|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ 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_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 4 then > printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel); > else > printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel, Re(value), Im(value), postlabel) else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value), Im(value), postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number -1 > if vallen = 5 then # if number 0 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 0; > fi;# end if -1; > 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 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 -1 > 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 0 > 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 1 > 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 2 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 3 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 3 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 2 > 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 2 > 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 3 > 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 4 > 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 5 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 6 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 6 > else > printf(" 0.0 Seconds\n"); > fi;# end if 5 > 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 5 > 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 6 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 6; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 5; > 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 5 > 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 6 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 6; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 5; > 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_complex := proc(file,x) > fprintf(file,""); > fprintf(file,"%g + %g I",Re(x),Im(x)); > fprintf(file,""); > end; logitem_complex := proc(file, x) fprintf(file, ""); fprintf(file, "%g + %g I", Re(x), Im(x)); fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 5 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 6 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 7 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 8 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 9 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 10 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 11 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 11 > 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 20 # Begin Function number 21 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 21 # Begin Function number 22 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 22 # Begin Function number 23 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 11 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 11; > if (errflag) then # if number 11 > quit; > fi;# end if 11 > 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 23 # Begin Function number 24 > 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 11 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 12 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 12 > fi;# end if 11; > 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 24 # Begin Function number 25 > 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 11 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 11; > 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 25 # Begin Function number 26 > 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 11 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 11; > 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 26 # Begin Function number 27 > 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 11 > 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 11; > 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 27 # Begin Function number 28 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalc(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalc(in_val); ret end proc # End Function number 28 # Begin Function number 29 > 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 11 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 11; > 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 29 # Begin Function number 30 > 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 30 # Begin Function number 31 > 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 11 > 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 12 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13 > 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 14 > if (rcs > glob__0) then # if number 15 > rad_c := float_abs( sqrt(rcs) * float_abs(glob_h)); > 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 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 13 > fi;# end if 12 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 11; > 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 := float_abs(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 31 # Begin Function number 32 > 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 32 # Begin Function number 33 > 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 33 # Begin Function number 34 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 11 > if (array_fact_1[nnn] = 0) then # if number 12 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 12; > else > ret := factorial_2(nnn); > fi;# end if 11; > 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 34 # Begin Function number 35 > 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 11 > if (array_fact_2[mmm,nnn] = 0) then # if number 12 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 12; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 11; > 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 35 # Begin Function number 36 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 36 # Begin Function number 37 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 37 # Begin Function number 38 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 38 # Begin Function number 39 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 39 # Begin Function number 40 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 40 # Begin Function number 41 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 41 # Begin Function number 42 > 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 42 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return( cos(c(x)) ); > end; exact_soln_y1 := proc(x) return cos(c(x)) end proc > exact_soln_y2 := proc(x) > return( sin(c(x)) + c(10.0) * c(x) + c(10.0)); > end; exact_soln_y2 := proc(x) return sin(c(x)) + c(10.0)*c(x) + c(10.0) end proc > exact_soln_y2p := proc(x) > return( cos(c(x)) + c(10.0)); > end; exact_soln_y2p := proc(x) return cos(c(x)) + c(10.0) end proc > exact_soln_y2pp := proc(x) > return( neg(sin(c(x)))); > end; exact_soln_y2pp := proc(x) return neg(sin(c(x))) end proc > exact_soln_y2ppp := proc(x) > return( neg(cos(c(x)))); > end; exact_soln_y2ppp := proc(x) return neg(cos(c(x))) end proc > exact_soln_y2pppp := proc(x) > return( sin(c(x))); > end; exact_soln_y2pppp := proc(x) return sin(c(x)) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 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0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it 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 := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) 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 ((float_abs(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_complex(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 ((float_abs(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_complex(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 ((float_abs(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_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[2,1] + array_given_rad_poles[2,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 4 > glob_least_given_sing := rad_given; > fi;# end if 4; > elif > (glob_type_given_pole = 3) then # if number 4 > omniout_str(ALWAYS,"NO POLE (given) for Equation 2"); > elif > (glob_type_given_pole = 5) then # if number 5 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 2"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 2"); > fi;# end if 5; > if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," "); > if ((float_abs(array_rad_test_poles[2,1]) < glob_least_ratio_sing)) then # if number 6 > glob_least_ratio_sing := array_rad_test_poles[2,1]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," "); > if ((float_abs(array_rad_test_poles[2,2]) < glob_least_3_sing)) then # if number 6 > glob_least_3_sing := array_rad_test_poles[2,2]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," "); > if ((float_abs(array_rad_test_poles[2,3]) < glob_least_6_sing)) then # if number 6 > glob_least_6_sing := array_rad_test_poles[2,3]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2"); > fi;# end if 5 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) 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 float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(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 float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(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 float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[2, 1] - array_given_rad_poles[2, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[2, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 2") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2") end if; if array_rad_test_poles[2, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 2 ", 4, array_rad_test_poles[2, 1], 4, " "); if float_abs(array_rad_test_poles[2, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[2, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[2, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 2] and array_rad_test_poles[2, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_rad_test_poles[2, 2], 4, " "); if float_abs(array_rad_test_poles[2, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[2, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 3] and array_rad_test_poles[2, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_rad_test_poles[2, 3], 4, " "); if float_abs(array_rad_test_poles[2, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[2, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[2, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 2") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 5 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 5; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_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_y2[1]) < min_size) then # if number 5 > min_size := float_abs(array_y2[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > if (float_abs(array_y1[1]) < min_size) then # if number 5 > min_size := float_abs(array_y1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > if (min_size < glob__1) then # if number 5 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_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_y2[1]) < min_size then min_size := float_abs(array_y2[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if float_abs(array_y1[1]) < min_size then min_size := float_abs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if 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_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_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_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 5 > max_estimated_step_error := est_tmp; > fi;# end if 5; > est_tmp := float_abs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 5 > max_estimated_step_error := est_tmp; > fi;# end if 5; > 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_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_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_y2[no_terms - 3] + array_y2[no_terms - 2]*hn_div_ho + array_y2[no_terms - 1]*hn_div_ho_2 + array_y2[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; est_tmp := float_abs(array_y1[no_terms - 3] + array_y1[no_terms - 2]*hn_div_ho + array_y1[no_terms - 1]*hn_div_ho_2 + array_y1[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; 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_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_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_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5 > est_tmp := c(glob_prec) * c(float_abs(array_y2[1])); > fi;# end if 5; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5 > array_max_est_error[1] := c(est_tmp); > fi;# end if 5 > ; > est_tmp := c(float_abs(array_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5 > est_tmp := c(glob_prec) * c(float_abs(array_y1[1])); > fi;# end if 5; > if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5 > array_max_est_error[2] := c(est_tmp); > fi;# end if 5 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_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_y2[no_terms - 3])) + c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y2[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if; est_tmp := c(float_abs(array_y1[no_terms - 3])) + c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y1[1])) end if; if c(array_max_est_error[2]) <= c(est_tmp) then array_max_est_error[2] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 5 > ret := true; > else > ret := false; > fi;# end if 5; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_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_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_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 > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y2(ind_var)); > omniout_complex(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 5 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 6 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > 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; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > ; > term_no := 1; > numeric_val := array_y1[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y1(ind_var)); > omniout_complex(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 5 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 6 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > 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; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > #BOTTOM DISPLAY ALOT > 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_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_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; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y2(ind_var)); omniout_complex(ALWAYS, "y2[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 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; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); term_no := 1; numeric_val := array_y1[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y1(ind_var)); omniout_complex(ALWAYS, "y1[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 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; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " ") 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_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_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)); > if (c(percent_done) < glob__100) then # if number 5 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 5; > #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_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_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); 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 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_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_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 - 5 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,1]) then # if number 8 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[2,1] := glob_larger_float; > array_ord_test_poles[2,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[2,1]) then # if number 10 > array_rad_test_poles[2,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > array_rad_test_poles[2,1] := rad_c; > array_ord_test_poles[2,1] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test2 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 5 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 9 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 9; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 10 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 11 > found_sing := 0; > fi;# end if 11; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 11 > if (rad_c < array_rad_test_poles[1,2]) then # if number 12 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 13 > glob_min_pole_est := rad_c; > fi;# end if 13; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 12; > fi;# end if 11; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[2,2] := glob_larger_float; > array_ord_test_poles[2,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 11 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 11; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 12 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 13 > found_sing := 0; > fi;# end if 13; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 13 > if (rad_c < array_rad_test_poles[2,2]) then # if number 14 > array_rad_test_poles[2,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > array_rad_test_poles[2,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 15 > glob_min_pole_est := rad_c; > fi;# end if 15; > array_ord_test_poles[2,2] := tmp_ord; > fi;# end if 14; > fi;# end if 13; > #BOTTOM general radius test2 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 5 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 13 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 13; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 14 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 15 > found_sing := 0; > fi;# end if 15; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 15 > if (rad_c < array_rad_test_poles[1,3]) then # if number 16 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 17 > glob_min_pole_est := rad_c; > fi;# end if 17; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 16; > fi;# end if 15; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[2,3] := glob_larger_float; > array_ord_test_poles[2,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 15 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 15; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 16 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 17 > found_sing := 0; > fi;# end if 17; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 17 > if (rad_c < array_rad_test_poles[2,3]) then # if number 18 > array_rad_test_poles[2,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > array_rad_test_poles[2,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 19 > glob_min_pole_est := rad_c; > fi;# end if 19; > array_ord_test_poles[2,3] := tmp_ord; > fi;# end if 18; > fi;# end if 17; > #BOTTOM general radius test2 > ; > if (true) then # if number 17 > display_poles(); > fi;# end if 17 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_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 - 15; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[2, 1] := glob_larger_float; array_ord_test_poles[2, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[2, 1] then array_rad_test_poles[2, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no], last_no); array_rad_test_poles[2, 1] := rad_c; array_ord_test_poles[2, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 15; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[2, 2] := glob_larger_float; array_ord_test_poles[2, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[2, 2] then array_rad_test_poles[2, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no], last_no); array_rad_test_poles[2, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[2, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 15; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5], array_y2_higher[1, last_no - 4], array_y2_higher[1, last_no - 3], array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y2_higher[1, last_no - 5], array_y2_higher[1, last_no - 4], array_y2_higher[1, last_no - 3], array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[2, 3] := glob_larger_float; array_ord_test_poles[2, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y1_higher[1, last_no - 5], array_y1_higher[1, last_no - 4], array_y1_higher[1, last_no - 3], array_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[2, 3] then array_rad_test_poles[2, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y1_higher[1, last_no - 5], array_y1_higher[1, last_no - 4], array_y1_higher[1, last_no - 3], array_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no], last_no); array_rad_test_poles[2, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[2, 3] := tmp_ord end if end if; display_poles() 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_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_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 add CONST FULL $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_y1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp1[1]) * (expt((glob_h) , c(5))) * c(factorial_3(0,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[2,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[3,4] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[4,3] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[5,2] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(1); > array_y2_higher[6,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre diff $eq_no = 2 i = 1 order_d = 4 > array_tmp3[1] := array_y2_higher[5,1]; > #emit pre neg FULL $eq_no = 2 > array_tmp4[1] := neg(array_tmp3[1]); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[2,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y1_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp1[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,7]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp1[2]) * (expt((glob_h) , c(5))) * c(factorial_3(1,6)); > if (7 <= ATS_MAX_TERMS) then # if number 3 > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(6); > array_y2_higher[2,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[3,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[4,4] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[5,3] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[6,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre diff $eq_no = 2 i = 2 order_d = 4 > array_tmp3[2] := array_y2_higher[5,2]; > #emit pre neg FULL $eq_no = 2 > array_tmp4[2] := neg(array_tmp3[2]); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[2,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y1_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp1[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,8]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp1[3]) * (expt((glob_h) , c(5))) * c(factorial_3(2,7)); > if (8 <= ATS_MAX_TERMS) then # if number 3 > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(7); > array_y2_higher[2,7] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(6); > array_y2_higher[3,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[4,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[5,4] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[6,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre diff $eq_no = 2 i = 3 order_d = 4 > array_tmp3[3] := array_y2_higher[5,3]; > #emit pre neg FULL $eq_no = 2 > array_tmp4[3] := neg(array_tmp3[3]); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[2,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y1_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp1[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,9]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp1[4]) * (expt((glob_h) , c(5))) * c(factorial_3(3,8)); > if (9 <= ATS_MAX_TERMS) then # if number 3 > array_y2[9] := temporary; > array_y2_higher[1,9] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(8); > array_y2_higher[2,8] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(7); > array_y2_higher[3,7] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(6); > array_y2_higher[4,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[5,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[6,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre diff $eq_no = 2 i = 4 order_d = 4 > array_tmp3[4] := array_y2_higher[5,4]; > #emit pre neg FULL $eq_no = 2 > array_tmp4[4] := neg(array_tmp3[4]); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[2,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y1_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp1[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,10]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp1[5]) * (expt((glob_h) , c(5))) * c(factorial_3(4,9)); > if (10 <= ATS_MAX_TERMS) then # if number 3 > array_y2[10] := temporary; > array_y2_higher[1,10] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(9); > array_y2_higher[2,9] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(8); > array_y2_higher[3,8] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(7); > array_y2_higher[4,7] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(6); > array_y2_higher[5,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[6,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre diff $eq_no = 2 i = 5 order_d = 4 > array_tmp3[5] := array_y2_higher[5,5]; > #emit pre neg FULL $eq_no = 2 > array_tmp4[5] := neg(array_tmp3[5]); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[2,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y1_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp1[kkk] := array_y1[kkk]; > #emit assign $eq_no = 1 > order_d := 5; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp1[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y2[kkk + order_d] := c(temporary); > array_y2_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y2_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > #emit diff $eq_no = 2 > if (kkk <= ATS_MAX_TERMS) then # if number 1 > array_tmp3[kkk] := array_y2_higher[5,kkk]; > fi;# end if 1; > #emit neg FULL $eq_no = 2 > array_tmp4[kkk] := neg(array_tmp3[kkk]); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2 > temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y1[kkk + order_d] := c(temporary); > array_y1_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y1_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > 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_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; if not array_y2_set_initial[1, 6] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp1[1])*expt(glob_h, c(5))*c(factorial_3(0, 5)); if 6 <= ATS_MAX_TERMS then array_y2[6] := temporary; array_y2_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[2, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[3, 4] := c(temporary); temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[4, 3] := c(temporary); temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[5, 2] := c(temporary); temporary := c(temporary)*c(1)/c(glob_h); array_y2_higher[6, 1] := c(temporary) end if end if; kkk := 2; array_tmp3[1] := array_y2_higher[5, 1]; array_tmp4[1] := neg(array_tmp3[1]); if not array_y1_set_initial[2, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y1[2] := temporary; array_y1_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y1_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_y1[2]; if not array_y2_set_initial[1, 7] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp1[2])*expt(glob_h, c(5))*c(factorial_3(1, 6)); if 7 <= ATS_MAX_TERMS then array_y2[7] := temporary; array_y2_higher[1, 7] := temporary end if; temporary := c(temporary)*c(6)/c(glob_h); array_y2_higher[2, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[3, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[4, 4] := c(temporary); temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[5, 3] := c(temporary); temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[6, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[2] := array_y2_higher[5, 2]; array_tmp4[2] := neg(array_tmp3[2]); if not array_y1_set_initial[2, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y1[3] := temporary; array_y1_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y1_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := array_y1[3]; if not array_y2_set_initial[1, 8] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp1[3])*expt(glob_h, c(5))*c(factorial_3(2, 7)); if 8 <= ATS_MAX_TERMS then array_y2[8] := temporary; array_y2_higher[1, 8] := temporary end if; temporary := c(temporary)*c(7)/c(glob_h); array_y2_higher[2, 7] := c(temporary); temporary := c(temporary)*c(6)/c(glob_h); array_y2_higher[3, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[4, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[5, 4] := c(temporary); temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[6, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[3] := array_y2_higher[5, 3]; array_tmp4[3] := neg(array_tmp3[3]); if not array_y1_set_initial[2, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y1[4] := temporary; array_y1_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y1_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := array_y1[4]; if not array_y2_set_initial[1, 9] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp1[4])*expt(glob_h, c(5))*c(factorial_3(3, 8)); if 9 <= ATS_MAX_TERMS then array_y2[9] := temporary; array_y2_higher[1, 9] := temporary end if; temporary := c(temporary)*c(8)/c(glob_h); array_y2_higher[2, 8] := c(temporary); temporary := c(temporary)*c(7)/c(glob_h); array_y2_higher[3, 7] := c(temporary); temporary := c(temporary)*c(6)/c(glob_h); array_y2_higher[4, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[5, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[6, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[4] := array_y2_higher[5, 4]; array_tmp4[4] := neg(array_tmp3[4]); if not array_y1_set_initial[2, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y1[5] := temporary; array_y1_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y1_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := array_y1[5]; if not array_y2_set_initial[1, 10] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp1[5])*expt(glob_h, c(5))*c(factorial_3(4, 9)); if 10 <= ATS_MAX_TERMS then array_y2[10] := temporary; array_y2_higher[1, 10] := temporary end if; temporary := c(temporary)*c(9)/c(glob_h); array_y2_higher[2, 9] := c(temporary); temporary := c(temporary)*c(8)/c(glob_h); array_y2_higher[3, 8] := c(temporary); temporary := c(temporary)*c(7)/c(glob_h); array_y2_higher[4, 7] := c(temporary); temporary := c(temporary)*c(6)/c(glob_h); array_y2_higher[5, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[6, 5] := c(temporary) end if end if; kkk := 6; array_tmp3[5] := array_y2_higher[5, 5]; array_tmp4[5] := neg(array_tmp3[5]); if not array_y1_set_initial[2, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y1[6] := temporary; array_y1_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y1_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := array_y1[kkk]; order_d := 5; if kkk + order_d <= ATS_MAX_TERMS then if not array_y2_set_initial[1, kkk + order_d] then temporary := c(array_tmp1[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y2[kkk + order_d] := c(temporary); array_y2_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y2_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; if kkk <= ATS_MAX_TERMS then array_tmp3[kkk] := array_y2_higher[5, kkk] end if; array_tmp4[kkk] := neg(array_tmp3[kkk]); order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y1_set_initial[2, kkk + order_d] then temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y1[kkk + order_d] := c(temporary); array_y1_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y1_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > 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_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_5, > array_const_0D0, > array_const_1, > array_const_4, > #END CONST > array_y2_init, > array_y1_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_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=64; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y2_init:= Array(0..(40),[]); > array_y1_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > array_1st_rel_error:= Array(0..(3),[]); > array_last_rel_error:= Array(0..(3),[]); > array_est_rel_error:= Array(0..(3),[]); > array_max_est_error:= Array(0..(3),[]); > array_type_pole:= Array(0..(3),[]); > array_type_real_pole:= Array(0..(3),[]); > array_type_complex_pole:= Array(0..(3),[]); > array_est_digits:= Array(0..(3),[]); > array_y2:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_y1:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y2_higher := Array(0..(6) ,(0..40+ 1),[]); > array_y2_higher_work := Array(0..(6) ,(0..40+ 1),[]); > array_y2_higher_work2 := Array(0..(6) ,(0..40+ 1),[]); > array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]); > array_y1_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y1_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y1_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y1_set_initial := Array(0..(3) ,(0..40+ 1),[]); > array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(40) ,(0..40+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 40) do # do number 1 > array_y2_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y1_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=6) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=6) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=6) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y1_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y1_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y1_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y1_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=40) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y2); > zero_ats_ar(array_x); > zero_ats_ar(array_y1); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_5); > array_const_5[1] := c(5); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_4); > array_const_4[1] := c(4); > 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_h := 0.1; > glob_nxt := 1; > 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_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 := 10000; > 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_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := true; > array_y2_set_initial[1,5] := true; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y2_set_initial[1,31] := false; > array_y2_set_initial[1,32] := false; > array_y2_set_initial[1,33] := false; > array_y2_set_initial[1,34] := false; > array_y2_set_initial[1,35] := false; > array_y2_set_initial[1,36] := false; > array_y2_set_initial[1,37] := false; > array_y2_set_initial[1,38] := false; > array_y2_set_initial[1,39] := false; > array_y2_set_initial[1,40] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > array_y1_set_initial[2,31] := false; > array_y1_set_initial[2,32] := false; > array_y1_set_initial[2,33] := false; > array_y1_set_initial[2,34] := false; > array_y1_set_initial[2,35] := false; > array_y1_set_initial[2,36] := false; > array_y1_set_initial[2,37] := false; > array_y1_set_initial[2,38] := false; > array_y1_set_initial[2,39] := false; > array_y1_set_initial[2,40] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 40; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest7postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 5 ) = y1 ; "); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=64;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_h := c(0.1);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 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:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return( cos(c(x)) );"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return( sin(c(x)) + c(10.0) * c(x) + c(10.0));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return( cos(c(x)) + c(10.0));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"return( neg(sin(c(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"return( neg(cos(c(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"return( sin(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > 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 := 0.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); > array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); > glob_look_poles := true; > glob_max_h := c(0.1); > 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:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 18 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 18; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 17; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 17 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 17; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 17 > 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 := 5; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 18 > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 18; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 18 > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 18; > term_no := term_no + 1; > od;# end do number 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; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 18 > 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 19 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 19; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 18; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 18 > omniout_str(INFO," "); > fi;# end if 18; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 18 > 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 19 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 19; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 18; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > if (glob_subiter_method = 1 ) then # if number 18 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 19 > subiter := 1; > while (subiter <= 6) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 6 + ATS_MAX_TERMS) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 19; > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 19 > display_alot(current_iter); > fi;# end if 19; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 19 > check_for_pole(); > fi;# end if 19; > if (true) then # if number 19 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 19; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2; > order_diff := 6; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 6; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[6,iii] := array_y2_higher[6,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 := 6; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 5; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 5; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[4,iii] := array_y2_higher[4,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 := 4; > calc_term := 3; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[4,iii] := array_y2_higher[4,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 := 4; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[4,iii] := array_y2_higher[4,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 := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 3; > calc_term := 4; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 3; > calc_term := 3; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 5; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 4; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 6; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 6; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 5; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =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_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 19 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 19; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 19 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 19; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 5 ) = y1 ; "); > omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 19 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T15:50:21-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest7") > ; > logitem_str(html_log_file,"diff ( y2 , x , 5 ) = y1 ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 20 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 20; > if (glob_min_good_digits <> -16) then # if number 20 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 20; > if (glob_good_digits <> -16) then # if number 20 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 20; > 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 20 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 21 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 22 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 23 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 24 > 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 25 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 25; > if (glob_least_ratio_sing < glob_large_float) then # if number 25 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 25; > if (glob_least_3_sing < glob_large_float) then # if number 25 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 25; > if (glob_least_6_sing < glob_large_float) then # if number 25 > glob_least_6_sing := 0.0; > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 25; > 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 25 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 25; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"mtest7 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest7 maple results") > ; > logitem_str(html_log_file,"Poor Accuracy - Not sure of algorithm for multiple equations") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; ") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > glob_desired_digits_correct := 0.0; > logditto(html_log_file) > ; > if (array_est_digits[2] <> -16) then # if number 25 > logitem_integer(html_log_file,array_est_digits[2]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 25; > if (glob_min_good_digits <> -16) then # if number 25 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 25; > if (glob_good_digits <> -16) then # if number 25 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 25; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logditto(html_log_file) > ; > if (glob_type_given_pole = 0) then # if number 25 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 4) then # if number 26 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 5) then # if number 27 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 3) then # if number 28 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 1) then # if number 29 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 2) then # if number 30 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > fi;# end if 30; > if (glob_least_ratio_sing < glob_large_float) then # if number 30 > glob_least_ratio_sing := 0; > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 30; > if (glob_least_3_sing < glob_large_float) then # if number 30 > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 30; > if (glob_least_6_sing < glob_large_float) then # if number 30 > glob_least_6_sing := 0.0; > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 30; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > if (c(glob_percent_done) < glob__100) then # if number 30 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 30; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 29; > if (glob_html_log) then # if number 29 > fclose(html_log_file); > fi;# end if 29 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` 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, h_new, ratio; 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_h, glob_nxt, 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_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_5, array_const_0D0, array_const_1, array_const_4, array_y2_init, array_y1_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_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 64; max_terms := 40; glob_html_log := true; array_y2_init := Array(0 .. 