 368.54820006707614125809726702143 absolute error = 22.802580924644474036210637811805 relative error = 6.595190123074512417021374628051 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9143.6MB, alloc=44.3MB, time=49.92 TOP MAIN SOLVE Loop t[1] = 7.19 x1[1] (closed_form) = 2.0000013573604168883606094650458 x1[1] (numeric) = 1.8819622448477964902731177057958 absolute error = 0.11803911251262039808749175925004 relative error = 5.9019516200932641520104247474898 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 352.70994261057275628030460073594 x2[1] (numeric) = 375.97494967751978646442855124632 absolute error = 23.265007066947030184123950510386 relative error = 6.5960735029899447491739274408299 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.2 x1[1] (closed_form) = 2.0000013438544550780228625631655 x1[1] (numeric) = 1.8807678727028690939896791153742 absolute error = 0.11923347115158598403318344779133 relative error = 5.9616695517712057762918987513388 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 359.8149547452186317254573438115 x2[1] (numeric) = 383.55174758759700579587465759633 absolute error = 23.736792842378374070417313784831 relative error = 6.596944493089832665299773756486 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.21 x1[1] (closed_form) = 2.0000013304828798330753634482684 x1[1] (numeric) = 1.8795614969183245011873292560591 absolute error = 0.12043983356455533188803419220934 relative error = 6.0219876721520164123554642979759 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 367.06349764595858548465358260708 x2[1] (numeric) = 391.28162515498700927901825660803 absolute error = 24.218127509028423794364674000951 relative error = 6.5978032859010622392937584478884 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9182.1MB, alloc=44.3MB, time=50.13 TOP MAIN SOLVE Loop t[1] = 7.22 x1[1] (closed_form) = 2.0000013172443539848506008563226 x1[1] (numeric) = 1.8783429968555789409019515717753 absolute error = 0.12165832038877504394864928454733 relative error = 6.0829120130979996774516333400199 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 374.45847082660210946160335848332 x2[1] (numeric) = 399.16767497667488426509440839445 absolute error = 24.709204150072774803491049911133 relative error = 6.598650070734998763095402273365 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.23 x1[1] (closed_form) = 2.0000013041375536697316106637996 x1[1] (numeric) = 1.877112250663610718473835126793 absolute error = 0.12288905347394295125777553700659 relative error = 6.1444486670940208862690158484895 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 382.00283237502308009964009553212 x2[1] (numeric) = 407.21305212608591426589988212977 absolute error = 25.21021975106283416625978659765 relative error = 6.5994850337426928086237767890582 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9220.6MB, alloc=44.3MB, time=50.33 TOP MAIN SOLVE Loop t[1] = 7.24 x1[1] (closed_form) = 2.0000012911611681967645109679039 x1[1] (numeric) = 1.8758691352667750118353520801543 absolute error = 0.12413215589439318492915888774967 relative error = 6.2066037878567606146586388833728 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 389.69960013643434969603160380136 x2[1] (numeric) = 415.42097541521185251827551008292 absolute error = 25.721375278777502822243906281567 relative error = 6.6003083579691677990215669850436 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.25 x1[1] (closed_form) = 2.0000012783138999165883144522807 x1[1] (numeric) = 1.8746135263524962044653716938325 absolute error = 0.12538775196140371212294275844814 relative error = 6.2693835909500914959089815094653 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 397.55185292056607008111727654051 x2[1] (numeric) = 423.79472868223402309873220925499 absolute error = 26.24287576166795301761493271448 relative error = 6.6011202234068022894455196298441 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9259.1MB, alloc=44.3MB, time=50.55 TOP MAIN SOLVE Loop t[1] = 7.26 x1[1] (closed_form) = 2.0000012655944640916689109102113 x1[1] (numeric) = 1.8733452983588365242334498926333 absolute error = 0.12665596723562756743546101757801 relative error = 6.3327943544066397877642100172452 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 405.56273173323063608767528352994 x2[1] (numeric) = 432.33766210515832153588439080102 absolute error = 26.774930371927685448209107271077 relative error = 6.6019208070478200623143033865292 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.27 x1[1] (closed_form) = 2.0000012530015887678242432154128 x1[1] (numeric) = 1.8720643244619397449873192926311 absolute error = 0.12793692853964902283692392278171 relative error = 6.3968424193555938668603254045818 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 413.73544103276689120899885530985 x2[1] (numeric) = 441.05319354198759203064822027804 absolute error = 27.317752509220700821649364968195 relative error = 6.6027102829359010427135193774467 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.28 x1[1] (closed_form) = 2.0000012405340146470278291509735 x1[1] (numeric) = 1.8707704765633486952433748302561 absolute error = 0.12923076397066595178445432071742 relative error = 6.4615341906568224319518818558779 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 422.07325001186618988076409106017 x2[1] (numeric) = 449.94480989796747375486581171572 absolute error = 27.871559886101283874101720655558 relative error = 6.6034888222169259368373683787456 