|\^/| Maple 18 (X86 64 WINDOWS) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 21 # Begin Function number 22 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 22 # Begin Function number 23 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 23 # Begin Function number 24 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 24 # Begin Function number 25 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 27 # Begin Function number 28 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 28 # Begin Function number 29 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 29 # Begin Function number 30 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 30 # Begin Function number 31 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 31 # Begin Function number 32 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 32 # Begin Function number 33 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 35 # Begin Function number 36 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 36 # Begin Function number 37 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 37 # Begin Function number 38 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 38 # Begin Function number 39 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 39 # Begin Function number 40 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 40 # Begin Function number 41 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 41 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return((c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *c( x)) ; > end; exact_soln_y := proc(x) return (c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02)))*c(x) end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if (rad_given < glob_least_given_sing) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])* (array_x[1] - array_given_rad_poles[1, 1]) + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if rad_given < glob_least_given_sing then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if array_rad_test_poles[1, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if array_rad_test_poles[1, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if array_rad_test_poles[1, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 3 > if (iter >= 0) then # if number 4 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5 > relerr := abserr*glob__100/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 6 > glob_good_digits := -int_trunc(log10(c(relerr))) + 3; > else > glob_good_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 5; > if (glob_good_digits < glob_min_good_digits) then # if number 5 > glob_min_good_digits := glob_good_digits; > fi;# end if 5; > if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5 > glob_min_apfp_est_good_digits := glob_apfp_est_good_digits; > fi;# end if 5; > if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5 > est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*27*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 6 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 5; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > array_est_rel_error[1] := est_rel_err; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," "); > omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," "); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_float(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if c(glob_prec) < c(float_abs(closed_form_val_y)) then relerr := abserr*glob__100/float_abs(closed_form_val_y); if c(glob_prec) < c(relerr) then glob_good_digits := -int_trunc(log10(c(relerr))) + 3 else glob_good_digits := Digits end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits end if; if glob_prec < evalf(float_abs(numeric_val)) then est_rel_err := evalf(array_max_est_error[1]*100.0* sqrt(glob_iter)*27*ATS_MAX_TERMS/float_abs(numeric_val)) ; if glob_prec < evalf(est_rel_err) then glob_est_digits := -int_trunc(log10(est_rel_err)) + 3 else glob_est_digits := Digits end if else relerr := glob__m1; glob_est_digits := -16 end if; array_est_digits[1] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; array_est_rel_error[1] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr((glob_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr((left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(glob_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre sin ID_CONST $eq_no = 1 > array_tmp1[1] := sin(array_const_0D1[1]); > #emit pre add CONST CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre cos ID_CONST $eq_no = 1 > array_tmp3[1] := cos(array_const_0D05[1]); > #emit pre add CONST CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp2[1] + array_tmp3[1]; > #emit pre tan ID_CONST $eq_no = 1 > array_tmp5[1] := tan(array_const_0D02[1]); > #emit pre sub CONST CONST $eq_no = 1 i = 1 > array_tmp6[1] := array_tmp4[1] - array_tmp5[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp6[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp6[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp6[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp6[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp6[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (false) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp6[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := sin(array_const_0D1[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := cos(array_const_0D05[1]); array_tmp4[1] := array_tmp2[1] + array_tmp3[1]; array_tmp5[1] := tan(array_const_0D02[1]); array_tmp6[1] := array_tmp4[1] - array_tmp5[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp6[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp6[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp6[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp6[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp6[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6 end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D05, > array_const_0D02, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1_g:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3_g:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_tmp5_g:= Array(0..(30),[]); > array_tmp5:= Array(0..(30),[]); > array_tmp6:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(30) ,(0..30+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp5_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp6[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=30) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1_g); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3_g); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5_g); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_tmp6); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_0D1); > array_const_0D1[1] := c(0.1); > zero_ats_ar(array_const_0D05); > array_const_0D05[1] := c(0.05); > zero_ats_ar(array_const_0D02); > array_const_0D02[1] := c(0.02); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(-5.0);"); > omniout_str(ALWAYS,"x_end := c(5.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 3;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=100000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.005);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return((c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *c( x)) ;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(-5.0); > x_end := c(5.0) ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=100000; > glob_upper_ratio_limit:=c(1.0000001); > glob_lower_ratio_limit:=c(0.9999999); > glob_look_poles:=true; > glob_h:=c(0.005); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > glob_check_sign := c(my_check_sign(x_start,x_end)); > glob__pi := arccos(glob__m1); > glob_prec = expt(10.0,c(-Digits)); > if (glob_optimize) then # if number 9 > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > found_h := false; > glob_min_pole_est := glob_larger_float; > last_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > glob_min_h := float_abs(glob_min_h) * glob_check_sign; > glob_max_h := float_abs(glob_max_h) * glob_check_sign; > glob_h := float_abs(glob_min_h) * glob_check_sign; > glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign)); > display_max := c(x_end) - c(x_start)/glob__10; > if ((glob_display_interval) > (display_max)) then # if number 10 > glob_display_interval := c(display_max); > fi;# end if 10; > chk_data(); > min_value := glob_larger_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := glob_small_float; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > glob_h := glob_check_sign * float_abs(glob_min_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 10; > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if ( not found_h) then # if number 10 > est_answer := est_size_answer(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (estimated_step_error < est_needed_step_err) then # if number 11 > omniout_str(ALWAYS,"Double H and LOOP"); > glob_h := glob_h*glob__2; > else > omniout_str(ALWAYS,"Found H for OPTIMAL"); > found_h := true; > glob_h_reason := 3; > glob_h := glob_h/glob__2; > fi;# end if 11; > fi;# end if 10; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 10 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 10; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MAX H"); > glob_h := glob_check_sign * float_abs(glob_max_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 9; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > atomall(); > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (reached_interval()) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2015-05-02T21:19:53-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"add_sub_sin_c_cos_c_tan_c") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"add_sub_sin_c_cos_c_tan_c diffeq.mxt") > ; > logitem_str(html_log_file,"add_sub_sin_c_cos_c_tan_c maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > fi;# end if 14 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1_g := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3_g := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_tmp5_g := Array(0 .. 30, []); array_tmp5 := Array(0 .. 30, []); array_tmp6 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp5_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 30 do term := 1; while term <= 30 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1_g); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3_g); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5_g); zero_ats_ar(array_tmp5); zero_ats_ar(array_tmp6); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_0D1); array_const_0D1[1] := c(0.1); zero_ats_ar(array_const_0D05); array_const_0D05[1] := c(0.05); zero_ats_ar(array_const_0D02); array_const_0D02[1] := c(0.02); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/add_sub_sin_c_cos_c_tan_cpost\ ode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( 0.1 ) + \ cos ( 0.05 ) - tan ( 0.02 ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(-5.0);"); omniout_str(ALWAYS, "x_end := c(5.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 3;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=100000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.005);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return((c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *c( x)) ;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(-5.0); x_end := c(5.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 3; glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 100000; glob_upper_ratio_limit := c(1.0000001); glob_lower_ratio_limit := c(0.9999999); glob_look_poles := true; glob_h := c(0.005); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; glob_check_sign := c(my_check_sign(x_start, x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0, c(-Digits)); if glob_optimize then omniout_str(ALWAYS, "START of Optimize"); found_h := false; glob_min_pole_est := glob_larger_float; last_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; glob_min_h := float_abs(glob_min_h)*glob_check_sign; glob_max_h := float_abs(glob_max_h)*glob_check_sign; glob_h := float_abs(glob_min_h)*glob_check_sign; glob_display_interval := c(float_abs(c(glob_display_interval))*glob_check_sign); display_max := c(x_end) - c(x_start)/glob__10; if display_max < glob_display_interval then glob_display_interval := c(display_max) end if; chk_data(); min_value := glob_larger_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := glob_small_float; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]*expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); glob_h := float_abs(glob_min_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if; if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"); glob_h_reason := 2; glob_h := glob_display_interval; found_h := true end if; if glob_look_poles then check_for_pole() end if; if not found_h then est_answer := est_size_answer(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if estimated_step_error < est_needed_step_err then omniout_str(ALWAYS, "Double H and LOOP"); glob_h := glob_h*glob__2 else omniout_str(ALWAYS, "Found H for OPTIMAL"); found_h := true; glob_h_reason := 3; glob_h := glob_h/glob__2 end if end if; opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR MAX H"); glob_h := float_abs(glob_max_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if else found_h := true; glob_h := glob_check_sign*glob_h end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec - glob_orig_start_sec < glob_max_sec do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); track_estimated_error(); atomall(); track_estimated_error(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin ( 0.1 ) +\ cos ( 0.05 ) - tan ( 0.02 ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2015-05-02T21:19:53-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c"); logitem_str(html_log_file, "diff ( y , x , 1 ) = si\ n ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; "); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 308.maple.seems.ok "); logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c diffeq.mxt\ "); logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c maple res\ ults"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode################# diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(-5.0); x_end := c(5.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 3; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=100000; glob_upper_ratio_limit:=c(1.0000001); glob_lower_ratio_limit:=c(0.9999999); glob_look_poles:=true; glob_h:=c(0.005); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return((c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *c( x)) ; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = -5.392905049741959874861393478458 y[1] (numeric) = -5.392905049741959874861393478458 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.99 y[1] (closed_form) = -5.3821192396424759551116706915011 y[1] (numeric) = -5.382119239642475955111670691501 absolute error = 1e-31 relative error = 1.8580041717292538407038400857301e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.98 y[1] (closed_form) = -5.3713334295429920353619479045442 y[1] (numeric) = -5.371333429542992035361947904544 absolute error = 2e-31 relative error = 3.7234702076019986606876152722061e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.97 y[1] (closed_form) = -5.3605476194435081156122251175873 y[1] (numeric) = -5.360547619443508115612225117587 memory used=4.3MB, alloc=40.3MB, time=0.13 absolute error = 3e-31 relative error = 5.5964431490516961761240414654687e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.96 y[1] (closed_form) = -5.3497618093440241958625023306303 y[1] (numeric) = -5.34976180934402419586250233063 absolute error = 3e-31 relative error = 5.6077263005618810474468721942298e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.95 y[1] (closed_form) = -5.3389759992445402761127795436734 y[1] (numeric) = -5.338975999244540276112779543673 absolute error = 4e-31 relative error = 7.4920733874173548808987167901360e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.94 y[1] (closed_form) = -5.3281901891450563563630567567165 y[1] (numeric) = -5.328190189145056356363056756716 absolute error = 5e-31 relative error = 9.3840494098471423735953056961471e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.93 y[1] (closed_form) = -5.3174043790455724366133339697596 y[1] (numeric) = -5.317404379045572436613333969759 absolute error = 6e-31 relative error = 1.1283700791394292087357600845185e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.92 y[1] (closed_form) = -5.3066185689460885168636111828027 y[1] (numeric) = -5.306618568946088516863611182802 absolute error = 7e-31 relative error = 1.3191074333029031840606734592389e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.91 y[1] (closed_form) = -5.2958327588466045971138883958458 y[1] (numeric) = -5.295832758846604597113888395845 absolute error = 8e-31 relative error = 1.5106217216992222672280508395590e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (closed_form) = -5.2850469487471206773641656088888 y[1] (numeric) = -5.285046948747120677364165608888 absolute error = 8e-31 relative error = 1.5137046231720778228754550249459e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.89 y[1] (closed_form) = -5.2742611386476367576144428219319 y[1] (numeric) = -5.274261138647636757614442821931 absolute error = 9e-31 relative error = 1.7064001503550263800819930112503e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.88 y[1] (closed_form) = -5.263475328548152837864720034975 y[1] (numeric) = -5.263475328548152837864720034974 absolute error = 1.0e-30 relative error = 1.8998854133051181690803610712691e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.87 y[1] (closed_form) = -5.2526895184486689181149972480181 y[1] (numeric) = -5.252689518448668918114997248017 absolute error = 1.1e-30 relative error = 2.0941652769244095136803651397480e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.86 y[1] (closed_form) = -5.2419037083491849983652744610612 y[1] (numeric) = -5.24190370834918499836527446106 absolute error = 1.2e-30 relative error = 2.2892446461553028802746079080971e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.85 y[1] (closed_form) = -5.2311178982497010786155516741043 y[1] (numeric) = -5.231117898249701078615551674103 absolute error = 1.3e-30 relative error = 2.4851284663933339514733630177590e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.84 y[1] (closed_form) = -5.2203320881502171588658288871473 y[1] (numeric) = -5.220332088150217158865828887146 absolute error = 1.3e-30 relative error = 2.4902630293404276166623575694486e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.83 y[1] (closed_form) = -5.2095462780507332391161061001904 y[1] (numeric) = -5.209546278050733239116106100189 absolute error = 1.4e-30 relative error = 2.6873741498344859898875831964618e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.82 y[1] (closed_form) = -5.1987604679512493193663833132335 y[1] (numeric) = -5.198760467951249319366383313232 absolute error = 1.5e-30 relative error = 2.8853031587953246883129134941265e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.81 y[1] (closed_form) = -5.1879746578517653996166605262766 y[1] (numeric) = -5.187974657851765399616660526275 absolute error = 1.6e-30 relative error = 3.0840551573984121962951058720310e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.8 y[1] (closed_form) = -5.1771888477522814798669377393197 y[1] (numeric) = -5.177188847752281479866937739318 absolute error = 1.7e-30 relative error = 3.2836352893290125688938907181768e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.79 y[1] (closed_form) = -5.1664030376527975601172149523628 y[1] (numeric) = -5.166403037652797560117214952361 absolute error = 1.8e-30 relative error = 3.4840487412259202499377644363315e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.78 y[1] (closed_form) = -5.1556172275533136403674921654058 y[1] (numeric) = -5.155617227553313640367492165404 absolute error = 1.8e-30 relative error = 3.4913375461238824261928643619306e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.77 y[1] (closed_form) = -5.1448314174538297206177693784489 y[1] (numeric) = -5.144831417453829720617769378447 absolute error = 1.9e-30 relative error = 3.6930267404958187974241316253265e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.76 y[1] (closed_form) = -5.134045607354345800868046591492 y[1] (numeric) = -5.13404560735434580086804659149 absolute error = 2.0e-30 relative error = 3.8955633684575532206353621965518e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.75 y[1] (closed_form) = -5.1232597972548618811183238045351 y[1] (numeric) = -5.123259797254861881118323804533 absolute error = 2.1e-30 relative error = 4.0989527822212317887864295280770e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.74 y[1] (closed_form) = -5.1124739871553779613686010175782 y[1] (numeric) = -5.112473987155377961368601017576 absolute error = 2.2e-30 relative error = 4.3032003791653478192503705614230e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.73 y[1] (closed_form) = -5.1016881770558940416188782306213 y[1] (numeric) = -5.101688177055894041618878230619 absolute error = 2.3e-30 relative error = 4.5083116023121873847268441149946e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.72 y[1] (closed_form) = -5.0909023669564101218691554436644 y[1] (numeric) = -5.090902366956410121869155443662 absolute error = 2.4e-30 relative error = 4.7142919408113440670061840819287e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.71 y[1] (closed_form) = -5.0801165568569262021194326567074 y[1] (numeric) = -5.080116556856926202119432656705 absolute error = 2.4e-30 relative error = 4.7243010532122174089743500778565e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.7 y[1] (closed_form) = -5.0693307467574422823697098697505 y[1] (numeric) = -5.069330746757442282369709869748 absolute error = 2.5e-30 relative error = 4.9316174558132854601660436318050e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.69 y[1] (closed_form) = -5.0585449366579583626199870827936 y[1] (numeric) = -5.058544936657958362619987082791 absolute error = 2.6e-30 relative error = 5.1398179368902642493159107190325e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.68 y[1] (closed_form) = -5.0477591265584744428702642958367 y[1] (numeric) = -5.047759126558474442870264295834 absolute error = 2.7e-30 relative error = 5.3489081636128711529493242468038e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.67 y[1] (closed_form) = -5.0369733164589905231205415088798 y[1] (numeric) = -5.036973316458990523120541508877 absolute error = 2.8e-30 relative error = 5.5588938516918917906454076397904e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.66 y[1] (closed_form) = -5.0261875063595066033708187219229 y[1] (numeric) = -5.02618750635950660337081872192 absolute error = 2.9e-30 relative error = 5.7697807659000069375161523348928e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.65 y[1] (closed_form) = -5.0154016962600226836210959349659 y[1] (numeric) = -5.015401696260022683621095934963 absolute error = 2.9e-30 relative error = 5.7821888965793617911452193291615e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.64 y[1] (closed_form) = -5.004615886160538763871373148009 y[1] (numeric) = -5.004615886160538763871373148006 absolute error = 3.0e-30 relative error = 5.9944660454282176714087254490043e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.63 y[1] (closed_form) = -4.9938300760610548441216503610521 y[1] (numeric) = -4.993830076061054844121650361049 absolute error = 3.1e-30 relative error = 6.2076601582029865360362207961467e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.62 y[1] (closed_form) = -4.9830442659615709243719275740952 y[1] (numeric) = -4.983044265961570924371927574092 absolute error = 3.2e-30 relative error = 6.4217771892148756121989001058308e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.61 y[1] (closed_form) = -4.9722584558620870046222047871383 y[1] (numeric) = -4.972258455862087004622204787135 absolute error = 3.3e-30 relative error = 6.6368231444393976127700942932143e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.6 y[1] (closed_form) = -4.9614726457626030848724820001814 y[1] (numeric) = -4.961472645762603084872482000178 absolute error = 3.4e-30 relative error = 6.8528040820779392742133371509776e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.59 y[1] (closed_form) = -4.9506868356631191651227592132244 y[1] (numeric) = -4.950686835663119165122759213221 absolute error = 3.4e-30 relative error = 6.8677339384659086408238237242914e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.58 y[1] (closed_form) = -4.9399010255636352453730364262675 y[1] (numeric) = -4.939901025563635245373036426264 absolute error = 3.5e-30 relative error = 7.0851621963431044384044906325932e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.57 y[1] (closed_form) = -4.9291152154641513256233136393106 y[1] (numeric) = -4.929115215464151325623313639307 absolute error = 3.6e-30 relative error = 7.3035420002066336968060794967300e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.56 y[1] (closed_form) = -4.9183294053646674058735908523537 y[1] (numeric) = -4.91832940536466740587359085235 absolute error = 3.7e-30 relative error = 7.5228796102274591361655700664112e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.55 y[1] (closed_form) = -4.9075435952651834861238680653968 y[1] (numeric) = -4.907543595265183486123868065393 absolute error = 3.8e-30 relative error = 7.7431813416110134785552122429922e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.54 y[1] (closed_form) = -4.8967577851656995663741452784399 y[1] (numeric) = -4.896757785165699566374145278436 absolute error = 3.9e-30 relative error = 7.9644535652033059458011964555933e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.53 y[1] (closed_form) = -4.8859719750662156466244224914829 y[1] (numeric) = -4.885971975066215646624422491479 absolute error = 3.9e-30 relative error = 7.9820351404024302414872918120075e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.52 y[1] (closed_form) = -4.875186164966731726874699704526 y[1] (numeric) = -4.875186164966731726874699704522 absolute error = 4.0e-30 relative error = 8.2048148822380324470019132989322e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.51 y[1] (closed_form) = -4.8644003548672478071249769175691 y[1] (numeric) = -4.864400354867247807124976917565 absolute error = 4.1e-30 relative error = 8.4285825608445242410110563889030e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.5 y[1] (closed_form) = -4.8536145447677638873752541306122 y[1] (numeric) = -4.853614544767763887375254130608 absolute error = 4.2e-30 relative error = 8.6533447624670448874380178926071e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.49 y[1] (closed_form) = -4.8428287346682799676255313436553 y[1] (numeric) = -4.842828734668279967625531343651 absolute error = 4.3e-30 relative error = 8.8791081320255233095728945923187e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.48 y[1] (closed_form) = -4.8320429245687960478758085566984 y[1] (numeric) = -4.832042924568796047875808556694 absolute error = 4.4e-30 relative error = 9.1058793737695306532351591344398e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.47 y[1] (closed_form) = -4.8212571144693121281260857697415 y[1] (numeric) = -4.821257114469312128126085769737 absolute error = 4.5e-30 relative error = 9.3336652519419228172270087528119e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.46 y[1] (closed_form) = -4.8104713043698282083763629827845 y[1] (numeric) = -4.81047130436982820837636298278 absolute error = 4.5e-30 relative error = 9.3545927525068150208530782791637e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.45 y[1] (closed_form) = -4.7996854942703442886266401958276 y[1] (numeric) = -4.799685494270344288626640195823 absolute error = 4.6e-30 relative error = 9.5839612939041107100035832197414e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.44 y[1] (closed_form) = -4.7888996841708603688769174088707 y[1] (numeric) = -4.788899684170860368876917408866 absolute error = 4.7e-30 relative error = 9.8143630269293221455016129573488e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.43 y[1] (closed_form) = -4.7781138740713764491271946219138 y[1] (numeric) = -4.778113874071376449127194621909 absolute error = 4.8e-30 relative error = 1.0045804948365482616825818901446e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.42 y[1] (closed_form) = -4.7673280639718925293774718349569 y[1] (numeric) = -4.767328063971892529377471834952 absolute error = 4.9e-30 relative error = 1.0278294118314928882137917180133e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.41 y[1] (closed_form) = -4.756542253872408609627749048 y[1] (numeric) = -4.756542253872408609627749047995 absolute error = 5.0e-30 relative error = 1.0511837660917207103301771006568e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.4 y[1] (closed_form) = -4.745756443772924689878026261043 y[1] (numeric) = -4.745756443772924689878026261038 absolute error = 5.0e-30 relative error = 1.0535728201055655301263820486129e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.39 y[1] (closed_form) = -4.7349706336734407701283034740861 y[1] (numeric) = -4.734970633673440770128303474081 absolute error = 5.1e-30 relative error = 1.0770922133562136900244197344361e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.38 y[1] (closed_form) = -4.7241848235739568503785806871292 y[1] (numeric) = -4.724184823573956850378580687124 absolute error = 5.2e-30 relative error = 1.1007190010965908369539553092357e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.37 y[1] (closed_form) = -4.7133990134744729306288579001723 y[1] (numeric) = -4.713399013474472930628857900167 absolute error = 5.3e-30 relative error = 1.1244539205886401905055940216774e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.36 y[1] (closed_form) = -4.7026132033749890108791351132154 y[1] (numeric) = -4.70261320337498901087913511321 absolute error = 5.4e-30 relative error = 1.1482977158581760089817815355524e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.35 y[1] (closed_form) = -4.6918273932755050911294123262585 y[1] (numeric) = -4.691827393275505091129412326253 absolute error = 5.5e-30 relative error = 1.1722511377726292335199285322497e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.34 y[1] (closed_form) = -4.6810415831760211713796895393015 y[1] (numeric) = -4.681041583176021171379689539296 absolute