40, []); array_y1_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_est_rel_error := Array(0 .. 3, []); array_max_est_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_est_digits := Array(0 .. 3, []); array_y2 := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_y1 := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y2_higher := Array(0 .. 6, 0 .. 41, []); array_y2_higher_work := Array(0 .. 6, 0 .. 41, []); array_y2_higher_work2 := Array(0 .. 6, 0 .. 41, []); array_y2_set_initial := Array(0 .. 3, 0 .. 41, []); array_y1_higher := Array(0 .. 2, 0 .. 41, []); array_y1_higher_work := Array(0 .. 2, 0 .. 41, []); array_y1_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y1_set_initial := Array(0 .. 3, 0 .. 41, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_rad_test_poles := Array(0 .. 3, 0 .. 5, []); array_ord_test_poles := Array(0 .. 3, 0 .. 5, []); array_fact_2 := Array(0 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y2_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_y1_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 40 do array_y2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_y1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= 40 do array_y2_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= 40 do array_y2_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= 40 do array_y2_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_y2_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 <= 40 do array_y1_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y1_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y1_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_y1_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 40 do term := 1; while term <= 40 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y2); zero_ats_ar(array_x); zero_ats_ar(array_y1); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_m1); zero_ats_ar(array_const_5); array_const_5[1] := c(5); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_4); array_const_4[1] := c(4); 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_h := 0.1; glob_nxt := 1; 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_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 := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := true; array_y2_set_initial[1, 5] := true; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y2_set_initial[1, 31] := false; array_y2_set_initial[1, 32] := false; array_y2_set_initial[1, 33] := false; array_y2_set_initial[1, 34] := false; array_y2_set_initial[1, 35] := false; array_y2_set_initial[1, 36] := false; array_y2_set_initial[1, 37] := false; array_y2_set_initial[1, 38] := false; array_y2_set_initial[1, 39] := false; array_y2_set_initial[1, 40] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; array_y1_set_initial[2, 31] := false; array_y1_set_initial[2, 32] := false; array_y1_set_initial[2, 33] := false; array_y1_set_initial[2, 34] := false; array_y1_set_initial[2, 35] := false; array_y1_set_initial[2, 36] := false; array_y1_set_initial[2, 37] := false; array_y1_set_initial[2, 38] := false; array_y1_set_initial[2, 39] := false; array_y1_set_initial[2, 40] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 40; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest7postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ; "); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( diff ( y2\ , x , 4 ) ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=64;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); omniout_str(ALWAYS, "array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_h := c(0.1);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 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:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return(\t cos(c(x)) );"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(\tsin(c(x)) + c(10.0) * c(x) + c(10.0));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return(\tcos(c(x)) + c(10.0));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "return( neg(sin(c(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "return(\tneg(cos(c(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "return( sin(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "next_delta := proc()"); omniout_str(ALWAYS, "global glob_nxt, x_delta;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * 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* I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); 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 := 0.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); array_y2_init[4] := exact_soln_y2ppp(x_start); array_y2_init[5] := exact_soln_y2pppp(x_start); glob_look_poles := true; glob_max_h := c(0.1); glob_type_given_pole := 3; glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); 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_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; 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 := 5; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; 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; found_h := true; glob_h := next_delta(); 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_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); 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_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 6 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 6 + ATS_MAX_TERMS do atomall(); subiter := subiter + 1 end do end if; if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 6; ord := 6; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[6, iii] := array_y2_higher[6, 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 := 6; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 5; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, 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 := 5; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 5; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, 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 := 5; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 4; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, 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 := 4; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 4; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, 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 := 4; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 4; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, 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 := 4; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 3; calc_term := 4; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 3; calc_term := 4; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 3; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 3; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 3; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 3; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 3; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 3; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 5; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 5; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 4; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 4; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 6; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 6; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 5; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 5; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 4; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 4; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do 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 ( y2 , x , 5 ) = y1 ; "); omniout_str(INFO, "diff ( y1 , x , 1 ) = neg ( diff ( \ y2 , x , 4 ) ) ; "); 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, "2017-11-26T15:50:21-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest7"); logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; 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 glob_least_ratio_sing := 0; 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 glob_least_6_sing := 0.; 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, " 309 "); logitem_str(html_log_file, "mtest7 diffeq.mxt"); logitem_str(html_log_file, "mtest7 maple results"); logitem_str(html_log_file, "Poor Accuracy - Not sure of algor\ ithm for multiple equations"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = n\ eg ( diff ( y2 , x , 4 ) ) ; "); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); glob_desired_digits_correct := 0.; logditto(html_log_file); if array_est_digits[2] <> -16 then logitem_integer(html_log_file, array_est_digits[2]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logditto(html_log_file); if glob_type_given_pole = 0 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 4 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 5 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 3 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 1 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 2 then logditto(html_log_file); logditto(html_log_file) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logditto(html_log_file) else logditto(html_log_file) end if; if glob_least_3_sing < glob_large_float then logditto(html_log_file) else logditto(html_log_file) end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logditto(html_log_file) else logditto(html_log_file) end if; logditto(html_log_file); logditto(html_log_file); if c(glob_percent_done) < glob__100 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.5MB, alloc=40.3MB, time=0.07 ##############ECHO OF PROBLEM################# ##############temp/mtest7postcpx.cpx################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=64; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); glob_look_poles := true; glob_max_h := c(0.1); 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:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return( cos(c(x)) ); end; exact_soln_y2 := proc(x) return( sin(c(x)) + c(10.0) * c(x) + c(10.0)); end; exact_soln_y2p := proc(x) return( cos(c(x)) + c(10.0)); end; exact_soln_y2pp := proc(x) return( neg(sin(c(x)))); end; exact_soln_y2ppp := proc(x) return( neg(cos(c(x)))); end; exact_soln_y2pppp := proc(x) return( sin(c(x))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion memory used=53.5MB, alloc=40.3MB, time=0.66 memory used=100.0MB, alloc=40.3MB, time=1.20 x[1] = 0.1 0.1 h = 0.0001 0.005 y2[1] (numeric) = 11.1003329998 1.09966633349 y2[1] (closed_form) = 11.1003329998 1.09966633349 absolute error = 0 relative error = 0 % Correct digits = 62 h = 0.0001 0.005 y1[1] (numeric) = 0.999983333337 -0.00999998888889 y1[1] (closed_form) = 0.999983333337 -0.00999998888889 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1414 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1414 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=145.8MB, alloc=40.3MB, time=1.74 memory used=192.3MB, alloc=40.3MB, time=2.29 x[1] = 0.1001 0.105 h = 0.0001 0.003 y2[1] (numeric) = 11.1014738411 1.14366603417 y2[1] (closed_form) = 11.1014843031 1.15466646612 absolute error = 0.011 relative error = 0.09856 % Correct digits = 3 h = 0.0001 0.003 y1[1] (numeric) = 1.00048412347 -0.0105122476776 y1[1] (closed_form) = 1.00048412347 -0.0105122476776 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1452 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1452 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=238.0MB, alloc=40.3MB, time=2.82 memory used=284.7MB, alloc=40.3MB, time=3.38 x[1] = 0.1002 0.108 h = 0.001 0.001 y2[1] (numeric) = 11.1026163718 1.18766731208 y2[1] (closed_form) = 11.1026163718 1.18766731208 absolute error = 5.369e-13 relative error = 4.808e-12 % Correct digits = 13 h = 0.001 0.001 y1[1] (numeric) = 1.00079256889 -0.0108245151295 y1[1] (closed_form) = 1.00079256889 -0.0108245151295 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1475 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1475 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=330.6MB, alloc=40.3MB, time=3.93 memory used=377.0MB, alloc=40.3MB, time=4.48 x[1] = 0.1012 0.109 h = 0.001 0.003 y2[1] (numeric) = 11.1037605975 1.23167023111 y2[1] (closed_form) = 11.1136280969 1.19865717918 absolute error = 0.03446 relative error = 0.3082 % Correct digits = 3 h = 0.001 0.003 y1[1] (numeric) = 1.00079960894 -0.0110337996083 y1[1] (closed_form) = 1.00079960894 -0.0110337996083 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1489 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1489 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=422.8MB, alloc=40.3MB, time=5.02 memory used=469.3MB, alloc=40.3MB, time=5.57 memory used=515.8MB, alloc=40.3MB, time=6.12 x[1] = 0.1022 0.112 h = 0.0001 0.004 y2[1] (numeric) = 11.1049065238 1.27567485514 y2[1] (closed_form) = 11.1246627347 1.23164867691 absolute error = 0.04826 relative error = 0.4311 % Correct digits = 2 h = 0.0001 0.004 y1[1] (numeric) = 1.00102792236 -0.0114503883919 y1[1] (closed_form) = 1.00102792236 -0.0114503883919 absolute error = 1e-63 relative error = 9.989e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1518 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1518 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=561.6MB, alloc=40.3MB, time=6.65 memory used=608.1MB, alloc=40.3MB, time=7.20 x[1] = 0.1023 0.116 h = 0.003 0.006 y2[1] (numeric) = 11.106054156 1.31968124811 y2[1] (closed_form) = 11.1258095055 1.27565250577 absolute error = 0.04826 relative error = 0.4309 % Correct digits = 2 h = 0.003 0.006 y1[1] (numeric) = 1.00147225055 -0.0118726973391 y1[1] (closed_form) = 1.00147225055 -0.0118726973391 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.155 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.155 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=653.8MB, alloc=40.3MB, time=7.73 memory used=700.2MB, alloc=40.3MB, time=8.28 x[1] = 0.1053 0.122 h = 0.0001 0.005 y2[1] (numeric) = 11.1072034999 1.36368947394 y2[1] (closed_form) = 11.1588886778 1.34162544034 absolute error = 0.0562 relative error = 0.5 % Correct digits = 2 h = 0.0001 0.005 y1[1] (numeric) = 1.00187103916 -0.0128547054021 y1[1] (closed_form) = 1.00187103916 -0.0128547054021 absolute error = 1e-65 relative error = 9.981e-64 % Correct digits = 65 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1616 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1616 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=746.0MB, alloc=40.3MB, time=8.82 memory used=792.7MB, alloc=40.3MB, time=9.37 x[1] = 0.1054 0.127 h = 0.0001 0.003 y2[1] (numeric) = 11.108354561 1.40769959662 y2[1] (closed_form) = 11.1600545238 1.39663499766 absolute error = 0.05287 relative error = 0.4701 % Correct digits = 2 h = 0.0001 0.003 y1[1] (numeric) = 1.00248109187 -0.0133969752478 y1[1] (closed_form) = 1.00248109187 -0.0133969752478 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1656 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1656 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=838.6MB, alloc=44.3MB, time=9.91 memory used=885.2MB, alloc=44.3MB, time=10.48 x[1] = 0.1055 0.13 h = 0.001 0.001 y2[1] (numeric) = 11.1095073449 1.45171168014 y2[1] (closed_form) = 11.1611954781 1.42964164314 absolute error = 0.0562 relative error = 0.4995 % Correct digits = 2 h = 0.001 0.001 y1[1] (numeric) = 1.00285489407 -0.0137281638158 y1[1] (closed_form) = 1.00285489407 -0.0137281638158 absolute error = 1e-65 relative error = 9.971e-64 % Correct digits = 65 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1681 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1681 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=931.5MB, alloc=44.3MB, time=11.02 memory used=977.4MB, alloc=44.3MB, time=11.57 memory used=1023.9MB, alloc=44.3MB, time=12.12 x[1] = 0.1065 0.131 h = 0.001 0.003 y2[1] (numeric) = 11.1106618573 1.49572578851 y2[1] (closed_form) = 11.1722121911 1.44063066333 absolute error = 0.08261 relative error = 0.7333 % Correct digits = 2 h = 0.001 0.003 y1[1] (numeric) = 1.00287832643 -0.0139650037997 y1[1] (closed_form) = 1.00287832643 -0.0139650037997 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1695 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1695 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1069.8MB, alloc=44.3MB, time=12.65 memory used=1116.3MB, alloc=44.3MB, time=13.20 x[1] = 0.1075 0.134 h = 0.0001 0.004 y2[1] (numeric) = 11.111818104 1.53974198577 y2[1] (closed_form) = 11.1832577896 1.47362553714 absolute error = 0.09734 relative error = 0.8629 % Correct digits = 2 h = 0.0001 0.004 y1[1] (numeric) = 1.00316697577 -0.014420336423 y1[1] (closed_form) = 1.00316697577 -0.014420336423 absolute error = 1.000e-63 relative error = 9.968e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1725 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1725 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1162.0MB, alloc=44.3MB, time=13.73 memory used=1208.4MB, alloc=44.3MB, time=14.28 x[1] = 0.1076 0.138 h = 0.003 0.006 y2[1] (numeric) = 11.1129760906 1.58376033597 y2[1] (closed_form) = 11.1844167075 1.51763779872 absolute error = 0.09734 relative error = 0.8625 % Correct digits = 2 h = 0.003 0.006 y1[1] (numeric) = 1.00369866804 -0.014867247953 y1[1] (closed_form) = 1.00369866804 -0.014867247953 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1759 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1759 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1254.1MB, alloc=44.3MB, time=14.81 memory used=1300.5MB, alloc=44.3MB, time=15.36 x[1] = 0.1106 0.144 h = 0.0001 0.005 y2[1] (numeric) = 11.114135823 1.62778090319 y2[1] (closed_form) = 11.2175209979 1.58361530388 absolute error = 0.1124 relative error = 0.9924 % Correct digits = 2 h = 0.0001 0.005 y1[1] (numeric) = 1.00421252288 -0.015948936748 y1[1] (closed_form) = 1.00421252288 -0.015948936748 absolute error = 1e-63 relative error = 9.957e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1826 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1826 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1346.6MB, alloc=44.3MB, time=15.90 memory used=1392.9MB, alloc=44.3MB, time=16.45 memory used=1439.4MB, alloc=44.3MB, time=17.00 x[1] = 0.1107 0.149 h = 0.0001 0.003 y2[1] (numeric) = 11.1152973069 1.67180375151 y2[1] (closed_form) = 11.2187026307 1.63863653119 absolute error = 0.1086 relative error = 0.9578 % Correct digits = 2 h = 0.0001 0.003 y1[1] (numeric) = 1.00493198983 -0.0165216071589 y1[1] (closed_form) = 1.00493198983 -0.0165216071589 absolute error = 1e-63 relative error = 9.950e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1869 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1869 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1485.6MB, alloc=44.3MB, time=17.54 memory used=1532.3MB, alloc=44.3MB, time=18.12 x[1] = 0.1108 0.152 h = 0.001 0.001 y2[1] (numeric) = 11.1164605484 1.71582894507 y2[1] (closed_form) = 11.219853236 1.67165031411 absolute error = 0.1124 relative error = 0.9912 % Correct digits = 2 h = 0.001 0.001 y1[1] (numeric) = 1.005371242 -0.0168719550168 y1[1] (closed_form) = 1.005371242 -0.0168719550168 absolute error = 1e-63 relative error = 9.945e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1895 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1895 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1578.1MB, alloc=44.3MB, time=18.66 memory used=1624.4MB, alloc=44.3MB, time=19.20 x[1] = 0.1118 0.153 h = 0.001 0.003 y2[1] (numeric) = 11.1176255533 1.75985654798 y2[1] (closed_form) = 11.2308756312 1.6826387012 absolute error = 0.1371 relative error = 1.207 % Correct digits = 2 h = 0.001 0.003 y1[1] (numeric) = 1.00541102212 -0.0171364639514 y1[1] (closed_form) = 1.00541102212 -0.0171364639514 absolute error = 1e-63 relative error = 9.945e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1909 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1909 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1670.2MB, alloc=44.3MB, time=19.74 memory used=1716.8MB, alloc=44.3MB, time=20.29 x[1] = 0.1128 0.156 h = 0.0001 0.004 y2[1] (numeric) = 11.1187923275 1.80388662438 y2[1] (closed_form) = 11.2419333654 1.71563807267 absolute error = 0.1515 relative error = 1.332 % Correct digits = 2 h = 0.0001 0.004 y1[1] (numeric) = 1.00576003279 -0.0176308153291 y1[1] (closed_form) = 1.00576003279 -0.0176308153291 absolute error = 1e-63 relative error = 9.941e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.194 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.194 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1762.6MB, alloc=44.3MB, time=20.82 memory used=1809.0MB, alloc=44.3MB, time=21.37 x[1] = 0.1129 0.16 h = 0.003 0.006 y2[1] (numeric) = 11.1199608772 1.84791923845 y2[1] (closed_form) = 11.2431054388 1.75966055917 absolute error = 0.1515 relative error = 1.331 % Correct digits = 2 h = 0.003 0.006 y1[1] (numeric) = 1.00637922732 -0.0181026571991 y1[1] (closed_form) = 1.00637922732 -0.0181026571991 absolute error = 1e-63 relative error = 9.935e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1975 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1975 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1855.2MB, alloc=44.3MB, time=21.91 memory used=1901.3MB, alloc=44.3MB, time=22.45 memory used=1947.7MB, alloc=44.3MB, time=23.00 x[1] = 0.1159 0.166 h = 0.0001 0.005 y2[1] (numeric) = 11.1211312084 1.89195445434 y2[1] (closed_form) = 11.2762376567 1.82564463623 absolute error = 0.1687 relative error = 1.477 % Correct digits = 2 h = 0.0001 0.005 y1[1] (numeric) = 1.0070081304 -0.0192846397327 y1[1] (closed_form) = 1.0070081304 -0.0192846397327 absolute error = 1.000e-63 relative error = 9.929e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2044 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2044 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1993.6MB, alloc=44.3MB, time=23.54 memory used=2040.2MB, alloc=44.3MB, time=24.09 x[1] = 0.116 0.171 h = 0.0001 0.003 y2[1] (numeric) = 11.1223033272 1.93599233625 y2[1] (closed_form) = 11.2774363301 1.88067978046 absolute error = 0.1647 relative error = 1.441 % Correct digits = 2 h = 0.0001 0.003 y1[1] (numeric) = 1.00783720606 -0.0198881395948 y1[1] (closed_form) = 1.00783720606 -0.0198881395948 absolute error = 1.000e-63 relative error = 9.921e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2088 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2088 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2086.1MB, alloc=44.3MB, time=24.63 memory used=2132.8MB, alloc=44.3MB, time=25.19 x[1] = 0.1161 0.174 h = 0.001 0.001 y2[1] (numeric) = 11.1234772398 1.98003294839 y2[1] (closed_form) = 11.2785973579 1.91370203975 absolute error = 0.1687 relative error = 1.475 % Correct digits = 2 h = 0.001 0.001 y1[1] (numeric) = 1.00834202675 -0.0202579089155 y1[1] (closed_form) = 1.00834202675 -0.0202579089155 absolute error = 1e-65 relative error = 9.915e-64 % Correct digits = 65 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2116 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2116 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2178.7MB, alloc=44.3MB, time=25.73 memory used=2225.1MB, alloc=44.3MB, time=26.28 x[1] = 0.1171 0.175 h = 0.001 0.003 y2[1] (numeric) = 11.1246529525 2.02407635497 y2[1] (closed_form) = 11.2896261318 1.92469000593 absolute error = 0.1926 relative error = 1.682 % Correct digits = 2 h = 0.001 0.003 y1[1] (numeric) = 1.00839811108 -0.0205502166739 y1[1] (closed_form) = 1.00839811108 -0.0205502166739 absolute error = 1.000e-63 relative error = 9.917e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.213 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.213 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2270.9MB, alloc=44.3MB, time=26.82 memory used=2317.4MB, alloc=44.3MB, time=27.36 memory used=2363.7MB, alloc=44.3MB, time=27.91 x[1] = 0.1181 0.178 h = 0.0001 0.004 y2[1] (numeric) = 11.1258304716 2.0681226202 y2[1] (closed_form) = 11.3006971836 1.95769499587 absolute error = 0.2068 relative error = 1.803 % Correct digits = 2 h = 0.0001 0.004 y1[1] (numeric) = 1.00880752691 -0.0210838935875 y1[1] (closed_form) = 1.00880752691 -0.0210838935875 absolute error = 1.000e-63 relative error = 9.913e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2162 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2162 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2409.4MB, alloc=44.3MB, time=28.44 memory used=2455.7MB, alloc=44.3MB, time=28.99 x[1] = 0.1182 0.182 h = 0.003 0.006 y2[1] (numeric) = 11.1270098035 2.11217180832 y2[1] (closed_form) = 11.301883429 2.0017295011 absolute error = 0.2068 relative error = 1.802 % Correct digits = 2 h = 0.003 0.006 y1[1] (numeric) = 1.00951439597 -0.0215810253281 y1[1] (closed_form) = 1.00951439597 -0.0215810253281 absolute error = 1.000e-63 relative error = 9.905e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2198 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2198 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2501.4MB, alloc=44.3MB, time=29.52 memory used=2547.8MB, alloc=44.3MB, time=30.07 x[1] = 0.1212 0.188 h = 0.0001 0.005 y2[1] (numeric) = 11.1281909546 2.15622398357 y2[1] (closed_form) = 11.3350463981 2.06772214785 absolute error = 0.225 relative error = 1.953 % Correct digits = 2 h = 0.0001 0.005 y1[1] (numeric) = 1.01025835835 -0.0228639871644 y1[1] (closed_form) = 1.01025835835 -0.0228639871644 absolute error = 1.000e-63 relative error = 9.896e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2268 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2268 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2593.5MB, alloc=44.3MB, time=30.60 memory used=2640.1MB, alloc=44.3MB, time=31.15 x[1] = 0.1213 0.193 h = 0.0001 0.003 y2[1] (numeric) = 11.1293739313 2.20027921021 y2[1] (closed_form) = 11.3362633769 2.12277345831 absolute error = 0.2209 relative error = 1.916 % Correct digits = 2 h = 0.0001 0.003 y1[1] (numeric) = 1.01119727997 -0.0234987849821 y1[1] (closed_form) = 1.01119727997 -0.0234987849821 absolute error = 1.000e-63 relative error = 9.887e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2314 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2314 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2686.1MB, alloc=44.3MB, time=31.70 memory used=2732.8MB, alloc=44.3MB, time=32.26 x[1] = 0.1214 0.196 h = 0.001 0.001 y2[1] (numeric) = 11.1305587404 2.2443375525 y2[1] (closed_form) = 11.3374356055 2.15580553433 absolute error = 0.225 relative error = 1.95 % Correct digits = 2 h = 0.001 0.001 y1[1] (numeric) = 1.01176781311 -0.0238882620851 y1[1] (closed_form) = 1.01176781311 -0.0238882620851 absolute error = 1.000e-63 relative error = 9.881e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2343 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2343 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2779.3MB, alloc=44.3MB, time=32.81 memory used=2825.5MB, alloc=44.3MB, time=33.35 memory used=2872.1MB, alloc=44.3MB, time=33.91 x[1] = 0.1224 0.197 h = 0.0001 0.004 y2[1] (numeric) = 11.1317453883 2.2883990747 y2[1] (closed_form) = 11.3484714577 2.1667932901 absolute error = 0.2485 relative error = 2.151 % Correct digits = 2 h = 0.0001 0.004 y1[1] (numeric) = 1.01184015904 -0.0242085150168 y1[1] (closed_form) = 1.01184015904 -0.0242085150168 absolute error = 1e-63 relative error = 9.880e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2357 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2357 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2917.9MB, alloc=44.3MB, time=34.44 memory used=2964.3MB, alloc=44.3MB, time=34.99 x[1] = 0.1225 0.201 h = 0.003 0.006 y2[1] (numeric) = 11.1329338818 2.33246384108 y2[1] (closed_form) = 11.3496705507 2.21083976422 absolute error = 0.2485 relative error = 2.149 % Correct digits = 2 h = 0.003 0.006 y1[1] (numeric) = 1.01262296704 -0.0247266799437 y1[1] (closed_form) = 1.01262296704 -0.0247266799437 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2394 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2394 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3010.1MB, alloc=44.3MB, time=35.52 memory used=3056.7MB, alloc=44.3MB, time=36.07 x[1] = 0.1255 0.207 h = 0.0001 0.005 y2[1] (numeric) = 11.1341242278 2.37653191592 y2[1] (closed_form) = 11.3828621282 2.27684179712 absolute error = 0.268 relative error = 2.308 % Correct digits = 2 h = 0.0001 0.005 y1[1] (numeric) = 1.01346721491 -0.0260957947093 y1[1] (closed_form) = 1.01346721491 -0.0260957947093 absolute error = 1e-63 relative error = 9.864e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2465 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2465 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3102.5MB, alloc=44.3MB, time=36.60 memory used=3149.0MB, alloc=44.3MB, time=37.15 x[1] = 0.1256 0.212 h = 0.0001 0.003 y2[1] (numeric) = 11.1353164329 2.42060336349 y2[1] (closed_form) = 11.3840956568 2.33190906523 absolute error = 0.2641 relative error = 2.273 % Correct digits = 2 h = 0.0001 0.003 y1[1] (numeric) = 1.01450129208 -0.0267566252526 y1[1] (closed_form) = 1.01450129208 -0.0267566252526 absolute error = 1.000e-63 relative error = 9.854e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2513 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2513 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3195.1MB, alloc=44.3MB, time=37.68 memory used=3241.6MB, alloc=44.3MB, time=38.24 memory used=3288.2MB, alloc=44.3MB, time=38.81 x[1] = 0.1257 0.215 h = 0.001 0.001 y2[1] (numeric) = 11.1365105043 2.46467824809 y2[1] (closed_form) = 11.3852780167 2.36495081209 absolute error = 0.268 relative error = 2.305 % Correct digits = 2 h = 0.001 0.001 y1[1] (numeric) = 1.01512876276 -0.0271625284212 y1[1] (closed_form) = 1.01512876276 -0.0271625284212 absolute error = 1e-63 relative error = 9.847e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2542 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2542 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3334.1MB, alloc=44.3MB, time=39.34 memory used=3380.5MB, alloc=44.3MB, time=39.90 x[1] = 0.1267 0.216 h = 0.001 0.003 y2[1] (numeric) = 11.1377064488 2.50875663398 y2[1] (closed_form) = 11.3963205233 2.3759386497 absolute error = 0.2907 relative error = 2.497 % Correct digits = 2 h = 0.001 0.003 y1[1] (numeric) = 1.01521540828 -0.0275067724077 y1[1] (closed_form) = 1.01521540828 -0.0275067724077 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2556 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2556 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3426.2MB, alloc=44.3MB, time=40.43 memory used=3472.6MB, alloc=44.3MB, time=40.98 x[1] = 0.1277 0.219 h = 0.0001 0.004 y2[1] (numeric) = 11.1389042737 2.55283858545 y2[1] (closed_form) = 11.4074194286 2.40895726787 absolute error = 0.3046 relative error = 2.613 % Correct digits = 2 h = 0.0001 0.004 y1[1] (numeric) = 1.01573788214 -0.0281138296284 y1[1] (closed_form) = 1.01573788214 -0.0281138296284 absolute error = 1e-63 relative error = 9.841e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.259 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.259 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3518.4MB, alloc=44.3MB, time=41.51 memory used=3564.7MB, alloc=44.3MB, time=42.06 x[1] = 0.1278 0.223 h = 0.003 0.006 y2[1] (numeric) = 11.140103986 2.59692416679 y2[1] (closed_form) = 11.4086345891 2.4530191172 absolute error = 0.3047 relative error = 2.611 % Correct digits = 2 h = 0.003 0.006 y1[1] (numeric) = 1.01660878108 -0.0286580356999 y1[1] (closed_form) = 1.01660878108 -0.0286580356999 absolute error = 1e-63 relative error = 9.833e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2629 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2629 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3610.5MB, alloc=44.3MB, time=42.59 memory used=3657.1MB, alloc=44.3MB, time=43.14 x[1] = 0.1308 0.229 h = 0.0001 0.005 y2[1] (numeric) = 11.141305593 2.64101344227 y2[1] (closed_form) = 11.4418621922 2.51903346283 absolute error = 0.3244 relative error = 2.769 % Correct digits = 2 h = 0.0001 0.005 y1[1] (numeric) = 1.01756819591 -0.0301295987246 y1[1] (closed_form) = 1.01756819591 -0.0301295987246 absolute error = 1e-63 relative error = 9.823e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2701 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2701 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3703.5MB, alloc=44.3MB, time=43.68 memory used=3749.6MB, alloc=44.3MB, time=44.22 memory used=3796.2MB, alloc=44.3MB, time=44.77 x[1] = 0.1309 0.234 h = 0.0001 0.003 y2[1] (numeric) = 11.1425091022 2.68510647617 y2[1] (closed_form) = 11.443116386 2.57412110684 absolute error = 0.3204 relative error = 2.732 % Correct digits = 2 h = 0.0001 0.003 y1[1] (numeric) = 1.01871268108 -0.0308227013598 y1[1] (closed_form) = 1.01871268108 -0.0308227013598 absolute error = 1e-63 relative error = 9.812e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.275 Order of pole (three term test) = 33.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.275 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3842.3MB, alloc=44.3MB, time=45.32 memory used=3889.1MB, alloc=44.3MB, time=45.89 x[1] = 0.131 0.237 h = 0.001 0.001 y2[1] (numeric) = 11.1437145208 2.72920333278 y2[1] (closed_form) = 11.4443113991 2.60717517931 absolute error = 0.3244 relative error = 2.764 % Correct digits = 2 h = 0.001 0.001 y1[1] (numeric) = 1.01940620362 -0.0312489074978 y1[1] (closed_form) = 1.01940620362 -0.0312489074978 absolute error = 1e-63 relative error = 9.805e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.278 Order of pole (three term test) = 33.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.278 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3935.0MB, alloc=44.3MB, time=46.43 memory used=3981.5MB, alloc=44.3MB, time=46.98 x[1] = 0.132 0.238 h = 0.001 0.003 y2[1] (numeric) = 11.1449218565 2.77330407636 y2[1] (closed_form) = 11.4553622917 2.61816320194 absolute error = 0.347 relative error = 2.953 % Correct digits = 2 h = 0.001 0.003 y1[1] (numeric) = 1.01950903603 -0.0316214135167 y1[1] (closed_form) = 1.01950903603 -0.0316214135167 absolute error = 1.000e-63 relative error = 9.804e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2794 Order of pole (three term test) = 33.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2794 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4027.2MB, alloc=44.3MB, time=47.52 memory used=4073.8MB, alloc=44.3MB, time=48.06 x[1] = 0.133 0.241 h = 0.0001 0.004 y2[1] (numeric) = 11.1461311169 2.81740877119 y2[1] (closed_form) = 11.4664779254 2.65119065712 absolute error = 0.3609 relative error = 3.067 % Correct digits = 2 h = 0.0001 0.004 y1[1] (numeric) = 1.02009214664 -0.0322688500487 y1[1] (closed_form) = 1.02009214664 -0.0322688500487 absolute error = 1.000e-63 relative error = 9.799e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2828 Order of pole (three term test) = 33.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2828 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4119.7MB, alloc=44.3MB, time=48.60 memory used=4166.0MB, alloc=44.3MB, time=49.15 memory used=4212.5MB, alloc=44.3MB, time=49.70 x[1] = 0.1331 0.245 h = 0.003 0.006 y2[1] (numeric) = 11.1473423097 2.86151748151 y2[1] (closed_form) = 11.4677101988 2.69526968339 absolute error = 0.3609 relative error = 3.064 % Correct digits = 2 h = 0.003 0.006 y1[1] (numeric) = 1.02105140668 -0.0328395484898 y1[1] (closed_form) = 1.02105140668 -0.0328395484898 absolute error = 1.000e-63 relative error = 9.789e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2869 Order of pole (three term test) = 33.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2869 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4258.3MB, alloc=44.3MB, time=50.23 memory used=4304.9MB, alloc=44.3MB, time=50.79 x[1] = 0.1361 0.251 h = 0.0001 0.005 y2[1] (numeric) = 11.1485554426 2.90563027159 y2[1] (closed_form) = 11.5009767016 2.76129833109 absolute error = 0.3808 relative error = 3.22 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.02212608268 -0.0344144544453 y1[1] (closed_form) = 1.02212608268 -0.0344144544453 absolute error = 1e-63 relative error = 9.778e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2942 Order of pole (three term test) = 33.