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9297.7MB, alloc=44.3MB, time=50.75 TOP MAIN SOLVE Loop t[1] = 7.29 x1[1] (closed_form) = 2.000001228190494961477909342611 x1[1] (numeric) = 1.8694636252771953057204552626058 absolute error = 0.13053760291329965575745408000525 relative error = 6.5268761375413658282780713357564 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 430.57949390529306390285044291822 x2[1] (numeric) = 459.01606852045263850442137948931 absolute error = 28.436574615159574601570936571091 relative error = 6.6042565931888673901814059910299 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.3 x1[1] (closed_form) = 2.0000012159697953489196281061038 x1[1] (numeric) = 1.868143639917261914710998921161 absolute error = 0.13185757605253343420862918494277 relative error = 6.5928747942583645427343935337669 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 439.25757532402359870419693935847 x2[1] (numeric) = 468.27059862195139056509387425831 absolute error = 29.013023297927791860896934899833 relative error = 6.6050137613508403529433735623913 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9336.1MB, alloc=44.3MB, time=50.95 TOP MAIN SOLVE Loop t[1] = 7.31 x1[1] (closed_form) = 2.0000012038706937292077793230811 x1[1] (numeric) = 1.8668103884839125374093285530155 absolute error = 0.13319081538678119179845077006557 relative error = 6.6595367607284895632385745280105 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 448.11096561633519258995518965571 x2[1] (numeric) = 477.71210273191787142792861665081 absolute error = 29.601137115582678837973426995101 relative error = 6.6057604894513242279805496935988 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.32 x1[1] (closed_form) = 2.0000011918919801820977735168957 x1[1] (numeric) = 1.865463737650892792313107432909 absolute error = 0.13453745424108738978466608398678 relative error = 6.7268687032039399458712344595974 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 457.14320625639215302274963262314 x2[1] (numeric) = 487.34435817787261147467541618999 absolute error = 30.201151921480458451925783566845 relative error = 6.6064969375355692619429016763721 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.33 x1[1] (closed_form) = 2.0000011800324568262526051234452 x1[1] (numeric) = 1.8641035527519971646796067936754 absolute error = 0.13589762728045966157299832976978 relative error = 6.7948773549350735900980539517125 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 466.35791026088258269128512293962 x2[1] (numeric) = 497.17121859644390254278530957367 absolute error = 30.813308335561319851500186634049 relative error = 6.6072232629921995230716113731614 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9374.8MB, alloc=44.3MB, time=51.17 TOP MAIN SOLVE Loop t[1] = 7.34 x1[1] (closed_form) = 2.0000011682909376994537205528397 x1[1] (numeric) = 1.8627296977676022737520195510276 absolute error = 0.13727147052333542570170100181214 relative error = 6.8635695168437378857065241386657 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 475.75876363427322900947901060851 x2[1] (numeric) = 507.19661547493443406646028635471 absolute error = 31.437851840661205056981275746204 relative error = 6.607939620599024689832381585761 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.35 x1[1] (closed_form) = 2.0000011566662486400038080289008 x1[1] (numeric) = 1.8613420353110647970713206393318 absolute error = 0.13865912135518384293248738956904 relative error = 6.9329520582033675650831191776779 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 485.3495268432604182562449521056 x2[1] (numeric) = 517.42455972402984606299054830842 absolute error = 32.075032880769427806745596202818 relative error = 6.6086461625680727532427391667378 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9413.3MB, alloc=44.3MB, time=51.38 TOP MAIN SOLVE Loop t[1] = 7.36 x1[1] (closed_form) = 2.0000011451572271693096493866406 x1[1] (numeric) = 1.8599404266149826916547700435485 absolute error = 0.14006071854224447765487934309201 relative error = 7.0030319173259177711829028327317 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 495.13403632100687438919821186113 x2[1] (numeric) = 527.85914328227830947648990732299 absolute error = 32.725106961271435087291695461859 relative error = 6.6093430385898556126435108081802 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.37 x1[1] (closed_form) = 2.000001133762722375633292015055 x1[1] (numeric) = 1.8585247315173183381517273571285 absolute error = 0.14147640224540403748156465792648 relative error = 7.0738161022557010350708453265473 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 505.11620600176613731657214660382 x2[1] (numeric) = 538.50454075298295328722120545687 absolute error = 33.388334751216815970649058853053 relative error = 6.6100303958768794199390062127167 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9451.8MB, alloc=44.3MB, time=51.59 TOP MAIN SOLVE Loop t[1] = 7.38 x1[1] (closed_form) = 2.0000011224815947989999159655514 x1[1] (numeric) = 1.8570948084473822202796293622357 absolute error = 0.14290631403421257872028660331571 relative error = 7.1453116914701975473108364494266 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 515.30002888650845085659218620403 x2[1] (numeric) = 549.36501107416192342772417853866 absolute error = 34.064982187653472571131992334632 relative error = 6.6107083792064114011618685362369 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.39 x1[1] (closed_form) = 