error = 5.5e-30 relative error = 1.1749521772605846004174398883148e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.33 y[1] (closed_form) = -4.6702557730765372516299667523446 y[1] (numeric) = -4.670255773076537251629966752339 absolute error = 5.6e-30 relative error = 1.1990777961848099151184320405460e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.32 y[1] (closed_form) = -4.6594699629770533318802439653877 y[1] (numeric) = -4.659469962977053331880243965382 absolute error = 5.7e-30 relative error = 1.2233151077892399766467436008894e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.31 y[1] (closed_form) = -4.6486841528775694121305211784308 y[1] (numeric) = -4.648684152877569412130521178425 absolute error = 5.8e-30 relative error = 1.2476648895171244700150937299583e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.3 y[1] (closed_form) = -4.6378983427780854923807983914739 y[1] (numeric) = -4.637898342778085492380798391468 absolute error = 5.9e-30 relative error = 1.2721279260437433098642268828833e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.29 y[1] (closed_form) = -4.627112532678601572631075604517 y[1] (numeric) = -4.627112532678601572631075604511 absolute error = 6.0e-30 relative error = 1.2967050093606960370786240598312e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.28 y[1] (closed_form) = -4.61632672257911765288135281756 y[1] (numeric) = -4.616326722579117652881352817554 absolute error = 6.0e-30 relative error = 1.2997346939620060745484339291299e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.27 y[1] (closed_form) = -4.6055409124796337331316300306031 y[1] (numeric) = -4.605540912479633733131630030597 absolute error = 6.1e-30 relative error = 1.3244915452755680950160231468276e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.26 y[1] (closed_form) = -4.5947551023801498133819072436462 y[1] (numeric) = -4.59475510238014981338190724364 absolute error = 6.2e-30 relative error = 1.3493646259380200780210188866741e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.25 y[1] (closed_form) = -4.5839692922806658936321844566893 y[1] (numeric) = -4.583969292280665893632184456683 absolute error = 6.3e-30 relative error = 1.3743547563918247762401557829435e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.24 y[1] (closed_form) = -4.5731834821811819738824616697324 y[1] (numeric) = -4.573183482181181973882461669726 absolute error = 6.4e-30 relative error = 1.3994627648194681758659867211763e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.23 y[1] (closed_form) = -4.5623976720816980541327388827755 y[1] (numeric) = -4.562397672081698054132738882769 absolute error = 6.5e-30 relative error = 1.4246894872349491329368570491881e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.22 y[1] (closed_form) = -4.5516118619822141343830160958186 y[1] (numeric) = -4.551611861982214134383016095812 absolute error = 6.6e-30 relative error = 1.4500357675765698101834187057686e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.21 y[1] (closed_form) = -4.5408260518827302146332933088616 y[1] (numeric) = -4.540826051882730214633293308855 absolute error = 6.6e-30 relative error = 1.4534800330577493109201964224094e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.2 y[1] (closed_form) = -4.5300402417832462948835705219047 y[1] (numeric) = -4.530040241783246294883570521898 absolute error = 6.7e-30 relative error = 1.4790155588910510394345591806242e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.19 y[1] (closed_form) = -4.5192544316837623751338477349478 y[1] (numeric) = -4.519254431683762375133847734941 absolute error = 6.8e-30 relative error = 1.5046729726758243752449332169211e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.18 y[1] (closed_form) = -4.5084686215842784553841249479909 y[1] (numeric) = -4.508468621584278455384124947984 absolute error = 6.9e-30 relative error = 1.5304531492059794016572707653534e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.17 y[1] (closed_form) = -4.497682811484794535634402161034 y[1] (numeric) = -4.497682811484794535634402161027 absolute error = 7.0e-30 relative error = 1.5563569716667346919852550166559e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.16 y[1] (closed_form) = -4.4868970013853106158846793740771 y[1] (numeric) = -4.48689700138531061588467937407 absolute error = 7.1e-30 relative error = 1.5823853317354743827475084230128e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.15 y[1] (closed_form) = -4.4761111912858266961349565871201 y[1] (numeric) = -4.476111191285826696134956587113 absolute error = 7.1e-30 relative error = 1.5861983084384514294529241059598e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.14 y[1] (closed_form) = -4.4653253811863427763852338001632 y[1] (numeric) = -4.465325381186342776385233800156 absolute error = 7.2e-30 relative error = 1.6124244899006915939325499178771e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.13 y[1] (closed_form) = -4.4545395710868588566355110132063 y[1] (numeric) = -4.454539571086858856635511013199 absolute error = 7.3e-30 relative error = 1.6387776746629910328164354189562e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.12 y[1] (closed_form) = -4.4437537609873749368857882262494 y[1] (numeric) = -4.443753760987374936885788226242 absolute error = 7.4e-30 relative error = 1.6652587875066608573259708496522e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.11 y[1] (closed_form) = -4.4329679508878910171360654392925 y[1] (numeric) = -4.432967950887891017136065439285 absolute error = 7.5e-30 relative error = 1.6918687622133169096920003700353e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.1 y[1] (closed_form) = -4.4221821407884070973863426523356 y[1] (numeric) = -4.422182140788407097386342652328 absolute error = 7.6e-30 relative error = 1.7186085416746395769476202783226e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.09 y[1] (closed_form) = -4.4113963306889231776366198653786 y[1] (numeric) = -4.411396330688923177636619865371 absolute error = 7.6e-30 relative error = 1.7228105185491496981626511347489e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.08 y[1] (closed_form) = -4.4006105205894392578868970784217 y[1] (numeric) = -4.400610520589439257886897078414 absolute error = 7.7e-30 relative error = 1.7497572129988509882687168532845e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.07 y[1] (closed_form) = -4.3898247104899553381371742914648 y[1] (numeric) = -4.389824710489955338137174291457 absolute error = 7.8e-30 relative error = 1.7768363236374942994563848603633e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.06 y[1] (closed_form) = -4.3790389003904714183874515045079 y[1] (numeric) = -4.3790389003904714183874515045 absolute error = 7.9e-30 relative error = 1.8040488289098255087287211827480e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.05 y[1] (closed_form) = -4.368253090290987498637728717551 y[1] (numeric) = -4.368253090290987498637728717543 absolute error = 8.0e-30 relative error = 1.8313957169242423042196863264777e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.04 y[1] (closed_form) = -4.3574672801915035788880059305941 y[1] (numeric) = -4.357467280191503578888005930586 absolute error = 8.1e-30 relative error = 1.8588779855723938363219928818100e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.03 y[1] (closed_form) = -4.3466814700920196591382831436371 y[1] (numeric) = -4.346681470092019659138283143629 absolute error = 8.1e-30 relative error = 1.8634905860328712403823452214672e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.02 y[1] (closed_form) = -4.3358956599925357393885603566802 y[1] (numeric) = -4.335895659992535739388560356672 absolute error = 8.2e-30 relative error = 1.8911894203685972301970081748235e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.01 y[1] (closed_form) = -4.3251098498930518196388375697233 y[1] (numeric) = -4.325109849893051819638837569715 absolute error = 8.3e-30 relative error = 1.9190264035040026513823178262016e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4 y[1] (closed_form) = -4.3143240397935678998891147827664 y[1] (numeric) = -4.314324039793567899889114782758 absolute error = 8.4e-30 relative error = 1.9470025715550850996735540258366e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.99 y[1] (closed_form) = -4.3035382296940839801393919958095 y[1] (numeric) = -4.303538229694083980139391995801 absolute error = 8.5e-30 relative error = 1.9751189710249699662519643417605e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.98 y[1] (closed_form) = -4.2927524195946000603896692088526 y[1] (numeric) = -4.292752419594600060389669208844 absolute error = 8.6e-30 relative error = 2.0033766589344019929639345085181e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.97 y[1] (closed_form) = -4.2819666094951161406399464218957 y[1] (numeric) = -4.281966609495116140639946421887 absolute error = 8.7e-30 relative error = 2.0317767029542089921026652302721e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.96 y[1] (closed_form) = -4.2711807993956322208902236349387 y[1] (numeric) = -4.27118079939563222089022363493 absolute error = 8.7e-30 relative error = 2.0369074522040933582443386273182e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.95 y[1] (closed_form) = -4.2603949892961483011405008479818 y[1] (numeric) = -4.260394989296148301140500847973 absolute error = 8.8e-30 relative error = 2.0655361819993669532401778694831e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.94 y[1] (closed_form) = -4.2496091791966643813907780610249 y[1] (numeric) = -4.249609179196664381390778061016 absolute error = 8.9e-30 relative error = 2.0943102352961393989720366001868e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.93 y[1] (closed_form) = -4.238823369097180461641055274068 y[1] (numeric) = -4.238823369097180461641055274059 absolute error = 9.0e-30 relative error = 2.1232307214341167935371363422427e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.92 y[1] (closed_form) = -4.2280375589976965418913324871111 y[1] (numeric) = -4.228037558997696541891332487102 absolute error = 9.1e-30 relative error = 2.1522987610727981544010376135949e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.91 y[1] (closed_form) = -4.2172517488982126221416097001542 y[1] (numeric) = -4.217251748898212622141609700145 absolute error = 9.2e-30 relative error = 2.1815154863362298035558028300690e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.9 y[1] (closed_form) = -4.2064659387987287023918869131972 y[1] (numeric) = -4.206465938798728702391886913188 absolute error = 9.2e-30 relative error = 2.1871091157883739825392792475820e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.89 y[1] (closed_form) = -4.1956801286992447826421641262403 y[1] (numeric) = -4.195680128699244782642164126231 absolute error = 9.3e-30 relative error = 2.2165655423506293826617765259249e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.88 y[1] (closed_form) = -4.1848943185997608628924413392834 y[1] (numeric) = -4.184894318599760862892441339274 absolute error = 9.4e-30 relative error = 2.2461738061632056869086165737437e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.87 y[1] (closed_form) = -4.1741085085002769431427185523265 y[1] (numeric) = -4.174108508500276943142718552317 absolute error = 9.5e-30 relative error = 2.2759350842590511193427787923524e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.86 y[1] (closed_form) = -4.1633226984007930233929957653696 y[1] (numeric) = -4.16332269840079302339299576536 absolute error = 9.6e-30 relative error = 2.3058505658683465281107967737517e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.85 y[1] (closed_form) = -4.1525368883013091036432729784127 y[1] (numeric) = -4.152536888301309103643272978403 absolute error = 9.7e-30 relative error = 2.3359214525769110039373499134959e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.84 y[1] (closed_form) = -4.1417510782018251838935501914557 y[1] (numeric) = -4.141751078201825183893550191446 absolute error = 9.7e-30 relative error = 2.3420045813596633763434367622291e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.83 y[1] (closed_form) = -4.1309652681023412641438274044988 y[1] (numeric) = -4.130965268102341264143827404489 absolute error = 9.8e-30 relative error = 2.3723268931045423320652529470594e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.82 y[1] (closed_form) = -4.1201794580028573443941046175419 y[1] (numeric) = -4.120179458002857344394104617532 absolute error = 9.9e-30 relative error = 2.4028079604082949995971309967318e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.81 y[1] (closed_form) = -4.109393647903373424644381830585 y[1] (numeric) = -4.109393647903373424644381830575 absolute error = 1.00e-29 relative error = 2.4334490333146920380871816345914e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.8 y[1] (closed_form) = -4.0986078378038895048946590436281 y[1] (numeric) = -4.098607837803889504894659043618 absolute error = 1.01e-29 relative error = 2.4642513750258595873061272758082e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.79 y[1] (closed_form) = -4.0878220277044055851449362566712 y[1] (numeric) = -4.087822027704405585144936256661 absolute error = 1.02e-29 relative error = 2.4952162620758723478665976961343e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.78 y[1] (closed_form) = -4.0770362176049216653952134697142 y[1] (numeric) = -4.077036217604921665395213469704 absolute error = 1.02e-29 relative error = 2.5018173632982952905858214995633e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.77 y[1] (closed_form) = -4.0662504075054377456454906827573 y[1] (numeric) = -4.066250407505437745645490682747 absolute error = 1.03e-29 relative error = 2.5330461648373596724311742410152e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.76 y[1] (closed_form) = -4.0554645974059538258957678958004 y[1] (numeric) = -4.05546459740595382589576789579 absolute error = 1.04e-29 relative error = 2.5644410770229084392863426885386e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.75 y[1] (closed_form) = -4.0446787873064699061460451088435 y[1] (numeric) = -4.044678787306469906146045108833 absolute error = 1.05e-29 relative error = 2.5960034287401134662314053677821e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.74 y[1] (closed_form) = -4.0338929772069859863963223218866 y[1] (numeric) = -4.033892977206985986396322321876 absolute error = 1.06e-29 relative error = 2.6277345630868222633740352271286e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.73 y[1] (closed_form) = -4.0231071671075020666465995349297 y[1] (numeric) = -4.023107167107502066646599534919 absolute error = 1.07e-29 relative error = 2.6596358375640764159973226192329e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.72 y[1] (closed_form) = -4.0123213570080181468968767479728 y[1] (numeric) = -4.012321357008018146896876747962 absolute error = 1.08e-29 relative error = 2.6917086242697029027744986532303e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.71 y[1] (closed_form) = -4.0015355469085342271471539610158 y[1] (numeric) = -4.001535546908534227147153961005 absolute error = 1.08e-29 relative error = 2.6989639035804029105986886765544e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.7 y[1] (closed_form) = -3.9907497368090503073974311740589 y[1] (numeric) = -3.990749736809050307397431174048 absolute error = 1.09e-29 relative error = 2.7313163487709688013438531379175e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=52.4MB, alloc=40.3MB, time=0.75 TOP MAIN SOLVE Loop x[1] = -3.69 y[1] (closed_form) = -3.979963926709566387647708387102 y[1] (numeric) = -3.979963926709566387647708387091 absolute error = 1.10e-29 relative error = 2.7638441459679876237461729622148e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.68 y[1] (closed_form) = -3.9691781166100824678979856001451 y[1] (numeric) = -3.969178116610082467897985600134 absolute error = 1.11e-29 relative error = 2.7965487246715119832267662638181e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.67 y[1] (closed_form) = -3.9583923065105985481482628131882 y[1] (numeric) = -3.958392306510598548148262813177 absolute error = 1.12e-29 relative error = 2.8294315299619765299524854144764e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.66 y[1] (closed_form) = -3.9476064964111146283985400262313 y[1] (numeric) = -3.94760649641111462839854002622 absolute error = 1.13e-29 relative error = 2.8624940227130447080810773473788e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.65 y[1] (closed_form) = -3.9368206863116307086488172392743 y[1] (numeric) = -3.936820686311630708648817239263 absolute error = 1.13e-29 relative error = 2.8703364720903407209799296140840e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.64 y[1] (closed_form) = -3.9260348762121467888990944523174 y[1] (numeric) = -3.926034876212146788899094452306 absolute error = 1.14e-29 relative error = 2.9036930031041300544582045911221e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.63 y[1] (closed_form) = -3.9152490661126628691493716653605 y[1] (numeric) = -3.915249066112662869149371665349 absolute error = 1.15e-29 relative error = 2.9372333166579402658068832870420e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.62 y[1] (closed_form) = -3.9044632560131789493996488784036 y[1] (numeric) = -3.904463256013178949399648878392 absolute error = 1.16e-29 relative error = 2.9709589358114952849530684950940e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.61 y[1] (closed_form) = -3.8936774459136950296499260914467 y[1] (numeric) = -3.893677445913695029649926091435 absolute error = 1.17e-29 relative error = 3.0048714005005270632080968344925e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.6 y[1] (closed_form) = -3.8828916358142111099002033044898 y[1] (numeric) = -3.882891635814211109900203304478 absolute error = 1.18e-29 relative error = 3.0389722677711645735645419979989e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.59 y[1] (closed_form) = -3.8721058257147271901504805175328 y[1] (numeric) = -3.872105825714727190150480517521 absolute error = 1.18e-29 relative error = 3.0474373715811121071956410007789e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.58 y[1] (closed_form) = -3.8613200156152432704007577305759 y[1] (numeric) = -3.861320015615243270400757730564 absolute error = 1.19e-29 relative error = 3.0818476458506933607495734114732e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.57 y[1] (closed_form) = -3.850534205515759350651034943619 y[1] (numeric) = -3.850534205515759350651034943607 absolute error = 1.20e-29 relative error = 3.1164506947660425765082897572415e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.56 y[1] (closed_form) = -3.8397483954162754309013121566621 y[1] (numeric) = -3.83974839541627543090131215665 absolute error = 1.21e-29 relative error = 3.1512481428326016193218303521432e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.55 y[1] (closed_form) = -3.8289625853167915111515893697052 y[1] (numeric) = -3.828962585316791511151589369693 absolute error = 1.22e-29 relative error = 3.1862416328600990229399542743402e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.54 y[1] (closed_form) = -3.8181767752173075914018665827483 y[1] (numeric) = -3.818176775217307591401866582736 absolute error = 1.23e-29 relative error = 3.2214328262210851124542257893180e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.53 y[1] (closed_form) = -3.8073909651178236716521437957913 y[1] (numeric) = -3.807390965117823671652143795779 absolute error = 1.23e-29 relative error = 3.2305586982500400277869573071348e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.52 y[1] (closed_form) = -3.7966051550183397519024210088344 y[1] (numeric) = -3.796605155018339751902421008822 absolute error = 1.24e-29 relative error = 3.2660757423272531433917843506999e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.51 y[1] (closed_form) = -3.7858193449188558321526982218775 y[1] (numeric) = -3.785819344918855832152698221865 absolute error = 1.25e-29 relative error = 3.3017951627239945388576075597555e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.5 y[1] (closed_form) = -3.7750335348193719124029754349206 y[1] (numeric) = -3.775033534819371912402975434908 absolute error = 1.26e-29 relative error = 3.3377186940944315994403783300056e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.49 y[1] (closed_form) = -3.7642477247198879926532526479637 y[1] (numeric) = -3.764247724719887992653252647951 absolute error = 1.27e-29 relative error = 3.3738480909741548322900990760165e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.48 y[1] (closed_form) = -3.7534619146204040729035298610068 y[1] (numeric) = -3.753461914620404072903529860994 absolute error = 1.28e-29 relative error = 3.4101851280658304975125193665446e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.47 y[1] (closed_form) = -3.7426761045209201531538070740499 y[1] (numeric) = -3.742676104520920153153807074037 absolute error = 1.29e-29 relative error = 3.4467316005297924778082677279116e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.46 y[1] (closed_form) = -3.7318902944214362334040842870929 y[1] (numeric) = -3.73189029442143623340408428708 absolute error = 1.29e-29 relative error = 3.4566932525544450572238985594952e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.45 y[1] (closed_form) = -3.721104484321952313654361500136 y[1] (numeric) = -3.721104484321952313654361500123 absolute error = 1.30e-29 relative error = 3.4935863947848317868538581554004e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.44 y[1] (closed_form) = -3.7103186742224683939046387131791 y[1] (numeric) = -3.710318674222468393904638713166 absolute error = 1.31e-29 relative error = 3.5306940320281858811909686791887e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.43 y[1] (closed_form) = -3.6995328641229844741549159262222 y[1] (numeric) = -3.699532864122984474154915926209 absolute error = 1.32e-29 relative error = 3.5680180403341834396350011302295e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.42 y[1] (closed_form) = -3.6887470540235005544051931392653 y[1] (numeric) = -3.688747054023500554405193139252 absolute error = 1.33e-29 relative error = 3.6055603176946020364325074552529e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.41 y[1] (closed_form) = -3.6779612439240166346554703523084 y[1] (numeric) = -3.677961243924016634655470352295 absolute error = 1.34e-29 relative error = 3.6433227843650524138563921164935e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.4 y[1] (closed_form) = -3.6671754338245327149057475653514 y[1] (numeric) = -3.667175433824532714905747565338 absolute error = 1.34e-29 relative error = 3.6540384396131849209559697403656e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.39 y[1] (closed_form) = -3.6563896237250487951560247783945 y[1] (numeric) = -3.656389623725048795156024778381 absolute error = 1.35e-29 relative error = 3.6921666970071146011508609845195e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.38 y[1] (closed_form) = -3.6456038136255648754063019914376 y[1] (numeric) = -3.645603813625564875406301991424 absolute error = 1.36e-29 relative error = 3.7305205653915409066723492182837e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.37 y[1] (closed_form) = -3.6348180035260809556565792044807 y[1] (numeric) = -3.634818003526080955656579204467 absolute error = 1.37e-29 relative error = 3.7691020531729074276568729905272e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.36 y[1] (closed_form) = -3.6240321934265970359068564175238 y[1] (numeric) = -3.62403219342659703590685641751 absolute error = 1.38e-29 relative error = 3.8079131926672582731710665471294e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.35 y[1] (closed_form) = -3.6132463833271131161571336305669 y[1] (numeric) = -3.613246383327113116157133630553 absolute error = 1.39e-29 relative error = 3.8469560404570977804495239458605e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.34 y[1] (closed_form) = -3.6024605732276291964074108436099 y[1] (numeric) = -3.602460573227629196407410843596 absolute error = 1.39e-29 relative error = 3.8584738729135561570376961732434e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.33 y[1] (closed_form) = -3.591674763128145276657688056653 y[1] (numeric) = -3.591674763128145276657688056639 absolute error = 1.40e-29 relative error = 3.8979030461563265258729810327059e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.32 y[1] (closed_form) = -3.5808889530286613569079652696961 y[1] (numeric) = -3.580888953028661356907965269682 absolute error = 1.41e-29 relative error = 3.9375697445391135836771531503580e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.31 y[1] (closed_form) = -3.5701031429291774371582424827392 y[1] (numeric) = -3.570103142929177437158242482725 absolute error = 1.42e-29 relative error = 3.9774761208577482974197190572406e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.3 y[1] (closed_form) = -3.5593173328296935174085196957823 y[1] (numeric) = -3.559317332829693517408519695768 absolute error = 1.43e-29 relative error = 4.0176243540025565548819368787104e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.29 y[1] (closed_form) = -3.5485315227302095976587969088254 y[1] (numeric) = -3.548531522730209597658796908811 absolute error = 1.44e-29 relative error = 4.0580166493549320357937730455995e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.28 y[1] (closed_form) = -3.5377457126307256779090741218684 y[1] (numeric) = -3.537745712630725677909074121854 absolute error = 1.44e-29 relative error = 4.0703886513346726822443638170800e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.27 y[1] (closed_form) = -3.5269599025312417581593513349115 y[1] (numeric) = -3.526959902531241758159351334897 absolute error = 1.45e-29 relative error = 4.1111893530724820074656375964221e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.26 y[1] (closed_form) = -3.5161740924317578384096285479546 y[1] (numeric) = -3.51617409243175783840962854794 absolute error = 1.46e-29 relative error = 4.1522403658638975248661829940424e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.25 y[1] (closed_form) = -3.5053882823322739186599057609977 y[1] (numeric) = -3.505388282332273918659905760983 absolute error = 1.47e-29 relative error = 4.1935440002724909839122702094942e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.24 y[1] (closed_form) = -3.4946024722327899989101829740408 y[1] (numeric) = -3.494602472232789998910182974026 absolute error = 1.48e-29 relative error = 4.2351025953873103285080246299796e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.23 y[1] (closed_form) = -3.4838166621333060791604601870839 y[1] (numeric) = -3.483816662133306079160460187069 absolute error = 1.49e-29 relative error = 4.2769185192644505359186134431616e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.22 y[1] (closed_form) = -3.473030852033822159410737400127 y[1] (numeric) = -3.473030852033822159410737400112 absolute error = 1.50e-29 relative error = 4.3189941693768524837479015657422e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.21 y[1] (closed_form) = -3.46224504193433823966101461317 y[1] (numeric) = -3.462245041934338239661014613155 absolute error = 1.50e-29 relative error = 4.3324489798733535818281130970997e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.2 y[1] (closed_form) = -3.4514592318348543199112918262131 y[1] (numeric) = -3.451459231834854319911291826198 absolute error = 1.51e-29 relative error = 4.3749611354883608638498014568650e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.19 y[1] (closed_form) = -3.4406734217353704001615690392562 y[1] (numeric) = -3.440673421735370400161569039241 absolute error = 1.52e-29 relative error = 4.4177398249943713263230364521147e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.18 y[1] (closed_form) = -3.4298876116358864804118462522993 y[1] (numeric) = -3.429887611635886480411846252284 absolute error = 1.53e-29 relative error = 4.4607875628620548105728326737496e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.17 y[1] (closed_form) = -3.4191018015364025606621234653424 y[1] (numeric) = -3.419101801536402560662123465327 absolute error = 1.54e-29 relative error = 4.5041068952904176858904509535652e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.16 y[1] (closed_form) = -3.4083159914369186409124006783855 y[1] (numeric) = -3.40831599143691864091240067837 absolute error = 1.55e-29 relative error = 4.5477004007088334907986870705948e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.15 y[1] (closed_form) = -3.3975301813374347211626778914285 y[1] (numeric) = -3.397530181337434721162677891413 absolute error = 1.55e-29 relative error = 4.5621375448380678828329686168507e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.14 y[1] (closed_form) = -3.3867443712379508014129551044716 y[1] (numeric) = -3.386744371237950801412955104456 absolute error = 1.56e-29 relative error = 4.6061935268819119737499913259101e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.13 y[1] (closed_form) = -3.3759585611384668816632323175147 y[1] (numeric) = -3.375958561138466881663232317499 absolute error = 1.57e-29 relative error = 4.6505310167982406914460365442925e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.12 y[1] (closed_form) = -3.3651727510389829619135095305578 y[1] (numeric) = -3.365172751038982961913509530542 absolute error = 1.58e-29 relative error = 4.6951527213935202342555179499722e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.11 y[1] (closed_form) = -3.3543869409394990421637867436009 y[1] (numeric) = -3.354386940939499042163786743585 absolute error = 1.59e-29 relative error = 4.7400613822884478770187580785181e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.1 y[1] (closed_form) = -3.343601130840015122414063956644 y[1] (numeric) = -3.343601130840015122414063956628 absolute error = 1.60e-29 relative error = 4.7852597764794718271546642724094e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.09 y[1] (closed_form) = -3.332815320740531202664341169687 y[1] (numeric) = -3.332815320740531202664341169671 absolute error = 1.60e-29 relative error = 4.8007460540732565256244204674658e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.08 y[1] (closed_form) = -3.3220295106410472829146183827301 y[1] (numeric) = -3.322029510641047282914618382714 absolute error = 1.61e-29 relative error = 4.8464349724856014385813574236193e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.07 y[1] (closed_form) = -3.3112437005415633631648955957732 y[1] (numeric) = -3.311243700541563363164895595757 absolute