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2942 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4350.7MB, alloc=44.3MB, time=51.32 memory used=4397.2MB, alloc=44.3MB, time=51.88 x[1] = 0.1362 0.256 h = 0.0001 0.003 y2[1] (numeric) = 11.1497705237 2.94974720569 y2[1] (closed_form) = 11.5022528632 2.81640861127 absolute error = 0.3769 relative error = 3.182 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.023381336 -0.035140412088 y1[1] (closed_form) = 1.023381336 -0.035140412088 absolute error = 1.000e-63 relative error = 9.766e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2993 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2993 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4443.0MB, alloc=44.3MB, time=52.41 memory used=4489.8MB, alloc=44.3MB, time=52.97 x[1] = 0.1363 0.259 h = 0.001 0.001 y2[1] (numeric) = 11.1509875608 2.99386834803 y2[1] (closed_form) = 11.5034613305 2.84947635629 absolute error = 0.3809 relative error = 3.214 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.02414112719 -0.0355872772541 y1[1] (closed_form) = 1.02414112719 -0.0355872772541 absolute error = 2.000e-63 relative error = 1.952e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3024 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3024 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4535.8MB, alloc=44.3MB, time=53.52 memory used=4582.4MB, alloc=44.3MB, time=54.08 x[1] = 0.1373 0.26 h = 0.001 0.003 y2[1] (numeric) = 11.1522065622 3.03799376286 y2[1] (closed_form) = 11.5145213187 2.86046476933 absolute error = 0.4035 relative error = 3.401 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.0242601065 -0.0359882391217 y1[1] (closed_form) = 1.0242601065 -0.0359882391217 absolute error = 2e-63 relative error = 1.951e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3038 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3038 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4628.4MB, alloc=44.3MB, time=54.61 memory used=4674.8MB, alloc=44.3MB, time=55.16 memory used=4721.3MB, alloc=44.3MB, time=55.71 x[1] = 0.1383 0.263 h = 0.0001 0.004 y2[1] (numeric) = 11.1534275359 3.08212351439 y2[1] (closed_form) = 11.5256548956 2.89350218162 absolute error = 0.4173 relative error = 3.512 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.02490396873 -0.0366764861378 y1[1] (closed_form) = 1.02490396873 -0.0366764861378 absolute error = 1.000e-63 relative error = 9.751e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3073 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3073 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4767.1MB, alloc=44.3MB, time=56.25 memory used=4813.6MB, alloc=44.3MB, time=56.80 x[1] = 0.1384 0.267 h = 0.003 0.006 y2[1] (numeric) = 11.1546504904 3.12625766683 y2[1] (closed_form) = 11.5269053391 2.93760019037 absolute error = 0.4173 relative error = 3.508 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.02595189411 -0.0372741608594 y1[1] (closed_form) = 1.02595189411 -0.0372741608594 absolute error = 1e-63 relative error = 9.741e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3114 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3114 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4859.5MB, alloc=44.3MB, time=57.33 memory used=4906.1MB, alloc=44.3MB, time=57.88 x[1] = 0.1414 0.273 h = 0.0001 0.005 y2[1] (numeric) = 11.1558754341 3.17039628438 y2[1] (closed_form) = 11.5602136369 3.00364512693 absolute error = 0.4374 relative error = 3.662 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.02714195396 -0.0389533784147 y1[1] (closed_form) = 1.02714195396 -0.0389533784147 absolute error = 1e-63 relative error = 9.729e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3189 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3189 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4952.0MB, alloc=44.3MB, time=58.42 memory used=4998.6MB, alloc=44.3MB, time=58.97 x[1] = 0.1415 0.278 h = 0.0001 0.003 y2[1] (numeric) = 11.1571023754 3.21453943123 y2[1] (closed_form) = 11.5615130838 3.05878030878 absolute error = 0.4334 relative error = 3.624 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.02850837843 -0.0397128147928 y1[1] (closed_form) = 1.02850837843 -0.0397128147928 absolute error = 1.000e-63 relative error = 9.716e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3242 Order of pole (three term test) = 33.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3242 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5044.5MB, alloc=44.3MB, time=59.50 memory used=5091.2MB, alloc=44.3MB, time=60.07 x[1] = 0.1416 0.281 h = 0.001 0.001 y2[1] (numeric) = 11.158331323 3.25868717156 y2[1] (closed_form) = 11.5627358159 3.0918630764 absolute error = 0.4375 relative error = 3.655 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.02933468047 -0.0401807199198 y1[1] (closed_form) = 1.02933468047 -0.0401807199198 absolute error = 1.000e-63 relative error = 9.708e-62 % Correct digits = 63 memory used=5137.9MB, alloc=44.3MB, time=60.62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3273 Order of pole (three term test) = 33.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3273 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5184.0MB, alloc=44.3MB, time=61.17 memory used=5230.5MB, alloc=44.3MB, time=61.72 x[1] = 0.1426 0.282 h = 0.001 0.003 y2[1] (numeric) = 11.1595622858 3.30283956951 y2[1] (closed_form) = 11.5738056135 3.10285208326 absolute error = 0.46 relative error = 3.839 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.0294697674 -0.0406103481919 y1[1] (closed_form) = 1.0294697674 -0.0406103481919 absolute error = 1.000e-63 relative error = 9.707e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3288 Order of pole (three term test) = 33.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3288 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5276.2MB, alloc=44.3MB, time=62.25 memory used=5322.7MB, alloc=44.3MB, time=62.80 x[1] = 0.1436 0.285 h = 0.0001 0.004 y2[1] (numeric) = 11.1607952724 3.34699668924 y2[1] (closed_form) = 11.5849583587 3.13590057312 absolute error = 0.4738 relative error = 3.948 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.0301745143 -0.0413398696397 y1[1] (closed_form) = 1.0301745143 -0.0413398696397 absolute error = 1.000e-63 relative error = 9.701e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3324 Order of pole (three term test) = 33.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3324 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5368.5MB, alloc=44.3MB, time=63.34 memory used=5414.9MB, alloc=44.3MB, time=63.88 x[1] = 0.1437 0.289 h = 0.003 0.006 y2[1] (numeric) = 11.1620302919 3.39115859486 y2[1] (closed_form) = 11.5862280422 3.18001937432 absolute error = 0.4738 relative error = 3.944 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.0313114434 -0.04196503753 y1[1] (closed_form) = 1.0313114434 -0.04196503753 absolute error = 1.000e-63 relative error = 9.690e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3367 Order of pole (three term test) = 33.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3367 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5460.7MB, alloc=44.3MB, time=64.42 memory used=5507.2MB, alloc=44.3MB, time=64.97 x[1] = 0.1467 0.295 h = 0.0001 0.005 y2[1] (numeric) = 11.1632673535 3.43532535049 y2[1] (closed_form) = 11.6195810531 3.24608258421 absolute error = 0.494 relative error = 4.095 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.03261703805 -0.0437496098217 y1[1] (closed_form) = 1.03261703805 -0.0437496098217 absolute error = 1.000e-63 relative error = 9.680e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3443 Order of pole (three term test) = 33.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3443 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5553.4MB, alloc=44.3MB, time=65.50 memory used=5599.6MB, alloc=44.3MB, time=66.05 memory used=5646.2MB, alloc=44.3MB, time=66.60 x[1] = 0.1468 0.3 h = 0.0001 0.003 y2[1] (numeric) = 11.1645064662 3.47949702023 y2[1] (closed_form) = 11.6209051196 3.30124493914 absolute error = 0.49 relative error = 4.056 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.03409507953 -0.0445431898539 y1[1] (closed_form) = 1.03409507953 -0.0445431898539 absolute error = 1.000e-63 relative error = 9.666e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3497 Order of pole (three term test) = 33.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3497 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5692.2MB, alloc=44.3MB, time=67.14 memory used=5738.7MB, alloc=44.3MB, time=67.71 x[1] = 0.1469 0.303 h = 0.001 0.001 y2[1] (numeric) = 11.1657476395 3.52367366814 y2[1] (closed_form) = 11.622142937 3.33434408291 absolute error = 0.4941 relative error = 4.087 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.03498816002 -0.0450325409788 y1[1] (closed_form) = 1.03498816002 -0.0450325409788 absolute error = 1.000e-63 relative error = 9.657e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.353 Order of pole (three term test) = 33.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.353 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5784.6MB, alloc=44.3MB, time=68.25 memory used=5831.3MB, alloc=44.3MB, time=68.80 x[1] = 0.1479 0.304 h = 0.0001 0.004 y2[1] (numeric) = 11.1669908828 3.56785535827 y2[1] (closed_form) = 11.6332232624 3.34533388502 absolute error = 0.5166 relative error = 4.268 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.03513931598 -0.0454910630373 y1[1] (closed_form) = 1.03513931598 -0.0454910630373 absolute error = 3e-65 relative error = 2.895e-63 % Correct digits = 65 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3544 Order of pole (three term test) = 33.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3544 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5877.2MB, alloc=44.3MB, time=69.33 memory used=5923.6MB, alloc=44.3MB, time=69.88 x[1] = 0.148 0.308 h = 0.003 0.006 y2[1] (numeric) = 11.1682362057 3.61204215465 y2[1] (closed_form) = 11.6345100971 3.38947228362 absolute error = 0.5167 relative error = 4.264 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.03635349007 -0.04613926912 y1[1] (closed_form) = 1.03635349007 -0.04613926912 absolute error = 1.000e-63 relative error = 9.644e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3588 Order of pole (three term test) = 33.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3588 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5969.3MB, alloc=44.3MB, time=70.41 memory used=6015.8MB, alloc=44.3MB, time=70.96 x[1] = 0.151 0.314 h = 0.0001 0.005 y2[1] (numeric) = 11.1694836179 3.6562341213 y2[1] (closed_form) = 11.6679037013 3.45555339047 absolute error = 0.5373 relative error = 4.415 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.03775994886 -0.0480140405886 y1[1] (closed_form) = 1.03775994886 -0.0480140405886 absolute error = 1.001e-63 relative error = 9.634e-62 % Correct digits = 63 memory used=6062.3MB, alloc=44.3MB, time=71.51 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3666 Order of pole (three term test) = 33.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3666 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6108.3MB, alloc=44.3MB, time=72.05 memory used=6154.8MB, alloc=44.3MB, time=72.60 x[1] = 0.1511 0.319 h = 0.0001 0.003 y2[1] (numeric) = 11.1707331293 3.70043132221 y2[1] (closed_form) = 11.6692496806 3.51074127424 absolute error = 0.5334 relative error = 4.377 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.03933487464 -0.0488362369329 y1[1] (closed_form) = 1.03933487464 -0.0488362369329 absolute error = 1.000e-63 relative error = 9.615e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3721 Order of pole (three term test) = 33.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3721 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6200.8MB, alloc=44.3MB, time=73.14 memory used=6247.5MB, alloc=44.3MB, time=73.70 x[1] = 0.1512 0.322 h = 0.001 0.001 y2[1] (numeric) = 11.1719847497 3.74463382132 y2[1] (closed_form) = 11.670500931 3.54385579414 absolute error = 0.5374 relative error = 4.406 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.04028593203 -0.049343592276 y1[1] (closed_form) = 1.04028593203 -0.049343592276 absolute error = 1.001e-63 relative error = 9.610e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3755 Order of pole (three term test) = 33.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3755 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6293.4MB, alloc=44.3MB, time=74.25 memory used=6339.8MB, alloc=44.3MB, time=74.80 x[1] = 0.1522 0.323 h = 0.001 0.003 y2[1] (numeric) = 11.1732384894 3.78884168257 y2[1] (closed_form) = 11.6815908847 3.55484657762 absolute error = 0.5596 relative error = 4.583 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.04045123738 -0.0498269893422 y1[1] (closed_form) = 1.04045123738 -0.0498269893422 absolute error = 1.000e-63 relative error = 9.605e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.377 Order of pole (three term test) = 33.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.377 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6385.6MB, alloc=44.3MB, time=75.33 memory used=6432.0MB, alloc=44.3MB, time=75.88 x[1] = 0.1532 0.326 h = 0.0001 0.004 y2[1] (numeric) = 11.1744943585 3.83305496987 y2[1] (closed_form) = 11.6927824345 3.58791892786 absolute error = 0.5733 relative error = 4.688 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.04127019884 -0.0506339311263 y1[1] (closed_form) = 1.04127019884 -0.0506339311263 absolute error = 1.000e-63 relative error = 9.597e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3807 Order of pole (three term test) = 33.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3807 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6478.0MB, alloc=44.3MB, time=76.41 memory used=6524.3MB, alloc=44.3MB, time=76.96 memory used=6570.8MB, alloc=44.3MB, time=77.51 x[1] = 0.1533 0.33 h = 0.003 0.006 y2[1] (numeric) = 11.1757523675 3.8772737471 y2[1] (closed_form) = 11.6940905152 3.63208151371 absolute error = 0.5734 relative error = 4.683 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.04257410438 -0.0513106760591 y1[1] (closed_form) = 1.04257410438 -0.0513106760591 absolute error = 1.001e-63 relative error = 9.588e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3853 Order of pole (three term test) = 33.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3853 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6616.5MB, alloc=44.3MB, time=78.04 memory used=6663.1MB, alloc=44.3MB, time=78.59 x[1] = 0.1563 0.336 h = 0.0001 0.005 y2[1] (numeric) = 11.1770125268 3.92149807811 y2[1] (closed_form) = 11.7275343059 3.6981846166 absolute error = 0.5941 relative error = 4.831 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.04409646806 -0.0532929406906 y1[1] (closed_form) = 1.04409646806 -0.0532929406906 absolute error = 1.001e-63 relative error = 9.573e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3932 Order of pole (three term test) = 33.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3932 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6709.0MB, alloc=44.3MB, time=79.13 memory used=6755.5MB, alloc=44.3MB, time=79.68 x[1] = 0.1564 0.341 h = 0.0001 0.003 y2[1] (numeric) = 11.1782748471 3.96572802673 y2[1] (closed_form) = 11.7289074076 3.75340393466 absolute error = 0.5902 relative error = 4.792 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.04578396391 -0.0541506224751 y1[1] (closed_form) = 1.04578396391 -0.0541506224751 absolute error = 1.001e-63 relative error = 9.561e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3989 Order of pole (three term test) = 33.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3989 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6801.4MB, alloc=44.3MB, time=80.22 memory used=6848.1MB, alloc=44.3MB, time=80.78 x[1] = 0.1565 0.344 h = 0.001 0.001 y2[1] (numeric) = 11.1795393392 4.00996365675 y2[1] (closed_form) = 11.7301752828 3.78653737029 absolute error = 0.5942 relative error = 4.821 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.046802371 -0.0546802431283 y1[1] (closed_form) = 1.046802371 -0.0546802431283 absolute error = 1.001e-63 relative error = 9.552e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4024 Order of pole (three term test) = 33.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4024 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6894.1MB, alloc=44.3MB, time=81.32 memory used=6940.7MB, alloc=44.3MB, time=81.88 x[1] = 0.1575 0.345 h = 0.001 0.003 y2[1] (numeric) = 11.180806014 4.05420503193 y2[1] (closed_form) = 11.7412771123 3.79752932687 absolute error = 0.6164 relative error = 4.995 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.04698367824 -0.0551930026442 y1[1] (closed_form) = 1.04698367824 -0.0551930026442 absolute error = 2.001e-63 relative error = 1.908e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4039 Order of pole (three term test) = 33.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4039 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6987.0MB, alloc=44.3MB, time=82.42 memory used=7033.3MB, alloc=44.3MB, time=82.96 memory used=7080.0MB, alloc=44.3MB, time=83.52 x[1] = 0.1585 0.348 h = 0.0001 0.004 y2[1] (numeric) = 11.1820748827 4.098452216 y2[1] (closed_form) = 11.7524913874 3.83061597909 absolute error = 0.6302 relative error = 5.098 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.04786401178 -0.0560427270402 y1[1] (closed_form) = 1.04786401178 -0.0560427270402 absolute error = 1.002e-63 relative error = 9.547e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4077 Order of pole (three term test) = 33.1 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4077 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7125.8MB, alloc=44.3MB, time=84.05 memory used=7172.2MB, alloc=44.3MB, time=84.60 x[1] = 0.1586 0.352 h = 0.003 0.006 y2[1] (numeric) = 11.1833459565 4.14270527265 y2[1] (closed_form) = 11.7538218255 3.87480457816 absolute error = 0.6302 relative error = 5.092 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.04925808543 -0.0567486234603 y1[1] (closed_form) = 1.04925808543 -0.0567486234603 absolute error = 1.002e-63 relative error = 9.534e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4124 Order of pole (three term test) = 33.1 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4124 Order of pole (three term test) = 31.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7218.2MB, alloc=44.3MB, time=85.13 memory used=7264.7MB, alloc=44.3MB, time=85.68 x[1] = 0.1616 0.358 h = 0.0001 0.005 y2[1] (numeric) = 11.1846192467 4.18696426555 y2[1] (closed_form) = 11.787318796 3.94093165648 absolute error = 0.651 relative error = 5.238 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.05089658578 -0.0588396400566 y1[1] (closed_form) = 1.05089658578 -0.0588396400566 absolute error = 1.002e-63 relative error = 9.518e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4205 Order of pole (three term test) = 33.1 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4205 Order of pole (three term test) = 31.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7310.7MB, alloc=44.3MB, time=86.22 memory used=7357.4MB, alloc=44.3MB, time=86.77 x[1] = 0.1617 0.363 h = 0.0001 0.003 y2[1] (numeric) = 11.1858947649 4.23122925832 y2[1] (closed_form) = 11.7887204075 3.99618470143 absolute error = 0.647 relative error = 5.198 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.05269722104 -0.0597335918718 y1[1] (closed_form) = 1.05269722104 -0.0597335918718 absolute error = 1.002e-63 relative error = 9.507e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4264 Order of pole (three term test) = 33.1 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4264 Order of pole (three term test) = 31.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7403.4MB, alloc=44.3MB, time=87.30 memory used=7450.0MB, alloc=44.3MB, time=87.86 memory used=7496.8MB, alloc=44.3MB, time=88.43 x[1] = 0.1618 0.366 h = 0.001 0.001 y2[1] (numeric) = 11.1871725227 4.27550031457 y2[1] (closed_form) = 11.7900057605 4.02933841892 absolute error = 0.6512 relative error = 5.226 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.05378331863 -0.0602859568118 y1[1] (closed_form) = 1.05378331863 -0.0602859568118 absolute error = 1.002e-63 relative error = 9.491e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.43 Order of pole (three term test) = 33.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.43 Order of pole (three term test) = 31.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7542.7MB, alloc=44.3MB, time=88.96 memory used=7589.0MB, alloc=44.3MB, time=89.52 x[1] = 0.1628 0.367 h = 0.001 0.003 y2[1] (numeric) = 11.1884525322 4.31977749784 y2[1] (closed_form) = 11.8011201995 4.0403317439 absolute error = 0.6734 relative error = 5.399 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.05398059082 -0.0608283548403 y1[1] (closed_form) = 1.05398059082 -0.0608283548403 absolute error = 2.001e-63 relative error = 1.895e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4316 Order of pole (three term test) = 33.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4316 Order of pole (three term test) = 31.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7634.9MB, alloc=44.3MB, time=90.05 memory used=7681.5MB, alloc=44.3MB, time=90.60 x[1] = 0.1638 0.37 h = 0.0001 0.004 y2[1] (numeric) = 11.1897348051 4.36406087166 y2[1] (closed_form) = 11.8123584734 4.07343382218 absolute error = 0.6871 relative error = 5.499 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.05492249965 -0.0617214545662 y1[1] (closed_form) = 1.05492249965 -0.0617214545662 absolute error = 1.002e-63 relative error = 9.486e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4355 Order of pole (three term test) = 33.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4355 Order of pole (three term test) = 31.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7727.3MB, alloc=44.3MB, time=91.14 memory used=7773.7MB, alloc=44.3MB, time=91.68 x[1] = 0.1639 0.374 h = 0.003 0.006 y2[1] (numeric) = 11.1910193537 4.40835049948 y2[1] (closed_form) = 11.8137123963 4.11765026708 absolute error = 0.6872 relative error = 5.493 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.05640721236 -0.0624571494307 y1[1] (closed_form) = 1.05640721236 -0.0624571494307 absolute error = 2.001e-63 relative error = 1.891e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4403 Order of pole (three term test) = 33.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4403 Order of pole (three term test) = 31.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7819.5MB, alloc=44.3MB, time=92.22 memory used=7866.0MB, alloc=44.3MB, time=92.77 x[1] = 0.1669 0.38 h = 0.0001 0.005 y2[1] (numeric) = 11.1923061904 4.45264644477 y2[1] (closed_form) = 11.84726557 4.18380329876 absolute error = 0.708 relative error = 5.635 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.05816210876 -0.0646582534612 y1[1] (closed_form) = 1.05816210876 -0.0646582534612 absolute error = 1.003e-63 relative error = 9.463e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4486 Order of pole (three term test) = 33.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4486 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7912.5MB, alloc=44.3MB, time=93.31 memory used=7958.9MB, alloc=44.3MB, time=93.86 memory used=8005.4MB, alloc=44.3MB, time=94.40 x[1] = 0.167 0.385 h = 0.0001 0.003 y2[1] (numeric) = 11.1935953275 4.49694877091 y2[1] (closed_form) = 11.8486970995 4.23909237191 absolute error = 0.704 relative error = 5.595 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.0600764959 -0.0655893028202 y1[1] (closed_form) = 1.0600764959 -0.0655893028202 absolute error = 2.002e-63 relative error = 1.885e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4548 Order of pole (three term test) = 33.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4548 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8051.3MB, alloc=44.3MB, time=94.95 memory used=8098.0MB, alloc=44.3MB, time=95.51 x[1] = 0.1671 0.388 h = 0.001 0.001 y2[1] (numeric) = 11.1948867779 4.54125754127 y2[1] (closed_form) = 11.8500007958 4.27226774256 absolute error = 0.7082 relative error = 5.622 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.06123065034 -0.0661649171799 y1[1] (closed_form) = 1.06123065034 -0.0661649171799 absolute error = 1.003e-63 relative error = 9.435e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4585 Order of pole (three term test) = 33.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4585 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8144.0MB, alloc=44.3MB, time=96.06 memory used=8190.5MB, alloc=44.3MB, time=96.61 x[1] = 0.1681 0.389 h = 0.001 0.003 y2[1] (numeric) = 11.1961805541 4.58557281916 y2[1] (closed_form) = 11.861128584 4.28326262891 absolute error = 0.7304 relative error = 5.792 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.06144385093 -0.06673724702 y1[1] (closed_form) = 1.06144385093 -0.06673724702 absolute error = 1.003e-63 relative error = 9.433e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.46 Order of pole (three term test) = 33.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.46 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8236.3MB, alloc=44.3MB, time=97.14 memory used=8282.9MB, alloc=44.3MB, time=97.70 x[1] = 0.1691 0.392 h = 0.0001 0.004 y2[1] (numeric) = 11.1974766693 4.62989466784 y2[1] (closed_form) = 11.8723921447 4.31638125878 absolute error = 0.7442 relative error = 5.891 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.06244755619 -0.0676743489303 y1[1] (closed_form) = 1.06244755619 -0.0676743489303 absolute error = 1.003e-63 relative error = 9.423e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4641 Order of pole (three term test) = 33.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4641 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8328.8MB, alloc=44.3MB, time=98.23 memory used=8375.3MB, alloc=44.3MB, time=98.78 x[1] = 0.1692 0.396 h = 0.003 0.006 y2[1] (numeric) = 11.1987751367 4.67422315054 y2[1] (closed_form) = 11.8737706972 4.36062738934 absolute error = 0.7443 relative error = 5.884 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.0640234133 -0.0684405239204 y1[1] (closed_form) = 1.0640234133 -0.0684405239204 absolute error = 1.003e-63 relative error = 9.409e-62 % Correct digits = 63 memory used=8421.7MB, alloc=44.3MB, time=99.33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4691 Order of pole (three term test) = 33.13 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4691 Order of pole (three term test) = 31.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8467.6MB, alloc=44.3MB, time=99.86 memory used=8514.1MB, alloc=44.3MB, time=100.42 x[1] = 0.1722 0.402 h = 0.0001 0.005 y2[1] (numeric) = 11.2000759694 4.71855833044 y2[1] (closed_form) = 11.9073831291 4.42680835101 absolute error = 0.7651 relative error = 6.023 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.06589499251 -0.0707531281916 y1[1] (closed_form) = 1.06589499251 -0.0707531281916 absolute error = 1.004e-63 relative error = 9.399e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4776 Order of pole (three term test) = 33.13 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4776 Order of pole (three term test) = 31.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8560.0MB, alloc=44.3MB, time=100.95 memory used=8606.5MB, alloc=44.3MB, time=101.50 x[1] = 0.1723 0.407 h = 0.0001 0.003 y2[1] (numeric) = 11.2013791811 4.76290027068 y2[1] (closed_form) = 11.9088460068 4.48213576314 absolute error = 0.7611 relative error = 5.982 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.06792378719 -0.0717221460499 y1[1] (closed_form) = 1.06792378719 -0.0717221460499 absolute error = 1.004e-63 relative error = 9.381e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4839 Order of pole (three term test) = 33.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4839 Order of pole (three term test) = 31.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8652.5MB, alloc=44.3MB, time=102.05 memory used=8699.2MB, alloc=44.3MB, time=102.61 x[1] = 0.1724 0.41 h = 0.001 0.001 y2[1] (numeric) = 11.2026847854 4.80724903434 y2[1] (closed_form) = 11.9101689254 4.51533416384 absolute error = 0.7653 relative error = 6.009 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.06914639045 -0.0723215414344 y1[1] (closed_form) = 1.06914639045 -0.0723215414344 absolute error = 1.004e-63 relative error = 9.370e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4877 Order of pole (three term test) = 33.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4877 Order of pole (three term test) = 31.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8745.2MB, alloc=44.3MB, time=103.15 memory used=8791.7MB, alloc=44.3MB, time=103.70 x[1] = 0.1734 0.411 h = 0.0001 0.004 y2[1] (numeric) = 11.2039927961 4.85160468446 y2[1] (closed_form) = 11.921310809 4.52633080214 absolute error = 0.7876 relative error = 6.177 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.06937548317 -0.0729241137464 y1[1] (closed_form) = 1.06937548317 -0.0729241137464 absolute error = 1.004e-63 relative error = 9.367e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4893 Order of pole (three term test) = 33.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4893 Order of pole (three term test) = 31.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8838.0MB, alloc=44.3MB, time=104.24 memory used=8884.3MB, alloc=44.3MB, time=104.78 memory used=8930.7MB, alloc=44.3MB, time=105.33 x[1] = 0.1735 0.415 h = 0.003 0.006 y2[1] (numeric) = 11.2053032273 4.89596728403 y2[1] (closed_form) = 11.9227111087 4.57060427663 absolute error = 0.7877 relative error = 6.169 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.07103060008 -0.0737160031704 y1[1] (closed_form) = 1.07103060008 -0.0737160031704 absolute error = 1.004e-63 relative error = 9.352e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4945 Order of pole (three term test) = 33.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4945 Order of pole (three term test) = 31.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8976.5MB, alloc=44.3MB, time=105.86 memory used=9023.0MB, alloc=44.3MB, time=106.41 x[1] = 0.1765 0.421 h = 0.0001 0.005 y2[1] (numeric) = 11.2066160932 4.94033689598 y2[1] (closed_form) = 11.9563766553 4.63681161755 absolute error = 0.8089 relative error = 6.307 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.0730042189 -0.076124378964 y1[1] (closed_form) = 1.0730042189 -0.076124378964 absolute error = 1.005e-63 relative error = 9.343e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5032 Order of pole (three term test) = 33.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5032 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9069.0MB, alloc=44.3MB, time=106.94 memory used=9115.6MB, alloc=44.3MB, time=107.50 x[1] = 0.1766 0.426 h = 0.0001 0.003 y2[1] (numeric) = 11.2079314082 4.9847135832 y2[1] (closed_form) = 11.9578671852 4.69217428577 absolute error = 0.805 relative error = 6.267 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.07513251711 -0.0771254355981 y1[1] (closed_form) = 1.07513251711 -0.0771254355981 absolute error = 1.004e-63 relative error = 9.315e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5097 Order of pole (three term test) = 33.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5097 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9161.5MB, alloc=44.3MB, time=108.03 memory used=9208.2MB, alloc=44.3MB, time=108.59 x[1] = 0.1767 0.429 h = 0.001 0.001 y2[1] (numeric) = 11.2092491869 5.02909740851 y2[1] (closed_form) = 11.9592070676 4.72539386063 absolute error = 0.8091 relative error = 6.292 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.07641466469 -0.0777449248564 y1[1] (closed_form) = 1.07641466469 -0.0777449248564 absolute error = 1.004e-63 relative error = 9.303e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5136 Order of pole (three term test) = 33.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5136 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9254.3MB, alloc=44.3MB, time=109.14 memory used=9300.8MB, alloc=44.3MB, time=109.69 x[1] = 0.1777 0.43 h = 0.001 0.003 y2[1] (numeric) = 11.210569444 5.07348843469 y2[1] (closed_form) = 11.970361663 4.73639233778 absolute error = 0.8312 relative error = 6.457 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.07665777353 -0.0783736022804 y1[1] (closed_form) = 1.07665777353 -0.0783736022804 absolute error = 1.005e-63 relative error = 9.310e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5153 Order of pole (three term test) = 33.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5153 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9347.1MB, alloc=44.3MB, time=110.23 memory used=9393.3MB, alloc=44.3MB, time=110.78 memory used=9439.9MB, alloc=44.3MB, time=111.33 x[1] = 0.1787 0.433 h = 0.0001 0.004 y2[1] (numeric) = 11.2118921945 5.11788672446 y2[1] (closed_form) = 11.9816755291 4.76954510587 absolute error = 0.8449 relative error = 6.552 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.07777766086 -0.0793936255503 y1[1] (closed_form) = 1.07777766086 -0.0793936255503 absolute error = 1.005e-63 relative error = 9.299e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5195 Order of pole (three term test) = 33.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5195 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9485.7MB, alloc=44.3MB, time=111.86 memory used=9532.0MB, alloc=44.3MB, time=112.40 x[1] = 0.1788 0.437 h = 0.003 0.006 y2[1] (numeric) = 11.2132174536 5.16229234048 y2[1] (closed_form) = 11.9831026153 4.81385172486 absolute error = 0.8451 relative error = 6.544 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.07952496334 -0.0802173504665 y1[1] (closed_form) = 1.07952496334 -0.0802173504665 absolute error = 1.005e-63 relative error = 9.284e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5248 Order of pole (three term test) = 33.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5248 Order of pole (three term test) = 31.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9577.8MB, alloc=44.3MB, time=112.94 memory used=9624.3MB, alloc=44.3MB, time=113.49 x[1] = 0.1818 0.443 h = 0.0001 0.005 y2[1] (numeric) = 11.2145452366 5.20670534535 y2[1] (closed_form) = 12.0168331717 4.88009070846 absolute error = 0.8662 relative error = 6.679 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.08161588983 -0.0827400595285 y1[1] (closed_form) = 1.08161588983 -0.0827400595285 absolute error = 1.005e-63 relative error = 9.264e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5338 Order of pole (three term test) = 33.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5338 Order of pole (three term test) = 31.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9670.0MB, alloc=44.3MB, time=114.02 memory used=9716.6MB, alloc=44.3MB, time=114.57 x[1] = 0.1819 0.448 h = 0.0001 0.003 y2[1] (numeric) = 11.2158755591 5.25112580163 y2[1] (closed_form) = 12.0183577461 4.93549606078 absolute error = 0.8623 relative error = 6.637 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.08385994262 -0.0837808138071 y1[1] (closed_form) = 1.08385994262 -0.0837808138071 absolute error = 1.004e-63 relative error = 9.236e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5405 Order of pole (three term test) = 33.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5405 Order of pole (three term test) = 31.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9762.9MB, alloc=44.3MB, time=115.11 memory used=9809.4MB, alloc=44.3MB, time=115.66 memory used=9856.2MB, alloc=44.3MB, time=116.23 x[1] = 0.182 0.451 h = 0.001 0.001 y2[1] (numeric) = 11.2172084368 5.2955537718 y2[1] (closed_form) = 12.0197185082 4.968741255 absolute error = 0.8665 relative error = 6.662 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.0852113438 -0.0844251395041 y1[1] (closed_form) = 1.0852113438 -0.0844251395041 absolute error = 1.005e-63 relative error = 9.233e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5446 Order of pole (three term test) = 33.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5446 Order of pole (three term test) = 31.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9901.9MB, alloc=44.3MB, time=116.76 memory used=9948.2MB, alloc=44.3MB, time=117.31 x[1] = 0.183 0.452 h = 0.001 0.003 y2[1] (numeric) = 11.2185438857 5.33998931829 y2[1] (closed_form) = 12.0308886037 4.9797418411 absolute error = 0.8886 relative error = 6.825 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.0854702819 -0.085084684565 y1[1] (closed_form) = 1.0854702819 -0.085084684565 absolute error = 2.002e-63 relative error = 1.839e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5463 Order of pole (three term test) = 33.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5463 Order of pole (three term test) = 31.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9994.1MB, alloc=44.3MB, time=117.86 memory used=10040.9MB, alloc=44.3MB, time=118.41 x[1] = 0.184 0.455 h = 0.0001 0.004 y2[1] (numeric) = 11.2198819218 5.38443250345 y2[1] (closed_form) = 12.0422315158 5.01291440645 absolute error = 0.9024 relative error = 6.918 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.08665270596 -0.0861506915662 y1[1] (closed_form) = 1.08665270596 -0.0861506915662 absolute error = 2.002e-63 relative error = 1.837e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5507 Order of pole (three term test) = 33.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5507 Order of pole (three term test) = 31.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10086.8MB, alloc=44.3MB, time=118.94 memory used=10133.3MB, alloc=44.3MB, time=119.49 x[1] = 0.1841 0.459 h = 0.003 0.006 y2[1] (numeric) = 11.2212225615 5.42888338959 y2[1] (closed_form) = 12.0436865877 5.05725603382 absolute error = 0.9025 relative error = 6.909 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.08849279854 -0.0870070350314 y1[1] (closed_form) = 1.08849279854 -0.0870070350314 absolute error = 1.006e-63 relative error = 9.213e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5562 Order of pole (three term test) = 33.18 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5562 Order of pole (three term test) = 31.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10179.1MB, alloc=44.3MB, time=120.02 memory used=10225.7MB, alloc=44.3MB, time=120.57 x[1] = 0.1871 0.465 h = 0.0001 0.005 y2[1] (numeric) = 11.2225658215 5.47334203895 y2[1] (closed_form) = 12.0774853098 5.12352863456 absolute error = 0.9237 relative error = 7.041 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.09070139764 -0.0896457151636 y1[1] (closed_form) = 1.09070139764 -0.0896457151636 absolute error = 1.006e-63 relative error = 9.193e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5653 Order of pole (three term test) = 33.18 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5653 Order of pole (three term test) = 31.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10272.1MB, alloc=44.3MB, time=121.11 memory used=10318.3MB, alloc=44.3MB, time=121.66 memory used=10364.8MB, alloc=44.3MB, time=122.22 x[1] = 0.1872 0.47 h = 0.0001 0.003 y2[1] (numeric) = 11.2239117183 5.51780851371 y2[1] (closed_form) = 12.0790454286 5.17897901307 absolute error = 0.9198 relative error = 6.999 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.0930619854 -0.0907271649432 y1[1] (closed_form) = 1.0930619854 -0.0907271649432 absolute error = 1.007e-63 relative error = 9.183e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5723 Order of pole (three term test) = 33.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5723 Order of pole (three term test) = 31.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10410.8MB, alloc=44.3MB, time=122.76 memory used=10457.5MB, alloc=44.3MB, time=123.32 x[1] = 0.1873 0.473 h = 0.001 0.001 y2[1] (numeric) = 11.2252602691 5.56228287597 y2[1] (closed_form) = 12.0804279915 5.21225122207 absolute error = 0.924 relative error = 7.023 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.09448310605 -0.0913969360123 y1[1] (closed_form) = 1.09448310605 -0.0913969360123 absolute error = 1.007e-63 relative error = 9.170e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5766 Order of pole (three term test) = 33.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5766 Order of pole (three term test) = 31.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10503.4MB, alloc=44.3MB, time=123.86 memory used=10549.8MB, alloc=44.3MB, time=124.41 x[1] = 0.1883 0.474 h = 0.001 0.003 y2[1] (numeric) = 11.226611491 5.60676518777 y2[1] (closed_form) = 12.0916143542 5.22325410042 absolute error = 0.9462 relative error = 7.184 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.09475783765 -0.0920877098006 y1[1] (closed_form) = 1.09475783765 -0.0920877098006 absolute error = 1.007e-63 relative error = 9.168e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5783 Order of pole (three term test) = 33.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5783 Order of pole (three term test) = 31.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10595.6MB, alloc=44.3MB, time=124.94 memory used=10642.1MB, alloc=44.3MB, time=125.50 x[1] = 0.1893 0.477 h = 0.0001 0.004 y2[1] (numeric) = 11.2279654013 5.65125551108 y2[1] (closed_form) = 12.1029876644 5.25644759628 absolute error = 0.96 relative error = 7.275 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.09600308892 -0.0932004623123 y1[1] (closed_form) = 1.09600308892 -0.0932004623123 absolute error = 2.004e-63 relative error = 1.822e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5828 Order of pole (three term test) = 33.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5828 Order of pole (three term test) = 31.