2.0000011113127163172508869168088 x1[1] (numeric) = 1.8556505144116757378963939239841 absolute error = 0.14435059690104057935449299282471 relative error = 7.2175258345879088048135761383934 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 525.68957864017439161478699039224 x2[1] (numeric) = 560.44489922224408610335028074536 absolute error = 34.755320582069694488563290353127 relative error = 6.6113771309625147567724564217534 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.4 x1[1] (closed_form) = 2.0000011002549700332306002064136 x1[1] (numeric) = 1.8541917049795917379787597439802 absolute error = 0.14580939527537829525184046243344 relative error = 7.2904657530833254190979384971212 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 536.28901122119516152779241332696 x2[1] (numeric) = 571.74863795018188288577784481857 absolute error = 35.459626728986721357985431491618 relative error = 6.6120367911773631135364809492348 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9490.3MB, alloc=44.3MB, time=51.80 TOP MAIN SOLVE Loop t[1] = 7.41 x1[1] (closed_form) = 2.0000010893072501630958345196612 x1[1] (numeric) = 1.8527182342689713335477435432396 absolute error = 0.1472828550382788295480909764216 relative error = 7.364138741009080583342474444765 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 547.10256654393137391789836697361 x2[1] (numeric) = 583.28074956067661233172123048891 absolute error = 36.178183016745238413822863515291 relative error = 6.6126874975718458712882787051065 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.42 x1[1] (closed_form) = 2.0000010784684619257364460778166 x1[1] (numeric) = 1.8512299549315155662110711958483 absolute error = 0.14877112353694635952537488196827 relative error = 7.4385521657253614141755846595296 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 558.1345701746953307389120143163 x2[1] (numeric) = 595.0458477152254583825027389669 absolute error = 36.911277540530127643590724650595 relative error = 6.6133293855954756575230684257991 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9528.9MB, alloc=44.3MB, time=52.00 TOP MAIN SOLVE Loop t[1] = 7.43 x1[1] (closed_form) = 2.0000010677375214332963453031039 x1[1] (numeric) = 1.8497267181380504534766800680769 absolute error = 0.15027434959947097981966523502698 relative error = 7.5137134686366511099464160058224 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 569.38943506203522253817304737865 x2[1] (numeric) = 607.04863927971391504182116931432 absolute error = 37.659204217678692503648121935671 relative error = 6.6139625884656089717052742648084 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.44 x1[1] (closed_form) = 2.0000010571133555827838079668577 x1[1] (numeric) = 1.8482083735636439473297447450128 absolute error = 0.1517926835497116354540632218449 relative error = 7.5896301659358756003062911589121 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 580.87166330197338788547493811502 x2[1] (numeric) = 619.29392620729187554082022064039 absolute error = 38.422262905318487655345282525369 relative error = 6.6145872372059909695601927103233 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.45 x1[1] (closed_form) = 2.000001046594901948760281761626 x1[1] (numeric) = 1.8466747693725733157566812714215 absolute error = 0.15332627722232863300360049020447 relative error = 7.6663098493560291023857820544628 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 592.58584793890475110949309847825 x2[1] (numeric) = 631.78660745928656822911972687456 absolute error = 39.200759520381817119626628396306 relative error = 6.6152034606846352055551168242103 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9567.4MB, alloc=44.3MB, time=52.22 TOP MAIN SOLVE Loop t[1] = 7.46 x1[1] (closed_form) = 2.0000010361811086770969570884565 x1[1] (numeric) = 1.8451257522031414439417550834416 absolute error = 0.15487528397796723315520200501488 relative error = 7.7437601869293537467494292390552 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 604.53667480287582172911921853922 x2[1] (numeric) = 644.53168096492073674364029296969 absolute error = 39.99500616204491501452107443047 relative error = 6.6158113856510490193894483473218 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.47 x1[1] (closed_form) = 2.0000010258709343797884776279072 x1[1] (numeric) = 1.8435611671523405367537591673915 absolute error = 0.15643985871859384303471846051566 relative error = 7.8219889237541491917233814940075 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 616.72892438397919167685958424839 x2[1] (numeric) = 657.53424562061998469016215467106 absolute error = 40.805321236640793013302570422677 relative error = 6.6164111367728151197112653184982 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9605.9MB, alloc=44.3MB, time=52.42 TOP MAIN SOLVE Loop t[1] = 7.48 x1[1] (closed_form) = 2.0000010156633480308132719781841 x1[1] (numeric) = 1.8419808577603616888802308229774 absolute error = 0.15802015790298634193304115520672 relative error = 7.9010038827692889076964252049994 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 629.16747374461331310545185141366 x2[1] (numeric) = 670.79950332970904133489902337026 absolute error = 41.632029585095728229447171956604 relative error = 6.6170028366715397855644531439145 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.49 x1[1] (closed_form) = 2.0000010055573288630300923067858 x1[1] (numeric) = 1.8403846659949487735533117179929 absolute error = 0.15961633956238008947678058879285 