error = 1.62e-29 relative error = 4.8924215385748997385933884316043e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.06 y[1] (closed_form) = -3.3004578904420794434151728088163 y[1] (numeric) = -3.3004578904420794434151728088 absolute error = 1.63e-29 relative error = 4.9387086704556313608277202958507e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.05 y[1] (closed_form) = -3.2896720803425955236654500218594 y[1] (numeric) = -3.289672080342595523665450021843 absolute error = 1.64e-29 relative error = 4.9852993245126300756668674510101e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.04 y[1] (closed_form) = -3.2788862702431116039157272349025 y[1] (numeric) = -3.278886270243111603915727234886 absolute error = 1.65e-29 relative error = 5.0321964960305300978404826795588e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.03 y[1] (closed_form) = -3.2681004601436276841660044479455 y[1] (numeric) = -3.268100460143627684166004447929 absolute error = 1.65e-29 relative error = 5.0488044052583536295165238765212e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.02 y[1] (closed_form) = -3.2573146500441437644162816609886 y[1] (numeric) = -3.257314650044143764416281660972 absolute error = 1.66e-29 relative error = 5.0962224357953977695649632338202e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.01 y[1] (closed_form) = -3.2465288399446598446665588740317 y[1] (numeric) = -3.246528839944659844666558874015 absolute error = 1.67e-29 relative error = 5.1439555363027877178529271051212e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3 y[1] (closed_form) = -3.2357430298451759249168360870748 y[1] (numeric) = -3.235743029845175924916836087058 absolute error = 1.68e-29 relative error = 5.1920068574802269324628107355642e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.99 y[1] (closed_form) = -3.2249572197456920051671133001179 y[1] (numeric) = -3.224957219745692005167113300101 absolute error = 1.69e-29 relative error = 5.2403795921772476802807872331005e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.98 y[1] (closed_form) = -3.214171409646208085417390513161 y[1] (numeric) = -3.214171409646208085417390513144 absolute error = 1.70e-29 relative error = 5.2890769761004229297619716265934e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.97 y[1] (closed_form) = -3.2033855995467241656676677262041 y[1] (numeric) = -3.203385599546724165667667726187 absolute error = 1.71e-29 relative error = 5.3381022885348653526403357129718e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.96 y[1] (closed_form) = -3.1925997894472402459179449392471 y[1] (numeric) = -3.19259978944724024591794493923 absolute error = 1.71e-29 relative error = 5.3561364178880236815343909011915e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.95 y[1] (closed_form) = -3.1818139793477563261682221522902 y[1] (numeric) = -3.181813979347756326168222152273 absolute error = 1.72e-29 relative error = 5.4057214254636745301670910806117e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.94 y[1] (closed_form) = -3.1710281692482724064184993653333 y[1] (numeric) = -3.171028169248272406418499365316 absolute error = 1.73e-29 relative error = 5.4556437460160304866136191524090e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.93 y[1] (closed_form) = -3.1602423591487884866687765783764 y[1] (numeric) = -3.160242359148788486668776578359 absolute error = 1.74e-29 relative error = 5.5059068332615765861075637980752e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.92 y[1] (closed_form) = -3.1494565490493045669190537914195 y[1] (numeric) = -3.149456549049304566919053791402 absolute error = 1.75e-29 relative error = 5.5565141882279825903925628591226e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.91 y[1] (closed_form) = -3.1386707389498206471693310044626 y[1] (numeric) = -3.138670738949820647169331004445 absolute error = 1.76e-29 relative error = 5.6074693600670099417860498862254e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.9 y[1] (closed_form) = -3.1278849288503367274196082175056 y[1] (numeric) = -3.127884928850336727419608217488 absolute error = 1.76e-29 relative error = 5.6268054613086203208956569547988e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.89 y[1] (closed_form) = -3.1170991187508528076698854305487 y[1] (numeric) = -3.117099118750852807669885430531 absolute error = 1.77e-29 relative error = 5.6783564864928334592555456017973e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.88 y[1] (closed_form) = -3.1063133086513688879201626435918 y[1] (numeric) = -3.106313308651368887920162643574 absolute error = 1.78e-29 relative error = 5.7302655049074925221873779199556e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.87 y[1] (closed_form) = -3.0955274985518849681704398566349 y[1] (numeric) = -3.095527498551884968170439856617 absolute error = 1.79e-29 relative error = 5.7825362586421143660455644702961e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.86 y[1] (closed_form) = -3.084741688452401048420717069678 y[1] (numeric) = -3.08474168845240104842071706966 absolute error = 1.80e-29 relative error = 5.8351725421231321668538082692405e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.85 y[1] (closed_form) = -3.0739558783529171286709942827211 y[1] (numeric) = -3.073955878352917128670994282703 absolute error = 1.81e-29 relative error = 5.8881782030320869346852678141423e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.84 y[1] (closed_form) = -3.0631700682534332089212714957641 y[1] (numeric) = -3.063170068253433208921271495746 absolute error = 1.81e-29 relative error = 5.9089112248737492126243004472909e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.83 y[1] (closed_form) = -3.0523842581539492891715487088072 y[1] (numeric) = -3.052384258153949289171548708789 absolute error = 1.82e-29 relative error = 5.9625520448094478906375034949060e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.82 y[1] (closed_form) = -3.0415984480544653694218259218503 y[1] (numeric) = -3.041598448054465369421825921832 absolute error = 1.83e-29 relative error = 6.0165732960922082614025732308021e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.81 y[1] (closed_form) = -3.0308126379549814496721031348934 y[1] (numeric) = -3.030812637954981449672103134875 absolute error = 1.84e-29 relative error = 6.0709790402666608767994228224696e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.8 y[1] (closed_form) = -3.0200268278554975299223803479365 y[1] (numeric) = -3.020026827855497529922380347918 absolute error = 1.85e-29 relative error = 6.1257733968995024394491070540777e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.79 y[1] (closed_form) = -3.0092410177560136101726575609796 y[1] (numeric) = -3.009241017756013610172657560961 absolute error = 1.86e-29 relative error = 6.1809605446193177767414413518621e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.78 y[1] (closed_form) = -2.9984552076565296904229347740226 y[1] (numeric) = -2.998455207656529690422934774004 absolute error = 1.86e-29 relative error = 6.2031942156431282723412307092431e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.77 y[1] (closed_form) = -2.9876693975570457706732119870657 y[1] (numeric) = -2.987669397557045770673211987047 absolute error = 1.87e-29 relative error = 6.2590593240639661963031563147919e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.76 y[1] (closed_form) = -2.9768835874575618509234892001088 y[1] (numeric) = -2.97688358745756185092348920009 absolute error = 1.88e-29 relative error = 6.3153292521110420762358205116853e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.75 y[1] (closed_form) = -2.9660977773580779311737664131519 y[1] (numeric) = -2.966097777358077931173766413133 absolute error = 1.89e-29 relative error = 6.3720084159984603262043586300107e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.74 y[1] (closed_form) = -2.955311967258594011424043626195 y[1] (numeric) = -2.955311967258594011424043626176 absolute error = 1.90e-29 relative error = 6.4291012964106042568296014061340e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.73 y[1] (closed_form) = -2.9445261571591100916743208392381 y[1] (numeric) = -2.944526157159110091674320839219 absolute error = 1.91e-29 relative error = 6.4866124396829104140528313088223e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.72 y[1] (closed_form) = -2.9337403470596261719245980522812 y[1] (numeric) = -2.933740347059626171924598052262 absolute error = 1.92e-29 relative error = 6.5445464590086894106674084902069e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.71 y[1] (closed_form) = -2.9229545369601422521748752653242 y[1] (numeric) = -2.922954536960142252174875265305 absolute error = 1.92e-29 relative error = 6.5686960769386107738064026174772e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.7 y[1] (closed_form) = -2.9121687268606583324251524783673 y[1] (numeric) = -2.912168726860658332425152478348 absolute error = 1.93e-29 relative error = 6.6273632506196018383949898939412e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.69 y[1] (closed_form) = -2.9013829167611744126754296914104 y[1] (numeric) = -2.901382916761174412675429691391 absolute error = 1.94e-29 relative error = 6.6864666114655073346905555144680e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.68 y[1] (closed_form) = -2.8905971066616904929257069044535 y[1] (numeric) = -2.890597106661690492925706904434 absolute error = 1.95e-29 relative error = 6.7460110421684718272271328187302e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.67 y[1] (closed_form) = -2.8798112965622065731759841174966 y[1] (numeric) = -2.879811296562206573175984117477 absolute error = 1.96e-29 relative error = 6.8060014985695858665242837357583e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.66 y[1] (closed_form) = -2.8690254864627226534262613305397 y[1] (numeric) = -2.86902548646272265342626133052 absolute error = 1.97e-29 relative error = 6.8664430110338661767935936822378e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.65 y[1] (closed_form) = -2.8582396763632387336765385435827 y[1] (numeric) = -2.858239676363238733676538543563 absolute error = 1.97e-29 relative error = 6.8923541167358807661399846017936e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.64 y[1] (closed_form) = -2.8474538662637548139268157566258 y[1] (numeric) = -2.847453866263754813926815756606 absolute error = 1.98e-29 relative error = 6.9535806126967324988341215208450e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.63 y[1] (closed_form) = -2.8366680561642708941770929696689 y[1] (numeric) = -2.836668056164270894177092969649 absolute error = 1.99e-29 relative error = 7.0152727093873245488871492149463e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.62 y[1] (closed_form) = -2.825882246064786974427370182712 y[1] (numeric) = -2.825882246064786974427370182692 absolute error = 2.00e-29 relative error = 7.0774357381137226451237878074758e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.61 y[1] (closed_form) = -2.8150964359653030546776473957551 y[1] (numeric) = -2.815096435965303054677647395735 absolute error = 2.01e-29 relative error = 7.1400751118878326041668374237028e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.6 y[1] (closed_form) = -2.8043106258658191349279246087982 y[1] (numeric) = -2.804310625865819134927924608778 absolute error = 2.02e-29 relative error = 7.2031963269986664859717566523624e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.59 y[1] (closed_form) = -2.7935248157663352151782018218412 y[1] (numeric) = -2.793524815766335215178201821821 absolute error = 2.02e-29 relative error = 7.2310078958287771673847750178157e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.58 y[1] (closed_form) = -2.7827390056668512954284790348843 y[1] (numeric) = -2.782739005666851295428479034864 absolute error = 2.03e-29 relative error = 7.2949708753355901667355383396979e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.57 y[1] (closed_form) = -2.7719531955673673756787562479274 y[1] (numeric) = -2.771953195567367375678756247907 absolute error = 2.04e-29 relative error = 7.3594316212198880921512881465752e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.56 y[1] (closed_form) = -2.7611673854678834559290334609705 y[1] (numeric) = -2.76116738546788345592903346095 absolute error = 2.05e-29 relative error = 7.4243959666814070951093484988188e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.55 y[1] (closed_form) = -2.7503815753683995361793106740136 y[1] (numeric) = -2.750381575368399536179310673993 absolute error = 2.06e-29 relative error = 7.4898698364210556588749230499035e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.54 y[1] (closed_form) = -2.7395957652689156164295878870567 y[1] (numeric) = -2.739595765268915616429587887036 absolute error = 2.07e-29 relative error = 7.5558592484421187782606989754062e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.53 y[1] (closed_form) = -2.7288099551694316966798651000997 y[1] (numeric) = -2.728809955169431696679865100079 absolute error = 2.07e-29 relative error = 7.5857243047600718169099507500128e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.52 y[1] (closed_form) = -2.7180241450699477769301423131428 y[1] (numeric) = -2.718024145069947776930142313122 absolute error = 2.08e-29 relative error = 7.6526178171477267712036892927819e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.51 y[1] (closed_form) = -2.7072383349704638571804195261859 y[1] (numeric) = -2.707238334970463857180419526165 absolute error = 2.09e-29 relative error = 7.7200443455703431195555452741387e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.5 y[1] (closed_form) = -2.696452524870979937430696739229 y[1] (numeric) = -2.696452524870979937430696739208 absolute error = 2.10e-29 relative error = 7.7880102862203403986942161033464e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.49 y[1] (closed_form) = -2.6856667147714960176809739522721 y[1] (numeric) = -2.685666714771496017680973952251 absolute error = 2.11e-29 relative error = 7.8565221380402171740508682243549e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.48 y[1] (closed_form) = -2.6748809046720120979312511653152 y[1] (numeric) = -2.674880904672012097931251165294 absolute error = 2.12e-29 relative error = 7.9255865047941252137249127011780e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.47 y[1] (closed_form) = -2.6640950945725281781815283783583 y[1] (numeric) = -2.664095094572528178181528378337 absolute error = 2.13e-29 relative error = 7.9952100971897653023032004531171e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.46 y[1] (closed_form) = -2.6533092844730442584318055914013 y[1] (numeric) = -2.65330928447304425843180559138 absolute error = 2.13e-29 relative error = 8.0277109512433822344263841947967e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.45 y[1] (closed_form) = -2.6425234743735603386820828044444 y[1] (numeric) = -2.642523474373560338682082804423 absolute error = 2.14e-29 relative error = 8.0983197339706163523836843834603e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.44 y[1] (closed_form) = -2.6317376642740764189323600174875 y[1] (numeric) = -2.631737664274076418932360017466 absolute error = 2.15e-29 relative error = 8.1695072772120081270455526064572e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.43 y[1] (closed_form) = -2.6209518541745924991826372305306 y[1] (numeric) = -2.620951854174592499182637230509 absolute error = 2.16e-29 relative error = 8.2412807261590903689885884691496e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.42 y[1] (closed_form) = -2.6101660440751085794329144435737 y[1] (numeric) = -2.610166044075108579432914443552 absolute error = 2.17e-29 relative error = 8.3136473441057352740881783472360e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=100.8MB, alloc=40.3MB, time=1.38 TOP MAIN SOLVE Loop x[1] = -2.41 y[1] (closed_form) = -2.5993802339756246596831916566168 y[1] (numeric) = -2.599380233975624659683191656595 absolute error = 2.18e-29 relative error = 8.3866145148984104273628685562610e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.4 y[1] (closed_form) = -2.5885944238761407399334688696598 y[1] (numeric) = -2.588594423876140739933468869638 absolute error = 2.18e-29 relative error = 8.4215587420438204708102138419124e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.39 y[1] (closed_form) = -2.5778086137766568201837460827029 y[1] (numeric) = -2.577808613776656820183746082681 absolute error = 2.19e-29 relative error = 8.4955880289014472370693032806977e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.38 y[1] (closed_form) = -2.567022803677172900434023295746 y[1] (numeric) = -2.567022803677172900434023295724 absolute error = 2.20e-29 relative error = 8.5702394106066170853977968324140e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.37 y[1] (closed_form) = -2.5562369935776889806843005087891 y[1] (numeric) = -2.556236993577688980684300508767 absolute error = 2.21e-29 relative error = 8.6455207617776533459484717643135e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.36 y[1] (closed_form) = -2.5454511834782050609345777218322 y[1] (numeric) = -2.54545118347820506093457772181 absolute error = 2.22e-29 relative error = 8.7214400905009865239614405515682e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.35 y[1] (closed_form) = -2.5346653733787211411848549348753 y[1] (numeric) = -2.534665373378721141184854934853 absolute error = 2.23e-29 relative error = 8.7980055411709012609362218391399e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.34 y[1] (closed_form) = -2.5238795632792372214351321479183 y[1] (numeric) = -2.523879563279237221435132147896 absolute error = 2.23e-29 relative error = 8.8356038554494093859829578299057e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.33 y[1] (closed_form) = -2.5130937531797533016854093609614 y[1] (numeric) = -2.513093753179753301685409360939 absolute error = 2.24e-29 relative error = 8.9133164935282865793352974001104e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.32 y[1] (closed_form) = -2.5023079430802693819356865740045 y[1] (numeric) = -2.502307943080269381935686573982 absolute error = 2.25e-29 relative error = 8.9916990681423265071130881735065e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.31 y[1] (closed_form) = -2.4915221329807854621859637870476 y[1] (numeric) = -2.491522132980785462185963787025 absolute error = 2.26e-29 relative error = 9.0707602797660118022309463994861e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.3 y[1] (closed_form) = -2.4807363228813015424362410000907 y[1] (numeric) = -2.480736322881301542436241000068 absolute error = 2.27e-29 relative error = 9.1505089801864247955672207839524e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.29 y[1] (closed_form) = -2.4699505127818176226865182131338 y[1] (numeric) = -2.469950512781817622686518213111 absolute error = 2.28e-29 relative error = 9.2309541758070160683212792241783e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.28 y[1] (closed_form) = -2.4591647026823337029367954261768 y[1] (numeric) = -2.459164702682333702936795426154 absolute error = 2.28e-29 relative error = 9.2714408169289766651121620277935e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.27 y[1] (closed_form) = -2.4483788925828497831870726392199 y[1] (numeric) = -2.448378892582849783187072639197 absolute error = 2.29e-29 relative error = 9.3531275201618310850690973760559e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.26 y[1] (closed_form) = -2.437593082483365863437349852263 y[1] (numeric) = -2.43759308248336586343734985224 absolute error = 2.30e-29 relative error = 9.4355371145737373140522002937720e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.25 y[1] (closed_form) = -2.4268072723838819436876270653061 y[1] (numeric) = -2.426807272383881943687627065283 absolute error = 2.31e-29 relative error = 9.5186792387137493761818196818678e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.24 y[1] (closed_form) = -2.4160214622843980239379042783492 y[1] (numeric) = -2.416021462284398023937904278326 absolute error = 2.32e-29 relative error = 9.6025637032478686888661678145001e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.23 y[1] (closed_form) = -2.4052356521849141041881814913923 y[1] (numeric) = -2.405235652184914104188181491369 absolute error = 2.33e-29 relative error = 9.6872004948181684438167432846449e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.22 y[1] (closed_form) = -2.3944498420854301844384587044354 y[1] (numeric) = -2.394449842085430184438458704412 absolute error = 2.34e-29 relative error = 9.7725997800062186470101167319981e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.21 y[1] (closed_form) = -2.3836640319859462646887359174784 y[1] (numeric) = -2.383664031985946264688735917455 absolute error = 2.34e-29 relative error = 9.8168196885130341160011127353107e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.2 y[1] (closed_form) = -2.3728782218864623449390131305215 y[1] (numeric) = -2.372878221886462344939013130498 absolute error = 2.35e-29 relative error = 9.9035845089923159831879912569611e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.19 y[1] (closed_form) = -2.3620924117869784251892903435646 y[1] (numeric) = -2.362092411786978425189290343541 absolute error = 2.36e-29 relative error = 9.9911417022613629815820558838321e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.18 y[1] (closed_form) = -2.3513066016874945054395675566077 y[1] (numeric) = -2.351306601687494505439567556584 absolute error = 2.37e-29 relative error = 1.0079502172532878301062304589849e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.17 y[1] (closed_form) = -2.3405207915880105856898447696508 y[1] (numeric) = -2.340520791588010585689844769627 absolute error = 2.38e-29 relative error = 1.0168677025018877632703661578870e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.16 y[1] (closed_form) = -2.3297349814885266659401219826939 y[1] (numeric) = -2.32973498148852666594012198267 absolute error = 2.39e-29 relative error = 1.0258677570583451032230586688160e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.15 y[1] (closed_form) = -2.3189491713890427461903991957369 y[1] (numeric) = -2.318949171389042746190399195713 absolute error = 2.39e-29 relative error = 1.0306392349981513595171194068105e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.14 y[1] (closed_form) = -2.30816336128955882644067640878 y[1] (numeric) = -2.308163361289558826440676408756 absolute error = 2.40e-29 relative error = 1.0397877551696048596387471433039e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.13 y[1] (closed_form) = -2.2973775511900749066909536218231 y[1] (numeric) = -2.297377551190074906690953621799 absolute error = 2.41e-29 relative error = 1.0490221769389123832356953280273e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.12 y[1] (closed_form) = -2.2865917410905909869412308348662 y[1] (numeric) = -2.286591741090590986941230834842 absolute error = 2.42e-29 relative error = 1.0583437158947228079986524578896e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.11 y[1] (closed_form) = -2.2758059309911070671915080479093 y[1] (numeric) = -2.275805930991107067191508047885 absolute error = 2.43e-29 relative error = 1.0677536106700195874986992287932e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.1 y[1] (closed_form) = -2.2650201208916231474417852609524 y[1] (numeric) = -2.265020120891623147441785260928 absolute error = 2.44e-29 relative error = 1.0772531234907953839463654927531e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.09 y[1] (closed_form) = -2.2542343107921392276920624739954 y[1] (numeric) = -2.254234310792139227692062473971 absolute error = 2.44e-29 relative error = 1.0824074446558231130561567152065e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.08 y[1] (closed_form) = -2.2434485006926553079423396870385 y[1] (numeric) = -2.243448500692655307942339687014 absolute error = 2.45e-29 relative error = 1.0920687500709611937271537003891e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.07 y[1] (closed_form) = -2.2326626905931713881926169000816 y[1] (numeric) = -2.232662690593171388192616900057 absolute error = 2.46e-29 relative error = 1.1018234014321392558539091105494e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.06 y[1] (closed_form) = -2.2218768804936874684428941131247 y[1] (numeric) = -2.2218768804936874684428941131 absolute error = 2.47e-29 relative error = 1.1116727581463384642149048644975e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.05 y[1] (closed_form) = -2.2110910703942035486931713261678 y[1] (numeric) = -2.211091070394203548693171326143 absolute error = 2.48e-29 relative error = 1.1216182061455542502184469184843e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.04 y[1] (closed_form) = -2.2003052602947196289434485392109 y[1] (numeric) = -2.200305260294719628943448539186 absolute error = 2.49e-29 relative error = 1.1316611585369192105945727180983e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.03 y[1] (closed_form) = -2.1895194501952357091937257522539 y[1] (numeric) = -2.189519450195235709193725752229 absolute error = 2.49e-29 relative error = 1.1372358440469532953758267708968e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.02 y[1] (closed_form) = -2.178733640095751789444002965297 y[1] (numeric) = -2.178733640095751789444002965272 absolute error = 2.50e-29 relative error = 1.1474555466496258248901190628457e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.01 y[1] (closed_form) = -2.1679478299962678696942801783401 y[1] (numeric) = -2.167947829996267869694280178315 absolute error = 2.51e-29 relative error = 1.1577769378354095238523147606846e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = -2.1571620198967839499445573913832 y[1] (numeric) = -2.157162019896783949944557391358 absolute error = 2.52e-29 relative error = 1.1682015429330510598041324155020e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (closed_form) = -2.1463762097973000301948346044263 y[1] (numeric) = -2.146376209797300030194834604401 absolute error = 2.53e-29 relative error = 1.1787309179311714051625010015235e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (closed_form) = -2.1355903996978161104451118174694 y[1] (numeric) = -2.135590399697816110445111817444 absolute error = 2.54e-29 relative error = 1.1893666502525050873426712904341e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (closed_form) = -2.1248045895983321906953890305125 y[1] (numeric) = -2.124804589598332190695389030487 absolute error = 2.55e-29 relative error = 1.2001103595517203297480209731407e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (closed_form) = -2.1140187794988482709456662435555 y[1] (numeric) = -2.11401877949884827094566624353 absolute error = 2.55e-29 relative error = 1.2062333715902495151038782230037e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (closed_form) = -2.1032329693993643511959434565986 y[1] (numeric) = -2.103232969399364351195943456573 absolute error = 2.56e-29 relative error = 1.2171737687865733468044684508283e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (closed_form) = -2.0924471592998804314462206696417 y[1] (numeric) = -2.092447159299880431446220669616 absolute error = 2.57e-29 relative error = 1.2282269535828592798627967222386e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (closed_form) = -2.0816613492003965116964978826848 y[1] (numeric) = -2.081661349200396511696497882659 absolute error = 2.58e-29 relative error = 1.2393946791542362588595532658915e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (closed_form) = -2.0708755391009125919467750957279 y[1] (numeric) = -2.070875539100912591946775095702 absolute error = 2.59e-29 relative error = 1.2506787352003150813875260235408e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (closed_form) = -2.060089729001428672197052308771 y[1] (numeric) = -2.060089729001428672197052308745 absolute error = 2.60e-29 relative error = 1.2620809489013266664550587053540e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = -2.049303918901944752447329521814 y[1] (numeric) = -2.049303918901944752447329521788 absolute error = 2.60e-29 relative error = 1.2687234802113336489100853301191e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (closed_form) = -2.0385181088024608326976067348571 y[1] (numeric) = -2.038518108802460832697606734831 absolute error = 2.61e-29 relative error = 1.2803418270997158251821557086000e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (closed_form) = -2.0277322987029769129478839479002 y[1] (numeric) = -2.027732298702976912947883947874 absolute error = 2.62e-29 relative error = 1.2920837734230807905635034315329e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (closed_form) = -2.0169464886034929931981611609433 y[1] (numeric) = -2.016946488603492993198161160917 absolute error = 2.63e-29 relative error = 1.3039513020600646325799457825185e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (closed_form) = -2.0061606785040090734484383739864 y[1] (numeric) = -2.00616067850400907344843837396 absolute error = 2.64e-29 relative error = 1.3159464385318547524675326749126e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (closed_form) = -1.9953748684045251536987155870295 y[1] (numeric) = -1.995374868404525153698715587003 absolute error = 2.65e-29 relative error = 1.3280712521546912520295799661433e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (closed_form) = -1.9845890583050412339489928000725 y[1] (numeric) = -1.984589058305041233948992800046 absolute error = 2.65e-29 relative error = 1.3352890306990102262253929007420e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (closed_form) = -1.9738032482055573141992700131156 y[1] (numeric) = -1.973803248205557314199270013089 absolute error = 2.66e-29 relative error = 1.3476520531710971546010027865536e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (closed_form) = -1.9630174381060733944495472261587 y[1] (numeric) = -1.963017438106073394449547226132 absolute error = 2.67e-29 relative error = 1.3601509330329872360356853084730e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (closed_form) = -1.9522316280065894746998244392018 y[1] (numeric) = -1.952231628006589474699824439175 absolute error = 2.68e-29 relative error = 1.3727879220646219592541764770434e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (closed_form) = -1.9414458179071055549501016522449 y[1] (numeric) = -1.941445817907105554950101652218 absolute error = 2.69e-29 relative error = 1.3855653220854970682862064363758e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (closed_form) = -1.930660007807621635200378865288 