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10688.2MB, alloc=44.3MB, time=126.03 memory used=10734.8MB, alloc=44.3MB, time=126.58 memory used=10781.3MB, alloc=44.3MB, time=127.13 x[1] = 0.1894 0.481 h = 0.003 0.006 y2[1] (numeric) = 11.2293220177 5.6957539078 y2[1] (closed_form) = 12.1044719418 5.30082610534 absolute error = 0.9601 relative error = 7.266 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.09793661082 -0.0940902438952 y1[1] (closed_form) = 1.09793661082 -0.0940902438952 absolute error = 1.008e-63 relative error = 9.151e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5885 Order of pole (three term test) = 33.2 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5885 Order of pole (three term test) = 31.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10827.2MB, alloc=44.3MB, time=127.67 memory used=10873.7MB, alloc=44.3MB, time=128.21 x[1] = 0.1924 0.487 h = 0.0001 0.005 y2[1] (numeric) = 11.230681358 5.74026043978 y2[1] (closed_form) = 12.1383420246 5.36713429713 absolute error = 0.9814 relative error = 7.394 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.10026327411 -0.0968466132164 y1[1] (closed_form) = 1.10026327411 -0.0968466132164 absolute error = 2.004e-63 relative error = 1.815e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.598 Order of pole (three term test) = 33.2 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.598 Order of pole (three term test) = 31.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10919.7MB, alloc=44.3MB, time=128.75 memory used=10966.3MB, alloc=44.3MB, time=129.31 x[1] = 0.1925 0.492 h = 0.0001 0.003 y2[1] (numeric) = 11.2320434402 5.78477516876 y2[1] (closed_form) = 12.1399392142 5.42263205615 absolute error = 0.9775 relative error = 7.352 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.10274122087 -0.0979698020854 y1[1] (closed_form) = 1.10274122087 -0.0979698020854 absolute error = 1.008e-63 relative error = 9.109e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6052 Order of pole (three term test) = 33.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6052 Order of pole (three term test) = 31.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11012.3MB, alloc=44.3MB, time=129.84 memory used=11059.1MB, alloc=44.3MB, time=130.41 x[1] = 0.1926 0.495 h = 0.001 0.001 y2[1] (numeric) = 11.2334082826 5.82929815646 y2[1] (closed_form) = 12.1413445156 5.45593268258 absolute error = 0.9817 relative error = 7.375 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.10423255271 -0.0986656553211 y1[1] (closed_form) = 1.10423255271 -0.0986656553211 absolute error = 1.007e-63 relative error = 9.085e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6096 Order of pole (three term test) = 33.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6096 Order of pole (three term test) = 31.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11105.0MB, alloc=44.3MB, time=130.95 memory used=11151.5MB, alloc=44.3MB, time=131.50 x[1] = 0.1936 0.496 h = 0.001 0.003 y2[1] (numeric) = 11.2347759037 5.87382946447 y2[1] (closed_form) = 12.15254792 5.46693803373 absolute error = 1.004 relative error = 7.534 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.10452304197 -0.0993880368486 y1[1] (closed_form) = 1.10452304197 -0.0993880368486 absolute error = 1.3e-64 relative error = 1.172e-62 % Correct digits = 64 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6113 Order of pole (three term test) = 33.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6113 Order of pole (three term test) = 31.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11197.5MB, alloc=44.3MB, time=132.03 memory used=11243.8MB, alloc=44.3MB, time=132.58 memory used=11290.2MB, alloc=44.3MB, time=133.13 x[1] = 0.1946 0.499 h = 0.0001 0.004 y2[1] (numeric) = 11.2361463222 5.91836915434 y2[1] (closed_form) = 12.1639529993 5.50015359581 absolute error = 1.018 relative error = 7.623 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.10583142866 -0.100548332615 y1[1] (closed_form) = 1.10583142866 -0.100548332615 absolute error = 1.020e-63 relative error = 9.184e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.616 Order of pole (three term test) = 33.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.616 Order of pole (three term test) = 31.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11335.9MB, alloc=44.3MB, time=133.66 memory used=11382.4MB, alloc=44.3MB, time=134.21 x[1] = 0.1947 0.503 h = 0.003 0.006 y2[1] (numeric) = 11.2375195569 5.96291728754 y2[1] (closed_form) = 12.1654677243 5.54457086989 absolute error = 1.018 relative error = 7.614 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.10785905392 -0.101472408919 y1[1] (closed_form) = 1.10785905392 -0.101472408919 absolute error = 1.020e-63 relative error = 9.167e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6219 Order of pole (three term test) = 33.22 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6219 Order of pole (three term test) = 31.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11428.2MB, alloc=44.3MB, time=134.74 memory used=11474.9MB, alloc=44.3MB, time=135.30 x[1] = 0.1977 0.509 h = 0.0001 0.005 y2[1] (numeric) = 11.2388956271 6.00747392546 y2[1] (closed_form) = 12.1994124033 5.61091662619 absolute error = 1.039 relative error = 7.739 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.11030419934 -0.10434826674 y1[1] (closed_form) = 1.11030419934 -0.10434826674 absolute error = 1.020e-63 relative error = 9.145e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6317 Order of pole (three term test) = 33.22 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6317 Order of pole (three term test) = 31.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11520.7MB, alloc=44.3MB, time=135.83 memory used=11567.3MB, alloc=44.3MB, time=136.38 x[1] = 0.1978 0.514 h = 0.0001 0.003 y2[1] (numeric) = 11.2402745522 6.05203912942 y2[1] (closed_form) = 12.2010482181 5.66646413299 absolute error = 1.035 relative error = 7.696 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.1129003729 -0.105514284687 y1[1] (closed_form) = 1.1129003729 -0.105514284687 absolute error = 2.010e-63 relative error = 1.798e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6392 Order of pole (three term test) = 33.23 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6392 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11613.4MB, alloc=44.3MB, time=136.91 memory used=11660.1MB, alloc=44.3MB, time=137.48 x[1] = 0.1979 0.517 h = 0.001 0.001 y2[1] (numeric) = 11.2416563517 6.09661296064 y2[1] (closed_form) = 12.2024772125 5.69979458717 absolute error = 1.04 relative error = 7.719 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.11446243357 -0.106236885149 y1[1] (closed_form) = 1.11446243357 -0.106236885149 absolute error = 2.010e-63 relative error = 1.795e-61 % Correct digits = 63 memory used=11706.6MB, alloc=44.3MB, time=138.03 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6437 Order of pole (three term test) = 33.23 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6437 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11752.6MB, alloc=44.3MB, time=138.58 memory used=11799.2MB, alloc=44.3MB, time=139.13 x[1] = 0.1989 0.518 h = 0.0001 0.004 y2[1] (numeric) = 11.2430410455 6.14119548029 y2[1] (closed_form) = 12.213698442 5.71080258884 absolute error = 1.062 relative error = 7.875 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.11476864446 -0.106991271513 y1[1] (closed_form) = 1.11476864446 -0.106991271513 absolute error = 2.010e-63 relative error = 1.795e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6455 Order of pole (three term test) = 33.23 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6455 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11845.0MB, alloc=44.3MB, time=139.66 memory used=11891.4MB, alloc=44.3MB, time=140.21 x[1] = 0.199 0.522 h = 0.003 0.006 y2[1] (numeric) = 11.2444286538 6.18578674943 y2[1] (closed_form) = 12.2152398948 5.75525512996 absolute error = 1.062 relative error = 7.865 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.11687826023 -0.107944449662 y1[1] (closed_form) = 1.11687826023 -0.107944449662 absolute error = 2.010e-63 relative error = 1.791e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6516 Order of pole (three term test) = 33.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6516 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11937.2MB, alloc=44.3MB, time=140.74 memory used=11983.8MB, alloc=44.3MB, time=141.29 x[1] = 0.202 0.528 h = 0.0001 0.005 y2[1] (numeric) = 11.2458191967 6.23038682906 y2[1] (closed_form) = 12.2492509279 5.82163574248 absolute error = 1.083 relative error = 7.989 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.11942719981 -0.110923244089 y1[1] (closed_form) = 1.11942719981 -0.110923244089 absolute error = 2.022e-63 relative error = 1.798e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6616 Order of pole (three term test) = 33.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6616 Order of pole (three term test) = 31.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12029.8MB, alloc=44.3MB, time=141.82 memory used=12076.3MB, alloc=44.3MB, time=142.37 x[1] = 0.2021 0.533 h = 0.0001 0.003 y2[1] (numeric) = 11.247212695 6.27499578008 y2[1] (closed_form) = 12.2509206258 5.87722846243 absolute error = 1.08 relative error = 7.946 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.12212639623 -0.112125613455 y1[1] (closed_form) = 1.12212639623 -0.112125613455 absolute error = 2.010e-63 relative error = 1.782e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6694 Order of pole (three term test) = 33.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6694 Order of pole (three term test) = 31.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12122.5MB, alloc=44.3MB, time=142.92 memory used=12169.0MB, alloc=44.3MB, time=143.47 memory used=12215.7MB, alloc=44.3MB, time=144.04 x[1] = 0.2022 0.536 h = 0.001 0.001 y2[1] (numeric) = 11.2486091693 6.31961366333 y2[1] (closed_form) = 12.252370414 5.91058602486 absolute error = 1.084 relative error = 7.968 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.12375010223 -0.112870940099 y1[1] (closed_form) = 1.12375010223 -0.112870940099 absolute error = 1.044e-63 relative error = 9.244e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6741 Order of pole (three term test) = 33.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6741 Order of pole (three term test) = 31.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12261.5MB, alloc=44.3MB, time=144.57 memory used=12308.0MB, alloc=44.3MB, time=145.12 x[1] = 0.2032 0.537 h = 0.001 0.003 y2[1] (numeric) = 11.2500086408 6.36424053952 y2[1] (closed_form) = 12.2636075859 5.92159667324 absolute error = 1.106 relative error = 8.122 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.12407020471 -0.113653020395 y1[1] (closed_form) = 1.12407020471 -0.113653020395 absolute error = 2.010e-63 relative error = 1.779e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6759 Order of pole (three term test) = 33.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6759 Order of pole (three term test) = 31.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12353.8MB, alloc=44.3MB, time=145.66 memory used=12400.5MB, alloc=44.3MB, time=146.21 x[1] = 0.2042 0.54 h = 0.0001 0.004 y2[1] (numeric) = 11.2514111308 6.4088764693 y2[1] (closed_form) = 12.2750752016 5.95485674528 absolute error = 1.12 relative error = 8.208 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.12549754312 -0.114903269739 y1[1] (closed_form) = 1.12549754312 -0.114903269739 absolute error = 2.010e-63 relative error = 1.777e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6809 Order of pole (three term test) = 33.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6809 Order of pole (three term test) = 31.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12446.3MB, alloc=44.3MB, time=146.74 memory used=12492.8MB, alloc=44.3MB, time=147.29 x[1] = 0.2043 0.544 h = 0.003 0.006 y2[1] (numeric) = 11.2528166607 6.45352151324 y2[1] (closed_form) = 12.276649452 5.99935159987 absolute error = 1.12 relative error = 8.197 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.1277026207 -0.115892427998 y1[1] (closed_form) = 1.1277026207 -0.115892427998 absolute error = 2.010e-63 relative error = 1.773e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6872 Order of pole (three term test) = 33.26 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6872 Order of pole (three term test) = 31.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12538.5MB, alloc=44.3MB, time=147.82 memory used=12585.2MB, alloc=44.3MB, time=148.38 x[1] = 0.2073 0.55 h = 0.0001 0.005 y2[1] (numeric) = 11.2542252525 6.4981757318 y2[1] (closed_form) = 12.3107411939 6.06577348825 absolute error = 1.142 relative error = 8.318 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.1303709133 -0.118994272584 y1[1] (closed_form) = 1.1303709133 -0.118994272584 absolute error = 2.010e-63 relative error = 1.768e-61 % Correct digits = 63 memory used=12631.5MB, alloc=44.3MB, time=148.92 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6975 Order of pole (three term test) = 33.26 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.6975 Order of pole (three term test) = 31.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12677.6MB, alloc=44.3MB, time=149.46 memory used=12724.2MB, alloc=44.3MB, time=150.02 x[1] = 0.2074 0.555 h = 0.0001 0.003 y2[1] (numeric) = 11.2556369281 6.54283918536 y2[1] (closed_form) = 12.3124524597 6.12142041724 absolute error = 1.138 relative error = 8.274 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.13319008261 -0.120241613581 y1[1] (closed_form) = 1.13319008261 -0.120241613581 absolute error = 2.010e-63 relative error = 1.764e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7056 Order of pole (three term test) = 33.27 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7056 Order of pole (three term test) = 31.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12770.2MB, alloc=44.3MB, time=150.56 memory used=12817.0MB, alloc=44.3MB, time=151.12 x[1] = 0.2075 0.558 h = 0.001 0.001 y2[1] (numeric) = 11.2570517099 6.58751193421 y2[1] (closed_form) = 12.3139277479 6.15481046536 absolute error = 1.142 relative error = 8.296 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.13488555869 -0.121014994772 y1[1] (closed_form) = 1.13488555869 -0.121014994772 absolute error = 3.002e-63 relative error = 2.630e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7105 Order of pole (three term test) = 33.27 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7105 Order of pole (three term test) = 31.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12863.1MB, alloc=44.3MB, time=151.66 memory used=12909.4MB, alloc=44.3MB, time=152.22 x[1] = 0.2085 0.559 h = 0.001 0.003 y2[1] (numeric) = 11.2584696204 6.63219403855 y2[1] (closed_form) = 12.3251842236 6.16582409658 absolute error = 1.164 relative error = 8.448 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.13522132013 -0.121829867983 y1[1] (closed_form) = 1.13522132013 -0.121829867983 absolute error = 3.007e-63 relative error = 2.633e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7123 Order of pole (three term test) = 33.28 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7123 Order of pole (three term test) = 31.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12955.3MB, alloc=44.3MB, time=152.75 memory used=13001.8MB, alloc=44.3MB, time=153.30 x[1] = 0.2095 0.562 h = 0.0001 0.004 y2[1] (numeric) = 11.2598906824 6.67688555846 y2[1] (closed_form) = 12.336687628 6.19910951629 absolute error = 1.178 relative error = 8.532 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.13671278427 -0.123130140954 y1[1] (closed_form) = 1.13671278427 -0.123130140954 absolute error = 3.007e-63 relative error = 2.630e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7175 Order of pole (three term test) = 33.28 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7175 Order of pole (three term test) = 31.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13047.8MB, alloc=44.3MB, time=153.83 memory used=13094.3MB, alloc=44.3MB, time=154.38 memory used=13140.7MB, alloc=44.3MB, time=154.93 x[1] = 0.2096 0.566 h = 0.003 0.006 y2[1] (numeric) = 11.2613149191 6.72158655395 y2[1] (closed_form) = 12.338295986 6.24364859973 absolute error = 1.178 relative error = 8.521 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.13901409833 -0.124156244567 y1[1] (closed_form) = 1.13901409833 -0.124156244567 absolute error = 3.007e-63 relative error = 2.624e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7241 Order of pole (three term test) = 33.28 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7241 Order of pole (three term test) = 31.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13186.6MB, alloc=44.3MB, time=155.46 memory used=13233.1MB, alloc=44.3MB, time=156.01 x[1] = 0.2126 0.572 h = 0.0001 0.005 y2[1] (numeric) = 11.2627423537 6.76629708494 y2[1] (closed_form) = 12.3724718 6.31011373758 absolute error = 1.2 relative error = 8.639 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.14180223707 -0.127383175806 y1[1] (closed_form) = 1.14180223707 -0.127383175806 absolute error = 3.007e-63 relative error = 2.617e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7347 Order of pole (three term test) = 33.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7347 Order of pole (three term test) = 31.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13278.9MB, alloc=44.3MB, time=156.55 memory used=13325.6MB, alloc=44.3MB, time=157.10 x[1] = 0.2127 0.577 h = 0.0001 0.003 y2[1] (numeric) = 11.2641730099 6.81101721123 y2[1] (closed_form) = 12.3742262749 6.3658172843 absolute error = 1.196 relative error = 8.595 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.1447423737 -0.128676714606 y1[1] (closed_form) = 1.1447423737 -0.128676714606 absolute error = 3.002e-63 relative error = 2.606e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7431 Order of pole (three term test) = 33.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7431 Order of pole (three term test) = 31.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13371.3MB, alloc=44.3MB, time=157.64 memory used=13418.0MB, alloc=44.3MB, time=158.20 x[1] = 0.2128 0.58 h = 0.001 0.001 y2[1] (numeric) = 11.2656069115 6.85574699253 y2[1] (closed_form) = 12.3757280704 6.39924125286 absolute error = 1.2 relative error = 8.615 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.14651021251 -0.129478898361 y1[1] (closed_form) = 1.14651021251 -0.129478898361 absolute error = 3.007e-63 relative error = 2.606e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7482 Order of pole (three term test) = 33.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7482 Order of pole (three term test) = 31.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13464.2MB, alloc=44.3MB, time=158.74 memory used=13510.8MB, alloc=44.3MB, time=159.30 x[1] = 0.2138 0.581 h = 0.001 0.003 y2[1] (numeric) = 11.2670440827 6.90048648846 y2[1] (closed_form) = 12.3870046591 6.41025803602 absolute error = 1.223 relative error = 8.765 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.14686159593 -0.130327014312 y1[1] (closed_form) = 1.14686159593 -0.130327014312 absolute error = 3.002e-63 relative error = 2.601e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7501 Order of pole (three term test) = 33.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7501 Order of pole (three term test) = 31.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13556.9MB, alloc=44.3MB, time=159.84 memory used=13603.2MB, alloc=44.3MB, time=160.39 memory used=13649.7MB, alloc=44.3MB, time=160.94 x[1] = 0.2148 0.584 h = 0.0001 0.004 y2[1] (numeric) = 11.2684845479 6.94523575852 y2[1] (closed_form) = 12.3985453039 6.44356995069 absolute error = 1.236 relative error = 8.849 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.14841756257 -0.131678251571 y1[1] (closed_form) = 1.14841756257 -0.131678251571 absolute error = 3.007e-63 relative error = 2.601e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7554 Order of pole (three term test) = 33.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7554 Order of pole (three term test) = 31.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13695.4MB, alloc=44.3MB, time=161.48 memory used=13741.8MB, alloc=44.3MB, time=162.02 x[1] = 0.2149 0.588 h = 0.003 0.006 y2[1] (numeric) = 11.2699283317 6.98999486211 y2[1] (closed_form) = 12.4001891055 6.48815519056 absolute error = 1.237 relative error = 8.836 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.150815923 -0.132742305069 y1[1] (closed_form) = 1.150815923 -0.132742305069 absolute error = 3.007e-63 relative error = 2.595e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7622 Order of pole (three term test) = 33.31 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7622 Order of pole (three term test) = 31.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13787.7MB, alloc=44.3MB, time=162.55 memory used=13834.3MB, alloc=44.3MB, time=163.11 x[1] = 0.2179 0.594 h = 0.0001 0.005 y2[1] (numeric) = 11.2713754592 7.03476385856 y2[1] (closed_form) = 12.4344524032 6.55466555163 absolute error = 1.258 relative error = 8.952 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.15372442649 -0.136096444436 y1[1] (closed_form) = 1.15372442649 -0.136096444436 absolute error = 3.015e-63 relative error = 2.595e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7733 Order of pole (three term test) = 33.31 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7733 Order of pole (three term test) = 31.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13880.0MB, alloc=44.3MB, time=163.64 memory used=13926.6MB, alloc=44.3MB, time=164.19 x[1] = 0.218 0.599 h = 0.0001 0.003 y2[1] (numeric) = 11.2728259555 7.07954280705 y2[1] (closed_form) = 12.4362517613 6.61042814049 absolute error = 1.254 relative error = 8.907 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.15678656924 -0.137437456484 y1[1] (closed_form) = 1.15678656924 -0.137437456484 absolute error = 3.007e-63 relative error = 2.581e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.782 Order of pole (three term test) = 33.32 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.782 Order of pole (three term test) = 31.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13972.7MB, alloc=44.3MB, time=164.73 memory used=14019.5MB, alloc=44.3MB, time=165.29 x[1] = 0.2181 0.602 h = 0.001 0.001 y2[1] (numeric) = 11.2742798461 7.12433176668 y2[1] (closed_form) = 12.4377810915 6.64388747353 absolute error = 1.259 relative error = 8.927 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.15862738968 -0.138269220829 y1[1] (closed_form) = 1.15862738968 -0.138269220829 absolute error = 3.007e-63 relative error = 2.577e-61 % Correct digits = 63 memory used=14066.2MB, alloc=44.3MB, time=165.85 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7872 Order of pole (three term test) = 33.32 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7872 Order of pole (three term test) = 31.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14112.2MB, alloc=44.3MB, time=166.39 memory used=14158.7MB, alloc=44.3MB, time=166.94 x[1] = 0.2191 0.603 h = 0.001 0.003 y2[1] (numeric) = 11.2757371569 7.16913079645 y2[1] (closed_form) = 12.4490786123 6.65490757448 absolute error = 1.281 relative error = 9.075 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.1589943575 -0.139151048143 y1[1] (closed_form) = 1.1589943575 -0.139151048143 absolute error = 3.007e-63 relative error = 2.576e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7892 Order of pole (three term test) = 33.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7892 Order of pole (three term test) = 31.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14204.6MB, alloc=44.3MB, time=167.48 memory used=14251.2MB, alloc=44.3MB, time=168.03 x[1] = 0.2201 0.606 h = 0.0001 0.004 y2[1] (numeric) = 11.2771979139 7.21393995521 y2[1] (closed_form) = 12.4606579723 6.68824713478 absolute error = 1.295 relative error = 9.157 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.16061522089 -0.140554228629 y1[1] (closed_form) = 1.16061522089 -0.140554228629 absolute error = 3.007e-63 relative error = 2.572e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7947 Order of pole (three term test) = 33.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.7947 Order of pole (three term test) = 31.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14297.0MB, alloc=44.3MB, time=168.56 memory used=14343.3MB, alloc=44.3MB, time=169.12 x[1] = 0.2202 0.61 h = 0.003 0.006 y2[1] (numeric) = 11.2786621434 7.25875930175 y2[1] (closed_form) = 12.4623385804 6.73288047146 absolute error = 1.295 relative error = 9.144 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.16311147303 -0.141657276478 y1[1] (closed_form) = 1.16311147303 -0.141657276478 absolute error = 3.007e-63 relative error = 2.566e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8018 Order of pole (three term test) = 33.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8018 Order of pole (three term test) = 31.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14389.2MB, alloc=44.3MB, time=169.65 memory used=14435.8MB, alloc=44.3MB, time=170.20 x[1] = 0.2232 0.616 h = 0.0001 0.005 y2[1] (numeric) = 11.2801298722 7.30358889473 y2[1] (closed_form) = 12.4966928238 6.79943802968 absolute error = 1.317 relative error = 9.256 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.16614088506 -0.145140831516 y1[1] (closed_form) = 1.16614088506 -0.145140831516 absolute error = 4.005e-63 relative error = 3.408e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8133 Order of pole (three term test) = 33.34 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8133 Order of pole (three term test) = 31.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14482.0MB, alloc=44.3MB, time=170.74 memory used=14528.3MB, alloc=44.3MB, time=171.29 memory used=14574.8MB, alloc=44.3MB, time=171.83 x[1] = 0.2233 0.621 h = 0.0001 0.003 y2[1] (numeric) = 11.281601127 7.34842879269 y2[1] (closed_form) = 12.4985387736 6.85526210156 absolute error = 1.313 relative error = 9.211 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.16932611729 -0.146530642357 y1[1] (closed_form) = 1.16932611729 -0.146530642357 absolute error = 4.005e-63 relative error = 3.398e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8223 Order of pole (three term test) = 33.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8223 Order of pole (three term test) = 31.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14620.9MB, alloc=44.3MB, time=172.38 memory used=14667.6MB, alloc=44.3MB, time=172.94 x[1] = 0.2234 0.624 h = 0.001 0.001 y2[1] (numeric) = 11.2830759351 7.39327905407 y2[1] (closed_form) = 12.5000966865 6.88875825282 absolute error = 1.317 relative error = 9.231 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.17124056466 -0.147392795823 y1[1] (closed_form) = 1.17124056466 -0.147392795823 absolute error = 3.007e-63 relative error = 2.547e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8278 Order of pole (three term test) = 33.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8278 Order of pole (three term test) = 31.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14713.7MB, alloc=44.3MB, time=173.48 memory used=14760.2MB, alloc=44.3MB, time=174.03 x[1] = 0.2244 0.625 h = 0.0001 0.004 y2[1] (numeric) = 11.2845543241 7.4381397372 y2[1] (closed_form) = 12.5114159689 6.89978183405 absolute error = 1.34 relative error = 9.377 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.17162307852 -0.14830882213 y1[1] (closed_form) = 1.17162307852 -0.14830882213 absolute error = 4.011e-63 relative error = 3.397e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8298 Order of pole (three term test) = 33.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8298 Order of pole (three term test) = 31.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14806.1MB, alloc=44.3MB, time=174.57 memory used=14852.4MB, alloc=44.3MB, time=175.11 x[1] = 0.2245 0.629 h = 0.003 0.006 y2[1] (numeric) = 11.2860363217 7.48301090026 y2[1] (closed_form) = 12.513128767 6.94445859588 absolute error = 1.34 relative error = 9.364 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.17420477878 -0.149445121938 y1[1] (closed_form) = 1.17420477878 -0.149445121938 absolute error = 3.015e-63 relative error = 2.547e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8372 Order of pole (three term test) = 33.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8372 Order of pole (three term test) = 31.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14898.1MB, alloc=44.3MB, time=175.64 memory used=14944.8MB, alloc=44.3MB, time=176.19 x[1] = 0.2275 0.635 h = 0.0001 0.005 y2[1] (numeric) = 11.287521956 7.52789260136 y2[1] (closed_form) = 12.5475635115 7.01105950119 absolute error = 1.362 relative error = 9.475 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.17734029839 -0.153040458423 y1[1] (closed_form) = 1.17734029839 -0.153040458423 absolute error = 4.011e-63 relative error = 3.379e-61 % Correct digits = 62 memory used=14991.4MB, alloc=44.3MB, time=176.74 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8489 Order of pole (three term test) = 33.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8489 Order of pole (three term test) = 31.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15037.5MB, alloc=44.3MB, time=177.28 memory used=15084.1MB, alloc=44.3MB, time=177.83 x[1] = 0.2276 0.64 h = 0.0001 0.003 y2[1] (numeric) = 11.2890112554 7.57278489845 y2[1] (closed_form) = 12.5494501887 7.06693904662 absolute error = 1.358 relative error = 9.43 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.18063298733 -0.154471889345 y1[1] (closed_form) = 1.18063298733 -0.154471889345 absolute error = 3.015e-63 relative error = 2.532e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8583 Order of pole (three term test) = 33.37 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8583 Order of pole (three term test) = 31.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15130.1MB, alloc=44.3MB, time=178.38 memory used=15176.9MB, alloc=44.3MB, time=178.94 x[1] = 0.2277 0.643 h = 0.001 0.001 y2[1] (numeric) = 11.2905042486 7.6176878494 y2[1] (closed_form) = 12.5510330982 7.10046841948 absolute error = 1.363 relative error = 9.449 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.18261172293 -0.155359983885 y1[1] (closed_form) = 1.18261172293 -0.155359983885 absolute error = 3.015e-63 relative error = 2.528e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8639 Order of pole (three term test) = 33.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8639 Order of pole (three term test) = 31.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15222.8MB, alloc=44.3MB, time=179.48 memory used=15269.3MB, alloc=44.3MB, time=180.03 x[1] = 0.2287 0.644 h = 0.001 0.003 y2[1] (numeric) = 11.2920009646 7.66260151192 y2[1] (closed_form) = 12.5623717407 7.11149539674 absolute error = 1.385 relative error = 9.593 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.18300800258 -0.156305668146 y1[1] (closed_form) = 1.18300800258 -0.156305668146 absolute error = 3.007e-63 relative error = 2.520e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.866 Order of pole (three term test) = 33.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.866 Order of pole (three term test) = 31.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15315.1MB, alloc=44.3MB, time=180.57 memory used=15361.7MB, alloc=44.3MB, time=181.12 x[1] = 0.2297 0.647 h = 0.0001 0.004 y2[1] (numeric) = 11.2935014327 7.70752594362 y2[1] (closed_form) = 12.5740267873 7.14488997781 absolute error = 1.399 relative error = 9.671 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.18475138096 -0.157807456753 y1[1] (closed_form) = 1.18475138096 -0.157807456753 absolute error = 3.015e-63 relative error = 2.523e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.872 Order of pole (three term test) = 33.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.872 Order of pole (three term test) = 31.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15407.7MB, alloc=44.3MB, time=181.65 memory used=15453.9MB, alloc=44.3MB, time=182.20 memory used=15500.3MB, alloc=44.3MB, time=182.74 x[1] = 0.2298 0.651 h = 0.003 0.006 y2[1] (numeric) = 11.2950056825 7.75246120197 y2[1] (closed_form) = 12.5757789797 7.18961850002 absolute error = 1.399 relative error = 9.658 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.18743265414 -0.158984791963 y1[1] (closed_form) = 1.18743265414 -0.158984791963 absolute error = 3.007e-63 relative error = 2.510e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8796 Order of pole (three term test) = 33.39 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8796 Order of pole (three term test) = 31.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15546.2MB, alloc=44.3MB, time=183.28 memory used=15592.8MB, alloc=44.3MB, time=183.83 x[1] = 0.2328 0.657 h = 0.0001 0.005 y2[1] (numeric) = 11.2965137439 7.79740734432 y2[1] (closed_form) = 12.6103112298 7.25627031918 absolute error = 1.421 relative error = 9.766 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.19069018914 -0.162713877657 y1[1] (closed_form) = 1.19069018914 -0.162713877657 absolute error = 4.005e-63 relative error = 3.333e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8918 Order of pole (three term test) = 33.39 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.8918 Order of pole (three term test) = 31.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15638.8MB, alloc=44.3MB, time=184.36 memory used=15685.3MB, alloc=44.3MB, time=184.92 x[1] = 0.2329 0.662 h = 0.0001 0.003 y2[1] (numeric) = 11.2980256472 7.84236442792 y2[1] (closed_form) = 12.6122477437 7.31221595712 absolute error = 1.417 relative error = 9.721 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.19410811989 -0.164196696031 y1[1] (closed_form) = 1.19410811989 -0.164196696031 absolute error = 3.007e-63 relative error = 2.494e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9015 Order of pole (three term test) = 33.4 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9015 Order of pole (three term test) = 31.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15731.3MB, alloc=44.3MB, time=185.45 memory used=15778.0MB, alloc=44.3MB, time=186.02 x[1] = 0.233 0.665 h = 0.001 0.001 y2[1] (numeric) = 11.2995414228 7.88733250987 y2[1] (closed_form) = 12.6138612267 7.34578489363 absolute error = 1.422 relative error = 9.738 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.19616176422 -0.165116758738 y1[1] (closed_form) = 1.19616176422 -0.165116758738 absolute error = 4.005e-63 relative error = 3.317e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9074 Order of pole (three term test) = 33.41 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9074 Order of pole (three term test) = 31.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15824.2MB, alloc=44.3MB, time=186.56 memory used=15870.6MB, alloc=44.3MB, time=187.11 x[1] = 0.234 0.666 h = 0.001 0.003 y2[1] (numeric) = 11.3010611017 7.93231164712 y2[1] (closed_form) = 12.6252232014 7.35681565432 absolute error = 1.444 relative error = 9.881 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.19657352245 -0.166097601157 y1[1] (closed_form) = 1.19657352245 -0.166097601157 absolute error = 4.005e-63 relative error = 3.315e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9096 Order of pole (three term test) = 33.41 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9096 Order of pole (three term test) = 31.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15916.9MB, alloc=44.3MB, time=187.65 memory used=15963.1MB, alloc=44.3MB, time=188.20 memory used=16009.6MB, alloc=44.3MB, time=188.75 x[1] = 0.235 0.669 h = 0.0001 0.004 y2[1] (numeric) = 11.302584715 7.97730189653 y2[1] (closed_form) = 12.6369213047 7.39024121175 absolute error = 1.458 relative error = 9.958 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.19838303506 -0.167654344407 y1[1] (closed_form) = 1.19838303506 -0.167654344407 absolute error = 3.007e-63 relative error = 2.485e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9157 Order of pole (three term test) = 33.41 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9157 Order of pole (three term test) = 31.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16055.4MB, alloc=44.3MB, time=189.28 memory used=16101.8MB, alloc=44.3MB, time=189.83 x[1] = 0.2351 0.673 h = 0.003 0.006 y2[1] (numeric) = 11.3041122942 8.02230331479 y2[1] (closed_form) = 12.6387143372 7.43502347474 absolute error = 1.458 relative error = 9.944 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.20116482903 -0.168873877114 y1[1] (closed_form) = 1.20116482903 -0.168873877114 absolute error = 3.015e-63 relative error = 2.486e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9236 Order of pole (three term test) = 33.42 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9236 Order of pole (three term test) = 31.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16147.6MB, alloc=44.3MB, time=190.36 memory used=16194.1MB, alloc=44.3MB, time=190.92 x[1] = 0.2381 0.679 h = 0.0001 0.005 y2[1] (numeric) = 11.3056438711 8.0673159585 y2[1] (closed_form) = 12.6733477105 7.50172818346 absolute error = 1.48 relative error = 10.05 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.20454499492 -0.172739171907 y1[1] (closed_form) = 1.20454499492 -0.172739171907 absolute error = 3.015e-63 relative error = 2.478e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9363 Order of pole (three term test) = 33.42 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9363 Order of pole (three term test) = 31.58 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16240.1MB, alloc=44.3MB, time=191.45 memory used=16286.8MB, alloc=44.3MB, time=192.01 x[1] = 0.2382 0.684 h = 0.0001 0.003 y2[1] (numeric) = 11.3071794779 8.11233988409 y2[1] (closed_form) = 12.6753358747 7.55774240625 absolute error = 1.476 relative error = 10 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.20808937996 -0.174274850906 y1[1] (closed_form) = 1.20808937996 -0.174274850906 absolute error = 3.015e-63 relative error = 2.470e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9464 Order of pole (three term test) = 33.43 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9464 Order of pole (three term test) = 31.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16332.9MB, alloc=44.3MB, time=192.54 memory used=16379.5MB, alloc=44.3MB, time=193.10 x[1] = 0.2383 0.687 h = 0.001 0.001 y2[1] (numeric) = 11.3087191469 8.15737514788 y2[1] (closed_form) = 12.6769810434 7.5913523905 absolute error = 1.481 relative error = 10.02 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.21021865477 -0.175227780203 y1[1] (closed_form) = 1.21021865477 -0.175227780203 absolute error = 3.015e-63 relative error = 2.466e-61 % Correct digits = 63 memory used=16426.4MB, alloc=44.3MB, time=193.67 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9525 Order of pole (three term test) = 33.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9525 Order of pole (three term test) = 31.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16472.3MB, alloc=44.3MB, time=194.20 memory used=16518.8MB, alloc=44.3MB, time=194.76 x[1] = 0.2393 0.688 h = 0.001 0.003 y2[1] (numeric) = 11.310262911 8.20242180603 y2[1] (closed_form) = 12.6883672116 7.60238708693 absolute error = 1.503 relative error = 10.16 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.21064585055 -0.176244323998 y1[1] (closed_form) = 1.21064585055 -0.176244323998 absolute error = 3.027e-63 relative error = 2.474e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9548 Order of pole (three term test) = 33.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9548 Order of pole (three term test) = 31.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16564.6MB, alloc=44.3MB, time=195.30 memory used=16611.2MB, alloc=44.3MB, time=195.84 x[1] = 0.2403 0.691 h = 0.0001 0.004 y2[1] (numeric) = 11.3118108034 8.24747991458 y2[1] (closed_form) = 12.7001099448 7.63584478647 absolute error = 1.517 relative error = 10.24 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.21252195933 -0.177857153656 y1[1] (closed_form) = 1.21252195933 -0.177857153656 absolute error = 3.027e-63 relative error = 2.470e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9612 Order of pole (three term test) = 33.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9612 Order of pole (three term test) = 31.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16657.0MB, alloc=44.3MB, time=196.38 memory used=16703.3MB, alloc=44.3MB, time=196.92 x[1] = 0.2404 0.695 h = 0.003 0.006 y2[1] (numeric) = 11.3133628574 8.29254952942 y2[1] (closed_form) = 12.7019452942 7.68068278566 absolute error = 1.517 relative error = 10.22 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.21540525796 -0.179120088638 y1[1] (closed_form) = 1.21540525796 -0.179120088638 absolute error = 3.027e-63 relative error = 2.464e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9694 Order of pole (three term test) = 33.