relative error = 7.9808129655365205836682920093105 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 641.85729847037248618596512694846 x2[1] (numeric) = 684.33276108331286097966025929144 absolute error = 42.475462612940374793695132342981 relative error = 6.617586605958177973344508603961 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9644.4MB, alloc=44.3MB, time=52.64 TOP MAIN SOLVE Loop t[1] = 7.5 x1[1] (closed_form) = 2.0000009955518662661004495836002 x1[1] (numeric) = 1.8387724322355950852430853509943 absolute error = 0.16122856331627118085736423260585 relative error = 8.0614241530306288867378442548389 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 654.80347466034743890472108414894 x2[1] (numeric) = 698.13943308329495124711281222001 absolute error = 43.335958422947512342391728071069 relative error = 6.6181625632677454843958463163812 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.51 x1[1] (closed_form) = 2.0000009856459596854267375539123 x1[1] (numeric) = 1.8371439952575811559694917473755 absolute error = 0.16285699038837852945724580653679 relative error = 8.1428455064375395914655832700491 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 668.0111809576326456286548822379 x2[1] (numeric) = 712.22504290808214102548593073717 absolute error = 44.213861950449495396831048499272 relative error = 6.6187308252934282159071481990335 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.52 x1[1] (closed_form) = 2.0000009758386185220959391795014 x1[1] (numeric) = 1.8354991922158521490011487162341 absolute error = 0.16450178362276637309479046326732 relative error = 8.2250851679604448901885302111494 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 681.48570062085261444033898370965 x2[1] (numeric) = 726.59522572224215404122708747721 absolute error = 45.109525101389539600888103767556 relative error = 6.619291506820098385537394799871 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9682.9MB, alloc=44.3MB, time=52.84 TOP MAIN SOLVE Loop t[1] = 7.53 x1[1] (closed_form) = 2.0000009661288620338189098350915 x1[1] (numeric) = 1.8338378586287332176670140001177 absolute error = 0.1661631075001288161518958349738 relative error = 8.3081513616340304974903083441904 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 695.23242363753578137832765379686 x2[1] (numeric) = 741.25573053069785580594045230732 absolute error = 46.023306893162074427612798510465 relative error = 6.6198447207572474883124241754061 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.54 x1[1] (closed_form) = 2.0000009565157192368553311059233 x1[1] (numeric) = 1.8321598283614812008031989043062 absolute error = 0.16784112815423803605213220161703 relative error = 8.3920523941468859722154221815686 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 709.25684888018138931921753657054 x2[1] (numeric) = 756.21242247847989702137127622263 absolute error = 46.955573598298507702153739652094 relative error = 6.6203905781713456128444192789778 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9721.4MB, alloc=44.3MB, time=53.05 TOP MAIN SOLVE Loop t[1] = 7.55 x1[1] (closed_form) = 2.0000009469982288089145276000987 x1[1] (numeric) = 1.8304649336096710099907711208432 absolute error = 0.16953601338855779892375647925549 relative error = 8.4767966556721804987453022162167 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 723.56458630588180700092372447107 x2[1] (numeric) = 771.47128519693769256562106523986 absolute error = 47.906698891055885564697340768789 relative error = 6.6209291883176366129145742705527 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.56 x1[1] (closed_form) = 2.0000009375754389930224367764625 x1[1] (numeric) = 1.8287530048824150472094258041467 absolute error = 0.17124793269302394581301097231585 relative error = 8.5623926207066871958064976216801 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 738.16135920038016644347412059729 x2[1] (numeric) = 787.0384231973472592118554432512 absolute error = 48.877063996967092768381322653904 relative error = 6.6214606586713784999881654052283 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.57 x1[1] (closed_form) = 2.0000009282464075023451184048928 x1[1] (numeric) = 1.8270238709854139748348064000737 absolute error = 0.17297705726099352751031200481918 relative error = 8.6488488489182398559411091822656 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 753.05300646746097174346266372401 x2[1] (numeric) = 802.92006431287339468136558606001 absolute error = 49.867057845412422937902922335997 relative error = 6.6219850949585382923632444020446 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9760.1MB, alloc=44.3MB, time=53.26 TOP MAIN SOLVE Loop t[1] = 7.58 x1[1] (closed_form) = 2.000000919010201425959285930632 x1[1] (numeric) = 1.8252773590038371430423505551029 absolute error = 0.17472356000636428291693537552917 relative error = 8.7361739860017068620196475510554 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 768.24548496458946601129907930218 x2[1] (numeric) = 819.1225621898630230900056053074 absolute error = 50.877077225273557078706526005217 relative error = 6.6225026011859504274472995521548 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.59 x1[1] (closed_form) = 2.0000009098658971355604367172707 x1[1] (numeric) = 1.8235132942850309626461351321766 absolute error = 0.17648761558086617291430158509405 relative error = 8.8243767645435678789013034166106 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 783.74487188573404334030822158415 