y[1] (numeric) = -1.930660007807621635200378865261 absolute error = 2.70e-29 relative error = 1.3984854863524154746258568421811e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (closed_form) = -1.919874197708137715450656078331 y[1] (numeric) = -1.919874197708137715450656078304 absolute error = 2.70e-29 relative error = 1.4063421463881032020113953637664e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (closed_form) = -1.9090883876086537957009332913741 y[1] (numeric) = -1.909088387608653795700933291347 absolute error = 2.71e-29 relative error = 1.4195256843998602690651954291141e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (closed_form) = -1.8983025775091698759512105044172 y[1] (numeric) = -1.89830257750916987595121050439 absolute error = 2.72e-29 relative error = 1.4328590353435691209718795861135e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (closed_form) = -1.8875167674096859562014877174603 y[1] (numeric) = -1.887516767409685956201487717433 absolute error = 2.73e-29 relative error = 1.4463447674409203597574972763358e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (closed_form) = -1.8767309573102020364517649305034 y[1] (numeric) = -1.876730957310202036451764930476 absolute error = 2.74e-29 relative error = 1.4599855079531836817475473538019e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (closed_form) = -1.8659451472107181167020421435465 y[1] (numeric) = -1.865945147210718116702042143519 absolute error = 2.75e-29 relative error = 1.4737839448875540941652280680018e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (closed_form) = -1.8551593371112341969523193565896 y[1] (numeric) = -1.855159337111234196952319356562 absolute error = 2.76e-29 relative error = 1.4877428287630218369598585579482e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (closed_form) = -1.8443735270117502772025965696326 y[1] (numeric) = -1.844373527011750277202596569605 absolute error = 2.76e-29 relative error = 1.4964430792236243038426647483456e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = -1.8335877169122663574528737826757 y[1] (numeric) = -1.833587716912266357452873782648 absolute error = 2.77e-29 relative error = 1.5106994742878391389623934598228e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (closed_form) = -1.8228019068127824377031509957188 y[1] (numeric) = -1.822801906812782437703150995691 absolute error = 2.78e-29 relative error = 1.5251245840865417236101662980630e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (closed_form) = -1.8120160967132985179534282087619 y[1] (numeric) = -1.812016096713298517953428208734 absolute error = 2.79e-29 relative error = 1.5397214213828479104561269081871e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (closed_form) = -1.801230286613814598203705421805 y[1] (numeric) = -1.801230286613814598203705421777 absolute error = 2.80e-29 relative error = 1.5544930711018643510367696813066e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (closed_form) = -1.7904444765143306784539826348481 y[1] (numeric) = -1.79044447651433067845398263482 absolute error = 2.81e-29 relative error = 1.5694426925042424354798298372348e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (closed_form) = -1.7796586664148467587042598478911 y[1] (numeric) = -1.779658666414846758704259847863 absolute error = 2.81e-29 relative error = 1.5789544663982075411494045635212e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (closed_form) = -1.7688728563153628389545370609342 y[1] (numeric) = -1.768872856315362838954537060906 absolute error = 2.82e-29 relative error = 1.5942355551060801338790424950230e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (closed_form) = -1.7580870462158789192048142739773 y[1] (numeric) = -1.758087046215878919204814273949 absolute error = 2.83e-29 relative error = 1.6097041418349082185440134072795e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (closed_form) = -1.7473012361163949994550914870204 y[1] (numeric) = -1.747301236116394999455091486992 absolute error = 2.84e-29 relative error = 1.6253636987702650449949716147489e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (closed_form) = -1.7365154260169110797053687000635 y[1] (numeric) = -1.736515426016911079705368700035 absolute error = 2.85e-29 relative error = 1.6412177843632039438242025949820e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = -1.7257296159174271599556459131066 y[1] (numeric) = -1.725729615917427159955645913078 absolute error = 2.86e-29 relative error = 1.6572700460260545788887989624680e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (closed_form) = -1.7149438058179432402059231261496 y[1] (numeric) = -1.714943805817943240205923126121 absolute error = 2.86e-29 relative error = 1.6676931280765329095736341760685e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (closed_form) = -1.7041579957184593204562003391927 y[1] (numeric) = -1.704157995718459320456200339164 absolute error = 2.87e-29 relative error = 1.6841161483915293056248041151751e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (closed_form) = -1.6933721856189754007064775522358 y[1] (numeric) = -1.693372185618975400706477552207 absolute error = 2.88e-29 relative error = 1.7007483791563982672307660280283e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (closed_form) = -1.6825863755194914809567547652789 y[1] (numeric) = -1.68258637551949148095675476525 absolute error = 2.89e-29 relative error = 1.7175938436490219591137274525848e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (closed_form) = -1.671800565420007561207031978322 y[1] (numeric) = -1.671800565420007561207031978293 absolute error = 2.90e-29 relative error = 1.7346566689738085373435657987484e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (closed_form) = -1.6610147553205236414573091913651 y[1] (numeric) = -1.661014755320523641457309191336 absolute error = 2.91e-29 relative error = 1.7519410894326832529530124351219e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (closed_form) = -1.6502289452210397217075864044081 y[1] (numeric) = -1.650228945221039721707586404379 absolute error = 2.91e-29 relative error = 1.7633916847884524245409406209725e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (closed_form) = -1.6394431351215558019578636174512 y[1] (numeric) = -1.639443135121555801957863617422 absolute error = 2.92e-29 relative error = 1.7810925779889876225083890211287e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (closed_form) = -1.6286573250220718822081408304943 y[1] (numeric) = -1.628657325022071882208140830465 absolute error = 2.93e-29 relative error = 1.7990279201060862005813665391679e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (closed_form) = -1.6178715149225879624584180435374 y[1] (numeric) = -1.617871514922587962458418043508 absolute error = 2.94e-29 relative error = 1.8172024001180794263619837574475e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (closed_form) = -1.6070857048231040427086952565805 y[1] (numeric) = -1.607085704823104042708695256551 absolute error = 2.95e-29 relative error = 1.8356208328819114873879783880530e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.48 y[1] (closed_form) = -1.5962998947236201229589724696236 y[1] (numeric) = -1.596299894723620122958972469594 absolute error = 2.96e-29 relative error = 1.8542881633857953330224324055586e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (closed_form) = -1.5855140846241362032092496826667 y[1] (numeric) = -1.585514084624136203209249682637 absolute error = 2.97e-29 relative error = 1.8732094711754463058083755933704e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (closed_form) = -1.5747282745246522834595268957097 y[1] (numeric) = -1.57472827452465228345952689568 absolute error = 2.97e-29 relative error = 1.8860396730328123763961041933251e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (closed_form) = -1.5639424644251683637098041087528 y[1] (numeric) = -1.563942464425168363709804108723 absolute error = 2.98e-29 relative error = 1.9054409403067827904851201960569e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (closed_form) = -1.5531566543256844439600813217959 y[1] (numeric) = -1.553156654325684443960081321766 absolute error = 2.99e-29 relative error = 1.9251116696262250158809280877154e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.43 y[1] (closed_form) = -1.542370844226200524210358534839 y[1] (numeric) = -1.542370844226200524210358534809 absolute error = 3.00e-29 relative error = 1.9450575140410440556179360897468e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.42 y[1] (closed_form) = -1.5315850341267166044606357478821 y[1] (numeric) = -1.531585034126716604460635747852 absolute error = 3.01e-29 relative error = 1.9652842858419873071822258946238e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.41 y[1] (closed_form) = -1.5207992240272326847109129609252 y[1] (numeric) = -1.520799224027232684710912960895 absolute error = 3.02e-29 relative error = 1.9857979622074829452935269024067e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (closed_form) = -1.5100134139277487649611901739682 y[1] (numeric) = -1.510013413927748764961190173938 absolute error = 3.02e-29 relative error = 1.9999822333661078234741949517097e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.39 y[1] (closed_form) = -1.4992276038282648452114673870113 y[1] (numeric) = -1.499227603828264845211467386981 absolute error = 3.03e-29 relative error = 2.0210406960643740500208525859147e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.38 y[1] (closed_form) = -1.4884417937287809254617446000544 y[1] (numeric) = -1.488441793728780925461744600024 absolute error = 3.04e-29 relative error = 2.0424043538742093523145632293110e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.37 y[1] (closed_form) = -1.4776559836292970057120218130975 y[1] (numeric) = -1.477655983629297005712021813067 absolute error = 3.05e-29 relative error = 2.0640798899002466298242404514430e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36 y[1] (closed_form) = -1.4668701735298130859622990261406 y[1] (numeric) = -1.46687017352981308596229902611 absolute error = 3.06e-29 relative error = 2.0860741838090197496502364562535e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.35 y[1] (closed_form) = -1.4560843634303291662125762391837 y[1] (numeric) = -1.456084363430329166212576239153 absolute error = 3.07e-29 relative error = 2.1083943191090339527329138833574e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.34 y[1] (closed_form) = -1.4452985533308452464628534522267 y[1] (numeric) = -1.445298553330845246462853452196 absolute error = 3.07e-29 relative error = 2.1241286050725342061115177183079e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.33 y[1] (closed_form) = -1.4345127432313613267131306652698 y[1] (numeric) = -1.434512743231361326713130665239 absolute error = 3.08e-29 relative error = 2.1470705049730261750786059432785e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.32 y[1] (closed_form) = -1.4237269331318774069634078783129 y[1] (numeric) = -1.423726933131877406963407878282 absolute error = 3.09e-29 relative error = 2.1703600094174649920603470201425e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.31 y[1] (closed_form) = -1.412941123032393487213685091356 y[1] (numeric) = -1.412941123032393487213685091325 absolute error = 3.10e-29 relative error = 2.1940050788152540199883742203175e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.3 y[1] (closed_form) = -1.4021553129329095674639623043991 y[1] (numeric) = -1.402155312932909567463962304368 absolute error = 3.11e-29 relative error = 2.2180139185114705714229864543413e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.29 y[1] (closed_form) = -1.3913695028334256477142395174422 y[1] (numeric) = -1.391369502833425647714239517411 absolute error = 3.12e-29 relative error = 2.2423949882804966817945694206755e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.28 y[1] (closed_form) = -1.3805836927339417279645167304852 y[1] (numeric) = -1.380583692733941727964516730454 absolute error = 3.12e-29 relative error = 2.2599136991264380621210894942747e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27 y[1] (closed_form) = -1.3697978826344578082147939435283 y[1] (numeric) = -1.369797882634457808214793943497 absolute error = 3.13e-29 relative error = 2.2850086422824958237638635548814e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.26 y[1] (closed_form) = -1.3590120725349738884650711565714 y[1] (numeric) = -1.35901207253497388846507115654 absolute error = 3.14e-29 relative error = 2.3105019178696021213057292672438e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.25 y[1] (closed_form) = -1.3482262624354899687153483696145 y[1] (numeric) = -1.348226262435489968715348369583 absolute error = 3.15e-29 relative error = 2.3364030858661021196082648310039e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.24 y[1] (closed_form) = -1.3374404523360060489656255826576 y[1] (numeric) = -1.337440452336006048965625582626 absolute error = 3.16e-29 relative error = 2.3627220146367392146576154845021e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.23 y[1] (closed_form) = -1.3266546422365221292159027957007 y[1] (numeric) = -1.326654642236522129215902795669 absolute error = 3.17e-29 relative error = 2.3894688934686874819841913518784e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.22 y[1] (closed_form) = -1.3158688321370382094661800087438 y[1] (numeric) = -1.315868832137038209466180008712 absolute error = 3.18e-29 relative error = 2.4166542457241103110702192826542e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.21 y[1] (closed_form) = -1.3050830220375542897164572217868 y[1] (numeric) = -1.305083022037554289716457221755 absolute error = 3.18e-29 relative error = 2.4366265948623260987650144833375e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.2 y[1] (closed_form) = -1.2942972119380703699667344348299 y[1] (numeric) = -1.294297211938070369966734434798 absolute error = 3.19e-29 relative error = 2.4646580171669529634756497390551e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.19 y[1] (closed_form) = -1.283511401838586450217011647873 y[1] (numeric) = -1.283511401838586450217011647841 absolute error = 3.20e-29 relative error = 2.4931605558128340612066318057932e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18 y[1] (closed_form) = -1.2727255917391025304672888609161 y[1] (numeric) = -1.272725591739102530467288860884 absolute error = 3.21e-29 relative error = 2.5221461883340690758483084838319e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.17 y[1] (closed_form) = -1.2619397816396186107175660739592 y[1] (numeric) = -1.261939781639618610717566073927 absolute error = 3.22e-29 relative error = 2.5516273017531029796291591221790e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.16 y[1] (closed_form) = -1.2511539715401346909678432870023 y[1] (numeric) = -1.25115397154013469096784328697 absolute error = 3.23e-29 relative error = 2.5816167102310857438200244267044e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.15 y[1] (closed_form) = -1.2403681614406507712181205000453 y[1] (numeric) = -1.240368161440650771218120500013 absolute error = 3.23e-29 relative error = 2.6040655511896169242010681173716e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.14 y[1] (closed_form) = -1.2295823513411668514683977130884 y[1] (numeric) = -1.229582351341166851468397713056 absolute error = 3.24e-29 relative error = 2.6350410742850775785055618394781e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.13 y[1] (closed_form) = -1.2187965412416829317186749261315 y[1] (numeric) = -1.218796541241682931718674926099 absolute error = 3.25e-29 relative error = 2.6665648367273605452756218221530e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 memory used=149.2MB, alloc=40.3MB, time=2.00 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.12 y[1] (closed_form) = -1.2080107311421990119689521391746 y[1] (numeric) = -1.208010731142199011968952139142 absolute error = 3.26e-29 relative error = 2.6986515234989699935951471616612e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.11 y[1] (closed_form) = -1.1972249210427150922192293522177 y[1] (numeric) = -1.197224921042715092219229352185 absolute error = 3.27e-29 relative error = 2.7313163487709688013438531379174e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.1 y[1] (closed_form) = -1.1864391109432311724695065652608 y[1] (numeric) = -1.186439110943231172469506565228 absolute error = 3.28e-29 relative error = 2.7645750799570039510516264955601e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09 y[1] (closed_form) = -1.1756533008437472527197837783038 y[1] (numeric) = -1.175653300843747252719783778271 absolute error = 3.28e-29 relative error = 2.7899381540850498588594395826755e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.08 y[1] (closed_form) = -1.1648674907442633329700609913469 y[1] (numeric) = -1.164867490744263332970060991314 absolute error = 3.29e-29 relative error = 2.8243555821941049285387975066149e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.07 y[1] (closed_form) = -1.15408168064477941322033820439 y[1] (numeric) = -1.154081680644779413220338204357 absolute error = 3.30e-29 relative error = 2.8594163267164133640065546440858e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.06 y[1] (closed_form) = -1.1432958705452954934706154174331 y[1] (numeric) = -1.1432958705452954934706154174 absolute error = 3.31e-29 relative error = 2.8951385947202747888227600294336e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.05 y[1] (closed_form) = -1.1325100604458115737208926304762 y[1] (numeric) = -1.132510060445811573720892630443 absolute error = 3.32e-29 relative error = 2.9315412868765907169687978983117e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.04 y[1] (closed_form) = -1.1217242503463276539711698435193 y[1] (numeric) = -1.121724250346327653971169843486 absolute error = 3.33e-29 relative error = 2.9686440308051434898868749569760e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.03 y[1] (closed_form) = -1.1109384402468437342214470565623 y[1] (numeric) = -1.110938440246843734221447056529 absolute error = 3.33e-29 relative error = 2.9974658175119895431867475293741e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.02 y[1] (closed_form) = -1.1001526301473598144717242696054 y[1] (numeric) = -1.100152630147359814471724269572 absolute error = 3.34e-29 relative error = 3.0359423851512531432818256051795e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.01 y[1] (closed_form) = -1.0893668200478758947220014826485 y[1] (numeric) = -1.089366820047875894722001482615 absolute error = 3.35e-29 relative error = 3.0751808650209972107055190884265e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = -1.0785810099483919749722786956916 y[1] (numeric) = -1.078581009948391974972278695658 absolute error = 3.36e-29 relative error = 3.1152041144881361594776864413385e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (closed_form) = -1.0677951998489080552225559087347 y[1] (numeric) = -1.067795199848908055222555908701 absolute error = 3.37e-29 relative error = 3.1560359144495607435785844478447e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (closed_form) = -1.0570093897494241354728331217778 y[1] (numeric) = -1.057009389749424135472833121744 absolute error = 3.38e-29 relative error = 3.1977010164510144008243987401980e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (closed_form) = -1.0462235796499402157231103348209 y[1] (numeric) = -1.046223579649940215723110334787 absolute error = 3.39e-29 relative error = 3.2402251927205392674979617808472e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (closed_form) = -1.0354377695504562959733875478639 y[1] (numeric) = -1.03543776955045629597338754783 absolute error = 3.39e-29 relative error = 3.2739775384780448848677322160646e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (closed_form) = -1.024651959450972376223664760907 y[1] (numeric) = -1.024651959450972376223664760873 absolute error = 3.40e-29 relative error = 3.3181998713219495433033000941577e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (closed_form) = -1.0138661493514884564739419739501 y[1] (numeric) = -1.013866149351488456473941973916 absolute error = 3.41e-29 relative error = 3.3633631048646606838332417568910e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (closed_form) = -1.0030803392520045367242191869932 y[1] (numeric) = -1.003080339252004536724219186959 absolute error = 3.42e-29 relative error = 3.4094975907416236768476982940917e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.92 y[1] (closed_form) = -0.99229452915252061697449640003627 y[1] (numeric) = -0.99229452915252061697449640000208 absolute error = 3.419e-29 relative error = 3.4455495818565403497846176057636e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (closed_form) = -0.98150871905303669722477361307936 y[1] (numeric) = -0.98150871905303669722477361304516 absolute error = 3.420e-29 relative error = 3.4844316037249560653498455093465e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (closed_form) = -0.97072290895355277747505082612244 y[1] (numeric) = -0.97072290895355277747505082608824 absolute error = 3.420e-29 relative error = 3.5231475104330111327426215705614e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.89 y[1] (closed_form) = -0.95993709885406885772532803916552 y[1] (numeric) = -0.95993709885406885772532803913132 absolute error = 3.420e-29 relative error = 3.5627334375165281117622015882082e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (closed_form) = -0.94915128875458493797560525220861 y[1] (numeric) = -0.9491512887545849379756052521744 absolute error = 3.421e-29 relative error = 3.6042726175811396785623529883046e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (closed_form) = -0.93836547865510101822588246525169 y[1] (numeric) = -0.93836547865510101822588246521748 absolute error = 3.421e-29 relative error = 3.6457010384728769162469777352967e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.86 y[1] (closed_form) = -0.92757966855561709847615967829478 y[1] (numeric) = -0.92757966855561709847615967826056 absolute error = 3.422e-29 relative error = 3.6891709855268555986062579603615e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (closed_form) = -0.91679385845613317872643689133786 y[1] (numeric) = -0.91679385845613317872643689130364 absolute error = 3.422e-29 relative error = 3.7325729971212891938839786422481e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (closed_form) = -0.90600804835664925897671410438094 y[1] (numeric) = -0.90600804835664925897671410434672 absolute error = 3.422e-29 relative error = 3.7770083899441616842873593403701e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (closed_form) = -0.89522223825716533922699131742403 y[1] (numeric) = -0.8952222382571653392269913173898 absolute error = 3.423e-29 relative error = 3.8236315561864924246601121230285e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (closed_form) = -0.88443642815768141947726853046711 y[1] (numeric) = -0.88443642815768141947726853043288 absolute error = 3.423e-29 relative error = 3.8702612093107179420340159294069e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.81 y[1] (closed_form) = -0.8736506180581974997275457435102 y[1] (numeric) = -0.87365061805819749972754574347596 absolute error = 3.424e-29 relative error = 3.9191868342178785310301287386622e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (closed_form) = -0.86286480795871357997782295655328 y[1] (numeric) = -0.86286480795871357997782295651904 absolute error = 3.424e-29 relative error = 3.9681766696456020126680053478955e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (closed_form) = -0.85207899785922966022810016959636 y[1] (numeric) = -0.85207899785922966022810016956212 absolute error = 3.424e-29 relative error = 4.0184067540714957090308914915398e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (closed_form) = -0.84129318775974574047837738263945 y[1] (numeric) = -0.8412931877597457404783773826052 absolute error = 3.425e-29 relative error = 4.0711134356386852664114301211785e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (closed_form) = -0.83050737766026182072865459568253 y[1] (numeric) = -0.83050737766026182072865459564828 absolute error = 3.425e-29 relative error = 4.1239850386989279322089811617133e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (closed_form) = -0.81972156756077790097893180872562 y[1] (numeric) = -0.81972156756077790097893180869136 absolute error = 3.426e-29 relative error = 4.1794679261577202703518772509500e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (closed_form) = -0.8089357574612939812292090217687 y[1] (numeric) = -0.80893575746129398122920902173444 absolute error = 3.426e-29 relative error = 4.2351941651731565406232356142960e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (closed_form) = -0.79814994736181006147948623481178 y[1] (numeric) = -0.79814994736181006147948623477752 absolute error = 3.426e-29 relative error = 4.2924265187565775749559820415162e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (closed_form) = -0.78736413726232614172976344785487 y[1] (numeric) = -0.7873641372623261417297634478206 absolute error = 3.427e-29 relative error = 4.3524969424130963056629286670202e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (closed_form) = -0.77657832716284222198004066089795 y[1] (numeric) = -0.77657832716284222198004066086368 absolute error = 3.427e-29 relative error = 4.4129482888355004210193582318400e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (closed_form) = -0.76579251706335830223031787394104 y[1] (numeric) = -0.76579251706335830223031787390676 absolute error = 3.428e-29 relative error = 4.4764083268214833814090833001796e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (closed_form) = -0.75500670696387438248059508698412 y[1] (numeric) = -0.75500670696387438248059508694984 absolute error = 3.428e-29 relative error = 4.5403570172046474297149273473251e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.69 y[1] (closed_form) = -0.7442208968643904627308723000272 y[1] (numeric) = -0.74422089686439046273087229999292 absolute error = 3.428e-29 relative error = 4.6061592928163089866673175987356e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.68 y[1] (closed_form) = -0.73343508676490654298114951307029 y[1] (numeric) = -0.733435086764906542981149513036 absolute error = 3.429e-29 relative error = 4.6752603766543324977455299401916e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.67 y[1] (closed_form) = -0.72264927666542262323142672611337 y[1] (numeric) = -0.72264927666542262323142672607908 absolute error = 3.429e-29 relative error = 4.7450403822760389529357617303438e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.66 y[1] (closed_form) = -0.71186346656593870348170393915646 y[1] (numeric) = -0.71186346656593870348170393912216 absolute error = 3.430e-29 relative error = 4.8183396972827863577779872356562e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.65 y[1] (closed_form) = -0.70107765646645478373198115219954 y[1] (numeric) = -0.70107765646645478373198115216524 absolute error = 3.430e-29 relative error = 4.8924680003179061478976485777432e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.64 y[1] (closed_form) = -0.69029184636697086398225836524262 y[1] (numeric) = -0.69029184636697086398225836520832 absolute error = 3.430e-29 relative error = 4.9689128128228734314585493367705e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.63 y[1] (closed_form) = -0.67950603626748694423253557828571 y[1] (numeric) = -0.6795060362674869442325355782514 absolute error = 3.431e-29 relative error = 5.0492561020449712599999726852950e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.62 y[1] (closed_form) = -0.66872022616800302448281279132879 y[1] (numeric) = -0.66872022616800302448281279129448 absolute error = 3.431e-29 relative error = 5.1306957165940836996773915995740e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.61 y[1] (closed_form) = -0.65793441606851910473309000437188 y[1] (numeric) = -0.65793441606851910473309000433756 absolute error = 3.432e-29 relative error = 5.2163253907705324450270393572765e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6 y[1] (closed_form) = -0.64714860596903518498336721741496 y[1] (numeric) = -0.64714860596903518498336721738064 absolute error = 3.432e-29 relative error = 5.3032641472833746524441566798978e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.59 y[1] (closed_form) = -0.63636279586955126523364443045804 y[1] (numeric) = -0.63636279586955126523364443042372 absolute error = 3.432e-29 relative error = 5.3931499802881776126550745897266e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.58 y[1] (closed_form) = -0.62557698577006734548392164350113 y[1] (numeric) = -0.6255769857700673454839216434668 absolute error = 3.433e-29 relative error = 5.4877338490546856709189745243818e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.57 y[1] (closed_form) = -0.61479117567058342573419885654421 y[1] (numeric) = -0.61479117567058342573419885650988 absolute error = 3.433e-29 relative error = 5.5840098814942415598824653055113e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.56 y[1] (closed_form) = -0.6040053655710995059844760695873 y[1] (numeric) = -0.60400536557109950598447606955296 absolute error = 3.434e-29 relative error = 5.6853799580953760478562793577575e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.55 y[1] (closed_form) = -0.59321955547161558623475328263038 y[1] (numeric) = -0.59321955547161558623475328259604 absolute error = 3.434e-29 relative error = 5.7887505027880192487263935278986e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.54 y[1] (closed_form) = -0.58243374537213166648503049567346 y[1] (numeric) = -0.58243374537213166648503049563912 absolute error = 3.434e-29 relative error = 5.8959495861729825681472526673041e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.53 y[1] (closed_form) = -0.57164793527264774673530770871655 y[1] (numeric) = -0.5716479352726477467353077086822 absolute error = 3.435e-29 relative error = 6.0089432464435914801245804840509e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.52 y[1] (closed_form) = -0.56086212517316382698558492175963 y[1] (numeric) = -0.56086212517316382698558492172528 absolute error = 3.435e-29 relative error = 6.1244998473367374701269762625904e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.51 y[1] (closed_form) = -0.55007631507367990723586213480272 y[1] (numeric) = -0.55007631507367990723586213476836 absolute error = 3.436e-29 