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9694 Order of pole (three term test) = 31.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16749.1MB, alloc=44.3MB, time=197.46 memory used=16795.7MB, alloc=44.3MB, time=198.01 x[1] = 0.2434 0.701 h = 0.0001 0.005 y2[1] (numeric) = 11.3149191068 8.33763070631 y2[1] (closed_form) = 12.7366834669 7.74744236017 absolute error = 1.539 relative error = 10.33 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.21890869438 -0.18312414312 y1[1] (closed_form) = 1.21890869438 -0.18312414312 absolute error = 3.027e-63 relative error = 2.455e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9825 Order of pole (three term test) = 33.46 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9825 Order of pole (three term test) = 31.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16842.0MB, alloc=44.3MB, time=198.55 memory used=16888.3MB, alloc=44.3MB, time=199.09 memory used=16935.0MB, alloc=44.3MB, time=199.65 x[1] = 0.2435 0.706 h = 0.0001 0.003 y2[1] (numeric) = 11.3164795857 8.38272350087 y2[1] (closed_form) = 12.7387251346 7.80352767938 absolute error = 1.536 relative error = 10.28 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.22258079154 -0.184714209508 y1[1] (closed_form) = 1.22258079154 -0.184714209508 absolute error = 3.027e-63 relative error = 2.448e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9931 Order of pole (three term test) = 33.46 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9931 Order of pole (three term test) = 31.54 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16981.1MB, alloc=44.3MB, time=200.19 memory used=17027.8MB, alloc=44.3MB, time=200.76 x[1] = 0.2436 0.709 h = 0.001 0.001 y2[1] (numeric) = 11.3180443286 8.42782796855 y2[1] (closed_form) = 12.7404031249 7.83718020678 absolute error = 1.54 relative error = 10.3 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.22478644535 -0.185700936442 y1[1] (closed_form) = 1.22478644535 -0.185700936442 absolute error = 3.027e-63 relative error = 2.443e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9995 Order of pole (three term test) = 33.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.9995 Order of pole (three term test) = 31.54 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17073.8MB, alloc=44.3MB, time=201.30 memory used=17120.1MB, alloc=44.3MB, time=201.84 x[1] = 0.2446 0.71 h = 0.001 0.003 y2[1] (numeric) = 11.3196133703 8.47294416469 y2[1] (closed_form) = 12.7518143599 7.84821898741 absolute error = 1.563 relative error = 10.44 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.22522903638 -0.186753744708 y1[1] (closed_form) = 1.22522903638 -0.186753744708 absolute error = 3.027e-63 relative error = 2.442e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.002 Order of pole (three term test) = 33.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.002 Order of pole (three term test) = 31.54 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17166.1MB, alloc=44.3MB, time=202.38 memory used=17212.7MB, alloc=44.3MB, time=202.93 x[1] = 0.2456 0.713 h = 0.0001 0.004 y2[1] (numeric) = 11.3211867459 8.51807214447 y2[1] (closed_form) = 12.7636033239 7.88170999908 absolute error = 1.577 relative error = 10.51 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.22717222056 -0.188423833642 y1[1] (closed_form) = 1.22717222056 -0.188423833642 absolute error = 3.015e-63 relative error = 2.428e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.008 Order of pole (three term test) = 33.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.008 Order of pole (three term test) = 31.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17258.6MB, alloc=44.3MB, time=203.47 memory used=17304.9MB, alloc=44.3MB, time=204.02 x[1] = 0.2457 0.717 h = 0.003 0.006 y2[1] (numeric) = 11.3227644908 8.56321196292 y2[1] (closed_form) = 12.7654824994 7.92660574538 absolute error = 1.577 relative error = 10.49 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.23015804386 -0.189731419135 y1[1] (closed_form) = 1.23015804386 -0.189731419135 absolute error = 3.015e-63 relative error = 2.422e-61 % Correct digits = 63 memory used=17351.4MB, alloc=44.3MB, time=204.56 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.017 Order of pole (three term test) = 33.48 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.017 Order of pole (three term test) = 31.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17397.3MB, alloc=44.3MB, time=205.10 memory used=17443.9MB, alloc=44.3MB, time=205.65 x[1] = 0.2487 0.723 h = 0.0001 0.005 y2[1] (numeric) = 11.324346641 8.60836367491 y2[1] (closed_form) = 12.8003292082 7.99342216251 absolute error = 1.599 relative error = 10.6 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.2337854143 -0.19387687591 y1[1] (closed_form) = 1.2337854143 -0.19387687591 absolute error = 3.027e-63 relative error = 2.423e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.031 Order of pole (three term test) = 33.49 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.031 Order of pole (three term test) = 31.52 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17489.8MB, alloc=44.3MB, time=206.19 memory used=17536.3MB, alloc=44.3MB, time=206.74 x[1] = 0.2488 0.728 h = 0.0001 0.003 y2[1] (numeric) = 11.3259332325 8.6535273352 y2[1] (closed_form) = 12.8024262734 8.04958110964 absolute error = 1.595 relative error = 10.55 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.23758652693 -0.195522911033 y1[1] (closed_form) = 1.23758652693 -0.195522911033 absolute error = 3.027e-63 relative error = 2.416e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.042 Order of pole (three term test) = 33.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.042 Order of pole (three term test) = 31.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17582.3MB, alloc=44.3MB, time=207.28 memory used=17629.0MB, alloc=44.3MB, time=207.84 x[1] = 0.2489 0.731 h = 0.001 0.001 y2[1] (numeric) = 11.3275243018 8.69870299836 y2[1] (closed_form) = 12.8041382465 8.08327768734 absolute error = 1.6 relative error = 10.56 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.23986933524 -0.196544399873 y1[1] (closed_form) = 1.23986933524 -0.196544399873 absolute error = 3.027e-63 relative error = 2.411e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.048 Order of pole (three term test) = 33.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.048 Order of pole (three term test) = 31.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17675.0MB, alloc=44.3MB, time=208.38 memory used=17721.6MB, alloc=44.3MB, time=208.93 x[1] = 0.2499 0.732 h = 0.0001 0.004 y2[1] (numeric) = 11.3291198859 8.74389071882 y2[1] (closed_form) = 12.8155754338 8.09432069665 absolute error = 1.622 relative error = 10.7 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.24032727777 -0.197634055829 y1[1] (closed_form) = 1.24032727777 -0.197634055829 absolute error = 4.031e-63 relative error = 3.210e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.051 Order of pole (three term test) = 33.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.051 Order of pole (three term test) = 31.5 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17767.8MB, alloc=44.3MB, time=209.47 memory used=17814.0MB, alloc=44.3MB, time=210.02 memory used=17860.4MB, alloc=44.3MB, time=210.56 x[1] = 0.25 0.736 h = 0.003 0.006 y2[1] (numeric) = 11.330720022 8.78909055087 y2[1] (closed_form) = 12.8174928466 8.13926831948 absolute error = 1.623 relative error = 10.69 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.24340274838 -0.198979869842 y1[1] (closed_form) = 1.24340274838 -0.198979869842 absolute error = 4.020e-63 relative error = 3.192e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.06 Order of pole (three term test) = 33.51 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.06 Order of pole (three term test) = 31.5 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17906.4MB, alloc=44.3MB, time=211.10 memory used=17953.1MB, alloc=44.3MB, time=211.66 x[1] = 0.253 0.742 h = 0.0001 0.005 y2[1] (numeric) = 11.3323247476 8.83430254861 y2[1] (closed_form) = 12.8524353105 8.20613660291 absolute error = 1.645 relative error = 10.79 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.24713907531 -0.203247740885 y1[1] (closed_form) = 1.24713907531 -0.203247740885 absolute error = 4.020e-63 relative error = 3.181e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.074 Order of pole (three term test) = 33.52 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.074 Order of pole (three term test) = 31.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17999.1MB, alloc=44.3MB, time=212.20 memory used=18045.6MB, alloc=44.3MB, time=212.75 x[1] = 0.2531 0.747 h = 0.0001 0.003 y2[1] (numeric) = 11.3339341006 8.87952676602 y2[1] (closed_form) = 12.8545806908 8.26236166079 absolute error = 1.641 relative error = 10.74 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.25105301216 -0.204941701948 y1[1] (closed_form) = 1.25105301216 -0.204941701948 absolute error = 4.020e-63 relative error = 3.171e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.085 Order of pole (three term test) = 33.53 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.085 Order of pole (three term test) = 31.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18091.6MB, alloc=44.3MB, time=213.29 memory used=18138.3MB, alloc=44.3MB, time=213.85 x[1] = 0.2532 0.75 h = 0.001 0.001 y2[1] (numeric) = 11.3355481194 8.9247632569 y2[1] (closed_form) = 12.8563223149 8.29609779576 absolute error = 1.646 relative error = 10.76 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.25340330449 -0.205992978524 y1[1] (closed_form) = 1.25340330449 -0.205992978524 absolute error = 5.009e-63 relative error = 3.943e-61 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.092 Order of pole (three term test) = 33.53 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.092 Order of pole (three term test) = 31.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18184.4MB, alloc=44.3MB, time=214.39 memory used=18230.7MB, alloc=44.3MB, time=214.94 x[1] = 0.2542 0.751 h = 0.001 0.003 y2[1] (numeric) = 11.3371668426 8.97001207489 y2[1] (closed_form) = 12.8677825076 8.30714488128 absolute error = 1.668 relative error = 10.89 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.2538748736 -0.207114652195 y1[1] (closed_form) = 1.2538748736 -0.207114652195 absolute error = 4.011e-63 relative error = 3.156e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.094 Order of pole (three term test) = 33.53 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.094 Order of pole (three term test) = 31.47 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18276.9MB, alloc=44.3MB, time=215.48 memory used=18323.2MB, alloc=44.3MB, time=216.03 memory used=18369.8MB, alloc=44.3MB, time=216.58 x[1] = 0.2552 0.754 h = 0.0001 0.004 y2[1] (numeric) = 11.3387903092 9.01527327347 y2[1] (closed_form) = 12.8796614271 8.34070160535 absolute error = 1.682 relative error = 10.96 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.25594492087 -0.208893739119 y1[1] (closed_form) = 1.25594492087 -0.208893739119 absolute error = 4.011e-63 relative error = 3.151e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.102 Order of pole (three term test) = 33.54 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.102 Order of pole (three term test) = 31.47 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18415.7MB, alloc=44.3MB, time=217.12 memory used=18462.3MB, alloc=44.3MB, time=217.67 x[1] = 0.2553 0.758 h = 0.0001 0.004 y2[1] (numeric) = 11.3404185587 9.06054690595 y2[1] (closed_form) = 12.8816255397 8.38571077941 absolute error = 1.682 relative error = 10.95 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.25912492715 -0.210286631604 y1[1] (closed_form) = 1.25912492715 -0.210286631604 absolute error = 4.011e-63 relative error = 3.142e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.111 Order of pole (three term test) = 33.55 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.111 Order of pole (three term test) = 31.46 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18508.1MB, alloc=44.3MB, time=218.20 memory used=18554.5MB, alloc=44.3MB, time=218.75 x[1] = 0.2554 0.762 h = 0.003 0.006 y2[1] (numeric) = 11.3420516307 9.10583302549 y2[1] (closed_form) = 12.8835955516 8.43073257391 absolute error = 1.683 relative error = 10.93 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.26232489863 -0.211683893879 y1[1] (closed_form) = 1.26232489863 -0.211683893879 absolute error = 4.005e-63 relative error = 3.129e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.12 Order of pole (three term test) = 33.55 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.12 Order of pole (three term test) = 31.46 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18600.3MB, alloc=44.3MB, time=219.29 memory used=18647.0MB, alloc=44.3MB, time=219.84 x[1] = 0.2584 0.768 h = 0.0001 0.005 y2[1] (numeric) = 11.3436895655 9.15113168509 y2[1] (closed_form) = 12.9186717368 8.49767648463 absolute error = 1.705 relative error = 11.03 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.26621372943 -0.216119287686 y1[1] (closed_form) = 1.26621372943 -0.216119287686 absolute error = 4.005e-63 relative error = 3.118e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.135 Order of pole (three term test) = 33.56 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.135 Order of pole (three term test) = 31.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18693.1MB, alloc=44.3MB, time=220.37 memory used=18739.6MB, alloc=44.3MB, time=220.92 memory used=18786.4MB, alloc=44.3MB, time=221.48 x[1] = 0.2585 0.773 h = 0.0001 0.003 y2[1] (numeric) = 11.3453324036 9.19644293757 y2[1] (closed_form) = 12.9208835513 8.55399601698 absolute error = 1.701 relative error = 10.98 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.27028437459 -0.21787775553 y1[1] (closed_form) = 1.27028437459 -0.21787775553 absolute error = 4.011e-63 relative error = 3.112e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.147 Order of pole (three term test) = 33.57 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.147 Order of pole (three term test) = 31.44 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18832.3MB, alloc=44.3MB, time=222.02 memory used=18879.1MB, alloc=44.3MB, time=222.58 x[1] = 0.2586 0.776 h = 0.001 0.001 y2[1] (numeric) = 11.3469801857 9.24176683559 y2[1] (closed_form) = 12.9226659715 8.58778869102 absolute error = 1.706 relative error = 11 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.2727284224 -0.21896916811 y1[1] (closed_form) = 1.2727284224 -0.21896916811 absolute error = 3.015e-63 relative error = 2.335e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.154 Order of pole (three term test) = 33.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.154 Order of pole (three term test) = 31.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18925.0MB, alloc=44.3MB, time=223.12 memory used=18971.4MB, alloc=44.3MB, time=223.68 x[1] = 0.2596 0.777 h = 0.001 0.003 y2[1] (numeric) = 11.3486329531 9.28710343165 y2[1] (closed_form) = 12.9341584973 8.59884211311 absolute error = 1.728 relative error = 11.13 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.27321932576 -0.220134895664 y1[1] (closed_form) = 1.27321932576 -0.220134895664 absolute error = 3.015e-63 relative error = 2.333e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.157 Order of pole (three term test) = 33.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.157 Order of pole (three term test) = 31.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19017.3MB, alloc=44.3MB, time=224.21 memory used=19063.9MB, alloc=44.3MB, time=224.76 x[1] = 0.2606 0.78 h = 0.0001 0.004 y2[1] (numeric) = 11.3502907476 9.33245277807 y2[1] (closed_form) = 12.9460959666 8.63244393995 absolute error = 1.743 relative error = 11.2 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.2753721271 -0.221982918078 y1[1] (closed_form) = 1.2753721271 -0.221982918078 absolute error = 3.015e-63 relative error = 2.329e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.164 Order of pole (three term test) = 33.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.164 Order of pole (three term test) = 31.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19109.6MB, alloc=44.3MB, time=225.29 memory used=19156.0MB, alloc=44.3MB, time=225.84 x[1] = 0.2607 0.784 h = 0.003 0.006 y2[1] (numeric) = 11.351953611 9.377814927 y2[1] (closed_form) = 12.9481144909 8.67752976293 absolute error = 1.743 relative error = 11.18 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.27867800967 -0.223428835531 y1[1] (closed_form) = 1.27867800967 -0.223428835531 absolute error = 3.015e-63 relative error = 2.323e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.174 Order of pole (three term test) = 33.59 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.174 Order of pole (three term test) = 31.42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19202.2MB, alloc=44.3MB, time=226.38 memory used=19248.4MB, alloc=44.3MB, time=226.92 memory used=19294.8MB, alloc=44.3MB, time=227.48 x[1] = 0.2637 0.79 h = 0.0001 0.005 y2[1] (numeric) = 11.3536215859 9.42318993042 y2[1] (closed_form) = 12.9833108439 8.74453671147 absolute error = 1.765 relative error = 11.28 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.28269307582 -0.228014188885 y1[1] (closed_form) = 1.28269307582 -0.228014188885 absolute error = 3.015e-63 relative error = 2.314e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.189 Order of pole (three term test) = 33.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.189 Order of pole (three term test) = 31.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19340.8MB, alloc=44.3MB, time=228.02 memory used=19387.6MB, alloc=44.3MB, time=228.57 x[1] = 0.2638 0.795 h = 0.0001 0.003 y2[1] (numeric) = 11.3552947148 9.46857784015 y2[1] (closed_form) = 12.98558394 8.80093778119 absolute error = 1.762 relative error = 11.23 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.2868970587 -0.22983369543 y1[1] (closed_form) = 1.2868970587 -0.22983369543 absolute error = 3.015e-63 relative error = 2.306e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.202 Order of pole (three term test) = 33.61 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.202 Order of pole (three term test) = 31.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19433.6MB, alloc=44.3MB, time=229.12 memory used=19480.4MB, alloc=44.3MB, time=229.68 x[1] = 0.2639 0.798 h = 0.001 0.001 y2[1] (numeric) = 11.3569730411 9.51397870782 y2[1] (closed_form) = 12.98740395 8.83477921536 absolute error = 1.766 relative error = 11.24 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.28942083297 -0.230962962143 y1[1] (closed_form) = 1.28942083297 -0.230962962143 absolute error = 2.022e-63 relative error = 1.544e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.209 Order of pole (three term test) = 33.61 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.209 Order of pole (three term test) = 31.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19526.4MB, alloc=44.3MB, time=230.22 memory used=19572.9MB, alloc=44.3MB, time=230.77 x[1] = 0.2649 0.799 h = 0.001 0.003 y2[1] (numeric) = 11.3586566083 9.55939258488 y2[1] (closed_form) = 12.998925189 8.84583732432 absolute error = 1.789 relative error = 11.38 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.28992697687 -0.232167434898 y1[1] (closed_form) = 1.28992697687 -0.232167434898 absolute error = 2.040e-63 relative error = 1.556e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.212 Order of pole (three term test) = 33.62 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.212 Order of pole (three term test) = 31.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19618.8MB, alloc=44.3MB, time=231.31 memory used=19665.4MB, alloc=44.3MB, time=231.86 x[1] = 0.2659 0.802 h = 0.0001 0.004 y2[1] (numeric) = 11.3603454603 9.60481952261 y2[1] (closed_form) = 13.0109155917 8.87947731425 absolute error = 1.803 relative error = 11.45 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.29214902791 -0.234077851003 y1[1] (closed_form) = 1.29214902791 -0.234077851003 absolute error = 2.040e-63 relative error = 1.553e-61 % Correct digits = 63 memory used=19711.9MB, alloc=44.3MB, time=232.40 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 33.62 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.22 Order of pole (three term test) = 31.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19757.6MB, alloc=44.3MB, time=232.94 memory used=19803.9MB, alloc=44.3MB, time=233.48 x[1] = 0.266 0.806 h = 0.003 0.006 y2[1] (numeric) = 11.3620396415 9.65025957212 y2[1] (closed_form) = 13.0129842789 8.92462924691 absolute error = 1.803 relative error = 11.43 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.29556199159 -0.235573853852 y1[1] (closed_form) = 1.29556199159 -0.235573853852 absolute error = 2.040e-63 relative error = 1.549e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.23 Order of pole (three term test) = 33.63 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.23 Order of pole (three term test) = 31.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19849.8MB, alloc=44.3MB, time=234.02 memory used=19896.3MB, alloc=44.3MB, time=234.57 x[1] = 0.269 0.812 h = 0.0001 0.005 y2[1] (numeric) = 11.3637391965 9.69571278431 y2[1] (closed_form) = 13.048304803 8.99170121603 absolute error = 1.826 relative error = 11.52 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.29970405426 -0.240312193705 y1[1] (closed_form) = 1.29970405426 -0.240312193705 absolute error = 2.040e-63 relative error = 1.543e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.246 Order of pole (three term test) = 33.64 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.246 Order of pole (three term test) = 31.37 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19942.2MB, alloc=44.3MB, time=235.10 memory used=19988.8MB, alloc=44.3MB, time=235.66 x[1] = 0.2691 0.817 h = 0.0001 0.003 y2[1] (numeric) = 11.3654441706 9.74117920994 y2[1] (closed_form) = 13.0506412538 9.0481864446 absolute error = 1.822 relative error = 11.47 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.30404286723 -0.242194548948 y1[1] (closed_form) = 1.30404286723 -0.242194548948 absolute error = 2.062e-63 relative error = 1.554e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.259 Order of pole (three term test) = 33.65 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.259 Order of pole (three term test) = 31.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20034.8MB, alloc=44.3MB, time=236.19 memory used=20081.5MB, alloc=44.3MB, time=236.75 x[1] = 0.2692 0.82 h = 0.001 0.001 y2[1] (numeric) = 11.3671546092 9.78665889956 y2[1] (closed_form) = 13.0525001235 9.08207819905 absolute error = 1.827 relative error = 11.49 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.30664725523 -0.243362773241 y1[1] (closed_form) = 1.30664725523 -0.243362773241 absolute error = 2.040e-63 relative error = 1.535e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.267 Order of pole (three term test) = 33.65 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.267 Order of pole (three term test) = 31.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20127.8MB, alloc=44.3MB, time=237.30 memory used=20174.0MB, alloc=44.3MB, time=237.85 memory used=20220.6MB, alloc=44.3MB, time=238.41 x[1] = 0.2702 0.821 h = 0.001 0.003 y2[1] (numeric) = 11.3688705583 9.83215190353 y2[1] (closed_form) = 13.0640510159 9.09314112251 absolute error = 1.849 relative error = 11.62 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.30716858953 -0.244606658384 y1[1] (closed_form) = 1.30716858953 -0.244606658384 absolute error = 2.062e-63 relative error = 1.550e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.269 Order of pole (three term test) = 33.65 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.269 Order of pole (three term test) = 31.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20266.4MB, alloc=44.3MB, time=238.94 memory used=20313.1MB, alloc=44.3MB, time=239.49 x[1] = 0.2712 0.824 h = 0.0001 0.004 y2[1] (numeric) = 11.3705920642 9.87765827203 y2[1] (closed_form) = 13.0760961085 9.12682047089 absolute error = 1.863 relative error = 11.69 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.30946045781 -0.246580857406 y1[1] (closed_form) = 1.30946045781 -0.246580857406 absolute error = 3.041e-63 relative error = 2.283e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.277 Order of pole (three term test) = 33.66 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.277 Order of pole (three term test) = 31.35 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20359.0MB, alloc=44.3MB, time=240.02 memory used=20405.4MB, alloc=44.3MB, time=240.57 x[1] = 0.2713 0.828 h = 0.003 0.006 y2[1] (numeric) = 11.3723191736 9.92317805507 y2[1] (closed_form) = 13.0782166474 9.17204061288 absolute error = 1.864 relative error = 11.67 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.31298170976 -0.248128423675 y1[1] (closed_form) = 1.31298170976 -0.248128423675 absolute error = 3.041e-63 relative error = 2.276e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.288 Order of pole (three term test) = 33.67 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.288 Order of pole (three term test) = 31.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20451.1MB, alloc=44.3MB, time=241.10 memory used=20497.6MB, alloc=44.3MB, time=241.65 x[1] = 0.2743 0.834 h = 0.0001 0.005 y2[1] (numeric) = 11.3740519337 9.96871130243 y2[1] (closed_form) = 13.1136654175 9.239179586 absolute error = 1.886 relative error = 11.76 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.31725155233 -0.253022876346 y1[1] (closed_form) = 1.31725155233 -0.253022876346 absolute error = 2.062e-63 relative error = 1.537e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.305 Order of pole (three term test) = 33.68 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.305 Order of pole (three term test) = 31.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20543.5MB, alloc=44.3MB, time=242.18 memory used=20590.1MB, alloc=44.3MB, time=242.74 memory used=20636.6MB, alloc=44.3MB, time=243.29 x[1] = 0.2744 0.839 h = 0.0001 0.003 y2[1] (numeric) = 11.3757903921 10.0142580637 y2[1] (closed_form) = 13.116067345 9.29575161851 absolute error = 1.883 relative error = 11.71 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.32172673455 -0.254969950384 y1[1] (closed_form) = 1.32172673455 -0.254969950384 absolute error = 3.041e-63 relative error = 2.259e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.318 Order of pole (three term test) = 33.69 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.318 Order of pole (three term test) = 31.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20682.7MB, alloc=44.3MB, time=243.83 memory used=20729.5MB, alloc=44.3MB, time=244.39 x[1] = 0.2745 0.842 h = 0.001 0.001 y2[1] (numeric) = 11.3775345967 10.0598183884 y2[1] (closed_form) = 13.1179663734 9.32969526727 absolute error = 1.887 relative error = 11.72 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.32441265124 -0.256178272267 y1[1] (closed_form) = 1.32441265124 -0.256178272267 absolute error = 3.027e-63 relative error = 2.244e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.326 Order of pole (three term test) = 33.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.326 Order of pole (three term test) = 31.32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20775.4MB, alloc=44.3MB, time=244.93 memory used=20821.9MB, alloc=44.3MB, time=245.48 x[1] = 0.2755 0.843 h = 0.001 0.003 y2[1] (numeric) = 11.3792845959 10.1053923257 y2[1] (closed_form) = 13.1295478744 9.34076312815 absolute error = 1.91 relative error = 11.85 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.32494912353 -0.257462258499 y1[1] (closed_form) = 1.32494912353 -0.257462258499 absolute error = 3.027e-63 relative error = 2.242e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.329 Order of pole (three term test) = 33.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.329 Order of pole (three term test) = 31.32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20867.7MB, alloc=44.3MB, time=246.02 memory used=20914.5MB, alloc=44.3MB, time=246.57 x[1] = 0.2765 0.846 h = 0.0001 0.004 y2[1] (numeric) = 11.3810404386 10.1509799246 y2[1] (closed_form) = 13.1416494473 9.37448303553 absolute error = 1.924 relative error = 11.92 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.32731139356 -0.259501675023 y1[1] (closed_form) = 1.32731139356 -0.259501675023 absolute error = 3.027e-63 relative error = 2.238e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.338 Order of pole (three term test) = 33.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.338 Order of pole (three term test) = 31.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20960.4MB, alloc=44.3MB, time=247.10 memory used=21006.8MB, alloc=44.3MB, time=247.65 x[1] = 0.2766 0.85 h = 0.003 0.006 y2[1] (numeric) = 11.3828021738 10.196581234 y2[1] (closed_form) = 13.1438235661 9.41977350551 absolute error = 1.925 relative error = 11.9 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.33094217826 -0.261102331502 y1[1] (closed_form) = 1.33094217826 -0.261102331502 absolute error = 3.027e-63 relative error = 2.231e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.349 Order of pole (three term test) = 33.71 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.349 Order of pole (three term test) = 31.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21052.9MB, alloc=44.3MB, time=248.18 memory used=21099.3MB, alloc=44.3MB, time=248.73 memory used=21145.9MB, alloc=44.3MB, time=249.28 x[1] = 0.2796 0.856 h = 0.0001 0.005 y2[1] (numeric) = 11.3845698513 10.2421963024 y2[1] (closed_form) = 13.1794047314 9.4869814667 absolute error = 1.947 relative error = 11.99 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.33534060599 -0.266156124286 y1[1] (closed_form) = 1.33534060599 -0.266156124286 absolute error = 3.027e-63 relative error = 2.223e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.366 Order of pole (three term test) = 33.72 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.366 Order of pole (three term test) = 31.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21192.0MB, alloc=44.3MB, time=249.82 memory used=21238.6MB, alloc=44.3MB, time=250.37 x[1] = 0.2797 0.861 h = 0.0001 0.003 y2[1] (numeric) = 11.3863435212 10.2878251784 y2[1] (closed_form) = 13.1818743075 9.54364297253 absolute error = 1.944 relative error = 11.94 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.3399537437 -0.268169848527 y1[1] (closed_form) = 1.3399537437 -0.268169848527 absolute error = 3.027e-63 relative error = 2.215e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.38 Order of pole (three term test) = 33.73 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.38 Order of pole (three term test) = 31.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21284.6MB, alloc=44.3MB, time=250.92 memory used=21331.3MB, alloc=44.3MB, time=251.48 x[1] = 0.2798 0.864 h = 0.001 0.001 y2[1] (numeric) = 11.3881232339 10.3334679102 y2[1] (closed_form) = 13.1838148243 9.57764010393 absolute error = 1.948 relative error = 11.96 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.34272213184 -0.269419445304 y1[1] (closed_form) = 1.34272213184 -0.269419445304 absolute error = 3.027e-63 relative error = 2.210e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.389 Order of pole (three term test) = 33.74 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.389 Order of pole (three term test) = 31.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21377.3MB, alloc=44.3MB, time=252.02 memory used=21423.9MB, alloc=44.3MB, time=252.57 x[1] = 0.2808 0.865 h = 0.0001 0.004 y2[1] (numeric) = 11.3899090403 10.3791245457 y2[1] (closed_form) = 13.1954279039 9.58871302026 absolute error = 1.971 relative error = 12.08 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.34327368726 -0.270744243139 y1[1] (closed_form) = 1.34327368726 -0.270744243139 absolute error = 3.027e-63 relative error = 2.209e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.392 Order of pole (three term test) = 33.74 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.392 Order of pole (three term test) = 31.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21469.7MB, alloc=44.3MB, time=253.10 memory used=21516.2MB, alloc=44.3MB, time=253.65 x[1] = 0.2809 0.869 h = 0.003 0.006 y2[1] (numeric) = 11.3917009918 10.4247951329 y2[1] (closed_form) = 13.1976486852 9.63406640472 absolute error = 1.971 relative error = 12.07 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.34700043743 -0.272390532846 y1[1] (closed_form) = 1.34700043743 -0.272390532846 absolute error = 3.027e-63 relative error = 2.202e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.403 Order of pole (three term test) = 33.75 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.403 Order of pole (three term test) = 31.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21562.5MB, alloc=44.3MB, time=254.20 memory used=21608.7MB, alloc=44.3MB, time=254.74 memory used=21655.4MB, alloc=44.3MB, time=255.29 x[1] = 0.2839 0.875 h = 0.0001 0.005 y2[1] (numeric) = 11.3934991401 10.4704797192 y2[1] (closed_form) = 13.2333463388 9.70133698355 absolute error = 1.994 relative error = 12.15 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.35151216048 -0.277582597783 y1[1] (closed_form) = 1.35151216048 -0.277582597783 absolute error = 2.040e-63 relative error = 1.478e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.421 Order of pole (three term test) = 33.76 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.421 Order of pole (three term test) = 31.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21701.3MB, alloc=44.3MB, time=255.82 memory used=21748.1MB, alloc=44.3MB, time=256.38 x[1] = 0.284 0.88 h = 0.0001 0.003 y2[1] (numeric) = 11.3953035376 10.5161783523 y2[1] (closed_form) = 13.2358748135 9.75807850368 absolute error = 1.991 relative error = 12.11 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.35624617846 -0.279653616731 y1[1] (closed_form) = 1.35624617846 -0.279653616731 absolute error = 2.040e-63 relative error = 1.473e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.436 Order of pole (three term test) = 33.77 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.436 Order of pole (three term test) = 31.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21794.2MB, alloc=44.3MB, time=256.92 memory used=21841.0MB, alloc=44.3MB, time=257.49 x[1] = 0.2841 0.883 h = 0.001 0.001 y2[1] (numeric) = 11.3971142367 10.5618910791 y2[1] (closed_form) = 13.2378514677 9.79212347061 absolute error = 1.995 relative error = 12.12 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.35908684304 -0.280938715146 y1[1] (closed_form) = 1.35908684304 -0.280938715146 absolute error = 2.040e-63 relative error = 1.470e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.444 Order of pole (three term test) = 33.78 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.444 Order of pole (three term test) = 31.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21886.9MB, alloc=44.3MB, time=258.03 memory used=21933.3MB, alloc=44.3MB, time=258.58 x[1] = 0.2851 0.884 h = 0.001 0.003 y2[1] (numeric) = 11.3989312907 10.6076179468 y2[1] (closed_form) = 13.2494924558 9.80320122134 absolute error = 2.018 relative error = 12.24 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.35965183365 -0.28229904936 y1[1] (closed_form) = 1.35965183365 -0.28229904936 absolute error = 2.040e-63 relative error = 1.469e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.447 Order of pole (three term test) = 33.78 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.447 Order of pole (three term test) = 31.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21979.1MB, alloc=44.3MB, time=259.12 memory used=22025.7MB, alloc=44.3MB, time=259.66 x[1] = 0.2861 0.887 h = 0.0001 0.004 y2[1] (numeric) = 11.4007547531 10.653359002 y2[1] (closed_form) = 13.2617034951 9.83700053797 absolute error = 2.032 relative error = 12.31 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.36214753773 -0.284462941475 y1[1] (closed_form) = 1.36214753773 -0.284462941475 absolute error = 2.040e-63 relative error = 1.466e-61 % Correct digits = 63 memory used=22072.3MB, alloc=44.3MB, time=260.22 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.457 Order of pole (three term test) = 33.78 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.457 Order of pole (three term test) = 31.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22118.2MB, alloc=44.3MB, time=260.75 memory used=22164.6MB, alloc=44.3MB, time=261.30 x[1] = 0.2862 0.891 h = 0.003 0.006 y2[1] (numeric) = 11.4025846778 10.6991142914 y2[1] (closed_form) = 13.2639811561 9.882428267 absolute error = 2.033 relative error = 12.29 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.36598625611 -0.286165279694 y1[1] (closed_form) = 1.36598625611 -0.286165279694 absolute error = 3.027e-63 relative error = 2.169e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.469 Order of pole (three term test) = 33.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.469 Order of pole (three term test) = 31.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22210.6MB, alloc=44.3MB, time=261.83 memory used=22257.2MB, alloc=44.3MB, time=262.38 x[1] = 0.2892 0.897 h = 0.0001 0.005 y2[1] (numeric) = 11.4044211193 10.7448838612 y2[1] (closed_form) = 13.2998191073 9.94977157889 absolute error = 2.055 relative error = 12.37 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.37062816088 -0.291522954273 y1[1] (closed_form) = 1.37062816088 -0.291522954273 absolute error = 3.027e-63 relative error = 2.160e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.487 Order of pole (three term test) = 33.8 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.487 Order of pole (three term test) = 31.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22303.1MB, alloc=44.3MB, time=262.92 memory used=22349.7MB, alloc=44.3MB, time=263.48 x[1] = 0.2893 0.902 h = 0.0001 0.003 y2[1] (numeric) = 11.4062641325 10.7906677576 y2[1] (closed_form) = 13.3024193783 10.0066076339 absolute error = 2.052 relative error = 12.33 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.37550323701 -0.293664364581 y1[1] (closed_form) = 1.37550323701 -0.293664364581 absolute error = 3.027e-63 relative error = 2.152e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.502 Order of pole (three term test) = 33.82 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.502 Order of pole (three term test) = 31.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22395.8MB, alloc=44.3MB, time=264.01 memory used=22442.6MB, alloc=44.3MB, time=264.58 x[1] = 0.2894 0.905 h = 0.001 0.001 y2[1] (numeric) = 11.4081137726 10.8364660265 y2[1] (closed_form) = 13.3044400599 10.0407090952 absolute error = 2.057 relative error = 12.34 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.37842821701 -0.294993018434 y1[1] (closed_form) = 1.37842821701 -0.294993018434 absolute error = 4.031e-63 relative error = 2.860e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.512 Order of pole (three term test) = 33.82 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.512 Order of pole (three term test) = 31.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22488.8MB, alloc=44.3MB, time=265.12 memory used=22535.0MB, alloc=44.3MB, time=265.67 memory used=22581.6MB, alloc=44.3MB, time=266.22 x[1] = 0.2904 0.906 h = 0.001 0.003 y2[1] (numeric) = 11.4099700955 10.8822787135 y2[1] (closed_form) = 13.3161144723 10.0517921194 absolute error = 2.079 relative error = 12.46 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.37900819058 -0.29639554621 y1[1] (closed_form) = 1.37900819058 -0.29639554621 absolute error = 3.041e-63 relative error = 2.156e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.515 Order of pole (three term test) = 33.82 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.515 Order of pole (three term test) = 31.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22627.5MB, alloc=44.3MB, time=266.76 memory used=22673.9MB, alloc=44.3MB, time=267.31 x[1] = 0.2914 0.909 h = 0.0001 0.004 y2[1] (numeric) = 11.4118331574 10.9281058641 y2[1] (closed_form) = 13.3283872978 10.0856354821 absolute error = 2.094 relative error = 12.53 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.38157608051 -0.298629009893 y1[1] (closed_form) = 1.38157608051 -0.298629009893 absolute error = 3.059e-63 relative error = 2.164e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.524 Order of pole (three term test) = 33.83 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.524 Order of pole (three term test) = 31.