x2[1] (numeric) = 835.65239882946626504800062770346 absolute error = 51.90752694373222170769240611931 relative error = 6.623013279670947715164998523867 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9798.6MB, alloc=44.3MB, time=53.47 TOP MAIN SOLVE Loop t[1] = 7.6 x1[1] (closed_form) = 2.0000009008125801930992519036645 x1[1] (numeric) = 1.8217315004210534941955944803695 absolute error = 0.17826940039152669890365742329493 relative error = 8.9134660048951797786312994813997 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 799.55736719232486654386042021897 x2[1] (numeric) = 852.51618718060192251145471950029 absolute error = 52.958819988277055967594299281319 relative error = 6.6235172310704736827755864776091 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.61 x1[1] (closed_form) = 2.0000008918493452593370294378002 x1[1] (numeric) = 1.8199317992310335067744670726098 absolute error = 0.18006909261831175256256236519043 relative error = 9.0034506160548191264955885014455 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 815.68929609332110652084604516529 x2[1] (numeric) = 869.72067378530460701259575318048 absolute error = 54.031377691983500491749708015191 relative error = 6.624014554409685034468406256013 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9837.1MB, alloc=44.3MB, time=53.69 TOP MAIN SOLVE Loop t[1] = 7.62 x1[1] (closed_form) = 2.0000008829752960033110057547101 x1[1] (numeric) = 1.81811401074335224239314957278 absolute error = 0.18188687223194376091785618193011 relative error = 9.0943395965585894329165607907722 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 832.147111575378863213249147698 x2[1] (numeric) = 887.27274147751169333056895742298 absolute error = 55.125629902132830117319809724973 relative error = 6.6245053471100528230539135094186 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.63 x1[1] (closed_form) = 2.0000008741895450127005125551568 x1[1] (numeric) = 1.8162779531776461041360489884366 absolute error = 0.18372292101189890856446356672022 relative error = 9.1861420353802822626573956270908 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 848.93739698413186906022982416536 x2[1] (numeric) = 905.17941213636965738709342452026 absolute error = 56.242015152237788326863600354908 relative error = 6.6249897050169708059170336213046 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.64 x1[1] (closed_form) = 2.0000008654912137050850052260707 x1[1] (numeric) = 1.8144234429266284683177498344917 absolute error = 0.18557742256458523676725539157897 relative error = 9.278867112840282188195883042471 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 866.06686865761752164763636100034 x2[1] (numeric) = 923.44784949516116571250827798356 absolute error = 57.380980837543644064871916983217 relative error = 6.6254677224268793331884131166029 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9875.6MB, alloc=44.3MB, time=53.89 TOP MAIN SOLVE Loop t[1] = 7.65 x1[1] (closed_form) = 2.0000008568794322400850886316315 x1[1] (numeric) = 1.8125502945377288028140633842114 absolute error = 0.18745056234170343727102524742009 relative error = 9.3725241015236064785204956097246 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 883.54237861290165107882667309355 x2[1] (numeric) = 942.08536200697653295138085558521 absolute error = 58.542983394074881872554182491657 relative error = 6.6259394921139129928529571102172 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.66 x1[1] (closed_form) = 2.0000008483533394323777543043551 x1[1] (numeric) = 1.8106583206945472554644913267259 absolute error = 0.18934252765879217691326297762923 relative error = 9.46712236720717132808264399069 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 901.37091728697670779589294777119 x2[1] (numeric) = 961.09940576827586246288239657427 absolute error = 59.728488481299154666989448803077 relative error = 6.6264051053560801152872784045754 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9914.0MB, alloc=44.3MB, time=54.11 TOP MAIN SOLVE Loop t[1] = 7.67 x1[1] (closed_form) = 2.0000008399120826655771304874194 x1[1] (numeric) = 1.8087473321981228579894895162406 absolute error = 0.19125350771395980758764097117883 relative error = 9.5626713697963773533007540730617 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 919.55961633302976667221877887451 x2[1] (numeric) = 980.49758750151134219930262299866 absolute error = 60.937971168481575527083844124151 relative error = 6.6268646519609821185290549256171 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.68 x1[1] (closed_form) = 2.0000008315548178069721330314649 x1[1] (numeric) = 1.8068171379480134722273136572187 absolute error = 0.19318369360680433474481937424618 relative error = 9.6591806642711080159463244270007 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 938.11575147319889186208062569941 x2[1] (numeric) = 1000.2876675980027929795416104226 absolute error = 62.171916124803901117460984723228 relative error = 6.6273182202910805554601361961673 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.69 x1[1] (closed_form) = 2.0000008232807091231124908399089 x1[1] (numeric) = 1.8048675449231855866693038460801 memory used=9952.5MB, alloc=44.3MB, time=54.31 absolute error = 0.1951332783575235364431869938288 relative error = 9.756659901641235574042654790054 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 957.0467454089590029904963923128 x2[1] (numeric) = 1020.477563222283668463482230679 absolute error = 