relative error = 6.2464060092094046708481154367642e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (closed_form) = -0.5392905049741959874861393478458 y[1] (numeric) = -0.53929050497419598748613934781144 absolute error = 3.436e-29 relative error = 6.3713341293935927642650777454995e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (closed_form) = -0.52850469487471206773641656088888 y[1] (numeric) = -0.52850469487471206773641656085452 absolute error = 3.436e-29 relative error = 6.5013613565240742492500793321424e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (closed_form) = -0.51771888477522814798669377393197 y[1] (numeric) = -0.5177188847752281479866937738976 absolute error = 3.437e-29 relative error = 6.6387379349551859995813543519845e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (closed_form) = -0.50693307467574422823697098697505 y[1] (numeric) = -0.50693307467574422823697098694068 absolute error = 3.437e-29 relative error = 6.7799876782521048506362767850055e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (closed_form) = -0.49614726457626030848724820001814 y[1] (numeric) = -0.49614726457626030848724819998376 absolute error = 3.438e-29 relative error = 6.9293942453482221249251332720768e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (closed_form) = -0.48536145447677638873752541306122 y[1] (numeric) = -0.48536145447677638873752541302684 absolute error = 3.438e-29 relative error = 7.0833807841337381721456917892341e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.44 y[1] (closed_form) = -0.4745756443772924689878026261043 y[1] (numeric) = -0.47457564437729246898780262606992 absolute error = 3.438e-29 relative error = 7.2443667110458685851490029662622e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.43 y[1] (closed_form) = -0.46378983427780854923807983914739 y[1] (numeric) = -0.463789834277808549238079839113 absolute error = 3.439e-29 relative error = 7.4149965045159885468187733054839e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.42 y[1] (closed_form) = -0.45300402417832462948835705219047 y[1] (numeric) = -0.45300402417832462948835705215608 absolute error = 3.439e-29 relative error = 7.5915440403377977979335060032336e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.41 y[1] (closed_form) = -0.44221821407884070973863426523356 y[1] (numeric) = -0.44221821407884070973863426519916 absolute error = 3.440e-29 relative error = 7.7789649781062633482892286281972e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4 y[1] (closed_form) = -0.43143240397935678998891147827664 y[1] (numeric) = -0.43143240397935678998891147824224 absolute error = 3.440e-29 relative error = 7.9734391025589199319964593439022e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.39 y[1] (closed_form) = -0.42064659387987287023918869131972 y[1] (numeric) = -0.42064659387987287023918869128532 absolute error = 3.440e-29 relative error = 8.1778862590347896738425224040024e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.38 y[1] (closed_form) = -0.40986078378038895048946590436281 y[1] (numeric) = -0.4098607837803889504894659043284 absolute error = 3.441e-29 relative error = 8.3955336450138443959607761941149e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.37 y[1] (closed_form) = -0.39907497368090503073974311740589 y[1] (numeric) = -0.39907497368090503073974311737148 absolute error = 3.441e-29 relative error = 8.6224399597439482985543106858478e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.36 y[1] (closed_form) = -0.38828916358142111099002033044898 y[1] (numeric) = -0.38828916358142111099002033041456 absolute error = 3.442e-29 relative error = 8.8645275810748715781433504721289e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.35 y[1] (closed_form) = -0.37750335348193719124029754349206 y[1] (numeric) = -0.37750335348193719124029754345764 absolute error = 3.442e-29 relative error = 9.1177997976770107660903033427613e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.34 y[1] (closed_form) = -0.36671754338245327149057475653514 y[1] (numeric) = -0.36671754338245327149057475650072 absolute error = 3.442e-29 relative error = 9.3859703799616287297988416763720e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.33 y[1] (closed_form) = -0.35593173328296935174085196957823 y[1] (numeric) = -0.3559317332829693517408519695438 absolute error = 3.443e-29 relative error = 9.6732032523292323206003557156643e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.32 y[1] (closed_form) = -0.34514592318348543199112918262131 y[1] (numeric) = -0.34514592318348543199112918258688 absolute error = 3.443e-29 relative error = 9.9754908539645208306191168317789e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.31 y[1] (closed_form) = -0.3343601130840015122414063956644 y[1] (numeric) = -0.33436011308400151224140639562996 absolute error = 3.444e-29 relative error = 1.0300271668872063107950414846361e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3 y[1] (closed_form) = -0.32357430298451759249168360870748 y[1] (numeric) = -0.32357430298451759249168360867304 absolute error = 3.444e-29 relative error = 1.0643614057834465211548762007907e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.29 y[1] (closed_form) = -0.31278849288503367274196082175056 y[1] (numeric) = -0.31278849288503367274196082171612 absolute error = 3.444e-29 relative error = 1.1010635232242550218843546904731e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.28 y[1] (closed_form) = -0.30200268278554975299223803479365 y[1] (numeric) = -0.3020026827855497529922380347592 absolute error = 3.445e-29 relative error = 1.1407183433685830218325499352053e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.27 y[1] (closed_form) = -0.29121687268606583324251524783673 y[1] (numeric) = -0.29121687268606583324251524780228 absolute error = 3.445e-29 relative error = 1.1829671709007527633819036365092e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.26 y[1] (closed_form) = -0.28043106258658191349279246087982 y[1] (numeric) = -0.28043106258658191349279246084536 absolute error = 3.446e-29 relative error = 1.2288225021206635995375580902990e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.25 y[1] (closed_form) = -0.2696452524870979937430696739229 y[1] (numeric) = -0.26964525248709799374306967388844 absolute error = 3.446e-29 relative error = 1.2779754022054901435190604139110e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.24 y[1] (closed_form) = -0.25885944238761407399334688696598 y[1] (numeric) = -0.25885944238761407399334688693152 absolute error = 3.446e-29 relative error = 1.3312243772973855661656879311573e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.23 y[1] (closed_form) = -0.24807363228813015424362410000907 y[1] (numeric) = -0.2480736322881301542436240999746 absolute error = 3.447e-29 relative error = 1.3895068041719209810713748917306e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.22 y[1] (closed_form) = -0.23728782218864623449390131305215 y[1] (numeric) = -0.23728782218864623449390131301768 absolute error = 3.447e-29 relative error = 1.4526662043615537529382555686274e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.21 y[1] (closed_form) = -0.22650201208916231474417852609524 y[1] (numeric) = -0.22650201208916231474417852606076 absolute error = 3.448e-29 relative error = 1.5222822827033862638717492700872e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2 y[1] (closed_form) = -0.21571620198967839499445573913832 y[1] (numeric) = -0.21571620198967839499445573910384 absolute error = 3.448e-29 relative error = 1.5983963968385555770653367335916e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.19 y[1] (closed_form) = -0.2049303918901944752447329521814 y[1] (numeric) = -0.20493039189019447524473295214692 absolute error = 3.448e-29 relative error = 1.6825225229879532390161439300964e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.18 y[1] (closed_form) = -0.19414458179071055549501016522449 y[1] (numeric) = -0.19414458179071055549501016519 absolute error = 3.449e-29 relative error = 1.7765110765326689176651026018810e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.17 y[1] (closed_form) = -0.18335877169122663574528737826757 y[1] (numeric) = -0.18335877169122663574528737823308 absolute error = 3.449e-29 relative error = 1.8810117280934141481159909902270e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.16 y[1] (closed_form) = -0.17257296159174271599556459131066 y[1] (numeric) = -0.17257296159174271599556459127616 absolute error = 3.450e-29 relative error = 1.9991544261503105934148099372429e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.15 y[1] (closed_form) = -0.16178715149225879624584180435374 y[1] (numeric) = -0.16178715149225879624584180431924 absolute error = 3.450e-29 relative error = 2.1324313878936646329757972663925e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.14 y[1] (closed_form) = -0.15100134139277487649611901739682 y[1] (numeric) = -0.15100134139277487649611901736232 absolute error = 3.450e-29 relative error = 2.2847479156003549639026399282777e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.13 y[1] (closed_form) = -0.14021553129329095674639623043991 y[1] (numeric) = -0.1402155312932909567463962304054 absolute error = 3.451e-29 relative error = 2.4612109430170691131770823967626e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.12 y[1] (closed_form) = -0.12942972119380703699667344348299 y[1] (numeric) = -0.12942972119380703699667344344848 absolute error = 3.451e-29 relative error = 2.6663118549351582059418392631596e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.11 y[1] (closed_form) = -0.11864391109432311724695065652608 y[1] (numeric) = -0.11864391109432311724695065649156 absolute error = 3.452e-29 relative error = 2.9095467000035297679970166654492e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (closed_form) = -0.10785810099483919749722786956916 y[1] (numeric) = -0.10785810099483919749722786953464 absolute error = 3.452e-29 relative error = 3.2005013700038827447967183319942e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09 y[1] (closed_form) = -0.097072290895355277747505082612244 y[1] (numeric) = -0.097072290895355277747505082577722 absolute error = 3.4522e-29 relative error = 3.5563186653558014714778006391498e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.08 y[1] (closed_form) = -0.086286480795871357997782295655328 y[1] (numeric) = -0.086286480795871357997782295620806 absolute error = 3.4522e-29 relative error = 4.0008584985252766554125257190435e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.07 y[1] (closed_form) = -0.075500670696387438248059508698412 y[1] (numeric) = -0.07550067069638743824805950866389 absolute error = 3.4522e-29 relative error = 4.5724097126003161776143151074783e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06 y[1] (closed_form) = -0.064714860596903518498336721741496 y[1] (numeric) = -0.064714860596903518498336721706974 absolute error = 3.4522e-29 relative error = 5.3344779980337022072167009587247e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.05 y[1] (closed_form) = -0.05392905049741959874861393478458 y[1] (numeric) = -0.053929050497419598748613934750058 absolute error = 3.4522e-29 relative error = 6.4013735976404426486600411504696e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.04 y[1] (closed_form) = -0.043143240397935678998891147827664 y[1] (numeric) = -0.043143240397935678998891147793142 absolute error = 3.4522e-29 relative error = 8.0017169970505533108250514380870e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03 y[1] (closed_form) = -0.032357430298451759249168360870748 y[1] (numeric) = -0.032357430298451759249168360836226 absolute error = 3.4522e-29 relative error = 1.0668955996067404414433401917449e-25 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02 y[1] (closed_form) = -0.021571620198967839499445573913832 y[1] (numeric) = -0.02157162019896783949944557387931 absolute error = 3.4522e-29 relative error = 1.6003433994101106621650102876174e-25 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01 y[1] (closed_form) = -0.010785810099483919749722786956916 y[1] (numeric) = -0.010785810099483919749722786922394 absolute error = 3.4522e-29 relative error = 3.2006867988202213243300205752348e-25 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 0 y[1] (numeric) = 3.4522000000000000000000000000000e-29 absolute error = 3.4522000000000000000000000000000e-29 relative error = -1 % Desired digits = 8 Estimated correct digits = -16 Correct digits = -16 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (closed_form) = 0.010785810099483919749722786956916 y[1] (numeric) = 0.010785810099483919749722786991438 absolute error = 3.4522e-29 relative error = 3.2006867988202213243300205752348e-25 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (closed_form) = 0.021571620198967839499445573913832 y[1] (numeric) = 0.021571620198967839499445573948354 absolute error = 3.4522e-29 relative error = 1.6003433994101106621650102876174e-25 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (closed_form) = 0.032357430298451759249168360870748 y[1] (numeric) = 0.03235743029845175924916836090527 absolute error = 3.4522e-29 relative error = 1.0668955996067404414433401917449e-25 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (closed_form) = 0.043143240397935678998891147827664 y[1] (numeric) = 0.043143240397935678998891147862186 absolute error = 3.4522e-29 relative error = 8.0017169970505533108250514380870e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (closed_form) = 0.05392905049741959874861393478458 y[1] (numeric) = 0.053929050497419598748613934819102 absolute error = 3.4522e-29 relative error = 6.4013735976404426486600411504696e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (closed_form) = 0.064714860596903518498336721741496 y[1] (numeric) = 0.064714860596903518498336721776018 absolute error = 3.4522e-29 relative error = 5.3344779980337022072167009587247e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (closed_form) = 0.075500670696387438248059508698412 y[1] (numeric) = 0.075500670696387438248059508732934 absolute error = 3.4522e-29 relative error = 4.5724097126003161776143151074783e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (closed_form) = 0.086286480795871357997782295655328 y[1] (numeric) = 0.08628648079587135799778229568985 absolute error = 3.4522e-29 relative error = 4.0008584985252766554125257190435e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (closed_form) = 0.097072290895355277747505082612244 y[1] (numeric) = 0.097072290895355277747505082646766 absolute error = 3.4522e-29 relative error = 3.5563186653558014714778006391498e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.10785810099483919749722786956916 y[1] (numeric) = 0.10785810099483919749722786960368 absolute error = 3.452e-29 relative error = 3.2005013700038827447967183319942e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0.11864391109432311724695065652608 y[1] (numeric) = 0.1186439110943231172469506565606 absolute error = 3.452e-29 relative error = 2.9095467000035297679970166654492e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.12942972119380703699667344348299 y[1] (numeric) = 0.12942972119380703699667344351752 absolute error = 3.453e-29 relative error = 2.6678570950713130353860246234976e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.14021553129329095674639623043991 y[1] (numeric) = 0.14021553129329095674639623047444 absolute error = 3.453e-29 relative error = 2.4626373185273658788178688832284e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.15100134139277487649611901739682 y[1] (numeric) = 0.15100134139277487649611901743136 absolute error = 3.454e-29 relative error = 2.2873968986909061000926719745713e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.16178715149225879624584180435374 y[1] (numeric) = 0.16178715149225879624584180438828 absolute error = 3.454e-29 relative error = 2.1349037721115123600864938429332e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=197.5MB, alloc=40.3MB, time=2.62 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (closed_form) = 0.17257296159174271599556459131066 y[1] (numeric) = 0.1725729615917427159955645913452 absolute error = 3.454e-29 relative error = 2.0014722863545428375810879777498e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (closed_form) = 0.18335877169122663574528737826757 y[1] (numeric) = 0.18335877169122663574528737830212 absolute error = 3.455e-29 relative error = 1.8842840013229184928213246944721e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = 0.19414458179071055549501016522449 y[1] (numeric) = 0.19414458179071055549501016525904 absolute error = 3.455e-29 relative error = 1.7796015568049785765534733225570e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (closed_form) = 0.2049303918901944752447329521814 y[1] (numeric) = 0.20493039189019447524473295221596 absolute error = 3.456e-29 relative error = 1.6864262875424496502435595772660e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0.21571620198967839499445573913832 y[1] (numeric) = 0.21571620198967839499445573917288 absolute error = 3.456e-29 relative error = 1.6021049731653271677313815984027e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = 0.22650201208916231474417852609524 y[1] (numeric) = 0.2265020120891623147441785261298 absolute error = 3.456e-29 relative error = 1.5258142601574544454584586651454e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 0.23728782218864623449390131305215 y[1] (numeric) = 0.23728782218864623449390131308672 absolute error = 3.457e-29 relative error = 1.4568804956419760150587610968219e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 0.24807363228813015424362410000907 y[1] (numeric) = 0.24807363228813015424362410004364 absolute error = 3.457e-29 relative error = 1.3935378653966727100562062665253e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = 0.25885944238761407399334688696598 y[1] (numeric) = 0.25885944238761407399334688700056 absolute error = 3.458e-29 relative error = 1.3358600977058500544982440121712e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = 0.2696452524870979937430696739229 y[1] (numeric) = 0.26964525248709799374306967395748 absolute error = 3.458e-29 relative error = 1.2824256937976160523183142516844e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = 0.28043106258658191349279246087982 y[1] (numeric) = 0.2804310625865819134927924609144 absolute error = 3.458e-29 relative error = 1.2331016286515538964599175496965e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (closed_form) = 0.29121687268606583324251524783673 y[1] (numeric) = 0.29121687268606583324251524787132 absolute error = 3.459e-29 relative error = 1.1877745846576788994304803131162e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (closed_form) = 0.30200268278554975299223803479365 y[1] (numeric) = 0.30200268278554975299223803482824 absolute error = 3.459e-29 relative error = 1.1453540637770475101651060162192e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (closed_form) = 0.31278849288503367274196082175056 y[1] (numeric) = 0.31278849288503367274196082178516 absolute error = 3.460e-29 relative error = 1.1061788009163537676306234695229e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 0.32357430298451759249168360870748 y[1] (numeric) = 0.32357430298451759249168360874208 absolute error = 3.460e-29 relative error = 1.0693061742191419753762693538722e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (closed_form) = 0.3343601130840015122414063956644 y[1] (numeric) = 0.334360113084001512241406395699 absolute error = 3.460e-29 relative error = 1.0348124266636857826221961489085e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (closed_form) = 0.34514592318348543199112918262131 y[1] (numeric) = 0.34514592318348543199112918265592 absolute error = 3.461e-29 relative error = 1.0027642708559746324360372743185e-26 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (closed_form) = 0.35593173328296935174085196957823 y[1] (numeric) = 0.35593173328296935174085196961284 absolute error = 3.461e-29 relative error = 9.7237747476942994660464220539977e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (closed_form) = 0.36671754338245327149057475653514 y[1] (numeric) = 0.36671754338245327149057475656976 absolute error = 3.462e-29 relative error = 9.4405082671200344748877367471237e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (closed_form) = 0.37750335348193719124029754349206 y[1] (numeric) = 0.37750335348193719124029754352668 absolute error = 3.462e-29 relative error = 9.1707794594880334898909442686344e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (closed_form) = 0.38828916358142111099002033044898 y[1] (numeric) = 0.3882891635814211109900203304836 absolute error = 3.462e-29 relative error = 8.9160355856133658929495291500611e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (closed_form) = 0.39907497368090503073974311740589 y[1] (numeric) = 0.39907497368090503073974311744052 absolute error = 3.463e-29 relative error = 8.6775674456824449165630857033104e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (closed_form) = 0.40986078378038895048946590436281 y[1] (numeric) = 0.40986078378038895048946590439744 absolute error = 3.463e-29 relative error = 8.4492104076381700503377413426968e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (closed_form) = 0.42064659387987287023918869131972 y[1] (numeric) = 0.42064659387987287023918869135436 absolute error = 3.464e-29 relative error = 8.2349412794466602994739818626349e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0.43143240397935678998891147827664 y[1] (numeric) = 0.43143240397935678998891147831128 absolute error = 3.464e-29 relative error = 8.0290677474604937919871323160690e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (closed_form) = 0.44221821407884070973863426523356 y[1] (numeric) = 0.4422182140788407097386342652682 absolute error = 3.464e-29 relative error = 7.8332368267907256507191534790916e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (closed_form) = 0.45300402417832462948835705219047 y[1] (numeric) = 0.45300402417832462948835705222512 absolute error = 3.465e-29 relative error = 7.6489386739664057487175336729295e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (closed_form) = 0.46378983427780854923807983914739 y[1] (numeric) = 0.46378983427780854923807983918204 absolute error = 3.465e-29 relative error = 7.4710563792230009638636375410008e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (closed_form) = 0.4745756443772924689878026261043 y[1] (numeric) = 0.47457564437729246898780262613896 absolute error = 3.466e-29 relative error = 7.3033667889717802548360803609845e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (closed_form) = 0.48536145447677638873752541306122 y[1] (numeric) = 0.48536145447677638873752541309588 absolute error = 3.466e-29 relative error = 7.1410697492168518047286119085181e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (closed_form) = 0.49614726457626030848724820001814 y[1] (numeric) = 0.4961472645762603084872482000528 absolute error = 3.466e-29 relative error = 6.9858291024947463307127725192025e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (closed_form) = 0.50693307467574422823697098697505 y[1] (numeric) = 0.50693307467574422823697098700972 absolute error = 3.467e-29 relative error = 6.8391670877218642761582693085871e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (closed_form) = 0.51771888477522814798669377393197 y[1] (numeric) = 0.51771888477522814798669377396664 absolute error = 3.467e-29 relative error = 6.6966844400609921037383053646582e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (closed_form) = 0.52850469487471206773641656088888 y[1] (numeric) = 0.52850469487471206773641656092356 absolute error = 3.468e-29 relative error = 6.5619095414509573621650975331403e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 0.5392905049741959874861393478458 y[1] (numeric) = 0.53929050497419598748613934788048 absolute error = 3.468e-29 relative error = 6.4306713506219382149217955824774e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = 0.55007631507367990723586213480272 y[1] (numeric) = 0.5500763150736799072358621348374 absolute error = 3.468e-29 relative error = 6.3045797555117041322762701788994e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 0.56086212517316382698558492175963 y[1] (numeric) = 0.56086212517316382698558492179432 absolute error = 3.469e-29 relative error = 6.1851208065243500098604019373875e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 0.57164793527264774673530770871655 y[1] (numeric) = 0.57164793527264774673530770875124 absolute error = 3.469e-29 relative error = 6.0684204139484188775988849197009e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 0.58243374537213166648503049567346 y[1] (numeric) = 0.58243374537213166648503049570816 absolute error = 3.470e-29 relative error = 5.9577591916191757459146670808228e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 0.59321955547161558623475328263038 y[1] (numeric) = 0.59321955547161558623475328266508 absolute error = 3.470e-29 relative error = 5.8494362972260998232616731338987e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = 0.6040053655710995059844760695873 y[1] (numeric) = 0.604005365571099505984476069622 absolute error = 3.470e-29 relative error = 5.7449820776327766121320003993647e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (closed_form) = 0.61479117567058342573419885654421 y[1] (numeric) = 0.61479117567058342573419885657892 absolute error = 3.471e-29 relative error = 5.6458194869404347376498797190299e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (closed_form) = 0.62557698577006734548392164350113 y[1] (numeric) = 0.62557698577006734548392164353584 absolute error = 3.471e-29 relative error = 5.5484777716483582766559162755983e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (closed_form) = 0.63636279586955126523364443045804 y[1] (numeric) = 0.63636279586955126523364443049276 absolute error = 3.472e-29 relative error = 5.4560072061656622002151570441523e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0.64714860596903518498336721741496 y[1] (numeric) = 0.64714860596903518498336721744968 absolute error = 3.472e-29 relative error = 5.3650737527295678302115710934164e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (closed_form) = 0.65793441606851910473309000437188 y[1] (numeric) = 0.6579344160685191047330900044066 absolute error = 3.472e-29 relative error = 5.2771217239962962264376109115571e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (closed_form) = 0.66872022616800302448281279132879 y[1] (numeric) = 0.66872022616800302448281279136352 absolute error = 3.473e-29 relative error = 5.1935022511603767674087965681494e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (closed_form) = 0.67950603626748694423253557828571 y[1] (numeric) = 0.67950603626748694423253557832044 absolute error = 3.473e-29 relative error = 5.1110657074911644377673870988136e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (closed_form) = 0.69029184636697086398225836524262 y[1] (numeric) = 0.69029184636697086398225836527736 absolute error = 3.474e-29 relative error = 5.0326539684392601460311954507116e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (closed_form) = 0.70107765646645478373198115219954 y[1] (numeric) = 0.70107765646645478373198115223428 absolute error = 3.474e-29 relative error = 4.9552285227709638360922539822391e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (closed_form) = 0.71186346656593870348170393915646 y[1] (numeric) = 0.7118634665659387034817039391912 absolute error = 3.474e-29 relative error = 4.8801493027289795355454016491748e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (closed_form) = 0.72264927666542262323142672611337 y[1] (numeric) = 0.72264927666542262323142672614812 absolute error = 3.475e-29 relative error = 4.8086950505713722255619049323256e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = 0.73343508676490654298114951307029 y[1] (numeric) = 0.73343508676490654298114951310504 absolute error = 3.475e-29 relative error = 4.7379789468864991045977592715561e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (closed_form) = 0.7442208968643904627308723000272 y[1] (numeric) = 0.74422089686439046273087230006196 absolute error = 3.476e-29 relative error = 4.6706562724123366504246195954507e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 0.75500670696387438248059508698412 y[1] (numeric) = 0.75500670696387438248059508701888 absolute error = 3.476e-29 relative error = 4.6039326113778746982756964583728e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (closed_form) = 0.76579251706335830223031787394104 y[1] (numeric) = 0.7657925170633583022303178739758 absolute error = 3.476e-29 relative error = 4.5390884900908623785816725645929e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (closed_form) = 0.77657832716284222198004066089795 y[1] (numeric) = 0.77657832716284222198004066093272 absolute error = 3.477e-29 relative error = 4.4773332945086183145270815792552e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = 0.78736413726232614172976344785487 y[1] (numeric) = 0.78736413726232614172976344788964 absolute error = 3.477e-29 relative error = 4.4159999617071303924102722425530e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (closed_form) = 0.79814994736181006147948623481178 y[1] (numeric) = 0.79814994736181006147948623484656 absolute error = 3.478e-29 relative error = 4.3575771839566190326027161530629e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (closed_form) = 0.8089357574612939812292090217687 y[1] (numeric) = 0.80893575746129398122920902180348 absolute error = 3.478e-29 relative error = 4.2994761548371974455013466043553e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (closed_form) = 0.81972156756077790097893180872562 y[1] (numeric) = 0.8197215675607779009789318087604 absolute error = 3.478e-29 relative error = 4.2429041001682869527973815174559e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (closed_form) = 0.83050737766026182072865459568253 y[1] (numeric) = 0.83050737766026182072865459571732 absolute error = 3.479e-29 relative error = 4.1890055327397285477824950252848e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (closed_form) = 0.84129318775974574047837738263945 y[1] (numeric) = 0.84129318775974574047837738267424 absolute error = 3.479e-29 relative error = 4.1353003336020397202468220121401e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (closed_form) = 0.85207899785922966022810016959636 y[1] (numeric) = 