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22719.8MB, alloc=44.3MB, time=267.84 memory used=22766.2MB, alloc=44.3MB, time=268.39 x[1] = 0.2915 0.913 h = 0.003 0.006 y2[1] (numeric) = 11.413703015 10.9739475235 y2[1] (closed_form) = 13.330723687 10.1311397324 absolute error = 2.094 relative error = 12.51 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.38552812024 -0.300389068015 y1[1] (closed_form) = 1.38552812024 -0.300389068015 absolute error = 3.059e-63 relative error = 2.158e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.537 Order of pole (three term test) = 33.84 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.537 Order of pole (three term test) = 31.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22812.0MB, alloc=44.3MB, time=268.92 memory used=22858.6MB, alloc=44.3MB, time=269.47 x[1] = 0.2945 0.919 h = 0.0001 0.005 y2[1] (numeric) = 11.4155797255 11.0198037367 y2[1] (closed_form) = 13.3667063099 10.1985577638 absolute error = 2.117 relative error = 12.59 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.39030107357 -0.305915877496 y1[1] (closed_form) = 1.39030107357 -0.305915877496 absolute error = 3.059e-63 relative error = 2.149e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.556 Order of pole (three term test) = 33.85 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.556 Order of pole (three term test) = 31.17 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22904.5MB, alloc=44.3MB, time=270.00 memory used=22951.2MB, alloc=44.3MB, time=270.56 x[1] = 0.2946 0.924 h = 0.0001 0.003 y2[1] (numeric) = 11.4174633465 11.0656745484 y2[1] (closed_form) = 13.369380701 10.2554910972 absolute error = 2.113 relative error = 12.54 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.39531893111 -0.308129792437 y1[1] (closed_form) = 1.39531893111 -0.308129792437 absolute error = 3.059e-63 relative error = 2.141e-61 % Correct digits = 63 memory used=22997.9MB, alloc=44.3MB, time=271.11 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.572 Order of pole (three term test) = 33.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.572 Order of pole (three term test) = 31.16 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23044.1MB, alloc=44.3MB, time=271.66 memory used=23091.0MB, alloc=44.3MB, time=272.22 x[1] = 0.2947 0.927 h = 0.001 0.001 y2[1] (numeric) = 11.419353936 11.1115600033 y2[1] (closed_form) = 13.3714468321 10.2896506848 absolute error = 2.118 relative error = 12.55 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.39832925022 -0.309503289647 y1[1] (closed_form) = 1.39832925022 -0.309503289647 absolute error = 3.059e-63 relative error = 2.136e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.582 Order of pole (three term test) = 33.87 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.582 Order of pole (three term test) = 31.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23137.0MB, alloc=44.3MB, time=272.76 memory used=23183.4MB, alloc=44.3MB, time=273.31 x[1] = 0.2957 0.928 h = 0.001 0.003 y2[1] (numeric) = 11.4212515526 11.1574601455 y2[1] (closed_form) = 13.3831556846 10.3007390857 absolute error = 2.141 relative error = 12.68 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.39892414409 -0.310948785691 y1[1] (closed_form) = 1.39892414409 -0.310948785691 absolute error = 3.081e-63 relative error = 2.150e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.585 Order of pole (three term test) = 33.87 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.585 Order of pole (three term test) = 31.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23229.3MB, alloc=44.3MB, time=273.85 memory used=23275.9MB, alloc=44.3MB, time=274.40 x[1] = 0.2967 0.931 h = 0.0001 0.004 y2[1] (numeric) = 11.4231562554 11.2033750192 y2[1] (closed_form) = 13.3954922289 10.3346277167 absolute error = 2.155 relative error = 12.74 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.40156486972 -0.313253438106 y1[1] (closed_form) = 1.40156486972 -0.313253438106 absolute error = 2.119e-63 relative error = 1.475e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.595 Order of pole (three term test) = 33.88 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.595 Order of pole (three term test) = 31.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23321.7MB, alloc=44.3MB, time=274.93 memory used=23368.3MB, alloc=44.3MB, time=275.48 x[1] = 0.2968 0.935 h = 0.003 0.006 y2[1] (numeric) = 11.4250681038 11.2493046682 y2[1] (closed_form) = 13.3978892393 10.380210686 absolute error = 2.156 relative error = 12.72 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.40563162216 -0.315072940267 y1[1] (closed_form) = 1.40563162216 -0.315072940267 absolute error = 3.081e-63 relative error = 2.139e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.608 Order of pole (three term test) = 33.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.608 Order of pole (three term test) = 31.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23414.2MB, alloc=44.3MB, time=276.01 memory used=23460.8MB, alloc=44.3MB, time=276.56 memory used=23507.4MB, alloc=44.3MB, time=277.11 x[1] = 0.2998 0.941 h = 0.0001 0.005 y2[1] (numeric) = 11.4269871577 11.295249136 y2[1] (closed_form) = 13.4340209916 10.4477054238 absolute error = 2.179 relative error = 12.8 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.41053651121 -0.320772517585 y1[1] (closed_form) = 1.41053651121 -0.320772517585 absolute error = 3.105e-63 relative error = 2.146e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.628 Order of pole (three term test) = 33.9 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.628 Order of pole (three term test) = 31.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23553.4MB, alloc=44.3MB, time=277.65 memory used=23600.0MB, alloc=44.3MB, time=278.20 x[1] = 0.2999 0.946 h = 0.0001 0.003 y2[1] (numeric) = 11.4289134777 11.3412084661 y2[1] (closed_form) = 13.4367718832 10.5047388062 absolute error = 2.175 relative error = 12.75 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.41569892158 -0.323061116788 y1[1] (closed_form) = 1.41569892158 -0.323061116788 absolute error = 3.105e-63 relative error = 2.138e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.645 Order of pole (three term test) = 33.91 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.645 Order of pole (three term test) = 31.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23646.0MB, alloc=44.3MB, time=278.74 memory used=23692.8MB, alloc=44.3MB, time=279.31 x[1] = 0.3 0.949 h = 0.001 0.001 y2[1] (numeric) = 11.4308471247 11.3871827016 y2[1] (closed_form) = 13.4388849197 10.5389581678 absolute error = 2.18 relative error = 12.76 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.41879563195 -0.324480785622 y1[1] (closed_form) = 1.41879563195 -0.324480785622 absolute error = 3.105e-63 relative error = 2.133e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.655 Order of pole (three term test) = 33.92 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.655 Order of pole (three term test) = 31.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23738.8MB, alloc=44.3MB, time=279.86 memory used=23785.3MB, alloc=44.3MB, time=280.41 x[1] = 0.301 0.95 h = 0.001 0.003 y2[1] (numeric) = 11.43278816 11.4331718853 y2[1] (closed_form) = 13.4506292455 10.5500520432 absolute error = 2.203 relative error = 12.89 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.41940538022 -0.325970047709 y1[1] (closed_form) = 1.41940538022 -0.325970047709 absolute error = 3.105e-63 relative error = 2.132e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.658 Order of pole (three term test) = 33.92 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.658 Order of pole (three term test) = 31.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23831.1MB, alloc=44.3MB, time=280.94 memory used=23877.8MB, alloc=44.3MB, time=281.50 x[1] = 0.302 0.953 h = 0.0001 0.004 y2[1] (numeric) = 11.4347366455 11.4791760598 y2[1] (closed_form) = 13.4630314808 10.5839871704 absolute error = 2.217 relative error = 12.95 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.42211960806 -0.328347555463 y1[1] (closed_form) = 1.42211960806 -0.328347555463 absolute error = 3.105e-63 relative error = 2.127e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.669 Order of pole (three term test) = 33.93 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.669 Order of pole (three term test) = 31.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23924.1MB, alloc=44.3MB, time=282.04 memory used=23970.2MB, alloc=44.3MB, time=282.58 memory used=24016.7MB, alloc=44.3MB, time=283.13 x[1] = 0.3021 0.957 h = 0.003 0.006 y2[1] (numeric) = 11.4366926436 11.5251952675 y2[1] (closed_form) = 13.4654910513 10.6296510784 absolute error = 2.218 relative error = 12.93 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.42630250298 -0.330228279655 y1[1] (closed_form) = 1.42630250298 -0.330228279655 absolute error = 3.105e-63 relative error = 2.121e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.682 Order of pole (three term test) = 33.94 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.682 Order of pole (three term test) = 31.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24062.5MB, alloc=44.3MB, time=283.66 memory used=24109.2MB, alloc=44.3MB, time=284.22 x[1] = 0.3051 0.963 h = 0.0001 0.005 y2[1] (numeric) = 11.4386562172 11.5712295506 y2[1] (closed_form) = 13.5017764765 10.6972245095 absolute error = 2.241 relative error = 13.01 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.43134023474 -0.336104367285 y1[1] (closed_form) = 1.43134023474 -0.336104367285 absolute error = 3.105e-63 relative error = 2.112e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.703 Order of pole (three term test) = 33.95 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.703 Order of pole (three term test) = 31.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24155.2MB, alloc=44.3MB, time=284.75 memory used=24201.9MB, alloc=44.3MB, time=285.30 x[1] = 0.3052 0.968 h = 0.0001 0.003 y2[1] (numeric) = 11.4406274296 11.6172789509 y2[1] (closed_form) = 13.5046063072 10.7543607392 absolute error = 2.237 relative error = 12.96 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.43664901787 -0.338469898138 y1[1] (closed_form) = 1.43664901787 -0.338469898138 absolute error = 4.079e-63 relative error = 2.764e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.721 Order of pole (three term test) = 33.96 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.721 Order of pole (three term test) = 31.07 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24247.8MB, alloc=44.3MB, time=285.84 memory used=24294.6MB, alloc=44.3MB, time=286.40 x[1] = 0.3053 0.971 h = 0.001 0.001 y2[1] (numeric) = 11.4426063446 11.6633435101 y2[1] (closed_form) = 13.5067677407 10.788641539 absolute error = 2.242 relative error = 12.97 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.43983320027 -0.339937108066 y1[1] (closed_form) = 1.43983320027 -0.339937108066 absolute error = 3.081e-63 relative error = 2.082e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.731 Order of pole (three term test) = 33.97 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.731 Order of pole (three term test) = 31.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24340.7MB, alloc=44.3MB, time=286.95 memory used=24387.2MB, alloc=44.3MB, time=287.50 x[1] = 0.3063 0.972 h = 0.0001 0.004 y2[1] (numeric) = 11.4445930265 11.7094232695 y2[1] (closed_form) = 13.51854859 10.7997409807 absolute error = 2.265 relative error = 13.09 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.44045773362 -0.341470957387 y1[1] (closed_form) = 1.44045773362 -0.341470957387 absolute error = 3.105e-63 relative error = 2.097e-61 % Correct digits = 63 memory used=24433.7MB, alloc=44.3MB, time=288.04 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.735 Order of pole (three term test) = 33.97 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.735 Order of pole (three term test) = 31.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24479.7MB, alloc=44.3MB, time=288.58 memory used=24526.2MB, alloc=44.3MB, time=289.13 x[1] = 0.3064 0.976 h = 0.003 0.006 y2[1] (numeric) = 11.4465875402 11.7555182702 y2[1] (closed_form) = 13.5210625984 10.84547713 absolute error = 2.265 relative error = 13.07 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.4447425337 -0.343404437807 y1[1] (closed_form) = 1.4447425337 -0.343404437807 absolute error = 3.105e-63 relative error = 2.091e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.749 Order of pole (three term test) = 33.98 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.749 Order of pole (three term test) = 31.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24572.2MB, alloc=44.3MB, time=289.67 memory used=24618.9MB, alloc=44.3MB, time=290.22 x[1] = 0.3094 0.982 h = 0.0001 0.005 y2[1] (numeric) = 11.4485899511 11.8016285532 y2[1] (closed_form) = 13.5574830363 10.9131217946 absolute error = 2.288 relative error = 13.15 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.44989751851 -0.349433944067 y1[1] (closed_form) = 1.44989751851 -0.349433944067 absolute error = 3.132e-63 relative error = 2.100e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.771 Order of pole (three term test) = 34 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.771 Order of pole (three term test) = 31.04 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24664.8MB, alloc=44.3MB, time=290.76 memory used=24711.4MB, alloc=44.3MB, time=291.31 x[1] = 0.3095 0.987 h = 0.0001 0.003 y2[1] (numeric) = 11.4506003249 11.8477541591 y2[1] (closed_form) = 13.5603815426 10.9703497954 absolute error = 2.285 relative error = 13.1 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.45533474314 -0.351865773576 y1[1] (closed_form) = 1.45533474314 -0.351865773576 absolute error = 3.132e-63 relative error = 2.092e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.789 Order of pole (three term test) = 34.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.789 Order of pole (three term test) = 31.02 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24757.4MB, alloc=44.3MB, time=291.86 memory used=24804.4MB, alloc=44.3MB, time=292.42 x[1] = 0.3096 0.99 h = 0.001 0.001 y2[1] (numeric) = 11.4526187279 11.8938951281 y2[1] (closed_form) = 13.5625850977 11.0046854259 absolute error = 2.29 relative error = 13.11 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.45859569527 -0.353373974005 y1[1] (closed_form) = 1.45859569527 -0.353373974005 absolute error = 3.132e-63 relative error = 2.087e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 34.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.8 Order of pole (three term test) = 31.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24850.6MB, alloc=44.3MB, time=292.96 memory used=24897.1MB, alloc=44.3MB, time=293.52 memory used=24943.5MB, alloc=44.3MB, time=294.07 x[1] = 0.3106 0.991 h = 0.001 0.003 y2[1] (numeric) = 11.4546452271 11.9400515003 y2[1] (closed_form) = 13.5743981724 11.0157901804 absolute error = 2.312 relative error = 13.23 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.4592334417 -0.354946703337 y1[1] (closed_form) = 1.4592334417 -0.354946703337 absolute error = 3.105e-63 relative error = 2.067e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.803 Order of pole (three term test) = 34.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.803 Order of pole (three term test) = 31.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24989.4MB, alloc=44.3MB, time=294.60 memory used=25035.9MB, alloc=44.3MB, time=295.15 x[1] = 0.3116 0.994 h = 0.0001 0.004 y2[1] (numeric) = 11.4566798898 11.9862233156 y2[1] (closed_form) = 13.5869274443 11.0498159548 absolute error = 2.327 relative error = 13.29 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.46208718745 -0.357463491725 y1[1] (closed_form) = 1.46208718745 -0.357463491725 absolute error = 3.105e-63 relative error = 2.063e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.815 Order of pole (three term test) = 34.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.815 Order of pole (three term test) = 31.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25081.7MB, alloc=44.3MB, time=295.68 memory used=25128.1MB, alloc=44.3MB, time=296.23 x[1] = 0.3117 0.998 h = 0.003 0.006 y2[1] (numeric) = 11.4587227838 12.0324106134 y2[1] (closed_form) = 13.5895077209 11.0956372571 absolute error = 2.328 relative error = 13.27 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.46649091638 -0.35946163176 y1[1] (closed_form) = 1.46649091638 -0.35946163176 absolute error = 3.105e-63 relative error = 2.056e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.829 Order of pole (three term test) = 34.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.829 Order of pole (three term test) = 31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25174.1MB, alloc=44.3MB, time=296.76 memory used=25220.7MB, alloc=44.3MB, time=297.32 x[1] = 0.3147 1.004 h = 0.0001 0.005 y2[1] (numeric) = 11.4607739776 12.0786134332 y2[1] (closed_form) = 13.6260904997 11.163364369 absolute error = 2.351 relative error = 13.35 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.47178053067 -0.365674899012 y1[1] (closed_form) = 1.47178053067 -0.365674899012 absolute error = 4.079e-63 relative error = 2.690e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.852 Order of pole (three term test) = 34.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.852 Order of pole (three term test) = 30.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25266.6MB, alloc=44.3MB, time=297.86 memory used=25313.3MB, alloc=44.3MB, time=298.41 x[1] = 0.3148 1.009 h = 0.0001 0.003 y2[1] (numeric) = 11.4628335399 12.1248318138 y2[1] (closed_form) = 13.6290726096 11.2207005313 absolute error = 2.347 relative error = 13.3 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.47736767334 -0.368188004331 y1[1] (closed_form) = 1.47736767334 -0.368188004331 absolute error = 3.105e-63 relative error = 2.039e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.871 Order of pole (three term test) = 34.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.871 Order of pole (three term test) = 30.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25359.7MB, alloc=44.3MB, time=298.96 memory used=25406.0MB, alloc=44.3MB, time=299.51 memory used=25452.9MB, alloc=44.3MB, time=300.07 x[1] = 0.3149 1.012 h = 0.001 0.001 y2[1] (numeric) = 11.4649015403 12.171065794 y2[1] (closed_form) = 13.6313274144 11.2551007601 absolute error = 2.352 relative error = 13.31 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.48071820284 -0.369746393097 y1[1] (closed_form) = 1.48071820284 -0.369746393097 absolute error = 3.105e-63 relative error = 2.034e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.882 Order of pole (three term test) = 34.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.882 Order of pole (three term test) = 30.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25498.9MB, alloc=44.3MB, time=300.62 memory used=25545.4MB, alloc=44.3MB, time=301.17 x[1] = 0.3159 1.013 h = 0.001 0.003 y2[1] (numeric) = 11.4669780487 12.2173154122 y2[1] (closed_form) = 13.6431790144 11.266211249 absolute error = 2.375 relative error = 13.42 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.4813706059 -0.371365302207 y1[1] (closed_form) = 1.4813706059 -0.371365302207 absolute error = 3.105e-63 relative error = 2.033e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.886 Order of pole (three term test) = 34.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.886 Order of pole (three term test) = 30.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25591.2MB, alloc=44.3MB, time=301.70 memory used=25637.7MB, alloc=44.3MB, time=302.25 x[1] = 0.3169 1.016 h = 0.0001 0.004 y2[1] (numeric) = 11.4690631355 12.2635807067 y2[1] (closed_form) = 13.6557798338 11.3002870907 absolute error = 2.389 relative error = 13.48 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.48429987333 -0.373959986455 y1[1] (closed_form) = 1.48429987333 -0.373959986455 absolute error = 3.105e-63 relative error = 2.028e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.898 Order of pole (three term test) = 34.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.898 Order of pole (three term test) = 30.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25683.7MB, alloc=44.3MB, time=302.78 memory used=25730.2MB, alloc=44.3MB, time=303.34 x[1] = 0.317 1.02 h = 0.003 0.006 y2[1] (numeric) = 11.4711568717 12.3098617153 y2[1] (closed_form) = 13.6584284569 11.3461958316 absolute error = 2.39 relative error = 13.46 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.48882407287 -0.37602472413 y1[1] (closed_form) = 1.48882407287 -0.37602472413 absolute error = 3.105e-63 relative error = 2.022e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.913 Order of pole (three term test) = 34.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.913 Order of pole (three term test) = 30.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25776.1MB, alloc=44.3MB, time=303.86 memory used=25822.7MB, alloc=44.3MB, time=304.42 memory used=25869.3MB, alloc=44.3MB, time=304.97 x[1] = 0.32 1.026 h = 0.0001 0.005 y2[1] (numeric) = 11.4732593289 12.3561584756 y2[1] (closed_form) = 13.6951783799 11.4140073785 absolute error = 2.413 relative error = 13.54 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.49424927924 -0.382425818777 y1[1] (closed_form) = 1.49424927924 -0.382425818777 absolute error = 3.105e-63 relative error = 2.013e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.937 Order of pole (three term test) = 34.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.937 Order of pole (three term test) = 30.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25915.5MB, alloc=44.3MB, time=305.51 memory used=25962.3MB, alloc=44.3MB, time=306.07 x[1] = 0.3201 1.031 h = 0.0001 0.003 y2[1] (numeric) = 11.475370579 12.4024710251 y2[1] (closed_form) = 13.698246708 11.4714545847 absolute error = 2.41 relative error = 13.49 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.49998830116 -0.385022648709 y1[1] (closed_form) = 1.49998830116 -0.385022648709 absolute error = 3.105e-63 relative error = 2.005e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.957 Order of pole (three term test) = 34.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.957 Order of pole (three term test) = 30.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26008.3MB, alloc=44.3MB, time=306.61 memory used=26055.2MB, alloc=44.3MB, time=307.18 x[1] = 0.3202 1.034 h = 0.001 0.001 y2[1] (numeric) = 11.4774906948 12.4487994007 y2[1] (closed_form) = 13.7005543608 11.5059211254 absolute error = 2.415 relative error = 13.5 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.50342957217 -0.386632717719 y1[1] (closed_form) = 1.50342957217 -0.386632717719 absolute error = 3.105e-63 relative error = 2.000e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.968 Order of pole (three term test) = 34.13 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.968 Order of pole (three term test) = 30.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26101.2MB, alloc=44.3MB, time=307.72 memory used=26147.6MB, alloc=44.3MB, time=308.27 x[1] = 0.3212 1.035 h = 0.001 0.003 y2[1] (numeric) = 11.4796197492 12.4951436391 y2[1] (closed_form) = 13.7124455893 11.5170374231 absolute error = 2.438 relative error = 13.61 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.50409655175 -0.388298696857 y1[1] (closed_form) = 1.50409655175 -0.388298696857 absolute error = 3.105e-63 relative error = 1.999e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.973 Order of pole (three term test) = 34.13 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.973 Order of pole (three term test) = 30.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26193.5MB, alloc=44.3MB, time=308.80 memory used=26240.2MB, alloc=44.3MB, time=309.35 x[1] = 0.3222 1.038 h = 0.0001 0.004 y2[1] (numeric) = 11.481757816 12.541503777 y2[1] (closed_form) = 13.7251200926 11.5511645837 absolute error = 2.452 relative error = 13.67 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.50710207125 -0.390973143098 y1[1] (closed_form) = 1.50710207125 -0.390973143098 absolute error = 4.079e-63 relative error = 2.620e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.985 Order of pole (three term test) = 34.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 1.985 Order of pole (three term test) = 30.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26286.4MB, alloc=44.3MB, time=309.88 memory used=26332.7MB, alloc=44.3MB, time=310.43 memory used=26379.0MB, alloc=44.3MB, time=310.98 x[1] = 0.3223 1.042 h = 0.003 0.006 y2[1] (numeric) = 11.4839049693 12.5878798504 y2[1] (closed_form) = 13.7278391916 11.5971630726 absolute error = 2.453 relative error = 13.65 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.51174832255 -0.393106474897 y1[1] (closed_form) = 1.51174832255 -0.393106474897 absolute error = 3.105e-63 relative error = 1.988e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.001 Order of pole (three term test) = 34.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.001 Order of pole (three term test) = 30.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26424.9MB, alloc=44.3MB, time=311.52 memory used=26471.5MB, alloc=44.3MB, time=312.07 x[1] = 0.3253 1.048 h = 0.0001 0.005 y2[1] (numeric) = 11.4860612839 12.6342718953 y2[1] (closed_form) = 13.7647611582 11.6650610418 absolute error = 2.476 relative error = 13.72 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.51731010164 -0.399699580598 y1[1] (closed_form) = 1.51731010164 -0.399699580598 absolute error = 3.105e-63 relative error = 1.979e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.025 Order of pole (three term test) = 34.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.025 Order of pole (three term test) = 30.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26517.5MB, alloc=44.3MB, time=312.61 memory used=26564.0MB, alloc=44.3MB, time=313.16 x[1] = 0.3254 1.053 h = 0.0001 0.003 y2[1] (numeric) = 11.488226835 12.6806799472 y2[1] (closed_form) = 13.7679183843 11.7226222049 absolute error = 2.473 relative error = 13.68 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.52320301373 -0.402382657538 y1[1] (closed_form) = 1.52320301373 -0.402382657538 absolute error = 4.079e-63 relative error = 2.589e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.046 Order of pole (three term test) = 34.18 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.046 Order of pole (three term test) = 30.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26610.1MB, alloc=44.3MB, time=313.70 memory used=26657.0MB, alloc=44.3MB, time=314.26 x[1] = 0.3255 1.056 h = 0.001 0.001 y2[1] (numeric) = 11.4904016986 12.7271040416 y2[1] (closed_form) = 13.7702805229 11.757156789 absolute error = 2.478 relative error = 13.68 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.52673621971 -0.404045943426 y1[1] (closed_form) = 1.52673621971 -0.404045943426 absolute error = 4.061e-63 relative error = 2.571e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.058 Order of pole (three term test) = 34.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.058 Order of pole (three term test) = 30.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26703.1MB, alloc=44.3MB, time=314.81 memory used=26749.6MB, alloc=44.3MB, time=315.36 x[1] = 0.3265 1.057 h = 0.001 0.003 y2[1] (numeric) = 11.4925859509 12.7735442133 y2[1] (closed_form) = 13.7822125026 11.7682789634 absolute error = 2.501 relative error = 13.8 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.52741769136 -0.405759907701 y1[1] (closed_form) = 1.52741769136 -0.405759907701 absolute error = 4.079e-63 relative error = 2.581e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.063 Order of pole (three term test) = 34.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.063 Order of pole (three term test) = 30.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26795.8MB, alloc=44.3MB, time=315.90 memory used=26842.0MB, alloc=44.3MB, time=316.45 memory used=26888.6MB, alloc=44.3MB, time=317.00 x[1] = 0.3275 1.06 h = 0.0001 0.004 y2[1] (numeric) = 11.4947796689 12.8200004971 y2[1] (closed_form) = 13.7949628716 11.8024587008 absolute error = 2.515 relative error = 13.85 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.53050020949 -0.408516036216 y1[1] (closed_form) = 1.53050020949 -0.408516036216 absolute error = 4.079e-63 relative error = 2.575e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.075 Order of pole (three term test) = 34.2 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.075 Order of pole (three term test) = 30.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26934.4MB, alloc=44.3MB, time=317.54 memory used=26980.9MB, alloc=44.3MB, time=318.10 x[1] = 0.3276 1.064 h = 0.003 0.006 y2[1] (numeric) = 11.4969829301 12.8664729274 y2[1] (closed_form) = 13.7977546294 11.8485492717 absolute error = 2.516 relative error = 13.83 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.53527013335 -0.410720018362 y1[1] (closed_form) = 1.53527013335 -0.410720018362 absolute error = 3.105e-63 relative error = 1.954e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.092 Order of pole (three term test) = 34.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.092 Order of pole (three term test) = 30.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27026.8MB, alloc=44.3MB, time=318.63 memory used=27073.5MB, alloc=44.3MB, time=319.19 x[1] = 0.3306 1.07 h = 0.0001 0.005 y2[1] (numeric) = 11.4991958126 12.9129615383 y2[1] (closed_form) = 13.8348536372 11.9165356497 absolute error = 2.539 relative error = 13.91 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.54096948326 -0.417509438169 y1[1] (closed_form) = 1.54096948326 -0.417509438169 absolute error = 3.105e-63 relative error = 1.945e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.118 Order of pole (three term test) = 34.22 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.118 Order of pole (three term test) = 30.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27119.4MB, alloc=44.3MB, time=319.72 memory used=27166.0MB, alloc=44.3MB, time=320.28 x[1] = 0.3307 1.075 h = 0.0001 0.003 y2[1] (numeric) = 11.5014183949 12.9594663636 y2[1] (closed_form) = 13.8381025083 11.9742137139 absolute error = 2.536 relative error = 13.86 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.5470183465 -0.420281359725 y1[1] (closed_form) = 1.5470183465 -0.420281359725 absolute error = 3.105e-63 relative error = 1.937e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.139 Order of pole (three term test) = 34.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.139 Order of pole (three term test) = 30.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27212.1MB, alloc=44.3MB, time=320.81 memory used=27258.9MB, alloc=44.3MB, time=321.37 memory used=27305.6MB, alloc=44.3MB, time=321.93 x[1] = 0.3308 1.078 h = 0.001 0.001 y2[1] (numeric) = 11.5036507563 13.0059874368 y2[1] (closed_form) = 13.8405208114 12.0088180911 absolute error = 2.541 relative error = 13.87 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.55064471041 -0.421999444826 y1[1] (closed_form) = 1.55064471041 -0.421999444826 absolute error = 3.105e-63 relative error = 1.932e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.152 Order of pole (three term test) = 34.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.152 Order of pole (three term test) = 30.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27351.7MB, alloc=44.3MB, time=322.47 memory used=27398.3MB, alloc=44.3MB, time=323.02 x[1] = 0.3318 1.079 h = 0.0001 0.004 y2[1] (numeric) = 11.5058929763 13.0525247911 y2[1] (closed_form) = 13.8524946847 12.0199462032 absolute error = 2.564 relative error = 13.98 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.5513405851 -0.423762334605 y1[1] (closed_form) = 1.5513405851 -0.423762334605 absolute error = 3.132e-63 relative error = 1.948e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.157 Order of pole (three term test) = 34.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.157 Order of pole (three term test) = 30.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27444.2MB, alloc=44.3MB, time=323.56 memory used=27490.6MB, alloc=44.3MB, time=324.10 x[1] = 0.3319 1.083 h = 0.003 0.006 y2[1] (numeric) = 11.5081451355 13.0990784593 y2[1] (closed_form) = 13.8553496391 12.0661188251 absolute error = 2.564 relative error = 13.96 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.55621916659 -0.426027323161 y1[1] (closed_form) = 1.55621916659 -0.426027323161 absolute error = 3.132e-63 relative error = 1.941e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.174 Order of pole (three term test) = 34.27 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.174 Order of pole (three term test) = 30.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27536.4MB, alloc=44.3MB, time=324.63 memory used=27583.0MB, alloc=44.3MB, time=325.19 x[1] = 0.3349 1.089 h = 0.0001 0.005 y2[1] (numeric) = 11.5104073145 13.1456484741 y2[1] (closed_form) = 13.8926040324 12.1341850843 absolute error = 2.588 relative error = 14.03 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.5620401556 -0.432987606916 y1[1] (closed_form) = 1.5620401556 -0.432987606916 absolute error = 3.132e-63 relative error = 1.932e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.201 Order of pole (three term test) = 34.28 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.201 Order of pole (three term test) = 30.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27629.0MB, alloc=44.3MB, time=325.72 memory used=27675.7MB, alloc=44.3MB, time=326.28 x[1] = 0.335 1.094 h = 0.0001 0.003 y2[1] (numeric) = 11.5126795949 13.1922348676 y2[1] (closed_form) = 13.8959325999 12.1919672926 absolute error = 2.585 relative error = 13.98 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.56822604706 -0.435836249668 y1[1] (closed_form) = 1.56822604706 -0.435836249668 absolute error = 3.132e-63 relative error = 1.924e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.223 Order of pole (three term test) = 34.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.223 Order of pole (three term test) = 30.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27722.2MB, alloc=44.3MB, time=326.82 memory used=27768.5MB, alloc=44.3MB, time=327.38 memory used=27815.2MB, alloc=44.3MB, time=327.94 x[1] = 0.3351 1.097 h = 0.001 0.001 y2[1] (numeric) = 11.5149620587 13.2388376717 y2[1] (closed_form) = 13.8983997634 12.2266338578 absolute error = 2.589 relative error = 13.99 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.57193427948 -0.437601676763 y1[1] (closed_form) = 1.57193427948 -0.437601676763 absolute error = 4.100e-63 relative error = 2.513e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.237 Order of pole (three term test) = 34.31 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.237 Order of pole (three term test) = 30.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27861.1MB, alloc=44.3MB, time=328.48 memory used=27907.6MB, alloc=44.3MB, time=329.04 x[1] = 0.3361 1.098 h = 0.001 0.003 y2[1] (numeric) = 11.5172547885 13.2854569181 y2[1] (closed_form) = 13.9104105564 12.2377676423 absolute error = 2.612 relative error = 14.1 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.57264307537 -0.439407282554 y1[1] (closed_form) = 1.57264307537 -0.439407282554 absolute error = 4.079e-63 relative error = 2.498e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.241 Order of pole (three term test) = 34.31 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.241 Order of pole (three term test) = 30.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27953.5MB, alloc=44.3MB, time=329.57 memory used=28000.2MB, alloc=44.3MB, time=330.14 x[1] = 0.3371 1.101 h = 0.0001 0.004 y2[1] (numeric) = 11.5195578674 13.332092638 y2[1] (closed_form) = 13.9233074004 12.2720495499 absolute error = 2.627 relative error = 14.15 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.57587194149 -0.44231976453 y1[1] (closed_form) = 1.57587194149 -0.44231976453 absolute error = 3.105e-63 relative error = 1.897e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.255 Order of pole (three term test) = 34.32 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.255 Order of pole (three term test) = 30.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28046.1MB, alloc=44.3MB, time=330.68 memory used=28092.6MB, alloc=44.3MB, time=331.25 x[1] = 0.3372 1.105 h = 0.003 0.006 y2[1] (numeric) = 11.5218713793 13.3787448624 y2[1] (closed_form) = 13.9262391932 12.3183186913 absolute error = 2.628 relative error = 14.13 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.58087734412 -0.444659372678 y1[1] (closed_form) = 1.58087734412 -0.444659372678 absolute error = 4.100e-63 relative error = 2.497e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.273 Order of pole (three term test) = 34.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.273 Order of pole (three term test) = 30.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28138.4MB, alloc=44.3MB, time=331.80 memory used=28185.1MB, alloc=44.3MB, time=332.37 x[1] = 0.3402 1.111 h = 0.0001 0.005 y2[1] (numeric) = 11.5241954084 13.4254136218 y2[1] (closed_form) = 13.9636801757 12.3864771154 absolute error = 2.652 relative error = 14.21 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.58683786057 -0.451824290492 y1[1] (closed_form) = 1.58683786057 -0.451824290492 absolute error = 4.079e-63 relative error = 2.472e-61 % Correct digits = 63 memory used=28231.8MB, alloc=44.3MB, time=332.94 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.301 Order of pole (three term test) = 34.34 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.301 Order of pole (three term test) = 30.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28277.9MB, alloc=44.3MB, time=333.50 memory used=28324.8MB, alloc=44.3MB, time=334.07 x[1] = 0.3403 1.116 h = 0.0001 0.003 y2[1] (numeric) = 11.5265300398 13.4720989467 y2[1] (closed_form) = 13.9671056488 12.4443818235 absolute error = 2.648 relative error = 14.16 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.59318370566 -0.454766791343 y1[1] (closed_form) = 1.59318370566 -0.454766791343 absolute error = 3.132e-63 relative error = 1.890e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.324 Order of pole (three term test) = 34.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.324 Order of pole (three term test) = 30.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28370.9MB, alloc=44.3MB, time=334.64 memory used=28417.6MB, alloc=44.3MB, time=335.23 x[1] = 0.3404 1.119 h = 0.001 0.001 y2[1] (numeric) = 11.5288753589 13.5188008668 y2[1] (closed_form) = 13.9696321913 12.4791215089 absolute error = 2.653 relative error = 14.16 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.59698747101 -0.456590071714 y1[1] (closed_form) = 1.59698747101 -0.456590071714 absolute error = 4.100e-63 relative error = 2.468e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.338 Order of pole (three term test) = 34.37 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.338 Order of pole (three term test) = 30.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28463.6MB, alloc=44.3MB, time=335.81 memory used=28510.1MB, alloc=44.3MB, time=336.39 x[1] = 0.3414 1.12 h = 0.001 0.003 y2[1] (numeric) = 11.5312314519 13.5655194119 y2[1] (closed_form) = 13.9816870583 12.49026134 absolute error = 2.676 relative error = 14.27 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.59771050312 -0.458446422643 y1[1] (closed_form) = 1.59771050312 -0.458446422643 absolute error = 3.132e-63 relative error = 1.884e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.343 Order of pole (three term test) = 34.37 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.343 Order of pole (three term test) = 30.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28555.9MB, alloc=44.3MB, time=336.97 memory used=28602.6MB, alloc=44.3MB, time=337.56 x[1] = 0.3424 1.123 h = 0.0001 0.004 y2[1] (numeric) = 11.5335984055 13.6122546113 y2[1] (closed_form) = 13.9946662579 12.5245994859 absolute error = 2.691 relative error = 14.33 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.60101861699 -0.461446379376 y1[1] (closed_form) = 1.60101861699 -0.461446379376 absolute error = 3.132e-63 relative error = 1.880e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.357 Order of pole (three term test) = 34.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.357 Order of pole (three term test) = 30.