63.430817813324665472985838366194 relative error = 6.6277658972885196050575963690462 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.7 x1[1] (closed_form) = 2.0000008150889291962347043949731 x1[1] (numeric) = 1.8028983581627120522573362752329 absolute error = 0.19710245692621714397736811974014 relative error = 9.855118829911730111667610176375 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 976.3601707903014358354635757107 x2[1] (numeric) = 1041.0753514791592952190146834201 absolute error = 64.715180688857859383551107709374 relative error = 6.6282077684995116319566505550702 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.71 x1[1] (closed_form) = 2.0000008069786588415195798906299 x1[1] (numeric) = 1.800909380746275827200936570821 absolute error = 0.19909142623238301431864331980889 relative error = 9.9545672950574681593676778634331 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 996.06375324489490891645272396452 x2[1] (numeric) = 1062.0892726447442270921269774389 absolute error = 66.02551939984931817567425347436 relative error = 6.6286439180982933217981936689399 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9991.1MB, alloc=44.3MB, time=54.52 TOP MAIN SOLVE Loop t[1] = 7.72 x1[1] (closed_form) = 2.0000007989490870251730646569306 x1[1] (numeric) = 1.7989004137744777811722895420461 absolute error = 0.20110038517460924400077511488447 relative error = 10.055015242007838386857718325717 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1016.165374468439600765147148233 x2[1] (numeric) = 1083.5277334627711806765622591661 absolute error = 67.362358994331579911415110933091 relative error = 6.6290744289106597842214566480071 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.73 x1[1] (closed_form) = 2.0000007909994107833221918909905 x1[1] (numeric) = 1.796871256348946589643154625169 absolute error = 0.20312953465046419367903726582149 relative error = 10.156472715641242829396203682941 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1036.6730753774505207146117111345 x2[1] (numeric) = 1105.3993105074901282704600182857 absolute error = 68.726235130039607555848307151209 relative error = 6.6294993824370839009267763916642 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10029.6MB, alloc=44.3MB, time=54.73 TOP MAIN SOLVE Loop t[1] = 7.74 x1[1] (closed_form) = 2.000000783128835141718024221517 x1[1] (numeric) = 1.7948217055522487293365455704291 absolute error = 0.20517907757658641238147865108793 relative error = 10.258949861789593098787350765494 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1057.595059325731328592882523714 x2[1] (numeric) = 1127.7127536145027617473367457952 absolute error = 70.117694288771433154454222081194 relative error = 6.6299188588754280829908088734831 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.75 x1[1] (closed_form) = 2.0000007753365730362375663343241 x1[1] (numeric) = 1.7927515564275965657759778135912 absolute error = 0.20724921890897647046158852073291 relative error = 10.362456928252902029468347458208 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1078.939695385825235735748419471 x2[1] (numeric) = 1150.4769893809047159129026251401 absolute error = 71.5372939950794801771542056691 relative error = 6.6303329371432554895810250172583 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.76 x1[1] (closed_form) = 2.0000007676218452341766967838447 x1[1] (numeric) = 1.790660601958352503724128473445 absolute error = 0.20934016566349273045256831039964 relative error = 10.467004265824072219691792076906 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1100.7155216967556114323953464933 x2[1] (numeric) = 1173.7011247361356640379832946644 absolute error = 72.985603039380052605587948171009 relative error = 6.6307416948997476494007244104472 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10068.1MB, alloc=44.3MB, time=54.95 TOP MAIN SOLVE Loop t[1] = 7.77 x1[1] (closed_form) = 2.0000007599838802563262482182353 x1[1] (numeric) = 1.7885486330473271509088729096924 absolute error = 0.21145212693655310541737530854294 relative error = 10.572602329323983947511472193908 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1122.931248879395435683632448385 x2[1] (numeric) = 1197.3944505849656824412458846803 absolute error = 74.463201705570246757613436295272 relative error = 6.6311452085672353166112338580137 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.78 x1[1] (closed_form) = 2.0000007524219142998234435611568 x1[1] (numeric) = 1.786415438495869424835818857142 absolute error = 0.21358531392604487498762470401482 relative error = 10.679261678646985971225672209037 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1145.5957635208317915926735720145 x2[1] (numeric) = 1221.5664455240751365575760821349 absolute error = 75.970682003243344964902510120431 relative error = 6.63154355335234928463409677811 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10106.7MB, alloc=44.3MB, time=55.16 TOP MAIN SOLVE Loop t[1] = 7.79 x1[1] (closed_form) = 2.0000007449351911617709732295592 x1[1] (numeric) = 1.7842608049827465116805944205545 absolute error = 0.2157399399524446500903788090047 relative error = 10.786992979816893764229313526098 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1168.7181317291191896442470511558 x2[1] (numeric) = 1246.2267796337147794114367849904 absolute error = 77.508647904595589767189733834599 relative error = 6.631936803266797774141169296872 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.8 x1[1] (closed_form) = 