0.85207899785922966022810016963116 absolute error = 3.480e-29 relative error = 4.0841283598623846575430789692052e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = 0.86286480795871357997782295655328 y[1] (numeric) = 0.86286480795871357997782295658808 absolute error = 3.480e-29 relative error = 4.0330767553641048493237904820901e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (closed_form) = 0.8736506180581974997275457435102 y[1] (numeric) = 0.873650618058197499727545743545 absolute error = 3.480e-29 relative error = 3.9832856843102270116778177600890e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (closed_form) = 0.88443642815768141947726853046711 y[1] (numeric) = 0.88443642815768141947726853050192 absolute error = 3.481e-29 relative error = 3.9358396931377765574701751242376e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (closed_form) = 0.89522223825716533922699131742403 y[1] (numeric) = 0.89522223825716533922699131745884 absolute error = 3.481e-29 relative error = 3.8884199377987672013560766287649e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (closed_form) = 0.90600804835664925897671410438094 y[1] (numeric) = 0.90600804835664925897671410441576 absolute error = 3.482e-29 relative error = 3.8432329672079400890381604977115e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (closed_form) = 0.91679385845613317872643689133786 y[1] (numeric) = 0.91679385845613317872643689137268 absolute error = 3.482e-29 relative error = 3.7980184617113760879906527271501e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (closed_form) = 0.92757966855561709847615967829478 y[1] (numeric) = 0.9275796685556170984761596783296 absolute error = 3.482e-29 relative error = 3.7538554563426391567349474628809e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (closed_form) = 0.93836547865510101822588246525169 y[1] (numeric) = 0.93836547865510101822588246528652 absolute error = 3.483e-29 relative error = 3.7117733753291523821362827980235e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (closed_form) = 0.94915128875458493797560525220861 y[1] (numeric) = 0.94915128875458493797560525224344 absolute error = 3.483e-29 relative error = 3.6695941324276847414301886753186e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (closed_form) = 0.95993709885406885772532803916552 y[1] (numeric) = 0.95993709885406885772532803920036 absolute error = 3.484e-29 relative error = 3.6294044726045567080057047758238e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (closed_form) = 0.97072290895355277747505082612244 y[1] (numeric) = 0.97072290895355277747505082615728 absolute error = 3.484e-29 relative error = 3.5890777562422838556945302783146e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (closed_form) = 0.98150871905303669722477361307936 y[1] (numeric) = 0.9815087190530366972247736131142 absolute error = 3.484e-29 relative error = 3.5496373413385224946429420334980e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = 0.99229452915252061697449640003627 y[1] (numeric) = 0.99229452915252061697449640007112 absolute error = 3.485e-29 relative error = 3.5120620920649438780343352898761e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (closed_form) = 1.0030803392520045367242191869932 y[1] (numeric) = 1.003080339252004536724219187028 absolute error = 3.48e-29 relative error = 3.4693133379476170746871315974968e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (closed_form) = 1.0138661493514884564739419739501 y[1] (numeric) = 1.013866149351488456473941973985 absolute error = 3.49e-29 relative error = 3.4422689841576732511958984549999e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (closed_form) = 1.024651959450972376223664760907 y[1] (numeric) = 1.024651959450972376223664760942 absolute error = 3.50e-29 relative error = 3.4157939851843598239886912733976e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (closed_form) = 1.0354377695504562959733875478639 y[1] (numeric) = 1.035437769550456295973387547899 absolute error = 3.51e-29 relative error = 3.3898705486896570931816342414120e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (closed_form) = 1.0462235796499402157231103348209 y[1] (numeric) = 1.046223579649940215723110334856 absolute error = 3.51e-29 relative error = 3.3549234296310008344890400739745e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = 1.0570093897494241354728331217778 y[1] (numeric) = 1.057009389749424135472833121813 absolute error = 3.52e-29 relative error = 3.3301501709785712103260010548808e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (closed_form) = 1.0677951998489080552225559087347 y[1] (numeric) = 1.06779519984890805522255590877 absolute error = 3.53e-29 relative error = 3.3058773821979078411965587836475e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 1.0785810099483919749722786956916 y[1] (numeric) = 1.078581009948391974972278695727 absolute error = 3.54e-29 relative error = 3.2820900491928577394497053578388e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 1.0893668200478758947220014826485 y[1] (numeric) = 1.089366820047875894722001482684 absolute error = 3.55e-29 relative error = 3.2587737524849373426879381384818e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = 1.1001526301473598144717242696054 y[1] (numeric) = 1.100152630147359814471724269641 absolute error = 3.56e-29 relative error = 3.2359146380654075419411075312691e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = 1.1109384402468437342214470565623 y[1] (numeric) = 1.110938440246843734221447056598 absolute error = 3.57e-29 relative error = 3.2134993899452860868398464504100e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = 1.1217242503463276539711698435193 y[1] (numeric) = 1.121724250346327653971169843555 absolute error = 3.57e-29 relative error = 3.1826003573496583360048479268482e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = 1.1325100604458115737208926304762 y[1] (numeric) = 1.132510060445811573720892630512 absolute error = 3.58e-29 relative error = 3.1611198213910225201049085770952e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (closed_form) = 1.1432958705452954934706154174331 y[1] (numeric) = 1.143295870545295493470615417469 absolute error = 3.59e-29 relative error = 3.1400445785636817195993077056394e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = 1.15408168064477941322033820439 y[1] (numeric) = 1.154081680644779413220338204426 absolute error = 3.60e-29 relative error = 3.1193632655088145789162414299118e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = 1.1648674907442633329700609913469 y[1] (numeric) = 1.164867490744263332970060991383 absolute error = 3.61e-29 relative error = 3.0990649397327412741717504555865e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = 1.1756533008437472527197837783038 y[1] (numeric) = 1.17565330084374725271978377834 absolute error = 3.62e-29 relative error = 3.0791390603011830759363327101480e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 1.1864391109432311724695065652608 y[1] (numeric) = 1.186439110943231172469506565297 absolute error = 3.62e-29 relative error = 3.0511468870257177752460024127828e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = 1.1972249210427150922192293522177 y[1] (numeric) = 1.197224921042715092219229352254 absolute error = 3.63e-29 relative error = 3.0320117266173139904826259604404e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = 1.2080107311421990119689521391746 y[1] (numeric) = 1.208010731142199011968952139211 absolute error = 3.64e-29 relative error = 3.0132182655019174161614526590328e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = 1.2187965412416829317186749261315 y[1] (numeric) = 1.218796541241682931718674926168 absolute error = 3.65e-29 relative error = 2.9947574320168818431556983541102e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = 1.2295823513411668514683977130884 y[1] (numeric) = 1.229582351341166851468397713125 absolute error = 3.66e-29 relative error = 2.9766204728035135609044309668179e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = 1.2403681614406507712181205000453 y[1] (numeric) = 1.240368161440650771218120500082 absolute error = 3.67e-29 relative error = 2.9587989389677690748662290993046e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = 1.2511539715401346909678432870023 y[1] (numeric) = 1.251153971540134690967843287039 absolute error = 3.67e-29 relative error = 2.9332920515628745138760029863793e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = 1.2619397816396186107175660739592 y[1] (numeric) = 1.261939781639618610717566073996 absolute error = 3.68e-29 relative error = 2.9161454877178319767190389967759e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = 1.2727255917391025304672888609161 y[1] (numeric) = 1.272725591739102530467288860953 absolute error = 3.69e-29 relative error = 2.8992895435989766012088032103862e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = 1.283511401838586450217011647873 y[1] (numeric) = 1.28351140183858645021701164791 absolute error = 3.70e-29 relative error = 2.8827168926585893832701680254483e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 1.2942972119380703699667344348299 y[1] (numeric) = 1.294297211938070369966734434867 absolute error = 3.71e-29 relative error = 2.8664204525672086189638434269261e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = 1.3050830220375542897164572217868 y[1] (numeric) = 1.305083022037554289716457221824 absolute error = 3.72e-29 relative error = 2.8503933751219663796873754333382e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = 1.3158688321370382094661800087438 y[1] (numeric) = 1.315868832137038209466180008781 absolute error = 3.72e-29 relative error = 2.8270294949980158355915772740483e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = 1.3266546422365221292159027957007 y[1] (numeric) = 1.326654642236522129215902795738 absolute error = 3.73e-29 relative error = 2.8115832721256165008836068588348e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = 1.3374404523360060489656255826576 y[1] (numeric) = 1.337440452336006048965625582695 absolute error = 3.74e-29 relative error = 2.7963861818801913489935069341892e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = 1.3482262624354899687153483696145 y[1] (numeric) = 1.348226262435489968715348369652 absolute error = 3.75e-29 relative error = 2.7814322450786929995336486083380e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = 1.3590120725349738884650711565714 y[1] (numeric) = 1.359012072534973888465071156609 absolute error = 3.76e-29 relative error = 2.7667156723534089095890261289288e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (closed_form) = 1.3697978826344578082147939435283 y[1] (numeric) = 1.369797882634457808214793943566 absolute error = 3.77e-29 relative error = 2.7522308566789166950766024287230e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = 1.3805836927339417279645167304852 y[1] (numeric) = 1.380583692733941727964516730523 absolute error = 3.78e-29 relative error = 2.7379723662493384214159353488328e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = 1.3913695028334256477142395174422 y[1] (numeric) = 1.39136950283342564771423951748 absolute error = 3.78e-29 relative error = 2.7167477742629094414049591058184e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 1.4021553129329095674639623043991 y[1] (numeric) = 1.402155312932909567463962304437 absolute error = 3.79e-29 relative error = 2.7029815920123708892903918527182e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = 1.412941123032393487213685091356 y[1] (numeric) = 1.412941123032393487213685091394 absolute error = 3.80e-29 relative error = 2.6894255804832146051470393668408e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = 1.4237269331318774069634078783129 y[1] (numeric) = 1.423726933131877406963407878351 absolute error = 3.81e-29 relative error = 2.6760749630681364465210104034767e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = 1.4345127432313613267131306652698 y[1] (numeric) = 1.434512743231361326713130665308 absolute error = 3.82e-29 relative error = 2.6629251068171948015585307478324e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = 1.4452985533308452464628534522267 y[1] (numeric) = 1.445298553330845246462853452265 absolute error = 3.83e-29 relative error = 2.6499715170774612408492224303320e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = 1.4560843634303291662125762391837 y[1] (numeric) = 1.456084363430329166212576239222 absolute error = 3.83e-29 relative error = 2.6303420984324430094355244864035e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = 1.4668701735298130859622990261406 y[1] (numeric) = 1.466870173529813085962299026179 absolute error = 3.84e-29 relative error = 2.6178185836034757642669633960828e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = 1.4776559836292970057120218130975 y[1] (numeric) = 1.477655983629297005712021813136 absolute error = 3.85e-29 relative error = 2.6054778938085080409256805698543e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = 1.4884417937287809254617446000544 y[1] (numeric) = 1.488441793728780925461744600093 absolute error = 3.86e-29 relative error = 2.5933160545902789802415177845857e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = 1.4992276038282648452114673870113 y[1] (numeric) = 1.49922760382826484521146738705 absolute error = 3.87e-29 relative error = 2.5813292058643985391355443919108e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 1.5100134139277487649611901739682 y[1] (numeric) = 1.510013413927748764961190174007 absolute error = 3.88e-29 relative error = 2.5695135978346021043310849048456e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (closed_form) = 1.5207992240272326847109129609252 y[1] (numeric) = 1.520799224027232684710912960964 absolute error = 3.88e-29 relative error = 2.5512900971407396780592332388537e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = 1.5315850341267166044606357478821 y[1] (numeric) = 1.531585034126716604460635747921 absolute error = 3.89e-29 relative error = 2.5398524491446281145976274850785e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = 1.542370844226200524210358534839 y[1] (numeric) = 1.542370844226200524210358534878 absolute error = 3.90e-29 relative error = 2.5285747682533572723033169166709e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=245.9MB, alloc=40.3MB, time=3.23 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = 1.5531566543256844439600813217959 y[1] (numeric) = 1.553156654325684443960081321835 absolute error = 3.91e-29 relative error = 2.5174537218189096361519828839355e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = 1.5639424644251683637098041087528 y[1] (numeric) = 1.563942464425168363709804108792 absolute error = 3.92e-29 relative error = 2.5064860691283854156717017344104e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = 1.5747282745246522834595268957097 y[1] (numeric) = 1.574728274524652283459526895749 absolute error = 3.93e-29 relative error = 2.4956686582555396091706025184403e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = 1.5855140846241362032092496826667 y[1] (numeric) = 1.585514084624136203209249682706 absolute error = 3.93e-29 relative error = 2.4786913204442774349585576033487e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = 1.5962998947236201229589724696236 y[1] (numeric) = 1.596299894723620122958972469663 absolute error = 3.94e-29 relative error = 2.4682078931554167608474269182098e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = 1.6070857048231040427086952565805 y[1] (numeric) = 1.60708570482310404270869525662 absolute error = 3.95e-29 relative error = 2.4578651830113730085364456382405e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 1.6178715149225879624584180435374 y[1] (numeric) = 1.617871514922587962458418043577 absolute error = 3.96e-29 relative error = 2.4476603756692498395896107753374e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = 1.6286573250220718822081408304943 y[1] (numeric) = 1.628657325022071882208140830534 absolute error = 3.97e-29 relative error = 2.4375907313382806199003498841285e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = 1.6394431351215558019578636174512 y[1] (numeric) = 1.639443135121555801957863617491 absolute error = 3.98e-29 relative error = 2.4276535823274557320491055835933e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = 1.6502289452210397217075864044081 y[1] (numeric) = 1.650228945221039721707586404448 absolute error = 3.99e-29 relative error = 2.4178463306893213656076814699932e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = 1.6610147553205236414573091913651 y[1] (numeric) = 1.661014755320523641457309191405 absolute error = 3.99e-29 relative error = 2.4021460298406894086881510708373e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = 1.671800565420007561207031978322 y[1] (numeric) = 1.671800565420007561207031978362 absolute error = 4.00e-29 relative error = 2.3926298882397359135773321362047e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = 1.6825863755194914809567547652789 y[1] (numeric) = 1.682586375519491480956754765319 absolute error = 4.01e-29 relative error = 2.3832357484541792581474211366315e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = 1.6933721856189754007064775522358 y[1] (numeric) = 1.693372185618975400706477552276 absolute error = 4.02e-29 relative error = 2.3739612792391392480096109141229e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = 1.7041579957184593204562003391927 y[1] (numeric) = 1.704157995718459320456200339233 absolute error = 4.03e-29 relative error = 2.3648042083685934152153172767093e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = 1.7149438058179432402059231261496 y[1] (numeric) = 1.71494380581794324020592312619 absolute error = 4.04e-29 relative error = 2.3557623207794380960410776473136e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = 1.7257296159174271599556459131066 y[1] (numeric) = 1.725729615917427159955645913147 absolute error = 4.04e-29 relative error = 2.3410388062745666079408209120178e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = 1.7365154260169110797053687000635 y[1] (numeric) = 1.736515426016911079705368700104 absolute error = 4.05e-29 relative error = 2.3322568514635003412238668455008e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = 1.7473012361163949994550914870204 y[1] (numeric) = 1.747301236116394999455091487061 absolute error = 4.06e-29 relative error = 2.3235833158476324234787270267186e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = 1.7580870462158789192048142739773 y[1] (numeric) = 1.758087046215878919204814274018 absolute error = 4.07e-29 relative error = 2.3150162039816524556445705185962e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (closed_form) = 1.7688728563153628389545370609342 y[1] (numeric) = 1.768872856315362838954537060975 absolute error = 4.08e-29 relative error = 2.3065535690896478532718061630120e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (closed_form) = 1.7796586664148467587042598478911 y[1] (numeric) = 1.779658666414846758704259847932 absolute error = 4.09e-29 relative error = 2.2981935115902736097156813753743e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = 1.7904444765143306784539826348481 y[1] (numeric) = 1.790444476514330678453982634889 absolute error = 4.09e-29 relative error = 2.2843489723638261783318519694984e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = 1.801230286613814598203705421805 y[1] (numeric) = 1.801230286613814598203705421846 absolute error = 4.10e-29 relative error = 2.2762219969705870854466984619133e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (closed_form) = 1.8120160967132985179534282087619 y[1] (numeric) = 1.812016096713298517953428208803 absolute error = 4.11e-29 relative error = 2.2681917712844103627149396389423e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (closed_form) = 1.8228019068127824377031509957188 y[1] (numeric) = 1.82280190681278243770315099576 absolute error = 4.12e-29 relative error = 2.2602565778548747846308939381366e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 1.8335877169122663574528737826757 y[1] (numeric) = 1.833587716912266357452873782717 absolute error = 4.13e-29 relative error = 2.2524147396421572721713664220463e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = 1.8443735270117502772025965696326 y[1] (numeric) = 1.844373527011750277202596569674 absolute error = 4.14e-29 relative error = 2.2446646188354364557639971225184e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = 1.8551593371112341969523193565896 y[1] (numeric) = 1.855159337111234196952319356631 absolute error = 4.14e-29 relative error = 2.2316142431445327554397878369223e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (closed_form) = 1.8659451472107181167020421435465 y[1] (numeric) = 1.865945147210718116702042143588 absolute error = 4.15e-29 relative error = 2.2240739531939452693766169026209e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = 1.8767309573102020364517649305034 y[1] (numeric) = 1.876730957310202036451764930545 absolute error = 4.16e-29 relative error = 2.2166203332427898233831375882540e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = 1.8875167674096859562014877174603 y[1] (numeric) = 1.887516767409685956201487717502 absolute error = 4.17e-29 relative error = 2.2092518975196475824867266089085e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = 1.8983025775091698759512105044172 y[1] (numeric) = 1.898302577509169875951210504459 absolute error = 4.18e-29 relative error = 2.2019671940206319579641384816009e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = 1.9090883876086537957009332913741 y[1] (numeric) = 1.909088387608653795700933291416 absolute error = 4.19e-29 relative error = 2.1947648035555035156395457003647e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = 1.919874197708137715450656078331 y[1] (numeric) = 1.919874197708137715450656078373 absolute error = 4.20e-29 relative error = 2.1876433388259383142399483436367e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = 1.930660007807621635200378865288 y[1] (numeric) = 1.93066000780762163520037886533 absolute error = 4.20e-29 relative error = 2.1754218676593129605291106433928e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 1.9414458179071055549501016522449 y[1] (numeric) = 1.941445817907105554950101652287 absolute error = 4.21e-29 relative error = 2.1684869910706106533401223409450e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = 1.9522316280065894746998244392018 y[1] (numeric) = 1.952231628006589474699824439244 absolute error = 4.22e-29 relative error = 2.1616287429525017418106808705684e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = 1.9630174381060733944495472261587 y[1] (numeric) = 1.963017438106073394449547226201 absolute error = 4.23e-29 relative error = 2.1548458601983280930452991965696e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = 1.9738032482055573141992700131156 y[1] (numeric) = 1.973803248205557314199270013158 absolute error = 4.24e-29 relative error = 2.1481371073103202765068615845816e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = 1.9845890583050412339489928000725 y[1] (numeric) = 1.984589058305041233948992800115 absolute error = 4.25e-29 relative error = 2.1415012756493560231916678596806e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = 1.9953748684045251536987155870295 y[1] (numeric) = 1.995374868404525153698715587072 absolute error = 4.25e-29 relative error = 2.1299255930782784230663074928714e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = 2.0061606785040090734484383739864 y[1] (numeric) = 2.006160678504009073448438374029 absolute error = 4.26e-29 relative error = 2.1234590258127656232998822708817e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = 2.0169464886034929931981611609433 y[1] (numeric) = 2.016946488603492993198161160986 absolute error = 4.27e-29 relative error = 2.1170616196944775593598359282715e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = 2.0277322987029769129478839479002 y[1] (numeric) = 2.027732298702976912947883947943 absolute error = 4.28e-29 relative error = 2.1107322710880861769510666744125e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = 2.0385181088024608326976067348571 y[1] (numeric) = 2.0385181088024608326976067349 absolute error = 4.29e-29 relative error = 2.1044698997156248620810145555150e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 2.049303918901944752447329521814 y[1] (numeric) = 2.049303918901944752447329521857 absolute error = 4.30e-29 relative error = 2.0982734480418210347359103536585e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = 2.060089729001428672197052308771 y[1] (numeric) = 2.060089729001428672197052308814 absolute error = 4.30e-29 relative error = 2.0872877231829633329833663203932e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = 2.0708755391009125919467750957279 y[1] (numeric) = 2.070875539100912591946775095771 absolute error = 4.31e-29 relative error = 2.0812453083835359076371572051973e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = 2.0816613492003965116964978826848 y[1] (numeric) = 2.081661349200396511696497882728 absolute error = 4.32e-29 relative error = 2.0752655092815118752997170963765e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = 2.0924471592998804314462206696417 y[1] (numeric) = 2.092447159299880431446220669685 absolute error = 4.33e-29 relative error = 2.0693473575929107711307042051724e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = 2.1032329693993643511959434565986 y[1] (numeric) = 2.103232969399364351195943456642 absolute error = 4.34e-29 relative error = 2.0634899048959876270044504205448e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = 2.1140187794988482709456662435555 y[1] (numeric) = 2.114018779498848270945666243599 absolute error = 4.35e-29 relative error = 2.0576922221245432904713216745358e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = 2.1248045895983321906953890305125 y[1] (numeric) = 2.124804589598332190695389030556 absolute error = 4.35e-29 relative error = 2.0472470839411699742760357777107e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = 2.1355903996978161104451118174694 y[1] (numeric) = 2.135590399697816110445111817513 absolute error = 4.36e-29 relative error = 2.0415899980712292050449003253120e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = 2.1463762097973000301948346044263 y[1] (numeric) = 2.14637620979730003019483460447 absolute error = 4.37e-29 relative error = 2.0359897673356596998261380935405e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 2.1571620198967839499445573913832 y[1] (numeric) = 2.157162019896783949944557391427 absolute error = 4.38e-29 relative error = 2.0304455389074458896595634840867e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = 2.1679478299962678696942801783401 y[1] (numeric) = 2.167947829996267869694280178384 absolute error = 4.39e-29 relative error = 2.0249564769312541074548453384086e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = 2.178733640095751789444002965297 y[1] (numeric) = 2.178733640095751789444002965341 absolute error = 4.40e-29 relative error = 2.0195217621033414518066095506085e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = 2.1895194501952357091937257522539 y[1] (numeric) = 2.189519450195235709193725752298 absolute error = 4.41e-29 relative error = 2.0141405912638811375933317508655e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = 2.2003052602947196289434485392109 y[1] (numeric) = 2.200305260294719628943448539255 absolute error = 4.41e-29 relative error = 2.0042673530714111320168938501259e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = 2.2110910703942035486931713261678 y[1] (numeric) = 2.211091070394203548693171326212 absolute error = 4.42e-29 relative error = 1.9990130932110281395022320079437e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = 2.2218768804936874684428941131247 y[1] (numeric) = 2.221876880493687468442894113169 absolute error = 4.43e-29 relative error = 1.9938098455822993507983921253944e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = 2.2326626905931713881926169000816 y[1] (numeric) = 2.232662690593171388192616900126 absolute error = 4.44e-29 relative error = 1.9886568708775196325168115653818e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = 2.2434485006926553079423396870385 y[1] (numeric) = 2.243448500692655307942339687083 absolute error = 4.45e-29 relative error = 1.9835534440064397192187077415231e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = 2.2542343107921392276920624739954 y[1] (numeric) = 2.25423431079213922769206247404 absolute error = 4.46e-29 relative error = 1.9784988537561356902583848155004e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 2.2650201208916231474417852609524 y[1] (numeric) = 2.265020120891623147441785260997 absolute error = 4.46e-29 relative error = 1.9690774306430112345904877449503e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = 2.2758059309911070671915080479093 y[1] (numeric) = 2.275805930991107067191508047954 absolute error = 4.47e-29 relative error = 1.9641393578991718337939035196320e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = 2.2865917410905909869412308348662 y[1] (numeric) = 2.286591741090590986941230834911 absolute error = 4.48e-29 relative error = 1.9592478707472554462123814096469e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = 2.2973775511900749066909536218231 y[1] (numeric) = 2.297377551190074906690953621868 absolute error = 4.49e-29 relative error = 1.9544023130521645646175402584409e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = 2.30816336128955882644067640878 y[1] (numeric) = 2.308163361289558826440676408825 absolute error = 4.50e-29 relative error = 1.9496020409430091118226508936949e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = 2.3189491713890427461903991957369 y[1] (numeric) = 2.318949171389042746190399195782 absolute error = 4.51e-29 relative error = 1.9448464225278923144025977090860e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = 2.3297349814885266659401219826939 y[1] (numeric) = 2.329734981488526665940121982739 absolute error = 4.51e-29 relative error = 1.9358425039050779981322153122846e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = 2.3405207915880105856898447696508 y[1] (numeric) = 2.340520791588010585689844769696 absolute error = 4.52e-29 relative error = 1.9311941240792154159588466527938e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = 2.3513066016874945054395675566077 y[1] (numeric) = 2.351306601687494505439567556653 absolute error = 4.53e-29 relative error = 