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28648.7MB, alloc=44.3MB, time=338.12 memory used=28695.1MB, alloc=44.3MB, time=338.71 memory used=28741.5MB, alloc=44.3MB, time=339.30 x[1] = 0.3425 1.127 h = 0.003 0.006 y2[1] (numeric) = 11.5359763071 13.6590064938 y2[1] (closed_form) = 13.9976772318 12.5709675545 absolute error = 2.691 relative error = 14.31 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.60615257722 -0.463862841145 y1[1] (closed_form) = 1.60615257722 -0.463862841145 absolute error = 3.132e-63 relative error = 1.873e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.376 Order of pole (three term test) = 34.4 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.376 Order of pole (three term test) = 30.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28787.4MB, alloc=44.3MB, time=339.86 memory used=28834.0MB, alloc=44.3MB, time=340.45 x[1] = 0.3455 1.133 h = 0.0001 0.005 y2[1] (numeric) = 11.5383652444 13.7057750881 y2[1] (closed_form) = 14.0353100989 12.6392201277 absolute error = 2.715 relative error = 14.38 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.61225366766 -0.471237049766 y1[1] (closed_form) = 1.61225366766 -0.471237049766 absolute error = 3.132e-63 relative error = 1.865e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.405 Order of pole (three term test) = 34.41 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.405 Order of pole (three term test) = 30.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28880.0MB, alloc=44.3MB, time=341.03 memory used=28926.7MB, alloc=44.3MB, time=341.62 x[1] = 0.3456 1.138 h = 0.0001 0.003 y2[1] (numeric) = 11.5407653061 13.7525604225 y2[1] (closed_form) = 14.038835427 12.6972503739 absolute error = 2.712 relative error = 14.33 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.61876167334 -0.474276230234 y1[1] (closed_form) = 1.61876167334 -0.474276230234 absolute error = 3.132e-63 relative error = 1.857e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.43 Order of pole (three term test) = 34.43 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.43 Order of pole (three term test) = 30.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28972.7MB, alloc=44.3MB, time=342.18 memory used=29019.5MB, alloc=44.3MB, time=342.77 x[1] = 0.3457 1.141 h = 0.001 0.001 y2[1] (numeric) = 11.5431765813 13.7993625249 y2[1] (closed_form) = 14.0414231497 12.7320649845 absolute error = 2.717 relative error = 14.33 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.62266228062 -0.476159082261 y1[1] (closed_form) = 1.62266228062 -0.476159082261 absolute error = 3.132e-63 relative error = 1.852e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.444 Order of pole (three term test) = 34.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.444 Order of pole (three term test) = 30.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29065.5MB, alloc=44.3MB, time=343.34 memory used=29111.9MB, alloc=44.3MB, time=343.92 x[1] = 0.3467 1.142 h = 0.001 0.003 y2[1] (numeric) = 11.5455991597 13.8461814228 y2[1] (closed_form) = 14.0535232935 12.7432109026 absolute error = 2.74 relative error = 14.44 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.62339944566 -0.478067193304 y1[1] (closed_form) = 1.62339944566 -0.478067193304 absolute error = 3.132e-63 relative error = 1.851e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.449 Order of pole (three term test) = 34.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.449 Order of pole (three term test) = 30.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29158.2MB, alloc=44.3MB, time=344.48 memory used=29204.6MB, alloc=44.3MB, time=345.04 memory used=29251.4MB, alloc=44.3MB, time=345.63 x[1] = 0.3477 1.145 h = 0.0001 0.004 y2[1] (numeric) = 11.5480331317 13.8930171434 y2[1] (closed_form) = 14.0665872187 12.7776065698 absolute error = 2.754 relative error = 14.49 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.6267876159 -0.481156764054 y1[1] (closed_form) = 1.6267876159 -0.481156764054 absolute error = 2.236e-63 relative error = 1.318e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.464 Order of pole (three term test) = 34.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.464 Order of pole (three term test) = 30.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29297.3MB, alloc=44.3MB, time=346.17 memory used=29343.7MB, alloc=44.3MB, time=346.73 x[1] = 0.3478 1.149 h = 0.003 0.006 y2[1] (numeric) = 11.5504785882 13.9398697138 y2[1] (closed_form) = 14.0696797758 12.8240759999 absolute error = 2.755 relative error = 14.47 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.63205191084 -0.483652378496 y1[1] (closed_form) = 1.63205191084 -0.483652378496 absolute error = 3.162e-63 relative error = 1.858e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.484 Order of pole (three term test) = 34.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.484 Order of pole (three term test) = 30.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29389.7MB, alloc=44.3MB, time=347.27 memory used=29436.5MB, alloc=44.3MB, time=347.83 x[1] = 0.3508 1.155 h = 0.0001 0.005 y2[1] (numeric) = 11.5529356209 13.9867391603 y2[1] (closed_form) = 14.1075099321 12.8924247047 absolute error = 2.779 relative error = 14.54 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.63829463711 -0.491240662874 y1[1] (closed_form) = 1.63829463711 -0.491240662874 absolute error = 3.162e-63 relative error = 1.849e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.515 Order of pole (three term test) = 34.48 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.515 Order of pole (three term test) = 30.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29482.5MB, alloc=44.3MB, time=348.38 memory used=29529.2MB, alloc=44.3MB, time=348.94 x[1] = 0.3509 1.16 h = 0.0001 0.003 y2[1] (numeric) = 11.5554043218 14.0336255091 y2[1] (closed_form) = 14.1111381392 12.9505835612 absolute error = 2.776 relative error = 14.49 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.64496706174 -0.494379426373 y1[1] (closed_form) = 1.64496706174 -0.494379426373 absolute error = 2.236e-63 relative error = 1.302e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.54 Order of pole (three term test) = 34.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.54 Order of pole (three term test) = 30.58 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29575.3MB, alloc=44.3MB, time=349.48 memory used=29622.1MB, alloc=44.3MB, time=350.05 x[1] = 0.351 1.163 h = 0.001 0.001 y2[1] (numeric) = 11.5578847839 14.0805287861 y2[1] (closed_form) = 14.113788889 12.9854749218 absolute error = 2.781 relative error = 14.5 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.64896585022 -0.496323618183 y1[1] (closed_form) = 1.64896585022 -0.496323618183 absolute error = 2.193e-63 relative error = 1.274e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.555 Order of pole (three term test) = 34.51 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.555 Order of pole (three term test) = 30.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29668.8MB, alloc=44.3MB, time=350.61 memory used=29714.9MB, alloc=44.3MB, time=351.17 memory used=29761.2MB, alloc=44.3MB, time=351.73 x[1] = 0.352 1.164 h = 0.001 0.003 y2[1] (numeric) = 11.5603771005 14.1274490166 y2[1] (closed_form) = 14.1259355343 12.9966269595 absolute error = 2.804 relative error = 14.61 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.64971703927 -0.49828453121 y1[1] (closed_form) = 1.64971703927 -0.49828453121 absolute error = 2.236e-63 relative error = 1.298e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.561 Order of pole (three term test) = 34.51 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.561 Order of pole (three term test) = 30.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29807.1MB, alloc=44.3MB, time=352.28 memory used=29853.8MB, alloc=44.3MB, time=352.84 x[1] = 0.353 1.167 h = 0.0001 0.004 y2[1] (numeric) = 11.5628813658 14.1743862258 y2[1] (closed_form) = 14.1390866072 13.0310814376 absolute error = 2.819 relative error = 14.66 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.65318609007 -0.501465914766 y1[1] (closed_form) = 1.65318609007 -0.501465914766 absolute error = 3.162e-63 relative error = 1.830e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.576 Order of pole (three term test) = 34.52 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.576 Order of pole (three term test) = 30.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29899.7MB, alloc=44.3MB, time=353.38 memory used=29946.2MB, alloc=44.3MB, time=353.94 x[1] = 0.3531 1.171 h = 0.003 0.006 y2[1] (numeric) = 11.5653976744 14.2213404384 y2[1] (closed_form) = 14.1422632102 13.0776546908 absolute error = 2.819 relative error = 14.64 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.65858253782 -0.504043047413 y1[1] (closed_form) = 1.65858253782 -0.504043047413 absolute error = 2.193e-63 relative error = 1.265e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.597 Order of pole (three term test) = 34.54 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.597 Order of pole (three term test) = 30.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29992.0MB, alloc=44.3MB, time=354.49 memory used=30038.5MB, alloc=44.3MB, time=355.06 x[1] = 0.3561 1.177 h = 0.0001 0.005 y2[1] (numeric) = 11.5679261217 14.2683116788 y2[1] (closed_form) = 14.1802961727 13.1461015074 absolute error = 2.843 relative error = 14.7 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.6649679764 -0.511850323136 y1[1] (closed_form) = 1.6649679764 -0.511850323136 absolute error = 2.236e-63 relative error = 1.284e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.629 Order of pole (three term test) = 34.55 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.629 Order of pole (three term test) = 30.54 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30084.7MB, alloc=44.3MB, time=355.60 memory used=30131.0MB, alloc=44.3MB, time=356.16 memory used=30177.6MB, alloc=44.3MB, time=356.73 x[1] = 0.3562 1.182 h = 0.0001 0.003 y2[1] (numeric) = 11.5704668036 14.3152999709 y2[1] (closed_form) = 14.18403036 13.204392081 absolute error = 2.84 relative error = 14.65 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.67180713007 -0.515091656827 y1[1] (closed_form) = 1.67180713007 -0.515091656827 absolute error = 2.236e-63 relative error = 1.278e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.655 Order of pole (three term test) = 34.57 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.655 Order of pole (three term test) = 30.52 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30223.7MB, alloc=44.3MB, time=357.28 memory used=30270.6MB, alloc=44.3MB, time=357.86 x[1] = 0.3563 1.185 h = 0.001 0.001 y2[1] (numeric) = 11.5730198167 14.3623053383 y2[1] (closed_form) = 14.1867460301 13.2393620367 absolute error = 2.845 relative error = 14.66 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.67590546946 -0.51709900741 y1[1] (closed_form) = 1.67590546946 -0.51709900741 absolute error = 2.283e-63 relative error = 1.301e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.671 Order of pole (three term test) = 34.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.671 Order of pole (three term test) = 30.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30316.7MB, alloc=44.3MB, time=358.41 memory used=30363.4MB, alloc=44.3MB, time=358.97 x[1] = 0.3573 1.186 h = 0.0001 0.004 y2[1] (numeric) = 11.5755852582 14.4093278043 y2[1] (closed_form) = 14.1989404243 13.2505202187 absolute error = 2.868 relative error = 14.77 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.67667056769 -0.519113791637 y1[1] (closed_form) = 1.67667056769 -0.519113791637 absolute error = 2.283e-63 relative error = 1.300e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.677 Order of pole (three term test) = 34.59 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.677 Order of pole (three term test) = 30.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30409.5MB, alloc=44.3MB, time=359.52 memory used=30456.0MB, alloc=44.3MB, time=360.08 x[1] = 0.3574 1.19 h = 0.003 0.006 y2[1] (numeric) = 11.5781632261 14.4563673918 y2[1] (closed_form) = 14.202190114 13.2971858739 absolute error = 2.869 relative error = 14.74 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.68218326618 -0.521761434123 y1[1] (closed_form) = 1.68218326618 -0.521761434123 absolute error = 2.283e-63 relative error = 1.296e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.698 Order of pole (three term test) = 34.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.698 Order of pole (three term test) = 30.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30501.8MB, alloc=44.3MB, time=360.62 memory used=30548.4MB, alloc=44.3MB, time=361.19 x[1] = 0.3604 1.196 h = 0.0001 0.005 y2[1] (numeric) = 11.5807538188 14.5034241232 y2[1] (closed_form) = 14.2404009504 13.365721233 absolute error = 2.893 relative error = 14.81 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.68869511025 -0.529759530445 y1[1] (closed_form) = 1.68869511025 -0.529759530445 absolute error = 2.283e-63 relative error = 1.290e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.731 Order of pole (three term test) = 34.62 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.731 Order of pole (three term test) = 30.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30594.9MB, alloc=44.3MB, time=361.74 memory used=30641.1MB, alloc=44.3MB, time=362.30 memory used=30687.7MB, alloc=44.3MB, time=362.86 x[1] = 0.3605 1.201 h = 0.0001 0.003 y2[1] (numeric) = 11.5833571356 14.5504980206 y2[1] (closed_form) = 14.2442272854 13.4241290134 absolute error = 2.889 relative error = 14.76 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.69568094018 -0.53308958603 y1[1] (closed_form) = 1.69568094018 -0.53308958603 absolute error = 2.332e-63 relative error = 1.312e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.758 Order of pole (three term test) = 34.64 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.758 Order of pole (three term test) = 30.46 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30733.8MB, alloc=44.3MB, time=363.40 memory used=30780.6MB, alloc=44.3MB, time=363.98 x[1] = 0.3606 1.204 h = 0.001 0.001 y2[1] (numeric) = 11.5859732762 14.5975891058 y2[1] (closed_form) = 14.246999423 13.4591689194 absolute error = 2.894 relative error = 14.77 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.69986687271 -0.535151589235 y1[1] (closed_form) = 1.69986687271 -0.535151589235 absolute error = 2.332e-63 relative error = 1.309e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.775 Order of pole (three term test) = 34.65 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.775 Order of pole (three term test) = 30.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30826.6MB, alloc=44.3MB, time=364.53 memory used=30872.9MB, alloc=44.3MB, time=365.10 x[1] = 0.3616 1.205 h = 0.001 0.003 y2[1] (numeric) = 11.5886023412 14.6446974001 y2[1] (closed_form) = 14.259235861 13.4703329929 absolute error = 2.917 relative error = 14.87 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.70064450637 -0.537213457703 y1[1] (closed_form) = 1.70064450637 -0.537213457703 absolute error = 2.332e-63 relative error = 1.308e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.781 Order of pole (three term test) = 34.65 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.781 Order of pole (three term test) = 30.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30918.8MB, alloc=44.3MB, time=365.65 memory used=30965.4MB, alloc=44.3MB, time=366.22 x[1] = 0.3626 1.208 h = 0.0001 0.004 y2[1] (numeric) = 11.5912444316 14.6918229243 y2[1] (closed_form) = 14.2725549888 13.5049014674 absolute error = 2.932 relative error = 14.92 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.7042674619 -0.540570757159 y1[1] (closed_form) = 1.7042674619 -0.540570757159 absolute error = 2.332e-63 relative error = 1.305e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.798 Order of pole (three term test) = 34.66 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.798 Order of pole (three term test) = 30.44 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31011.3MB, alloc=44.3MB, time=366.77 memory used=31057.9MB, alloc=44.3MB, time=367.34 x[1] = 0.3627 1.212 h = 0.003 0.006 y2[1] (numeric) = 11.5938996493 14.7389656992 y2[1] (closed_form) = 14.2758934449 13.5516756313 absolute error = 2.933 relative error = 14.9 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.70991583633 -0.543304478862 y1[1] (closed_form) = 1.70991583633 -0.543304478862 absolute error = 2.283e-63 relative error = 1.272e-61 % Correct digits = 63 memory used=31104.5MB, alloc=44.3MB, time=367.91 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.82 Order of pole (three term test) = 34.68 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.82 Order of pole (three term test) = 30.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31150.4MB, alloc=44.3MB, time=368.46 memory used=31197.0MB, alloc=44.3MB, time=369.03 x[1] = 0.3657 1.218 h = 0.0001 0.005 y2[1] (numeric) = 11.5965680968 14.7861257447 y2[1] (closed_form) = 14.3143176391 13.6203128489 absolute error = 2.957 relative error = 14.97 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.71657249485 -0.551531056354 y1[1] (closed_form) = 1.71657249485 -0.551531056354 absolute error = 2.283e-63 relative error = 1.266e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.855 Order of pole (three term test) = 34.69 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.855 Order of pole (three term test) = 30.42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31242.9MB, alloc=44.3MB, time=369.59 memory used=31289.6MB, alloc=44.3MB, time=370.16 x[1] = 0.3658 1.223 h = 0.0001 0.003 y2[1] (numeric) = 11.599249877 14.8333030808 y2[1] (closed_form) = 14.3182558986 13.6788582614 absolute error = 2.954 relative error = 14.92 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.72372952933 -0.554969440997 y1[1] (closed_form) = 1.72372952933 -0.554969440997 absolute error = 1.487e-63 relative error = 8.209e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.883 Order of pole (three term test) = 34.72 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.883 Order of pole (three term test) = 30.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31335.6MB, alloc=44.3MB, time=370.73 memory used=31382.5MB, alloc=44.3MB, time=371.31 x[1] = 0.3659 1.226 h = 0.001 0.001 y2[1] (numeric) = 11.601945094 14.8804977266 y2[1] (closed_form) = 14.3210965857 13.713980275 absolute error = 2.959 relative error = 14.92 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.7280176664 -0.557098109841 y1[1] (closed_form) = 1.7280176664 -0.557098109841 absolute error = 2.283e-63 relative error = 1.257e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.901 Order of pole (three term test) = 34.73 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.901 Order of pole (three term test) = 30.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31428.6MB, alloc=44.3MB, time=371.88 memory used=31475.1MB, alloc=44.3MB, time=372.46 x[1] = 0.3669 1.227 h = 0.001 0.003 y2[1] (numeric) = 11.604653852 14.9277097013 y2[1] (closed_form) = 14.3333831558 13.7251505317 absolute error = 2.982 relative error = 15.03 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.72880899229 -0.559215914983 y1[1] (closed_form) = 1.72880899229 -0.559215914983 absolute error = 1.414e-63 relative error = 7.783e-62 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.907 Order of pole (three term test) = 34.73 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.907 Order of pole (three term test) = 30.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31521.0MB, alloc=44.3MB, time=373.02 memory used=31567.5MB, alloc=44.3MB, time=373.59 memory used=31614.0MB, alloc=44.3MB, time=374.17 x[1] = 0.3679 1.23 h = 0.0001 0.004 y2[1] (numeric) = 11.6073762562 14.9749390233 y2[1] (closed_form) = 14.3467966447 13.759781573 absolute error = 2.997 relative error = 15.08 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.7325152998 -0.56267164658 y1[1] (closed_form) = 1.7325152998 -0.56267164658 absolute error = 2.283e-63 relative error = 1.253e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.924 Order of pole (three term test) = 34.74 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.924 Order of pole (three term test) = 30.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31659.9MB, alloc=44.3MB, time=374.73 memory used=31706.3MB, alloc=44.3MB, time=375.30 x[1] = 0.368 1.234 h = 0.003 0.006 y2[1] (numeric) = 11.6101124125 15.0221857108 y2[1] (closed_form) = 14.3502265132 13.8066667889 absolute error = 2.998 relative error = 15.05 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.73830128785 -0.565494011167 y1[1] (closed_form) = 1.73830128785 -0.565494011167 absolute error = 2.283e-63 relative error = 1.249e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.948 Order of pole (three term test) = 34.76 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.948 Order of pole (three term test) = 30.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31752.2MB, alloc=44.3MB, time=375.86 memory used=31798.8MB, alloc=44.3MB, time=376.44 x[1] = 0.371 1.24 h = 0.0001 0.005 y2[1] (numeric) = 11.6128624273 15.0694497815 y2[1] (closed_form) = 14.3888699204 13.8754078381 absolute error = 3.022 relative error = 15.12 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.74510387715 -0.573954372964 y1[1] (closed_form) = 1.74510387715 -0.573954372964 absolute error = 2.283e-63 relative error = 1.242e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.984 Order of pole (three term test) = 34.77 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 2.984 Order of pole (three term test) = 30.35 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31844.6MB, alloc=44.3MB, time=377.00 memory used=31891.3MB, alloc=44.3MB, time=377.58 x[1] = 0.3711 1.245 h = 0.0001 0.003 y2[1] (numeric) = 11.6156264078 15.1167312528 y2[1] (closed_form) = 14.392923437 13.9340940934 absolute error = 3.019 relative error = 15.07 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.75243457734 -0.577504323451 y1[1] (closed_form) = 1.75243457734 -0.577504323451 absolute error = 2.283e-63 relative error = 1.237e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.014 Order of pole (three term test) = 34.8 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.014 Order of pole (three term test) = 30.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31937.4MB, alloc=44.3MB, time=378.16 memory used=31984.4MB, alloc=44.3MB, time=378.74 x[1] = 0.3712 1.248 h = 0.001 0.001 y2[1] (numeric) = 11.6184044618 15.1640301415 y2[1] (closed_form) = 14.3958347073 13.9693001208 absolute error = 3.023 relative error = 15.07 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.75682637758 -0.579701628512 y1[1] (closed_form) = 1.75682637758 -0.579701628512 absolute error = 2.283e-63 relative error = 1.234e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.032 Order of pole (three term test) = 34.81 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.032 Order of pole (three term test) = 30.32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32030.8MB, alloc=44.3MB, time=379.32 memory used=32076.9MB, alloc=44.3MB, time=379.89 memory used=32123.3MB, alloc=44.3MB, time=380.46 x[1] = 0.3722 1.249 h = 0.001 0.003 y2[1] (numeric) = 11.6211966978 15.2113464642 y2[1] (closed_form) = 14.408172725 13.9804765609 absolute error = 3.047 relative error = 15.18 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.75763126256 -0.581876520435 y1[1] (closed_form) = 1.75763126256 -0.581876520435 absolute error = 2.283e-63 relative error = 1.233e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.038 Order of pole (three term test) = 34.81 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.038 Order of pole (three term test) = 30.32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32169.3MB, alloc=44.3MB, time=381.03 memory used=32216.1MB, alloc=44.3MB, time=381.60 x[1] = 0.3732 1.252 h = 0.0001 0.004 y2[1] (numeric) = 11.6240032251 15.258680237 y2[1] (closed_form) = 14.4216832113 14.0151714843 absolute error = 3.062 relative error = 15.22 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.76142180591 -0.585433124095 y1[1] (closed_form) = 1.76142180591 -0.585433124095 absolute error = 3.195e-63 relative error = 1.721e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.056 Order of pole (three term test) = 34.82 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.056 Order of pole (three term test) = 30.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32262.0MB, alloc=44.3MB, time=382.16 memory used=32308.4MB, alloc=44.3MB, time=382.74 x[1] = 0.3733 1.256 h = 0.003 0.006 y2[1] (numeric) = 11.6268241537 15.3060314755 y2[1] (closed_form) = 14.4252072057 14.0621703245 absolute error = 3.062 relative error = 15.2 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.76734738731 -0.588346767742 y1[1] (closed_form) = 1.76734738731 -0.588346767742 absolute error = 2.283e-63 relative error = 1.225e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.081 Order of pole (three term test) = 34.84 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.081 Order of pole (three term test) = 30.29 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32354.2MB, alloc=44.3MB, time=383.29 memory used=32400.8MB, alloc=44.3MB, time=383.86 x[1] = 0.3763 1.262 h = 0.0001 0.005 y2[1] (numeric) = 11.629659594 15.353400195 y2[1] (closed_form) = 14.4640758052 14.1310171748 absolute error = 3.087 relative error = 15.27 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.77429703575 -0.597046357601 y1[1] (closed_form) = 1.77429703575 -0.597046357601 absolute error = 3.195e-63 relative error = 1.707e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.118 Order of pole (three term test) = 34.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.118 Order of pole (three term test) = 30.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32446.9MB, alloc=44.3MB, time=384.42 memory used=32493.4MB, alloc=44.3MB, time=385.16 memory used=32540.0MB, alloc=44.3MB, time=386.22 x[1] = 0.3764 1.267 h = 0.0001 0.003 y2[1] (numeric) = 11.6325096575 15.4007864102 y2[1] (closed_form) = 14.4682479968 14.1898475212 absolute error = 3.083 relative error = 15.22 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.78180391598 -0.600711202083 y1[1] (closed_form) = 1.78180391598 -0.600711202083 absolute error = 3.195e-63 relative error = 1.699e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.15 Order of pole (three term test) = 34.88 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.15 Order of pole (three term test) = 30.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32586.1MB, alloc=44.3MB, time=387.24 memory used=32633.0MB, alloc=44.3MB, time=388.32 x[1] = 0.3765 1.27 h = 0.001 0.001 y2[1] (numeric) = 11.635374456 15.4481901355 y2[1] (closed_form) = 14.4712319358 14.22513949 absolute error = 3.088 relative error = 15.22 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.78630086924 -0.602979169409 y1[1] (closed_form) = 1.78630086924 -0.602979169409 absolute error = 3.195e-63 relative error = 1.695e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.169 Order of pole (three term test) = 34.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.169 Order of pole (three term test) = 30.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32679.0MB, alloc=44.3MB, time=389.35 memory used=32725.3MB, alloc=44.3MB, time=390.41 x[1] = 0.3775 1.271 h = 0.001 0.003 y2[1] (numeric) = 11.6382541023 15.495611385 y2[1] (closed_form) = 14.4836227414 14.2363221047 absolute error = 3.112 relative error = 15.32 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.78711917307 -0.605212327408 y1[1] (closed_form) = 1.78711917307 -0.605212327408 absolute error = 4.148e-63 relative error = 2.199e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.175 Order of pole (three term test) = 34.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.175 Order of pole (three term test) = 30.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32771.2MB, alloc=44.3MB, time=391.43 memory used=32818.0MB, alloc=44.3MB, time=392.50 x[1] = 0.3785 1.274 h = 0.0001 0.004 y2[1] (numeric) = 11.6411487099 15.5430501721 y2[1] (closed_form) = 14.4972329206 14.271082232 absolute error = 3.127 relative error = 15.37 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.79099485099 -0.608872308692 y1[1] (closed_form) = 1.79099485099 -0.608872308692 absolute error = 4.148e-63 relative error = 2.193e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.194 Order of pole (three term test) = 34.91 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.194 Order of pole (three term test) = 30.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32863.9MB, alloc=44.3MB, time=393.04 memory used=32910.5MB, alloc=44.3MB, time=393.59 x[1] = 0.3786 1.278 h = 0.003 0.006 y2[1] (numeric) = 11.6440583928 15.5905065099 y2[1] (closed_form) = 14.500853824 14.3181972989 absolute error = 3.127 relative error = 15.35 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.79706204783 -0.611879941745 y1[1] (closed_form) = 1.79706204783 -0.611879941745 absolute error = 4.148e-63 relative error = 2.185e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.22 Order of pole (three term test) = 34.92 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.22 Order of pole (three term test) = 30.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32956.6MB, alloc=44.3MB, time=394.13 memory used=33002.9MB, alloc=44.3MB, time=394.68 memory used=33049.5MB, alloc=44.3MB, time=395.24 x[1] = 0.3816 1.284 h = 0.0001 0.005 y2[1] (numeric) = 11.6469832658 15.637980411 y2[1] (closed_form) = 14.5399537224 14.3871519154 absolute error = 3.152 relative error = 15.41 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.80415989502 -0.620824346788 y1[1] (closed_form) = 1.80415989502 -0.620824346788 absolute error = 4.123e-63 relative error = 2.161e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.259 Order of pole (three term test) = 34.94 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.259 Order of pole (three term test) = 30.21 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33095.5MB, alloc=44.3MB, time=395.78 memory used=33142.2MB, alloc=44.3MB, time=396.33 x[1] = 0.3817 1.289 h = 0.0001 0.003 y2[1] (numeric) = 11.6499234445 15.6854718877 y2[1] (closed_form) = 14.5442480947 14.446129639 absolute error = 3.149 relative error = 15.36 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.81184552312 -0.624607506889 y1[1] (closed_form) = 1.81184552312 -0.624607506889 absolute error = 4.148e-63 relative error = 2.165e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.292 Order of pole (three term test) = 34.97 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.292 Order of pole (three term test) = 30.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33188.3MB, alloc=44.3MB, time=396.88 memory used=33235.2MB, alloc=44.3MB, time=397.44 x[1] = 0.3818 1.292 h = 0.001 0.001 y2[1] (numeric) = 11.6528790451 15.7329809518 y2[1] (closed_form) = 14.5473068412 14.4815094993 absolute error = 3.153 relative error = 15.36 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.81644915075 -0.626948219266 y1[1] (closed_form) = 1.81644915075 -0.626948219266 absolute error = 5.099e-63 relative error = 2.654e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.312 Order of pole (three term test) = 34.98 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.312 Order of pole (three term test) = 30.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33281.3MB, alloc=44.3MB, time=397.98 memory used=33328.0MB, alloc=44.3MB, time=398.56 x[1] = 0.3828 1.293 h = 0.0001 0.004 y2[1] (numeric) = 11.6558501847 15.7805076145 y2[1] (closed_form) = 14.5597518005 14.4926982701 absolute error = 3.177 relative error = 15.46 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.8172807257 -0.629240852333 y1[1] (closed_form) = 1.8172807257 -0.629240852333 absolute error = 4.123e-63 relative error = 2.144e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.318 Order of pole (three term test) = 34.98 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.318 Order of pole (three term test) = 30.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33373.9MB, alloc=44.3MB, time=399.10 memory used=33420.4MB, alloc=44.3MB, time=399.64 x[1] = 0.3829 1.297 h = 0.003 0.006 y2[1] (numeric) = 11.6588369809 15.8280518866 y2[1] (closed_form) = 14.5634569756 14.5399166888 absolute error = 3.177 relative error = 15.44 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.82347263713 -0.632329896104 y1[1] (closed_form) = 1.82347263713 -0.632329896104 absolute error = 4.123e-63 relative error = 2.136e-61 % Correct digits = 63 memory used=33466.9MB, alloc=44.3MB, time=400.18 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.345 Order of pole (three term test) = 35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.345 Order of pole (three term test) = 30.16 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33513.0MB, alloc=44.3MB, time=400.72 memory used=33559.7MB, alloc=44.3MB, time=401.28 x[1] = 0.3859 1.303 h = 0.0001 0.005 y2[1] (numeric) = 11.661839552 15.8756137787 y2[1] (closed_form) = 14.6027596426 14.6089684936 absolute error = 3.202 relative error = 15.5 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.83070197896 -0.641487831439 y1[1] (closed_form) = 1.83070197896 -0.641487831439 absolute error = 4.123e-63 relative error = 2.125e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.386 Order of pole (three term test) = 35.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.386 Order of pole (three term test) = 30.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33605.6MB, alloc=44.3MB, time=401.81 memory used=33652.1MB, alloc=44.3MB, time=402.36 x[1] = 0.386 1.308 h = 0.0001 0.003 y2[1] (numeric) = 11.6648580174 15.9231933007 y2[1] (closed_form) = 14.6071602504 14.6680772494 absolute error = 3.199 relative error = 15.45 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.83854503131 -0.645373474713 y1[1] (closed_form) = 1.83854503131 -0.645373474713 absolute error = 4.123e-63 relative error = 2.116e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.42 Order of pole (three term test) = 35.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.42 Order of pole (three term test) = 30.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33698.1MB, alloc=44.3MB, time=402.90 memory used=33744.9MB, alloc=44.3MB, time=403.46 x[1] = 0.3861 1.311 h = 0.001 0.001 y2[1] (numeric) = 11.6678924967 15.9707904621 y2[1] (closed_form) = 14.6102840639 14.7035352694 absolute error = 3.204 relative error = 15.46 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.84324262448 -0.647777219775 y1[1] (closed_form) = 1.84324262448 -0.647777219775 absolute error = 4.123e-63 relative error = 2.110e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.44 Order of pole (three term test) = 35.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.44 Order of pole (three term test) = 30.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33791.0MB, alloc=44.3MB, time=404.00 memory used=33837.5MB, alloc=44.3MB, time=404.56 x[1] = 0.3871 1.312 h = 0.001 0.003 y2[1] (numeric) = 11.6709431107 16.0184052719 y2[1] (closed_form) = 14.6227766777 14.7147299847 absolute error = 3.227 relative error = 15.56 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.84408622712 -0.650121882632 y1[1] (closed_form) = 1.84408622712 -0.650121882632 absolute error = 5.099e-63 relative error = 2.608e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.447 Order of pole (three term test) = 35.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.447 Order of pole (three term test) = 30.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33883.4MB, alloc=44.3MB, time=405.09 memory used=33930.1MB, alloc=44.3MB, time=405.63 memory used=33976.5MB, alloc=44.3MB, time=406.18 x[1] = 0.3881 1.315 h = 0.0001 0.004 y2[1] (numeric) = 11.6740099807 16.0660377386 y2[1] (closed_form) = 14.6365789308 14.7496162478 absolute error = 3.242 relative error = 15.6 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.8481240679 -0.65398008457 y1[1] (closed_form) = 1.8481240679 -0.65398008457 absolute error = 5.099e-63 relative error = 2.601e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.468 Order of pole (three term test) = 35.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.468 Order of pole (three term test) = 30.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34022.5MB, alloc=44.3MB, time=406.72 memory used=34069.2MB, alloc=44.3MB, time=407.27 x[1] = 0.3882 1.319 h = 0.003 0.006 y2[1] (numeric) = 11.6770932288 16.1136878704 y2[1] (closed_form) = 14.6403863527 14.7969558519 absolute error = 3.243 relative error = 15.58 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.85446150561 -0.657168339072 y1[1] (closed_form) = 1.85446150561 -0.657168339072 absolute error = 5.080e-63 relative error = 2.582e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.496 Order of pole (three term test) = 35.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.496 Order of pole (three term test) = 30.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34115.1MB, alloc=44.3MB, time=407.80 memory used=34161.8MB, alloc=44.3MB, time=408.35 x[1] = 0.3912 1.325 h = 0.0001 0.005 y2[1] (numeric) = 11.6801929779 16.161355675 y2[1] (closed_form) = 14.6799320085 14.8661191429 absolute error = 3.267 relative error = 15.64 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.86184126469 -0.666581863328 y1[1] (closed_form) = 1.86184126469 -0.666581863328 absolute error = 4.123e-63 relative error = 2.085e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.538 Order of pole (three term test) = 35.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.538 Order of pole (three term test) = 30.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34207.8MB, alloc=44.3MB, time=408.89 memory used=34254.4MB, alloc=44.3MB, time=409.45 x[1] = 0.3913 1.33 h = 0.0001 0.003 y2[1] (numeric) = 11.6833093514 16.2090411594 y2[1] (closed_form) = 14.6844615216 14.9253815384 absolute error = 3.264 relative error = 15.59 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.86986803033 -0.670592413166 y1[1] (closed_form) = 1.86986803033 -0.670592413166 absolute error = 4.123e-63 relative error = 2.076e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.574 Order of pole (three term test) = 35.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.574 Order of pole (three term test) = 30.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34300.4MB, alloc=44.3MB, time=409.98 memory used=34347.2MB, alloc=44.3MB, time=410.54 x[1] = 0.3914 1.333 h = 0.001 0.001 y2[1] (numeric) = 11.6864424737 16.2567443305 y2[1] (closed_form) = 14.6876642448 14.960931166 absolute error = 3.269 relative error = 15.59 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.87467523962 -0.673072915352 y1[1] (closed_form) = 1.87467523962 -0.673072915352 absolute error = 4.123e-63 relative error = 2.070e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.596 Order of pole (three term test) = 35.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.596 Order of pole (three term test) = 30.04 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34393.6MB, alloc=44.3MB, time=411.09 memory used=34439.9MB, alloc=44.3MB, time=411.64 memory used=34486.4MB, alloc=44.3MB, time=412.19 x[1] = 0.3924 1.334 h = 0.001 0.003 y2[1] (numeric) = 11.6895924699 16.3044651943 y2[1] (closed_form) = 14.7002136243 14.9721319938 absolute error = 3.292 relative error = 15.69 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.87553183267 -0.675479385724 y1[1] (closed_form) = 1.87553183267 -0.675479385724 absolute error = 3.162e-63 relative error = 1.586e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.603 Order of pole (three term test) = 35.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.603 Order of pole (three term test) = 30.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34532.3MB, alloc=44.3MB, time=412.73 memory used=34578.8MB, alloc=44.3MB, time=413.28 x[1] = 0.3934 1.337 h = 0.0001 0.004 y2[1] (numeric) = 11.6927594658 16.3522037567 y2[1] (closed_form) = 14.7141236057 15.0070873125 absolute error = 3.307 relative error = 15.74 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.87965749225 -0.679448496513 y1[1] (closed_form) = 1.87965749225 -0.679448496513 absolute error = 4.123e-63 relative error = 2.063e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.625 Order of pole (three term test) = 35.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.625 Order of pole (three term test) = 30.04 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34624.6MB, alloc=44.3MB, time=413.81 memory used=34671.1MB, alloc=44.3MB, time=414.35 x[1] = 0.3935 1.341 h = 0.003 0.006 y2[1] (numeric) = 11.695943588 16.3999600228 y2[1] (closed_form) = 14.7180362661 15.0545507936 absolute error = 3.308 relative error = 15.71 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.88614260204 -0.682738893345 y1[1] (closed_form) = 1.88614260204 -0.682738893345 absolute error = 4.123e-63 relative error = 2.055e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.654 Order of pole (three term test) = 35.