2.0000007375229621636160752315421 x1[1] (numeric) = 1.782084517042811565239179066013 absolute error = 0.21791622048015059837689616552914 relative error = 10.895807006053600784978428019635 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1192.3076027598436725990921801889 x2[1] (numeric) = 1271.3853183459627865951542519308 absolute error = 79.077715586119113996062071741879 relative error = 6.6323250311477769057015472529806 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=10145.2MB, alloc=44.3MB, time=55.37 t[1] = 7.81 x1[1] (closed_form) = 2.0000007301844860762820559892815 x1[1] (numeric) = 1.7798863570454570126883956651198 absolute error = 0.2201143731390290635936603241617 relative error = 11.005714638850409444082820658084 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1216.3736127159483750006367500247 x2[1] (numeric) = 1297.0521263911260917435066818791 absolute error = 80.678513675177716742869931854338 relative error = 6.6327083086780206629768144924042 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.82 x1[1] (closed_form) = 2.0000007229190290460447649767158 x1[1] (numeric) = 1.7776661051728513124691840028405 absolute error = 0.22233461774617773357558097387531 relative error = 11.11672686906218950252142280722 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1240.9257883223005168493272724031 x2[1] (numeric) = 1323.2374718238646453546075331738 absolute error = 82.311683501564128505280260770729 relative error = 6.6330867064054966490446828895178 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.83 x1[1] (closed_form) = 2.0000007157258645211466107576851 x1[1] (numeric) = 1.775423539397956987950307980794 absolute error = 0.22457717632790753319630277689111 relative error = 11.228854798004472717726972629672 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1265.973950776509708570316285567 x2[1] (numeric) = 1349.9518301306491101368514995775 absolute error = 83.97787935413940156653521401046 relative error = 6.6334602937627538363890037098162 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10183.6MB, alloc=44.3MB, time=55.58 TOP MAIN SOLVE Loop t[1] = 7.84 x1[1] (closed_form) = 2.0000007086042731791407797649707 x1[1] (numeric) = 1.7731584354623277386575445203674 absolute error = 0.22684227314194544048323524460334 relative error = 11.342109638563593647920559238048 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1291.528119677537945941426146734 x2[1] (numeric) = 1377.2058884201950406191917650202 absolute error = 85.677768742657094677765618286251 relative error = 6.6338291390859284103236024941522 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.85 x1[1] (closed_form) = 2.0000007015535428549583921815683 x1[1] (numeric) = 1.7708705668536824087609746155632 absolute error = 0.22913013469986044619741756600509 relative error = 11.456502716317987629701597152087 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1317.5985170336727913615291534048 x2[1] (numeric) = 1405.0105496985497865615096043742 absolute error = 87.412032664876995199980450969411 relative error = 6.6341933096334137061196362744864 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10222.1MB, alloc=44.3MB, time=55.78 TOP MAIN SOLVE Loop t[1] = 7.86 x1[1] (closed_form) = 2.0000006945729684696914015798372 x1[1] (numeric) = 1.7685597047832535701985368427952 absolute error = 0.23144098978971489949286473704202 relative error = 11.572045470670758059625420577649 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1344.1955713514669841722098929176 x2[1] (numeric) = 1433.3769372305422220204938858115 absolute error = 89.181365879075237848283992893877 relative error = 6.6345528716042001418814347396872 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.87 x1[1] (closed_form) = 2.0000006876618519600841165491424 x1[1] (numeric) = 1.7662256181629084552752794393322 absolute error = 0.23377506949894350480883710981024 relative error = 11.688749455993626237440476659315 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1371.3299218072801103967637782681 x2[1] (numeric) = 1462.3163989893399483096575695505 absolute error = 90.98647718205983791289379128241 relative error = 6.6349078901558909522633922316282 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.88 x1[1] (closed_form) = 2.0000006808195022087262934053947 x1[1] (numeric) = 1.7638680735820399508125049225449 absolute error = 0.23613260723746225791378848284976 relative error = 11.806626342782378166922748076751 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1399.0124225030910041857281044074 x2[1] (numeric) = 1491.8405121958938633589049392898 absolute error = 92.828089692802859173176834882404 relative error = 6.635258429422399432438886126871 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10260.7MB, alloc=44.3MB, time=56.00 TOP MAIN SOLVE Loop t[1] = 7.89 x1[1] (closed_form) = 2.0000006740452349749408192335871 x1[1] (numeric) = 1.7614868352842253429269645953496 absolute error = 0.23851383876100963201385463823744 relative error = 11.925687918823923859950375671511 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1427.2541468082832626744492748122 x2[1] (numeric) = 1521.961087950085946227613935624 absolute error = 94.706941141802683553164660811838 relative error = 6.635604552531333307319053294899 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.9 x1[1] (closed_form) = 2.0000006673383728263590739740386 x1[1] (numeric) = 1.7590816651436504782951297464451 absolute error = 0.24091900219472234806394422759346 relative error = 