1.9265883899398286372916556874268e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = 2.3620924117869784251892903435646 y[1] (numeric) = 2.36209241178697842518929034361 absolute error = 4.54e-29 relative error = 1.9220247172994316922195988861270e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 2.3728782218864623449390131305215 y[1] (numeric) = 2.372878221886462344939013130567 absolute error = 4.55e-29 relative error = 1.9175025325921292648300153284754e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = 2.3836640319859462646887359174784 y[1] (numeric) = 2.383664031985946264688735917524 absolute error = 4.56e-29 relative error = 1.9130212726333092123489347894452e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = 2.3944498420854301844384587044354 y[1] (numeric) = 2.394449842085430184438458704481 absolute error = 4.56e-29 relative error = 1.9044040596935195312122278759791e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = 2.4052356521849141041881814913923 y[1] (numeric) = 2.405235652184914104188181491438 absolute error = 4.57e-29 relative error = 1.9000217279536064286799363438123e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = 2.4160214622843980239379042783492 y[1] (numeric) = 2.416021462284398023937904278395 absolute error = 4.58e-29 relative error = 1.8956785241756568359916831288970e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = 2.4268072723838819436876270653061 y[1] (numeric) = 2.426807272383881943687627065352 absolute error = 4.59e-29 relative error = 1.8913739266535112396828810536698e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = 2.437593082483365863437349852263 y[1] (numeric) = 2.437593082483365863437349852309 absolute error = 4.60e-29 relative error = 1.8871074229147474628104400587544e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = 2.4483788925828497831870726392199 y[1] (numeric) = 2.448378892582849783187072639266 absolute error = 4.61e-29 relative error = 1.8828785095172943800073597774506e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = 2.4591647026823337029367954261768 y[1] (numeric) = 2.459164702682333702936795426223 absolute error = 4.62e-29 relative error = 1.8786866918513979031937802003687e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = 2.4699505127818176226865182131338 y[1] (numeric) = 2.46995051278181762268651821318 absolute error = 4.62e-29 relative error = 1.8704828198345795717387855270046e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 2.4807363228813015424362410000907 y[1] (numeric) = 2.480736322881301542436241000137 absolute error = 4.63e-29 relative error = 1.8663813470600505199769265299427e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = 2.4915221329807854621859637870476 y[1] (numeric) = 2.491522132980785462185963787094 absolute error = 4.64e-29 relative error = 1.8623153848723139275376810306909e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = 2.5023079430802693819356865740045 y[1] (numeric) = 2.502307943080269381935686574051 absolute error = 4.65e-29 relative error = 1.8582844740827474781367048891913e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = 2.5130937531797533016854093609614 y[1] (numeric) = 2.513093753179753301685409361008 absolute error = 4.66e-29 relative error = 1.8542881633857953330224324055587e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = 2.5238795632792372214351321479183 y[1] (numeric) = 2.523879563279237221435132147965 absolute error = 4.67e-29 relative error = 1.8503260091905265395758032764870e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = 2.5346653733787211411848549348753 y[1] (numeric) = 2.534665373378721141184854934922 absolute error = 4.67e-29 relative error = 1.8424522814918434479180339008423e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = 2.5454511834782050609345777218322 y[1] (numeric) = 2.545451183478205060934577721879 absolute error = 4.68e-29 relative error = 1.8385738569164241861324117919522e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = 2.5562369935776889806843005087891 y[1] (numeric) = 2.556236993577688980684300508836 absolute error = 4.69e-29 relative error = 1.8347281616623164792985670848249e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = 2.567022803677172900434023295746 y[1] (numeric) = 2.567022803677172900434023295793 absolute error = 4.70e-29 relative error = 1.8309147831750500136986202323794e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = 2.5778086137766568201837460827029 y[1] (numeric) = 2.57780861377665682018374608275 absolute error = 4.71e-29 relative error = 1.8271333158048318030409323494103e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 2.5885944238761407399334688696598 y[1] (numeric) = 2.588594423876140739933468869707 absolute error = 4.72e-29 relative error = 1.8233833606626987441387251987994e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = 2.5993802339756246596831916566168 y[1] (numeric) = 2.599380233975624659683191656664 absolute error = 4.72e-29 relative error = 1.8158174546018576705115935589703e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = 2.6101660440751085794329144435737 y[1] (numeric) = 2.610166044075108579432914443621 absolute error = 4.73e-29 relative error = 1.8121452505815727118173771236141e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = 2.6209518541745924991826372305306 y[1] (numeric) = 2.620951854174592499182637230578 absolute error = 4.74e-29 relative error = 1.8085032704626892754169402473967e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = 2.6317376642740764189323600174875 y[1] (numeric) = 2.631737664274076418932360017535 absolute error = 4.75e-29 relative error = 1.8048911426398622606263430177057e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = 2.6425234743735603386820828044444 y[1] (numeric) = 2.642523474373560338682082804492 absolute error = 4.76e-29 relative error = 1.8013085015747726092217914796856e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = 2.6533092844730442584318055914013 y[1] (numeric) = 2.653309284473044258431805591449 absolute error = 4.77e-29 relative error = 1.7977549876728137679912606858770e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = 2.6640950945725281781815283783583 y[1] (numeric) = 2.664095094572528178181528378406 absolute error = 4.77e-29 relative error = 1.7904766273988347648819843268248e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = 2.6748809046720120979312511653152 y[1] (numeric) = 2.674880904672012097931251165363 absolute error = 4.78e-29 relative error = 1.7869954477790527604530699392279e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = 2.6856667147714960176809739522721 y[1] (numeric) = 2.68566671477149601768097395232 absolute error = 4.79e-29 relative error = 1.7835422294413573584693677153867e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 2.696452524870979937430696739229 y[1] (numeric) = 2.696452524870979937430696739277 absolute error = 4.80e-29 relative error = 1.7801166368503635197015351093363e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = 2.7072383349704638571804195261859 y[1] (numeric) = 2.707238334970463857180419526234 absolute error = 4.81e-29 relative error = 1.7767183398178636557446015678759e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = 2.7180241450699477769301423131428 y[1] (numeric) = 2.718024145069947776930142313191 absolute error = 4.82e-29 relative error = 1.7733470133967328383270087688081e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = 2.7288099551694316966798651000997 y[1] (numeric) = 2.728809955169431696679865100148 absolute error = 4.83e-29 relative error = 1.7700023377773500906123218416697e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = 2.7395957652689156164295878870567 y[1] (numeric) = 2.739595765268915616429587887105 absolute error = 4.83e-29 relative error = 1.7630338246364943815941630942615e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = 2.7503815753683995361793106740136 y[1] (numeric) = 2.750381575368399536179310674062 absolute error = 4.84e-29 relative error = 1.7597558256445587082016809495890e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = 2.7611673854678834559290334609705 y[1] (numeric) = 2.761167385467883455929033461019 absolute error = 4.85e-29 relative error = 1.7565034360197475322575775716718e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = 2.7719531955673673756787562479274 y[1] (numeric) = 2.771953195567367375678756247976 absolute error = 4.86e-29 relative error = 1.7532763568200321631301598231547e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = 2.7827390056668512954284790348843 y[1] (numeric) = 2.782739005666851295428479034933 absolute error = 4.87e-29 relative error = 1.7500742937381440449262104292773e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = 2.7935248157663352151782018218412 y[1] (numeric) = 2.79352481576633521517820182189 absolute error = 4.88e-29 relative error = 1.7468969570121006226157278260862e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 2.8043106258658191349279246087982 y[1] (numeric) = 2.804310625865819134927924608847 absolute error = 4.88e-29 relative error = 1.7401781225620540817595134882935e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = 2.8150964359653030546776473957551 y[1] (numeric) = 2.815096435965303054677647395804 absolute error = 4.89e-29 relative error = 1.7370630496085324096704395523337e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = 2.825882246064786974427370182712 y[1] (numeric) = 2.825882246064786974427370182761 absolute error = 4.90e-29 relative error = 1.7339717558378620480553280128316e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = 2.8366680561642708941770929696689 y[1] (numeric) = 2.836668056164270894177092969718 absolute error = 4.91e-29 relative error = 1.7309039700046112329163770173561e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = 2.8474538662637548139268157566258 y[1] (numeric) = 2.847453866263754813926815756675 absolute error = 4.92e-29 relative error = 1.7278594249731274694072665597251e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = 2.8582396763632387336765385435827 y[1] (numeric) = 2.858239676363238733676538543632 absolute error = 4.93e-29 relative error = 1.7248378576399945267548286338499e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = 2.8690254864627226534262613305397 y[1] (numeric) = 2.869025486462722653426261330589 absolute error = 4.93e-29 relative error = 1.7183535047917238706392089773316e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = 2.8798112965622065731759841174966 y[1] (numeric) = 2.879811296562206573175984117546 absolute error = 4.94e-29 relative error = 1.7153901736190690908484674313595e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = 2.8905971066616904929257069044535 y[1] (numeric) = 2.890597106661690492925706904503 absolute error = 4.95e-29 relative error = 1.7124489568581505407576567924469e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = 2.9013829167611744126754296914104 y[1] (numeric) = 2.90138291676117441267542969146 absolute error = 4.96e-29 relative error = 1.7095296078798410505188224408124e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 2.9121687268606583324251524783673 y[1] (numeric) = 2.912168726860658332425152478417 absolute error = 4.97e-29 relative error = 1.7066318837087782972447201954864e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = 2.9229545369601422521748752653242 y[1] (numeric) = 2.922954536960142252174875265374 absolute error = 4.98e-29 relative error = 1.7037555449559521694560356789082e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = 2.9337403470596261719245980522812 y[1] (numeric) = 2.933740347059626171924598052331 absolute error = 4.98e-29 relative error = 1.6974917378053788158918590771474e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=294.3MB, alloc=40.3MB, time=3.86 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = 2.9445261571591100916743208392381 y[1] (numeric) = 2.944526157159110091674320839288 absolute error = 4.99e-29 relative error = 1.6946699515192525113153732058127e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = 2.955311967258594011424043626195 y[1] (numeric) = 2.955311967258594011424043626245 absolute error = 5.00e-29 relative error = 1.6918687622133169096920003700353e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = 2.9660977773580779311737664131519 y[1] (numeric) = 2.966097777358077931173766413202 absolute error = 5.01e-29 relative error = 1.6890879451932426578986157003362e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = 2.9768835874575618509234892001088 y[1] (numeric) = 2.976883587457561850923489200159 absolute error = 5.02e-29 relative error = 1.6863272790211399586544584557798e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = 2.9876693975570457706732119870657 y[1] (numeric) = 2.987669397557045770673211987116 absolute error = 5.03e-29 relative error = 1.6835865454567780731232554151553e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = 2.9984552076565296904229347740226 y[1] (numeric) = 2.998455207656529690422934774073 absolute error = 5.04e-29 relative error = 1.6808655294000734673440754179885e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = 3.0092410177560136101726575609796 y[1] (numeric) = 3.00924101775601361017265756103 absolute error = 5.04e-29 relative error = 1.6748409217678151395041324953433e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 3.0200268278554975299223803479365 y[1] (numeric) = 3.020026827855497529922380347987 absolute error = 5.05e-29 relative error = 1.6721705759104047199577292228698e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = 3.0308126379549814496721031348934 y[1] (numeric) = 3.030812637954981449672103134944 absolute error = 5.06e-29 relative error = 1.6695192360733317411198412761791e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = 3.0415984480544653694218259218503 y[1] (numeric) = 3.041598448054465369421825921901 absolute error = 5.07e-29 relative error = 1.6668867000648904855361227475501e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = 3.0523842581539492891715487088072 y[1] (numeric) = 3.052384258153949289171548708858 absolute error = 5.08e-29 relative error = 1.6642727685512085321120064700067e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = 3.0631700682534332089212714957641 y[1] (numeric) = 3.063170068253433208921271495815 absolute error = 5.09e-29 relative error = 1.6616772450059327896274966451221e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = 3.0739558783529171286709942827211 y[1] (numeric) = 3.073955878352917128670994282772 absolute error = 5.09e-29 relative error = 1.6558467985322277622954703411041e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = 3.084741688452401048420717069678 y[1] (numeric) = 3.084741688452401048420717069729 absolute error = 5.10e-29 relative error = 1.6532988869348874472752456762848e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = 3.0955274985518849681704398566349 y[1] (numeric) = 3.095527498551884968170439856686 absolute error = 5.11e-29 relative error = 1.6507687308190616989102142147047e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = 3.1063133086513688879201626435918 y[1] (numeric) = 3.106313308651368887920162643643 absolute error = 5.12e-29 relative error = 1.6482561452318180737977176938299e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = 3.1170991187508528076698854305487 y[1] (numeric) = 3.1170991187508528076698854306 absolute error = 5.13e-29 relative error = 1.6457609477801263076825394879785e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 3.1278849288503367274196082175056 y[1] (numeric) = 3.127884928850336727419608217557 absolute error = 5.14e-29 relative error = 1.6432829585867220709888452697537e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = 3.1386707389498206471693310044626 y[1] (numeric) = 3.138670738949820647169331004514 absolute error = 5.14e-29 relative error = 1.6376359381104790398170622963181e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = 3.1494565490493045669190537914195 y[1] (numeric) = 3.149456549049304566919053791471 absolute error = 5.15e-29 relative error = 1.6352027468213777337440970699704e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = 3.1602423591487884866687765783764 y[1] (numeric) = 3.160242359148788486668776578428 absolute error = 5.16e-29 relative error = 1.6327861643465365048456913332223e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = 3.1710281692482724064184993653333 y[1] (numeric) = 3.171028169248272406418499365385 absolute error = 5.17e-29 relative error = 1.6303860212082588217221046831188e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = 3.1818139793477563261682221522902 y[1] (numeric) = 3.181813979347756326168222152342 absolute error = 5.18e-29 relative error = 1.6280021502268508178061355696261e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = 3.1925997894472402459179449392471 y[1] (numeric) = 3.192599789447240245917944939299 absolute error = 5.19e-29 relative error = 1.6256343864818036787814905717651e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = 3.2033855995467241656676677262041 y[1] (numeric) = 3.203385599546724165667667726256 absolute error = 5.19e-29 relative error = 1.6201608700290029929943475058669e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = 3.214171409646208085417390513161 y[1] (numeric) = 3.214171409646208085417390513213 absolute error = 5.20e-29 relative error = 1.6178353103365999549860148504874e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = 3.2249572197456920051671133001179 y[1] (numeric) = 3.22495721974569200516711330017 absolute error = 5.21e-29 relative error = 1.6155253062274236931516509754115e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 3.2357430298451759249168360870748 y[1] (numeric) = 3.235743029845175924916836087127 absolute error = 5.22e-29 relative error = 1.6132307021456419397295161928360e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = 3.2465288399446598446665588740317 y[1] (numeric) = 3.246528839944659844666558874084 absolute error = 5.23e-29 relative error = 1.6109513446026095667287909436996e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = 3.2573146500441437644162816609886 y[1] (numeric) = 3.257314650044143764416281661041 absolute error = 5.24e-29 relative error = 1.6086870821426436332843618882661e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = 3.2681004601436276841660044479455 y[1] (numeric) = 3.268100460143627684166004447998 absolute error = 5.25e-29 relative error = 1.6064377653094761548461666879840e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = 3.2788862702431116039157272349025 y[1] (numeric) = 3.278886270243111603915727234955 absolute error = 5.25e-29 relative error = 1.6011534305551686674946990344051e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = 3.2896720803425955236654500218594 y[1] (numeric) = 3.289672080342595523665450021912 absolute error = 5.26e-29 relative error = 1.5989435638375874510980318775801e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = 3.3004578904420794434151728088163 y[1] (numeric) = 3.300457890442079443415172808869 absolute error = 5.27e-29 relative error = 1.5967481406933237589915390158977e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = 3.3112437005415633631648955957732 y[1] (numeric) = 3.311243700541563363164895595826 absolute error = 5.28e-29 relative error = 1.5945670199799673222082154888192e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = 3.3220295106410472829146183827301 y[1] (numeric) = 3.322029510641047282914618382783 absolute error = 5.29e-29 relative error = 1.5924000623881261869624460106178e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = 3.332815320740531202664341169687 y[1] (numeric) = 3.33281532074053120266434116974 absolute error = 5.30e-29 relative error = 1.5902471304117662241130892798481e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = 3.343601130840015122414063956644 y[1] (numeric) = 3.343601130840015122414063956697 absolute error = 5.30e-29 relative error = 1.5851173009588250427449825402356e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = 3.3543869409394990421637867436009 y[1] (numeric) = 3.354386940939499042163786743654 absolute error = 5.31e-29 relative error = 1.5830016314435005174194720375428e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = 3.3651727510389829619135095305578 y[1] (numeric) = 3.365172751038982961913509530611 absolute error = 5.32e-29 relative error = 1.5808995239122485852050224996109e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = 3.3759585611384668816632323175147 y[1] (numeric) = 3.375958561138466881663232317568 absolute error = 5.33e-29 relative error = 1.5788108483780014576692595401961e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = 3.3867443712379508014129551044716 y[1] (numeric) = 3.386744371237950801412955104525 absolute error = 5.34e-29 relative error = 1.5767354765095775602451893384846e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = 3.3975301813374347211626778914285 y[1] (numeric) = 3.397530181337434721162677891482 absolute error = 5.35e-29 relative error = 1.5746732816053976240746052967840e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = 3.4083159914369186409124006783855 y[1] (numeric) = 3.408315991436918640912400678439 absolute error = 5.35e-29 relative error = 1.5696901383091780113401919888827e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = 3.4191018015364025606621234653424 y[1] (numeric) = 3.419101801536402560662123465396 absolute error = 5.36e-29 relative error = 1.5676631791400414802839491630590e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = 3.4298876116358864804118462522993 y[1] (numeric) = 3.429887611635886480411846252353 absolute error = 5.37e-29 relative error = 1.5656489681417800217500726443160e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = 3.4406734217353704001615690392562 y[1] (numeric) = 3.44067342173537040016156903931 absolute error = 5.38e-29 relative error = 1.5636473854256393247117063231827e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = 3.4514592318348543199112918262131 y[1] (numeric) = 3.451459231834854319911291826267 absolute error = 5.39e-29 relative error = 1.5616583126014745070298297915564e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = 3.46224504193433823966101461317 y[1] (numeric) = 3.462245041934338239661014613224 absolute error = 5.40e-29 relative error = 1.5596816327544072894581207149559e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = 3.473030852033822159410737400127 y[1] (numeric) = 3.473030852033822159410737400181 absolute error = 5.40e-29 relative error = 1.5548379009756668941492445636672e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = 3.4838166621333060791604601870839 y[1] (numeric) = 3.483816662133306079160460187138 absolute error = 5.41e-29 relative error = 1.5528945764577635838469596461412e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = 3.4946024722327899989101829740408 y[1] (numeric) = 3.494602472232789998910182974095 absolute error = 5.42e-29 relative error = 1.5509632477702177013860468577358e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = 3.5053882823322739186599057609977 y[1] (numeric) = 3.505388282332273918659905761052 absolute error = 5.43e-29 relative error = 1.5490438041822874858941243018744e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = 3.5161740924317578384096285479546 y[1] (numeric) = 3.516174092431757838409628548009 absolute error = 5.44e-29 relative error = 1.5471361363218905846076736635336e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = 3.5269599025312417581593513349115 y[1] (numeric) = 3.526959902531241758159351334966 absolute error = 5.45e-29 relative error = 1.5452401361548294441853603379656e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = 3.5377457126307256779090741218684 y[1] (numeric) = 3.537745712630725677909074121923 absolute error = 5.46e-29 relative error = 1.5433556969643967253509879473095e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = 3.5485315227302095976587969088254 y[1] (numeric) = 3.54853152273020959765879690888 absolute error = 5.46e-29 relative error = 1.5386646462137450635718056131231e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = 3.5593173328296935174085196957823 y[1] (numeric) = 3.559317332829693517408519695837 absolute error = 5.47e-29 relative error = 1.5368115535939849199443492815766e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = 3.5701031429291774371582424827392 y[1] (numeric) = 3.570103142929177437158242482794 absolute error = 5.48e-29 relative error = 1.5349696579084831457647929882872e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = 3.5808889530286613569079652696961 y[1] (numeric) = 3.580888953028661356907965269751 absolute error = 5.49e-29 relative error = 1.5331388579801229485381255883309e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = 3.591674763128145276657688056653 y[1] (numeric) = 3.591674763128145276657688056708 absolute error = 5.50e-29 relative error = 1.5313190538471282780215282628488e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = 3.6024605732276291964074108436099 y[1] (numeric) = 3.602460573227629196407410843665 absolute error = 5.51e-29 relative error = 1.5295101467448701025379644542857e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = 3.6132463833271131161571336305669 y[1] (numeric) = 3.613246383327113116157133630622 absolute error = 5.51e-29 relative error = 1.5249444448142884007393436648699e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = 3.6240321934265970359068564175238 y[1] (numeric) = 3.624032193426597035906856417579 absolute error = 5.52e-29 relative error = 1.5231652770669033092684266188517e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = 3.6348180035260809556565792044807 y[1] (numeric) = 3.634818003526080955656579204536 absolute error = 5.53e-29 relative error = 1.5213966681785531441563874188041e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = 3.6456038136255648754063019914376 y[1] (numeric) = 3.645603813625564875406301991493 absolute error = 5.54e-29 relative error = 1.5196385244315541634532951962714e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = 3.6563896237250487951560247783945 y[1] (numeric) = 3.65638962372504879515602477845 absolute error = 5.55e-29 relative error = 1.5178907532140360026953539603025e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = 3.6671754338245327149057475653514 y[1] (numeric) = 3.667175433824532714905747565407 absolute error = 5.56e-29 relative error = 1.5161532630036797134712829668980e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = 3.6779612439240166346554703523084 y[1] (numeric) = 3.677961243924016634655470352364 absolute error = 5.56e-29 relative error = 1.5117070657514695090329507587839e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = 3.6887470540235005544051931392653 y[1] (numeric) = 3.688747054023500554405193139321 absolute error = 5.57e-29 relative error = 1.5099978172600701761600801899067e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = 3.6995328641229844741549159262222 y[1] (numeric) = 3.699532864122984474154915926278 absolute error = 5.58e-29 relative error = 1.5082985352321775449366141141425e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = 3.7103186742224683939046387131791 y[1] (numeric) = 3.710318674222468393904638713235 absolute error = 5.59e-29 relative error = 1.5066091327509587080807263295164e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = 3.721104484321952313654361500136 y[1] (numeric) = 3.721104484321952313654361500192 absolute error = 5.60e-29 relative error = 1.5049295239073121543370465900186e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = 3.7318902944214362334040842870929 y[1] (numeric) = 3.731890294421436233404084287149 absolute error = 5.61e-29 relative error = 1.5032596237853051760485326293619e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = 3.7426761045209201531538070740499 y[1] (numeric) = 3.742676104520920153153807074106 absolute error = 5.61e-29 relative error = 1.4989274634862120775584792212081e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = 3.7534619146204040729035298610068 y[1] (numeric) = 3.753461914620404072903529861063 absolute error = 5.62e-29 relative error = 1.4972844077914037028140905343735e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = 3.7642477247198879926532526479637 y[1] (numeric) = 3.76424772471988799265325264802 absolute error = 5.63e-29 relative error = 1.4956507678885426539994691179506e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = 3.7750335348193719124029754349206 y[1] (numeric) = 3.775033534819371912402975434977 absolute error = 5.64e-29 relative error = 1.4940264630708408111780741096215e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = 3.7858193449188558321526982218775 y[1] (numeric) = 3.785819344918855832152698221934 absolute error = 5.65e-29 relative error = 1.4924114135512455315636386170095e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = 3.7966051550183397519024210088344 y[1] (numeric) = 3.796605155018339751902421008891 absolute error = 5.66e-29 relative error = 1.4908055404493752251288305987872e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = 3.8073909651178236716521437957913 y[1] (numeric) = 3.807390965117823671652143795848 absolute error = 5.67e-29 relative error = 1.4892087657786769884188656854841e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = 3.8181767752173075914018665827483 y[1] (numeric) = 3.818176775217307591401866582805 absolute error = 5.67e-29 relative error = 1.4850019613555733811069479858076e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = 3.8289625853167915111515893697052 y[1] (numeric) = 3.828962585316791511151589369762 absolute error = 5.68e-29 relative error = 1.4834305307086362664179459244469e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = 3.8397483954162754309013121566621 y[1] (numeric) = 3.839748395416275430901312156719 absolute error = 5.69e-29 relative error = 1.4818679283237605961934888184872e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = 3.850534205515759350651034943619 y[1] (numeric) = 3.850534205515759350651034943676 absolute error = 5.70e-29 relative error = 1.4803140800138702238414376346897e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = 3.8613200156152432704007577305759 y[1] (numeric) = 3.861320015615243270400757730633 absolute error = 5.71e-29 relative error = 1.4787689124207948815025264016397e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = 3.8721058257147271901504805175328 y[1] (numeric) = 3.87210582571472719015048051759 absolute error = 5.72e-29 relative error = 1.4772323530037255299287344512250e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = 3.8828916358142111099002033044898 y[1] (numeric) = 3.882891635814211109900203304547 absolute error = 5.72e-29 relative error = 1.4731289298009374034567101888605e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = 3.8936774459136950296499260914467 y[1] (numeric) = 3.893677445913695029649926091504 absolute error = 5.73e-29 relative error = 1.4716165063989760745455038343284e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = 3.9044632560131789493996488784036 y[1] (numeric) = 3.904463256013178949399648878461 absolute error = 5.74e-29 relative error = 1.4701124389274123220371218242965e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = 3.9152490661126628691493716653605 y[1] (numeric) = 3.915249066112662869149371665418 absolute error = 5.75e-29 relative error = 1.4686166583289701329034416435210e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = 3.9260348762121467888990944523174 y[1] (numeric) = 3.926034876212146788899094452375 absolute error = 5.76e-29 relative error = 1.4671290963052446590946717934091e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = 3.9368206863116307086488172392743 y[1] (numeric) = 3.936820686311630708648817239332 absolute error = 5.77e-29 relative error = 1.4656496853063067221286897232977e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = 3.9476064964111146283985400262313 y[1] (numeric) = 3.947606496411114628398540026289 absolute error = 5.77e-29 relative error = 1.4616451779694042447458244508297e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = 3.9583923065105985481482628131882 y[1] (numeric) = 3.958392306510598548148262813246 absolute error = 5.78e-29 relative error = 1.4601887717125200306361933656851e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = 3.9691781166100824678979856001451 y[1] (numeric) = 3.969178116610082467897985600203 absolute error = 5.79e-29 relative error = 1.4587402807070319263858537538294e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = 3.979963926709566387647708387102 y[1] (numeric) = 3.97996392670956638764770838716 absolute error = 5.80e-29 relative error = 1.4572996406013025652479821073496e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = 3.9907497368090503073974311740589 y[1] (numeric) = 3.990749736809050307397431174117 absolute error = 5.81e-29 relative error = 1.4558667877393879574135584157157e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = 4.0015355469085342271471539610158 y[1] (numeric) = 4.001535546908534227147153961074 absolute error = 5.82e-29 relative error = 1.4544416591516615684892933423654e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = 4.0123213570080181468968767479728 y[1] (numeric) = 4.012321357008018146896876748031 absolute error = 5.82e-29 relative error = 1.4505318697453398976062576075741e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = 4.0231071671075020666465995349297 y[1] (numeric) = 4.023107167107502066646599534988 absolute error = 5.83e-29 relative error = 1.4491286853269687388097561560867e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = 4.0338929772069859863963223218866 y[1] (numeric) = 4.033892977206985986396322321945 absolute error = 5.84e-29 relative error = 1.4477330045685888696324873326822e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = 4.0446787873064699061460451088435 y[1] (numeric) = 4.044678787306469906146045108902 absolute error = 5.85e-29 relative error = 1.4463447674409203597574972763358e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = 4.0554645974059538258957678958004 y[1] (numeric) = 4.055464597405953825895767895859 absolute error = 5.86e-29 relative error = 1.4449639145532926398286507841189e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = 4.0662504075054377456454906827573 y[1] (numeric) = 4.066250407505437745645490682816 absolute error = 5.87e-29 relative error = 1.4435903871451748812787371645397e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = 4.0770362176049216653952134697142 y[1] (numeric) = 4.077036217604921665395213469773 absolute error = 5.88e-29 relative error = 1.4422241270778408145730029821012e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = 4.0878220277044055851449362566712 y[1] (numeric) = 4.08782202770440558514493625673 absolute error = 5.88e-29 relative error = 1.4384187863731499417113327895363e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = 4.0986078378038895048946590436281 y[1] (numeric) = 4.098607837803889504894659043687 absolute error = 5.89e-29 relative error = 1.4370733266239913830923851143080e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = 4.109393647903373424644381830585 y[1] (numeric) = 4.109393647903373424644381830644 absolute error = 5.90e-29 relative error = 1.4357349296556683024714371644089e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = 4.1201794580028573443941046175419 y[1] (numeric) = 4.120179458002857344394104617601 absolute error = 5.91e-29 relative error = 1.4344035400013154997594994132005e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = 4.1309652681023412641438274044988 y[1] (numeric) = 4.130965268102341264143827404558 absolute error = 5.92e-29 relative error = 1.4330791027733561842679895353665e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = 4.1417510782018251838935501914557 y[1] (numeric) = 4.141751078201825183893550191515 absolute error = 5.93e-29 relative error = 1.4317615636559591568779979381462e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = 4.1525368883013091036432729784127 y[1] (numeric) = 4.152536888301309103643272978472 absolute error = 5.93e-29 relative error = 1.4280427024516579642627304110341e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = 4.1633226984007930233929957653696 y[1] (numeric) = 4.163322698400793023392995765429 absolute error = 5.94e-29 relative error = 1.4267450376310394142685555037589e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = 4.1741085085002769431427185523265 y[1] (numeric) = 4.174108508500276943142718552386 absolute error = 5.95e-29 relative error = 1.4254540790885635957988982962628e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = 4.1848943185997608628924413392834 y[1] (numeric) = 4.184894318599760862892441339343 absolute error = 5.96e-29 relative error = 1.4241697749715644568058888063311e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = 4.1956801286992447826421641262403 y[1] (numeric) = 4.1956801286992447826421641263 absolute error = 5.97e-29 relative error = 1.4228920739605653133861081569647e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = 4.2064659387987287023918869131972 y[1] (numeric) = 4.206465938798728702391886913257 absolute error = 5.98e-29 relative error = 1.4216209252624430886505315109283e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = 4.2172517488982126221416097001542 y[1] (numeric) = 4.217251748898212622141609700214 absolute error = 5.98e-29 relative error = 1.4179850661185493723112718395448e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = 4.2280375589976965418913324871111 y[1] (numeric) = 4.228037558997696541891332487171 absolute error = 5.99e-29 relative error = 1.4167329207501165873474961874102e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = 4.238823369097180461641055274068 y[1] (numeric) = 4.238823369097180461641055274128 absolute error = 6.00e-29 relative error = 1.4154871476227445290247575614952e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = 4.2496091791966643813907780610249 y[1] (numeric) = 4.249609179196664381390778061085 absolute error = 6.01e-29 relative error = 1.4142476982168312121148247154070e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = 4.2603949892961483011405008479818 y[1] (numeric) = 4.260394989296148301140500848042 absolute error = 6.02e-29 relative error = 1.4130145245041123930120307698055e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = 4.2711807993956322208902236349387 y[1] (numeric) = 4.271180799395632220890223634999 absolute error = 6.03e-29 relative error = 1.4117875789414578103693519451413e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = 4.2819666094951161406399464218957 y[1] (numeric) = 4.281966609495116140639946421956 absolute error = 6.03e-29 relative error = 1.4082314389441241634918472802920e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = 4.2927524195946000603896692088526 y[1] (numeric) = 4.292752419594600060389669208913 absolute error = 6.04e-29 relative error = 1.4070226767399753531979260966802e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = 4.3035382296940839801393919958095 y[1] (numeric) = 4.30353822969408398013939199587 absolute error = 6.05e-29 relative error = 1.4058199734942433289205157961942e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = 4.3143240397935678998891147827664 y[1] (numeric) = 4.314324039793567899889114782827 absolute error = 6.06e-29 relative error = 1.4046232837647399647644925472107e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = 4.3251098498930518196388375697233 y[1] (numeric) = 4.325109849893051819638837569784 absolute error = 6.07e-29 relative error = 1.4034325625625657944446589403667e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=342.8MB, alloc=40.3MB, time=4.50 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = 4.3358956599925357393885603566802 y[1] (numeric) = 4.335895659992535739388560356741 absolute error = 6.08e-29 relative error = 1.4022477653464720926338792320643e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (closed_form) = 4.3466814700920196591382831436371 y[1] (numeric) = 4.346681470092019659138283143698 absolute error = 6.09e-29 relative error = 1.4010688480173068955467262220660e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = 4.3574672801915035788880059305941 y[1] (numeric) = 4.357467280191503578888005930655 absolute error = 6.09e-29 relative error = 1.3976008558192442547161650185461e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = 4.368253090290987498637728717551 y[1] (numeric) = 4.368253090290987498637728717612 absolute error = 6.10e-29 relative error = 1.3964392341547347569675108239392e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = 4.3790389003904714183874515045079 y[1] (numeric) = 4.379038900390471418387451504569 absolute error = 6.11e-29 relative error = 1.3952833347644346656117071426063e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = 4.3898247104899553381371742914648 y[1] (numeric) = 4.389824710489955338137174291526 absolute error = 6.12e-29 relative error = 1.3941331154694186041888558135158e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = 4.4006105205894392578868970784217 y[1] (numeric) = 4.400610520589439257886897078483 absolute error = 6.13e-29 relative error = 1.3929885345042800724788615987837e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = 4.4113963306889231776366198653786 y[1] (numeric) = 4.41139633068892317763661986544 absolute error = 6.14e-29 relative error = 1.3918495505120762035156155220208e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = 4.4221821407884070973863426523356 y[1] (numeric) = 4.422182140788407097386342652397 absolute error = 6.14e-29 relative error = 1.3884547955108272371655774353817e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = 4.4329679508878910171360654392925 y[1] (numeric) = 4.432967950887891017136065439354 absolute error = 6.15e-29 relative error = 1.3873323850149198659474403034289e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = 4.4437537609873749368857882262494 y[1] (numeric) = 4.443753760987374936885788226311 absolute error = 6.16e-29 relative error = 1.3862154231136528217740514099807e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = 4.4545395710868588566355110132063 y[1] (numeric) = 4.454539571086858856635511013268 absolute error = 6.17e-29 relative error = 1.3851038702288568044489597993096e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = 4.4653253811863427763852338001632 y[1] (numeric) = 4.465325381186342776385233800225 absolute error = 6.18e-29 relative error = 1.3839976871647602847921053461778e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = 4.4761111912858266961349565871201 y[1] (numeric) = 4.476111191285826696134956587182 absolute error = 6.19e-29 relative error = 1.3828968351033823025793803120974e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = 4.4868970013853106158846793740771 y[1] (numeric) = 4.486897001385310615884679374139 absolute error = 6.19e-29 relative error = 1.3795725638651530181981798786548e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = 4.497682811484794535634402161034 y[1] (numeric) = 4.497682811484794535634402161096 absolute error = 6.20e-29 relative error = 1.3784876034762507271869401576095e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = 4.5084686215842784553841249479909 y[1] (numeric) = 4.508468621584278455384124948053 absolute error = 6.21e-29 relative error = 1.3774078342853814614915436888181e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = 4.5192544316837623751338477349478 y[1] (numeric) = 4.51925443168376237513384773501 absolute error = 6.22e-29 relative error = 1.3763332191240628844152183248896e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 4.5300402417832462948835705219047 y[1] (numeric) = 4.530040241783246294883570521967 absolute error = 6.23e-29 relative error = 1.3752637211777982053249707007893e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = 4.5408260518827302146332933088616 y[1] (numeric) = 4.540826051882730214633293308924 absolute error = 6.24e-29 relative error = 1.3741993039818720757790947993689e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = 4.5516118619822141343830160958186 y[1] (numeric) = 4.551611861982214134383016095881 absolute error = 6.24e-29 relative error = 1.3709429075269387296279595036358e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = 4.5623976720816980541327388827755 y[1] (numeric) = 4.562397672081698054132738882838 absolute error = 6.25e-29 relative error = 1.3698937377259126278239010088347e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = 4.5731834821811819738824616697324 y[1] (numeric) = 4.573183482181181973882461669795 absolute error = 6.26e-29 relative error = 1.3688495168390423095189182616506e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = 4.5839692922806658936321844566893 y[1] (numeric) = 4.583969292280665893632184456752 absolute error = 6.27e-29 relative error = 1.3678102099328160868294883744533e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = 4.5947551023801498133819072436462 y[1] (numeric) = 4.594755102380149813381907243709 absolute error = 6.28e-29 relative error = 1.3667757824017364661245159045667e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = 4.6055409124796337331316300306031 y[1] (numeric) = 4.605540912479633733131630030666 absolute error = 6.29e-29 relative error = 1.3657461999644792324017681300895e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = 4.61632672257911765288135281756 y[1] (numeric) = 4.616326722579117652881352817623 absolute error = 6.30e-29 relative error = 1.3647214286601063782758556255864e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = 4.627112532678601572631075604517 y[1] (numeric) = 4.62711253267860157263107560458 absolute error = 6.30e-29 relative error = 1.3615402598287308389325552628228e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 4.6378983427780854923807983914739 y[1] (numeric) = 4.637898342778085492380798391537 absolute error = 6.31e-29 relative error = 1.3605300361586475059734358696599e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = 4.6486841528775694121305211784308 y[1] (numeric) = 4.648684152877569412130521178494 absolute error = 6.32e-29 relative error = 1.3595245003014183880164469609200e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = 4.6594699629770533318802439653877 y[1] (numeric) = 4.659469962977053331880243965451 absolute error = 6.33e-29 relative error = 1.3585236197027875530129626304614e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = 4.6702557730765372516299667523446 y[1] (numeric) = 4.670255773076537251629966752408 absolute error = 6.34e-29 relative error = 1.3575273621092312253305105601896e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = 4.6810415831760211713796895393015 y[1] (numeric) = 4.681041583176021171379689539365 absolute error = 6.35e-29 relative error = 1.3565356955644931295728624165089e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = 4.6918273932755050911294123262585 y[1] (numeric) = 4.691827393275505091129412326322 absolute error = 6.35e-29 relative error = 1.3534172227011264787002811235974e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = 4.7026132033749890108791351132154 y[1] (numeric) = 4.702613203374989010879135113279 absolute error = 6.36e-29 relative error = 1.3524395320107406328007649196506e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = 4.7133990134744729306288579001723 y[1] (numeric) = 4.713399013474472930628857900236 absolute error = 6.37e-29 relative error = 1.3514663158772901912303082864312e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = 4.7241848235739568503785806871292 y[1] (numeric) = 4.724184823573956850378580687193 absolute error = 6.38e-29 relative error = 1.3504975436531249114935067063315e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = 4.7349706336734407701283034740861 y[1] (numeric) = 4.73497063367344077012830347415 absolute error = 6.39e-29 relative error = 1.3495331849698442116188317849111e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = 4.745756443772924689878026261043 y[1] (numeric) = 4.745756443772924689878026261107 absolute error = 6.40e-29 relative error = 1.3485732097351238785617690222245e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = 4.756542253872408609627749048 y[1] (numeric) = 4.756542253872408609627749048064 absolute error = 6.40e-29 relative error = 1.3455152205974025092226266888407e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = 4.7673280639718925293774718349569 y[1] (numeric) = 4.767328063971892529377471835021 absolute error = 6.41e-29 relative error = 1.3445686795591570231531438596868e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = 4.7781138740713764491271946219138 y[1] (numeric) = 4.778113874071376449127194621978 absolute error = 6.42e-29 relative error = 1.3436264118438833000004532780685e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = 4.7888996841708603688769174088707 y[1] (numeric) = 4.788899684170860368876917408935 absolute error = 6.43e-29 relative error = 1.3426883885777774765016036450160e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = 4.7996854942703442886266401958276 y[1] (numeric) = 4.799685494270344288626640195892 absolute error = 6.44e-29 relative error = 1.3417545811465754994005016507638e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = 4.8104713043698282083763629827845 y[1] (numeric) = 4.810471304369828208376362982849 absolute error = 6.45e-29 relative error = 1.3408249611926434863222745533468e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = 4.8212571144693121281260857697415 y[1] (numeric) = 4.821257114469312128126085769806 absolute error = 6.45e-29 relative error = 1.3378253527783422704692045879030e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = 4.8320429245687960478758085566984 y[1] (numeric) = 4.832042924568796047875808556763 absolute error = 6.46e-29 relative error = 1.3369086535125265459067983638291e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = 4.8428287346682799676255313436553 y[1] (numeric) = 4.84282873466827996762553134372 absolute error = 6.47e-29 relative error = 1.3359960375396543212310843723791e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = 4.8536145447677638873752541306122 y[1] (numeric) = 4.853614544767763887375254130677 absolute error = 6.48e-29 relative error = 1.3350874776377726397761513320022e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = 4.8644003548672478071249769175691 y[1] (numeric) = 4.864400354867247807124976917634 absolute error = 6.49e-29 relative error = 1.3341829468263649347356525844873e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = 4.875186164966731726874699704526 y[1] (numeric) = 4.875186164966731726874699704591 absolute error = 6.50e-29 relative error = 1.3332824183636802726378109110765e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = 4.8859719750662156466244224914829 y[1] (numeric) = 4.885971975066215646624422491548 absolute error = 6.51e-29 relative error = 1.3323858657440979710790325563120e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = 4.8967577851656995663741452784399 y[1] (numeric) = 4.896757785165699566374145278505 absolute error = 6.51e-29 relative error = 1.3294510951147056847991227929721e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = 4.9075435952651834861238680653968 y[1] (numeric) = 4.907543595265183486123868065462 absolute error = 6.52e-29 relative error = 1.3285669038764159968468416795871e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = 4.9183294053646674058735908523537 y[1] (numeric) = 4.918329405364667405873590852419 absolute error = 6.53e-29 relative error = 1.3276865906698731934908425009099e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = 4.9291152154641513256233136393106 y[1] (numeric) = 4.929115215464151325623313639376 absolute error = 6.54e-29 relative error = 1.3268101300375384549197711085726e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = 4.9399010255636352453730364262675 y[1] (numeric) = 4.939901025563635245373036426333 absolute error = 6.55e-29 relative error = 1.3259374967442095449014118183853e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = 4.9506868356631191651227592132244 y[1] (numeric) = 4.95068683566311916512275921329 absolute error = 6.56e-29 relative error = 1.3250686657745988436413024597456e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = 4.9614726457626030848724820001814 y[1] (numeric) = 4.961472645762603084872482000247 absolute error = 6.56e-29 relative error = 1.3221880817185671070246909326592e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = 4.9722584558620870046222047871383 y[1] (numeric) = 4.972258455862087004622204787204 absolute error = 6.57e-29 relative error = 1.3213311533020255247242278638308e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = 4.9830442659615709243719275740952 y[1] (numeric) = 4.983044265961570924371927574161 absolute error = 6.58e-29 relative error = 1.3204779345323087977583988342615e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = 4.9938300760610548441216503610521 y[1] (numeric) = 4.993830076061054844121650361118 absolute error = 6.59e-29 relative error = 1.3196284013728284281444740337615e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = 5.004615886160538763871373148009 y[1] (numeric) = 5.004615886160538763871373148075 absolute error = 6.60e-29 relative error = 1.3187825299942078877099195987809e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = 5.0154016962600226836210959349659 y[1] (numeric) = 5.015401696260022683621095935032 absolute error = 6.61e-29 relative error = 1.3179402967720545323955137850261e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = 5.0261875063595066033708187219229 y[1] (numeric) = 5.026187506359506603370818721989 absolute error = 6.61e-29 relative error = 1.3151120987103119261028195494359e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = 5.0369733164589905231205415088798 y[1] (numeric) = 5.036973316458990523120541508946 absolute error = 6.62e-29 relative error = 1.3142813320785829876454499491219e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = 5.0477591265584744428702642958367 y[1] (numeric) = 5.047759126558474442870264295903 absolute error = 6.63e-29 relative error = 1.3134541157316050275575562872707e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (closed_form) = 5.0585449366579583626199870827936 y[1] (numeric) = 5.05854493665795836261998708286 absolute error = 6.64e-29 relative error = 1.3126304269596674852099095067068e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 5.0693307467574422823697098697505 y[1] (numeric) = 5.069330746757442282369709869817 absolute error = 6.65e-29 relative error = 1.3118102432463339324041676060601e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = 5.0801165568569262021194326567074 y[1] (numeric) = 5.080116556856926202119432656774 absolute error = 6.66e-29 relative error = 1.3109935422663903309903821466052e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = 5.0909023669564101218691554436644 y[1] (numeric) = 5.090902366956410121869155443731 absolute error = 6.66e-29 relative error = 1.3082160135751479785942160827352e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = 5.1016881770558940416188782306213 y[1] (numeric) = 5.101688177055894041618878230688 absolute error = 6.67e-29 relative error = 1.3074103646705343415707847933484e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = 5.1124739871553779613686010175782 y[1] (numeric) = 5.112473987155377961368601017645 absolute error = 6.68e-29 relative error = 1.3066081151283874287542034250139e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = 5.1232597972548618811183238045351 y[1] (numeric) = 5.123259797254861881118323804602 absolute error = 6.69e-29 relative error = 1.3058092434790495555705339782303e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = 5.134045607354345800868046591492 y[1] (numeric) = 5.134045607354345800868046591559 absolute error = 6.70e-29 relative error = 1.3050137284332803289128463358449e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = 5.1448314174538297206177693784489 y[1] (numeric) = 5.144831417453829720617769378516 absolute error = 6.71e-29 relative error = 1.3042215488803654805639959582074e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = 5.1556172275533136403674921654058 y[1] (numeric) = 5.155617227553313640367492165473 absolute error = 6.72e-29 relative error = 1.3034326838862494391120026951207e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = 5.1664030376527975601172149523628 y[1] (numeric) = 5.16640303765279756011721495243 absolute error = 6.72e-29 relative error = 1.3007115300576768933100987228971e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 5.1771888477522814798669377393197 y[1] (numeric) = 5.177188847752281479866937739387 absolute error = 6.73e-29 relative error = 1.2999332645402502699209343843135e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = 5.1879746578517653996166605262766 y[1] (numeric) = 5.187974657851765399616660526344 absolute error = 6.74e-29 relative error = 1.2991582350540811376893133485931e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = 5.1987604679512493193663833132335 y[1] (numeric) = 5.198760467951249319366383313301 absolute error = 6.75e-29 relative error = 1.2983864214578961097408110723569e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = 5.2095462780507332391161061001904 y[1] (numeric) = 5.209546278050733239116106100258 absolute error = 6.76e-29 relative error = 1.2976178037772232351171473148630e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = 5.2203320881502171588658288871473 y[1] (numeric) = 5.220332088150217158865828887215 absolute error = 6.77e-29 relative error = 1.2968523622026688434464739034744e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = 5.2311178982497010786155516741043 y[1] (numeric) = 5.231117898249701078615551674172 absolute error = 6.77e-29 relative error = 1.2941784398063746808826667407868e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = 5.2419037083491849983652744610612 y[1] (numeric) = 5.241903708349184998365274461129 absolute error = 6.78e-29 relative error = 1.2934232250777461273551534680749e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = 5.2526895184486689181149972480181 y[1] (numeric) = 5.252689518448668918114997248086 absolute error = 6.79e-29 relative error = 1.2926711118469764179899708453535e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = 5.263475328548152837864720034975 y[1] (numeric) = 5.263475328548152837864720035043 absolute error = 6.80e-29 relative error = 1.2919220810474803549746455284630e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = 5.2742611386476367576144428219319 y[1] (numeric) = 5.274261138647636757614442822 absolute error = 6.81e-29 relative error = 1.2911761137686366275953747118461e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = 5.2850469487471206773641656088888 y[1] (numeric) = 5.285046948747120677364165608957 absolute error = 6.82e-29 relative error = 1.2904331912541963440013254087663e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = 5.2958327588466045971138883958458 y[1] (numeric) = 5.295832758846604597113888395914 absolute error = 6.82e-29 relative error = 1.2878050177485869828119133407240e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = 5.3066185689460885168636111828027 y[1] (numeric) = 5.306618568946088516863611182871 absolute error = 6.83e-29 relative error = 1.2870719670655469638763428180859e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = 5.3174043790455724366133339697596 y[1] (numeric) = 5.317404379045572436613333969828 absolute error = 6.84e-29 relative error = 1.2863418902189492979587664963510e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = 5.3281901891450563563630567567165 y[1] (numeric) = 5.328190189145056356363056756785 absolute error = 6.85e-29 relative error = 1.2856147691490585051825568803721e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = 5.3389759992445402761127795436734 y[1] (numeric) = 5.338975999244540276112779543742 absolute error = 6.86e-29 relative error = 1.2848905859420763620741299295083e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = 5.3497618093440241958625023306303 y[1] (numeric) = 5.349761809344024195862502330699 absolute error = 6.87e-29 relative error = 1.2841693228286707598653337324786e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = 5.3605476194435081156122251175873 y[1] (numeric) = 5.360547619443508115612225117656 absolute error = 6.87e-29 relative error = 1.2815854811328384243324054955923e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = 5.3713334295429920353619479045442 y[1] (numeric) = 5.371333429542992035361947904613 absolute error = 6.88e-29 relative error = 1.2808737514150875392765396536389e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 5.3821192396424759551116706915011 y[1] (numeric) = 5.38211923964247595511167069157 absolute error = 6.89e-29 relative error = 1.2801648743214558962449458190680e-27 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.005 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; Iterations = 2000 Total Elapsed Time = 4 Seconds Elapsed Time(since restart) = 4 Seconds Time to Timeout = 2 Minutes 55 Seconds Percent Done = 100 % > quit memory used=380.1MB, alloc=40.3MB, time=5.02