12.045946090375085850721452697555 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1456.0663917891406463498780909071 x2[1] (numeric) = 1552.690175955432788138501776286 absolute error = 96.623784166292141788623685378857 relative error = 6.6359463216210717478714334126729 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10299.2MB, alloc=44.3MB, time=56.20 TOP MAIN SOLVE Loop t[1] = 7.91 x1[1] (closed_form) = 2.0000006606982450711771290315325 x1[1] (numeric) = 1.7566523226412969842990193746947 absolute error = 0.24334833805694808687810965683779 relative error = 12.167412883353234799948750753175 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1485.4606827278242221474693868592 x2[1] (numeric) = 1584.0400693392348250511439274496 absolute error = 98.579386611410602903674540590406 relative error = 6.6362837978575404645021332856371 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.92 x1[1] (closed_form) = 2.0000006541241876910860079707575 x1[1] (numeric) = 1.7541985648408901667557549710675 absolute error = 0.24580208928329752433025299968999 relative error = 12.290100444538891253584007530467 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1515.4487777326389003892601110085 x2[1] (numeric) = 1616.023309570099406453886619788 absolute error = 100.5745318374605060646265087795 relative error = 6.6366170414506902168357436385793 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for 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=10337.8MB, alloc=44.3MB, time=56.42 t[1] = 7.93 x1[1] (closed_form) = 2.0000006476155432748693022682284 x1[1] (numeric) = 1.7517201463646051800005718282459 absolute error = 0.24828050125093809486873043998249 relative error = 12.414021042790413817249831085195 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1546.0426724414335336489445400963 x2[1] (numeric) = 1648.6526914748047859934151623509 absolute error = 102.61001903337125234447062225467 relative error = 6.6369461116706839898495697647984 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.94 x1[1] (closed_form) = 2.0000006411716609526615018269276 x1[1] (numeric) = 1.7492168193685290399200502532845 absolute error = 0.25078382180313191274145157364311 relative error = 12.539187070270895216208917924259 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1577.2546048200160002963334608236 x2[1] (numeric) = 1681.9412683565118573633206282825 absolute error = 104.68666353649585706698716745896 relative error = 6.6372710668637979981870365559236 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.95 x1[1] (closed_form) = 2.0000006347918963308604660319326 x1[1] (numeric) = 1.746688333517876026116421615807 absolute error = 0.25331230127402030474404441612563 relative error = 12.665611043687388931499009001645 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1609.0970600575027027343392278923 x2[1] (numeric) = 1715.9023572163709994323076237873 absolute error = 106.80529715886829669796839589496 relative error = 6.6375919644680415935830465360273 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10376.3MB, alloc=44.3MB, time=56.63 TOP MAIN SOLVE Loop t[1] = 7.96 x1[1] (closed_form) = 2.0000006284756114276875265398965 x1[1] (numeric) = 1.7441344359619539947225117619713 absolute error = 0.25586619251365743296501477792524 relative error = 12.793305605542590335929899596391 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1641.5827755605606853999816807928 x2[1] (numeric) = 1750.5495440806127541259810612287 absolute error = 108.9667685200520687259993804359 relative error = 6.6379088610285010646747251225689 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.97 x1[1] (closed_form) = 2.0000006222221746093887777589587 x1[1] (numeric) = 1.7415548713088790984777418130166 absolute error = 0.25844575091329551091103594594217 relative error = 12.922283525399097499099183834538 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1674.724746048540135967401322123 x2[1] (numeric) = 1785.8966894352532556278160227513 absolute error = 111.17194338671311966041470062825 relative error = 6.6382218122124122340370017835925 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10414.7MB, alloc=44.3MB, time=56.84 TOP MAIN SOLVE Loop t[1] = 7.98 x1[1] (closed_form) = 2.0000006160309605270711750949701 x1[1] (numeric) = 1.738949381600036385516122811634 absolute error = 0.26105123443092414155505228333604 relative error = 13.052557701156378088560799385568 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1708.5362287515353906893699766221 x2[1] (numeric) = 1821.9579337705883769135464065737 absolute error = 113.42170501905298622417642995163 relative error = 6.6385308728239666740660057732287 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 7.99 x1[1] (closed_form) = 2.0000006099013500541671245212185 x1[1] (numeric) = 1.736317706284283722904840110338 absolute error = 0.26368290361706633126228441088046 relative error = 13.184141160340570064900641399034 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 x2[1] (closed_form) = 1743.0307487134537375878428710633 x2[1] (numeric) = 1858.7477032376944766983698426392 absolute error = 115.71695452424073911052697157587 relative error = 6.6388360968188562813260238940642 % Desired digits = 12 Estimated correct digits = 11 Correct digits = 1 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; Iterations = 6500 Total Elapsed Time = 56 Seconds Elapsed Time(since restart) = 56 Seconds Time to Timeout = 2 Minutes 3 Seconds Percent Done = 100 % > quit memory used=10449.8MB, alloc=44.3MB, time=57.03