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.654 Order of pole (three term test) = 30.02 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34717.1MB, alloc=44.3MB, time=414.89 memory used=34763.7MB, alloc=44.3MB, time=415.44 x[1] = 0.3965 1.347 h = 0.0001 0.005 y2[1] (numeric) = 11.6991449638 16.4477339974 y2[1] (closed_form) = 14.7578313998 15.1238275224 absolute error = 3.333 relative error = 15.77 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.89367394757 -0.692414019454 y1[1] (closed_form) = 1.89367394757 -0.692414019454 absolute error = 4.123e-63 relative error = 2.045e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.698 Order of pole (three term test) = 35.2 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.698 Order of pole (three term test) = 30.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34809.6MB, alloc=44.3MB, time=415.97 memory used=34856.3MB, alloc=44.3MB, time=416.52 x[1] = 0.3966 1.352 h = 0.0001 0.003 y2[1] (numeric) = 11.7023637214 16.4955256849 y2[1] (closed_form) = 14.7624935874 15.1832469575 absolute error = 3.33 relative error = 15.72 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.90188715077 -0.696553176342 y1[1] (closed_form) = 1.90188715077 -0.696553176342 absolute error = 5.099e-63 relative error = 2.518e-61 % Correct digits = 63 memory used=34903.0MB, alloc=44.3MB, time=417.07 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.735 Order of pole (three term test) = 35.23 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.735 Order of pole (three term test) = 29.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34949.1MB, alloc=44.3MB, time=417.62 memory used=34995.9MB, alloc=44.3MB, time=418.18 x[1] = 0.3967 1.355 h = 0.001 0.001 y2[1] (numeric) = 11.7055999896 16.5433350889 y2[1] (closed_form) = 14.7657775188 15.2188902092 absolute error = 3.334 relative error = 15.73 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.9068055894 -0.699112687696 y1[1] (closed_form) = 1.9068055894 -0.699112687696 absolute error = 4.123e-63 relative error = 2.030e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.758 Order of pole (three term test) = 35.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.758 Order of pole (three term test) = 29.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35041.9MB, alloc=44.3MB, time=418.72 memory used=35088.6MB, alloc=44.3MB, time=419.27 x[1] = 0.3977 1.356 h = 0.001 0.003 y2[1] (numeric) = 11.7088538981 16.5911622128 y2[1] (closed_form) = 14.7783851064 15.2300971024 absolute error = 3.358 relative error = 15.82 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.90767500216 -0.701582262519 y1[1] (closed_form) = 1.90767500216 -0.701582262519 absolute error = 4.148e-63 relative error = 2.041e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.765 Order of pole (three term test) = 35.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.765 Order of pole (three term test) = 29.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35134.6MB, alloc=44.3MB, time=419.81 memory used=35181.3MB, alloc=44.3MB, time=420.36 x[1] = 0.3987 1.359 h = 0.0001 0.004 y2[1] (numeric) = 11.7121255772 16.6390070595 y2[1] (closed_form) = 14.7924057544 15.2651228241 absolute error = 3.373 relative error = 15.87 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.91188943585 -0.705665053945 y1[1] (closed_form) = 1.91188943585 -0.705665053945 absolute error = 4.148e-63 relative error = 2.036e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.788 Order of pole (three term test) = 35.26 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.788 Order of pole (three term test) = 29.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35227.3MB, alloc=44.3MB, time=420.90 memory used=35273.8MB, alloc=44.3MB, time=421.44 x[1] = 0.3988 1.363 h = 0.003 0.006 y2[1] (numeric) = 11.7154151581 16.686869631 y2[1] (closed_form) = 14.7964267219 15.3127129056 absolute error = 3.374 relative error = 15.84 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.91852440707 -0.709060605717 y1[1] (closed_form) = 1.91852440707 -0.709060605717 absolute error = 4.148e-63 relative error = 2.028e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.818 Order of pole (three term test) = 35.28 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.818 Order of pole (three term test) = 29.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35319.8MB, alloc=44.3MB, time=421.97 memory used=35366.4MB, alloc=44.3MB, time=422.52 memory used=35413.0MB, alloc=44.3MB, time=423.07 x[1] = 0.4018 1.369 h = 0.0001 0.005 y2[1] (numeric) = 11.7187227729 16.7347499294 y2[1] (closed_form) = 14.8364779628 15.3821050172 absolute error = 3.399 relative error = 15.9 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.92620851635 -0.719003501232 y1[1] (closed_form) = 1.92620851635 -0.719003501232 absolute error = 4.176e-63 relative error = 2.031e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.865 Order of pole (three term test) = 35.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.865 Order of pole (three term test) = 29.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35459.0MB, alloc=44.3MB, time=423.61 memory used=35505.7MB, alloc=44.3MB, time=424.16 x[1] = 0.4019 1.374 h = 0.0001 0.003 y2[1] (numeric) = 11.7220485541 16.7826479557 y2[1] (closed_form) = 14.8412766915 15.4416849323 absolute error = 3.395 relative error = 15.85 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.93461093635 -0.723275067769 y1[1] (closed_form) = 1.93461093635 -0.723275067769 absolute error = 3.195e-63 relative error = 1.547e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.903 Order of pole (three term test) = 35.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.903 Order of pole (three term test) = 29.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35551.8MB, alloc=44.3MB, time=424.70 memory used=35598.5MB, alloc=44.3MB, time=425.26 x[1] = 0.402 1.377 h = 0.001 0.001 y2[1] (numeric) = 11.7253926355 16.830563711 y2[1] (closed_form) = 14.8446441886 15.4774238483 absolute error = 3.4 relative error = 15.85 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.93964224984 -0.725915902298 y1[1] (closed_form) = 1.93964224984 -0.725915902298 absolute error = 4.148e-63 relative error = 2.003e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.927 Order of pole (three term test) = 35.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.927 Order of pole (three term test) = 29.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35644.7MB, alloc=44.3MB, time=425.80 memory used=35691.2MB, alloc=44.3MB, time=426.36 x[1] = 0.403 1.378 h = 0.001 0.003 y2[1] (numeric) = 11.7287551511 16.8784971953 y2[1] (closed_form) = 14.8573114545 15.4886367492 absolute error = 3.423 relative error = 15.95 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.94052430274 -0.728449910272 y1[1] (closed_form) = 1.94052430274 -0.728449910272 absolute error = 4.176e-63 relative error = 2.015e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.935 Order of pole (three term test) = 35.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.935 Order of pole (three term test) = 29.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35736.9MB, alloc=44.3MB, time=426.89 memory used=35783.5MB, alloc=44.3MB, time=427.44 x[1] = 0.404 1.381 h = 0.0001 0.004 y2[1] (numeric) = 11.7321362362 16.9264484084 y2[1] (closed_form) = 14.8714457743 15.5237342274 absolute error = 3.438 relative error = 15.99 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.94482847982 -0.732649226652 y1[1] (closed_form) = 1.94482847982 -0.732649226652 absolute error = 4.176e-63 relative error = 2.009e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.959 Order of pole (three term test) = 35.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.959 Order of pole (three term test) = 29.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35829.8MB, alloc=44.3MB, time=427.97 memory used=35876.0MB, alloc=44.3MB, time=428.52 memory used=35922.5MB, alloc=44.3MB, time=429.06 x[1] = 0.4041 1.385 h = 0.003 0.006 y2[1] (numeric) = 11.7355360266 16.9744173496 y2[1] (closed_form) = 14.8755781963 15.5714536653 absolute error = 3.439 relative error = 15.97 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.9516155456 -0.736153028866 y1[1] (closed_form) = 1.9516155456 -0.736153028866 absolute error = 4.176e-63 relative error = 2.002e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.99 Order of pole (three term test) = 35.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 3.99 Order of pole (three term test) = 29.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35968.5MB, alloc=44.3MB, time=429.60 memory used=36015.2MB, alloc=44.3MB, time=430.15 x[1] = 0.4071 1.391 h = 0.0001 0.005 y2[1] (numeric) = 11.7389546591 17.0224040177 y2[1] (closed_form) = 14.9158923175 15.6409630977 absolute error = 3.464 relative error = 16.03 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.95945360313 -0.74637001905 y1[1] (closed_form) = 1.95945360313 -0.74637001905 absolute error = 4.176e-63 relative error = 1.992e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.039 Order of pole (three term test) = 35.4 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.039 Order of pole (three term test) = 29.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36061.1MB, alloc=44.3MB, time=430.68 memory used=36107.7MB, alloc=44.3MB, time=431.24 x[1] = 0.4072 1.396 h = 0.0001 0.003 y2[1] (numeric) = 11.742392271 17.0704084107 y2[1] (closed_form) = 14.9208315534 15.7007069745 absolute error = 3.461 relative error = 15.98 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.96804807459 -0.750777902335 y1[1] (closed_form) = 1.96804807459 -0.750777902335 absolute error = 4.176e-63 relative error = 1.983e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.079 Order of pole (three term test) = 35.43 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.079 Order of pole (three term test) = 29.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36153.7MB, alloc=44.3MB, time=431.77 memory used=36200.3MB, alloc=44.3MB, time=432.33 x[1] = 0.4073 1.399 h = 0.001 0.001 y2[1] (numeric) = 11.7458490006 17.1184305264 y2[1] (closed_form) = 14.9242850338 15.7365436193 absolute error = 3.466 relative error = 15.98 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.97319394093 -0.753502437447 y1[1] (closed_form) = 1.97319394093 -0.753502437447 absolute error = 4.176e-63 relative error = 1.977e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.104 Order of pole (three term test) = 35.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.104 Order of pole (three term test) = 29.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36246.4MB, alloc=44.3MB, time=432.87 memory used=36292.8MB, alloc=44.3MB, time=433.42 x[1] = 0.4083 1.4 h = 0.003 0.006 y2[1] (numeric) = 11.749324987 17.1664703619 y2[1] (closed_form) = 14.9370134772 15.7477624586 absolute error = 3.489 relative error = 16.08 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.97408844515 -0.756102239592 y1[1] (closed_form) = 1.97408844515 -0.756102239592 absolute error = 4.176e-63 relative error = 1.976e-61 % Correct digits = 63 memory used=36339.2MB, alloc=44.3MB, time=433.96 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.112 Order of pole (three term test) = 35.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.112 Order of pole (three term test) = 29.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36385.4MB, alloc=44.3MB, time=434.50 memory used=36432.1MB, alloc=44.3MB, time=435.05 x[1] = 0.4113 1.406 h = 0.0001 0.005 y2[1] (numeric) = 11.7528203701 17.2145279138 y2[1] (closed_form) = 14.9775154495 15.8173468853 absolute error = 3.514 relative error = 16.13 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.98202599317 -0.766515443146 y1[1] (closed_form) = 1.98202599317 -0.766515443146 absolute error = 4.206e-63 relative error = 1.979e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.162 Order of pole (three term test) = 35.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.162 Order of pole (three term test) = 29.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36478.0MB, alloc=44.3MB, time=435.58 memory used=36524.6MB, alloc=44.3MB, time=436.13 x[1] = 0.4114 1.411 h = 0.0001 0.003 y2[1] (numeric) = 11.7563352906 17.2626031782 y2[1] (closed_form) = 14.9825579285 15.8772019299 absolute error = 3.511 relative error = 16.08 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.99075069374 -0.771024343915 y1[1] (closed_form) = 1.99075069374 -0.771024343915 absolute error = 4.206e-63 relative error = 1.970e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.204 Order of pole (three term test) = 35.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.204 Order of pole (three term test) = 29.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36570.9MB, alloc=44.3MB, time=436.69 memory used=36617.9MB, alloc=44.3MB, time=437.26 x[1] = 0.4115 1.414 h = 0.001 0.001 y2[1] (numeric) = 11.7598698899 17.3106961505 y2[1] (closed_form) = 14.9860745153 15.9131047711 absolute error = 3.516 relative error = 16.08 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.9959741684 -0.773810805567 y1[1] (closed_form) = 1.9959741684 -0.773810805567 absolute error = 4.206e-63 relative error = 1.965e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.229 Order of pole (three term test) = 35.52 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.229 Order of pole (three term test) = 29.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36664.0MB, alloc=44.3MB, time=437.80 memory used=36710.5MB, alloc=44.3MB, time=438.35 x[1] = 0.4125 1.415 h = 0.001 0.003 y2[1] (numeric) = 11.7634243105 17.3588068259 y2[1] (closed_form) = 14.9988460738 15.9243260625 absolute error = 3.539 relative error = 16.18 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.99687542396 -0.776456981128 y1[1] (closed_form) = 1.99687542396 -0.776456981128 absolute error = 4.206e-63 relative error = 1.963e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.238 Order of pole (three term test) = 35.52 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.238 Order of pole (three term test) = 29.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36756.5MB, alloc=44.3MB, time=438.88 memory used=36803.2MB, alloc=44.3MB, time=439.44 memory used=36849.9MB, alloc=44.3MB, time=439.98 x[1] = 0.4135 1.418 h = 0.0001 0.004 y2[1] (numeric) = 11.7669986954 17.4069351986 y2[1] (closed_form) = 15.0131811495 15.9595447102 absolute error = 3.554 relative error = 16.22 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.00133021574 -0.780861952185 y1[1] (closed_form) = 2.00133021574 -0.780861952185 absolute error = 3.270e-63 relative error = 1.522e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.263 Order of pole (three term test) = 35.53 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.263 Order of pole (three term test) = 29.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36895.9MB, alloc=44.3MB, time=440.52 memory used=36942.4MB, alloc=44.3MB, time=441.06 x[1] = 0.4136 1.422 h = 0.003 0.006 y2[1] (numeric) = 11.7705931887 17.4550812626 y2[1] (closed_form) = 15.0175124732 16.0074858417 absolute error = 3.555 relative error = 16.2 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.00837628302 -0.784559685562 y1[1] (closed_form) = 2.00837628302 -0.784559685562 absolute error = 4.206e-63 relative error = 1.951e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.297 Order of pole (three term test) = 35.56 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.297 Order of pole (three term test) = 29.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36988.4MB, alloc=44.3MB, time=441.60 memory used=37035.0MB, alloc=44.3MB, time=442.15 x[1] = 0.4166 1.428 h = 0.0001 0.005 y2[1] (numeric) = 11.7742079351 17.5032450111 y2[1] (closed_form) = 15.0582891419 16.0771906633 absolute error = 3.58 relative error = 16.25 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.016469624 -0.795258056813 y1[1] (closed_form) = 2.016469624 -0.795258056813 absolute error = 4.238e-63 relative error = 1.955e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.349 Order of pole (three term test) = 35.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.349 Order of pole (three term test) = 29.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37081.0MB, alloc=44.3MB, time=442.68 memory used=37127.7MB, alloc=44.3MB, time=443.24 x[1] = 0.4167 1.433 h = 0.0001 0.003 y2[1] (numeric) = 11.7778430802 17.5514264369 y2[1] (closed_form) = 15.063479146 16.1372155364 absolute error = 3.577 relative error = 16.2 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.02539118289 -0.799910187411 y1[1] (closed_form) = 2.02539118289 -0.799910187411 absolute error = 3.270e-63 relative error = 1.501e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.393 Order of pole (three term test) = 35.61 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.393 Order of pole (three term test) = 29.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37173.8MB, alloc=44.3MB, time=443.77 memory used=37220.5MB, alloc=44.3MB, time=444.33 x[1] = 0.4168 1.436 h = 0.001 0.001 y2[1] (numeric) = 11.7814987706 17.5996255322 y2[1] (closed_form) = 15.067085992 16.1732195822 absolute error = 3.582 relative error = 16.2 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.03073205346 -0.802784554454 y1[1] (closed_form) = 2.03073205346 -0.802784554454 absolute error = 3.270e-63 relative error = 1.497e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.419 Order of pole (three term test) = 35.63 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.419 Order of pole (three term test) = 29.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37267.0MB, alloc=44.3MB, time=444.88 memory used=37313.3MB, alloc=44.3MB, time=445.43 memory used=37359.9MB, alloc=44.3MB, time=445.98 x[1] = 0.4178 1.437 h = 0.001 0.003 y2[1] (numeric) = 11.7851751534 17.6478422886 y2[1] (closed_form) = 15.0799213222 16.1844466296 absolute error = 3.605 relative error = 16.3 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.03164538336 -0.805498891064 y1[1] (closed_form) = 2.03164538336 -0.805498891064 absolute error = 4.238e-63 relative error = 1.939e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.428 Order of pole (three term test) = 35.63 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.428 Order of pole (three term test) = 29.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37405.9MB, alloc=44.3MB, time=446.51 memory used=37452.5MB, alloc=44.3MB, time=447.06 x[1] = 0.4188 1.44 h = 0.0001 0.004 y2[1] (numeric) = 11.7888723769 17.6960766971 y2[1] (closed_form) = 15.0943785266 16.2197406215 absolute error = 3.62 relative error = 16.34 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.03619251354 -0.81002842917 y1[1] (closed_form) = 2.03619251354 -0.81002842917 absolute error = 4.206e-63 relative error = 1.919e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.455 Order of pole (three term test) = 35.64 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.455 Order of pole (three term test) = 29.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37498.4MB, alloc=44.3MB, time=447.60 memory used=37545.0MB, alloc=44.3MB, time=448.14 x[1] = 0.4189 1.444 h = 0.003 0.006 y2[1] (numeric) = 11.7925905901 17.7443287483 y2[1] (closed_form) = 15.0988302442 16.267818596 absolute error = 3.621 relative error = 16.31 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.04339681219 -0.813843219109 y1[1] (closed_form) = 2.04339681219 -0.813843219109 absolute error = 3.270e-63 relative error = 1.486e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.491 Order of pole (three term test) = 35.67 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.491 Order of pole (three term test) = 29.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37590.9MB, alloc=44.3MB, time=448.68 memory used=37637.7MB, alloc=44.3MB, time=449.23 x[1] = 0.4219 1.45 h = 0.0001 0.005 y2[1] (numeric) = 11.7963299427 17.792598432 y2[1] (closed_form) = 15.139888786 16.3376457238 absolute error = 3.646 relative error = 16.37 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.05164714102 -0.8248335232 y1[1] (closed_form) = 2.05164714102 -0.8248335232 absolute error = 3.311e-63 relative error = 1.497e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.545 Order of pole (three term test) = 35.69 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.545 Order of pole (three term test) = 29.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37683.7MB, alloc=44.3MB, time=449.76 memory used=37730.5MB, alloc=44.3MB, time=450.32 x[1] = 0.422 1.455 h = 0.0001 0.003 y2[1] (numeric) = 11.8000905854 17.8408857375 y2[1] (closed_form) = 15.1452305634 16.3978440188 absolute error = 3.643 relative error = 16.32 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.06076854081 -0.829633085305 y1[1] (closed_form) = 2.06076854081 -0.829633085305 absolute error = 3.311e-63 relative error = 1.490e-61 % Correct digits = 63 memory used=37777.2MB, alloc=44.3MB, time=450.87 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.591 Order of pole (three term test) = 35.72 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.591 Order of pole (three term test) = 29.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37823.3MB, alloc=44.3MB, time=451.42 memory used=37870.2MB, alloc=44.3MB, time=451.98 x[1] = 0.4221 1.458 h = 0.001 0.001 y2[1] (numeric) = 11.8038726698 17.8891906537 y2[1] (closed_form) = 15.1489302574 16.4339513985 absolute error = 3.648 relative error = 16.32 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.06622857195 -0.832597913813 y1[1] (closed_form) = 2.06622857195 -0.832597913813 absolute error = 4.238e-63 relative error = 1.902e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.618 Order of pole (three term test) = 35.74 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.618 Order of pole (three term test) = 29.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37916.1MB, alloc=44.3MB, time=452.51 memory used=37962.6MB, alloc=44.3MB, time=453.07 x[1] = 0.4231 1.459 h = 0.001 0.003 y2[1] (numeric) = 11.8076763481 17.9375131686 y2[1] (closed_form) = 15.1618309383 16.4451841003 absolute error = 3.671 relative error = 16.41 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.06715375957 -0.835381862006 y1[1] (closed_form) = 2.06715375957 -0.835381862006 absolute error = 4.238e-63 relative error = 1.901e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.628 Order of pole (three term test) = 35.74 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.628 Order of pole (three term test) = 29.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38008.5MB, alloc=44.3MB, time=453.60 memory used=38055.3MB, alloc=44.3MB, time=454.15 x[1] = 0.4241 1.462 h = 0.0001 0.004 y2[1] (numeric) = 11.8115017737 17.9858532699 y2[1] (closed_form) = 15.176413538 16.4805548105 absolute error = 3.686 relative error = 16.45 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.07179424493 -0.840039092751 y1[1] (closed_form) = 2.07179424493 -0.840039092751 absolute error = 4.238e-63 relative error = 1.896e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.656 Order of pole (three term test) = 35.76 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.656 Order of pole (three term test) = 29.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38101.3MB, alloc=44.3MB, time=454.68 memory used=38147.8MB, alloc=44.3MB, time=455.24 x[1] = 0.4242 1.466 h = 0.003 0.006 y2[1] (numeric) = 11.8153491007 18.0342109444 y2[1] (closed_form) = 15.1809891072 16.528772506 absolute error = 3.687 relative error = 16.43 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.07915916988 -0.843974358672 y1[1] (closed_form) = 2.07915916988 -0.843974358672 absolute error = 4.272e-63 relative error = 1.904e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.693 Order of pole (three term test) = 35.78 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.693 Order of pole (three term test) = 29.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38193.8MB, alloc=44.3MB, time=455.76 memory used=38240.5MB, alloc=44.3MB, time=456.31 memory used=38287.1MB, alloc=44.3MB, time=456.86 x[1] = 0.4272 1.472 h = 0.0001 0.005 y2[1] (numeric) = 11.8192184839 18.0825861787 y2[1] (closed_form) = 15.2223368558 16.5987238414 absolute error = 3.713 relative error = 16.48 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.08756768493 -0.855263530456 y1[1] (closed_form) = 2.08756768493 -0.855263530456 absolute error = 4.238e-63 relative error = 1.879e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.75 Order of pole (three term test) = 35.8 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.75 Order of pole (three term test) = 29.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38333.1MB, alloc=44.3MB, time=457.40 memory used=38379.9MB, alloc=44.3MB, time=457.95 x[1] = 0.4273 1.477 h = 0.0001 0.003 y2[1] (numeric) = 11.8231100793 18.1309789584 y2[1] (closed_form) = 15.2278347645 16.6590991953 absolute error = 3.709 relative error = 16.43 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.09689196493 -0.860214839571 y1[1] (closed_form) = 2.09689196493 -0.860214839571 absolute error = 3.311e-63 relative error = 1.461e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.797 Order of pole (three term test) = 35.84 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.797 Order of pole (three term test) = 29.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38426.1MB, alloc=44.3MB, time=458.49 memory used=38473.0MB, alloc=44.3MB, time=459.06 x[1] = 0.4274 1.48 h = 0.001 0.001 y2[1] (numeric) = 11.8270240434 18.1793892689 y2[1] (closed_form) = 15.2316299617 16.6953120638 absolute error = 3.714 relative error = 16.43 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.10247295456 -0.863272754653 y1[1] (closed_form) = 2.10247295456 -0.863272754653 absolute error = 4.238e-63 relative error = 1.865e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.826 Order of pole (three term test) = 35.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.826 Order of pole (three term test) = 29.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38519.1MB, alloc=44.3MB, time=459.60 memory used=38565.8MB, alloc=44.3MB, time=460.15 x[1] = 0.4284 1.481 h = 0.0001 0.004 y2[1] (numeric) = 11.8309605339 18.2278170946 y2[1] (closed_form) = 15.2445976031 16.7065503054 absolute error = 3.737 relative error = 16.52 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.10340977243 -0.866127799464 y1[1] (closed_form) = 2.10340977243 -0.866127799464 absolute error = 4.238e-63 relative error = 1.863e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.836 Order of pole (three term test) = 35.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.836 Order of pole (three term test) = 29.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38611.8MB, alloc=44.3MB, time=460.69 memory used=38658.1MB, alloc=44.3MB, time=461.24 x[1] = 0.4285 1.485 h = 0.003 0.006 y2[1] (numeric) = 11.8349197092 18.2762624195 y2[1] (closed_form) = 15.2492809048 16.7548921321 absolute error = 3.738 relative error = 16.5 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.11091640365 -0.870167622718 y1[1] (closed_form) = 2.11091640365 -0.870167622718 absolute error = 4.238e-63 relative error = 1.856e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.875 Order of pole (three term test) = 35.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.875 Order of pole (three term test) = 29.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38704.2MB, alloc=44.3MB, time=461.77 memory used=38750.5MB, alloc=44.3MB, time=462.33 memory used=38797.1MB, alloc=44.3MB, time=462.88 x[1] = 0.4315 1.491 h = 0.0001 0.005 y2[1] (numeric) = 11.8389017286 18.324725227 y2[1] (closed_form) = 15.2908820781 16.8249554625 absolute error = 3.764 relative error = 16.55 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.11946571737 -0.881717831422 y1[1] (closed_form) = 2.11946571737 -0.881717831422 absolute error = 3.311e-63 relative error = 1.442e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.934 Order of pole (three term test) = 35.91 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.934 Order of pole (three term test) = 29.52 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38843.0MB, alloc=44.3MB, time=463.42 memory used=38889.7MB, alloc=44.3MB, time=463.97 x[1] = 0.4316 1.496 h = 0.0001 0.003 y2[1] (numeric) = 11.8429067523 18.3732054999 y2[1] (closed_form) = 15.2965157859 16.8854881017 absolute error = 3.76 relative error = 16.5 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.12896898703 -0.886800836883 y1[1] (closed_form) = 2.12896898703 -0.886800836883 absolute error = 3.311e-63 relative error = 1.435e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.983 Order of pole (three term test) = 35.94 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 4.983 Order of pole (three term test) = 29.5 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38935.8MB, alloc=44.3MB, time=464.51 memory used=38982.6MB, alloc=44.3MB, time=465.07 x[1] = 0.4317 1.499 h = 0.001 0.001 y2[1] (numeric) = 11.8469349414 18.4217032203 y2[1] (closed_form) = 15.3003940754 16.9217946987 absolute error = 3.765 relative error = 16.5 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.13465671163 -0.88993956318 y1[1] (closed_form) = 2.13465671163 -0.88993956318 absolute error = 3.311e-63 relative error = 1.431e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.013 Order of pole (three term test) = 35.97 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.013 Order of pole (three term test) = 29.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39028.8MB, alloc=44.3MB, time=465.61 memory used=39075.3MB, alloc=44.3MB, time=466.16 x[1] = 0.4327 1.5 h = 0.001 0.003 y2[1] (numeric) = 11.8509864578 18.4702183696 y2[1] (closed_form) = 15.3134206038 16.9330384314 absolute error = 3.788 relative error = 16.59 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.13560422134 -0.892856886926 y1[1] (closed_form) = 2.13560422134 -0.892856886926 absolute error = 3.311e-63 relative error = 1.430e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.023 Order of pole (three term test) = 35.97 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.023 Order of pole (three term test) = 29.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39121.0MB, alloc=44.3MB, time=466.69 memory used=39167.7MB, alloc=44.3MB, time=467.25 x[1] = 0.4337 1.503 h = 0.0001 0.004 y2[1] (numeric) = 11.8550614645 18.5187509288 y2[1] (closed_form) = 15.3282445355 16.9685571626 absolute error = 3.803 relative error = 16.63 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.1404227814 -0.897759176755 y1[1] (closed_form) = 2.1404227814 -0.897759176755 absolute error = 3.311e-63 relative error = 1.426e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.054 Order of pole (three term test) = 35.98 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.054 Order of pole (three term test) = 29.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39214.2MB, alloc=44.3MB, time=467.82 memory used=39260.2MB, alloc=44.3MB, time=468.36 memory used=39306.8MB, alloc=44.3MB, time=468.90 x[1] = 0.4338 1.507 h = 0.003 0.006 y2[1] (numeric) = 11.8591601253 18.5673008781 y2[1] (closed_form) = 15.3330583262 17.0170442022 absolute error = 3.804 relative error = 16.61 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.14809465904 -0.901926056482 y1[1] (closed_form) = 2.14809465904 -0.901926056482 absolute error = 3.270e-63 relative error = 1.403e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.094 Order of pole (three term test) = 36.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.094 Order of pole (three term test) = 29.46 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39352.7MB, alloc=44.3MB, time=469.44 memory used=39399.3MB, alloc=44.3MB, time=469.99 x[1] = 0.4368 1.513 h = 0.0001 0.005 y2[1] (numeric) = 11.8632826046 18.6158681971 y2[1] (closed_form) = 15.3749627611 17.0872353406 absolute error = 3.83 relative error = 16.66 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.15680448203 -0.913788486239 y1[1] (closed_form) = 2.15680448203 -0.913788486239 absolute error = 3.270e-63 relative error = 1.396e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.156 Order of pole (three term test) = 36.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.156 Order of pole (three term test) = 29.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39445.3MB, alloc=44.3MB, time=470.53 memory used=39491.9MB, alloc=44.3MB, time=471.08 x[1] = 0.4369 1.518 h = 0.0001 0.003 y2[1] (numeric) = 11.8674290683 18.6644528649 y2[1] (closed_form) = 15.3807609664 17.1479519801 absolute error = 3.827 relative error = 16.61 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.16651649436 -0.919031543195 y1[1] (closed_form) = 2.16651649436 -0.919031543195 absolute error = 3.311e-63 relative error = 1.407e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.208 Order of pole (three term test) = 36.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.208 Order of pole (three term test) = 29.42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39537.9MB, alloc=44.3MB, time=471.64 memory used=39584.8MB, alloc=44.3MB, time=472.20 x[1] = 0.437 1.521 h = 0.001 0.001 y2[1] (numeric) = 11.8715996826 18.7130548596 y2[1] (closed_form) = 15.384739856 17.1843681782 absolute error = 3.831 relative error = 16.61 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.17232864536 -0.922268407721 y1[1] (closed_form) = 2.17232864536 -0.922268407721 absolute error = 4.238e-63 relative error = 1.796e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.239 Order of pole (three term test) = 36.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.239 Order of pole (three term test) = 29.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39631.0MB, alloc=44.3MB, time=472.74 memory used=39677.5MB, alloc=44.3MB, time=473.29 memory used=39723.9MB, alloc=44.3MB, time=473.84 x[1] = 0.438 1.522 h = 0.001 0.003 y2[1] (numeric) = 11.875794615 18.7616741591 y2[1] (closed_form) = 15.3978364278 17.1956172226 absolute error = 3.855 relative error = 16.7 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.17328735042 -0.925259688404 y1[1] (closed_form) = 2.17328735042 -0.925259688404 absolute error = 4.238e-63 relative error = 1.794e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.249 Order of pole (three term test) = 36.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.249 Order of pole (three term test) = 29.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39770.0MB, alloc=44.3MB, time=474.38 memory used=39816.8MB, alloc=44.3MB, time=474.93 x[1] = 0.439 1.525 h = 0.0001 0.004 y2[1] (numeric) = 11.8800140338 18.8103107403 y2[1] (closed_form) = 15.4127955047 17.2312166765 absolute error = 3.87 relative error = 16.74 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.17820228454 -0.930299047435 y1[1] (closed_form) = 2.17820228454 -0.930299047435 absolute error = 4.238e-63 relative error = 1.789e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.281 Order of pole (three term test) = 36.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.281 Order of pole (three term test) = 29.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39862.7MB, alloc=44.3MB, time=475.46 memory used=39909.3MB, alloc=44.3MB, time=476.01 x[1] = 0.4391 1.529 h = 0.003 0.006 y2[1] (numeric) = 11.8842581082 18.8589645797 y2[1] (closed_form) = 15.4177435025 17.2798519089 absolute error = 3.87 relative error = 16.71 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.1860419346 -0.934596672629 y1[1] (closed_form) = 2.1860419346 -0.934596672629 absolute error = 4.238e-63 relative error = 1.783e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.323 Order of pole (three term test) = 36.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.323 Order of pole (three term test) = 29.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39955.3MB, alloc=44.3MB, time=476.54 memory used=40001.9MB, alloc=44.3MB, time=477.09 x[1] = 0.4421 1.535 h = 0.0001 0.005 y2[1] (numeric) = 11.8885270083 18.9076356531 y2[1] (closed_form) = 15.4599590034 17.3501727254 absolute error = 3.896 relative error = 16.77 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.19491347133 -0.946778763074 y1[1] (closed_form) = 2.19491347133 -0.946778763074 absolute error = 4.238e-63 relative error = 1.773e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.388 Order of pole (three term test) = 36.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.388 Order of pole (three term test) = 29.37 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40047.9MB, alloc=44.3MB, time=477.62 memory used=40094.6MB, alloc=44.3MB, time=478.18 x[1] = 0.4422 1.54 h = 0.0001 0.003 y2[1] (numeric) = 11.8928209052 18.9563239354 y2[1] (closed_form) = 15.465926393 17.4110771321 absolute error = 3.893 relative error = 16.72 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.20483743149 -0.952186526969 y1[1] (closed_form) = 2.20483743149 -0.952186526969 absolute error = 4.238e-63 relative error = 1.765e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.442 Order of pole (three term test) = 36.2 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.442 Order of pole (three term test) = 29.35 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40141.0MB, alloc=44.3MB, time=478.72 memory used=40187.5MB, alloc=44.3MB, time=479.28 memory used=40234.5MB, alloc=44.3MB, time=479.84 x[1] = 0.4423 1.543 h = 0.001 0.001 y2[1] (numeric) = 11.8971399708 19.0050294012 y2[1] (closed_form) = 15.4700087373 17.4476051618 absolute error = 3.898 relative error = 16.71 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.21077590389 -0.955524360982 y1[1] (closed_form) = 2.21077590389 -0.955524360982 absolute error = 4.238e-63 relative error = 1.760e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.475 Order of pole (three term test) = 36.22 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.475 Order of pole (three term test) = 29.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40280.4MB, alloc=44.3MB, time=480.38 memory used=40326.8MB, alloc=44.3MB, time=480.93 x[1] = 0.4433 1.544 h = 0.001 0.003 y2[1] (numeric) = 11.901484378 19.0537520242 y2[1] (closed_form) = 15.4831770556 17.4588593653 absolute error = 3.921 relative error = 16.8 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.21174554377 -0.95859118598 y1[1] (closed_form) = 2.21174554377 -0.95859118598 absolute error = 4.272e-63 relative error = 1.772e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.486 Order of pole (three term test) = 36.22 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.486 Order of pole (three term test) = 29.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40372.7MB, alloc=44.3MB, time=481.46 memory used=40419.4MB, alloc=44.3MB, time=482.02 x[1] = 0.4443 1.547 h = 0.0001 0.004 y2[1] (numeric) = 11.9058543007 19.1024917775 y2[1] (closed_form) = 15.4982748445 17.4945409381 absolute error = 3.936 relative error = 16.84 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.21675791752 -0.963771058023 y1[1] (closed_form) = 2.21675791752 -0.963771058023 absolute error = 4.272e-63 relative error = 1.767e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.519 Order of pole (three term test) = 36.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.519 Order of pole (three term test) = 29.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40465.5MB, alloc=44.3MB, time=482.56 memory used=40512.1MB, alloc=44.3MB, time=483.10 x[1] = 0.4444 1.551 h = 0.003 0.006 y2[1] (numeric) = 11.9102499136 19.1512486335 y2[1] (closed_form) = 15.5033608633 17.5433273796 absolute error = 3.936 relative error = 16.81 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.224767912 -0.968203216414 y1[1] (closed_form) = 2.224767912 -0.968203216414 absolute error = 4.272e-63 relative error = 1.761e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.563 Order of pole (three term test) = 36.27 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.563 Order of pole (three term test) = 29.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40557.9MB, alloc=44.3MB, time=483.63 memory used=40604.5MB, alloc=44.3MB, time=484.18 x[1] = 0.4474 1.557 h = 0.0001 0.005 y2[1] (numeric) = 11.9146713924 19.2000225639 y2[1] (closed_form) = 15.5458954066 17.6137797308 absolute error = 3.963 relative error = 16.87 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.23380236612 -0.98071259064 y1[1] (closed_form) = 2.23380236612 -0.98071259064 absolute error = 3.354e-63 relative error = 1.375e-61 % Correct digits = 63 memory used=40651.1MB, alloc=44.3MB, time=484.73 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.63 Order of pole (three term test) = 36.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.63 Order of pole (three term test) = 29.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40697.2MB, alloc=44.3MB, time=485.27 memory used=40743.9MB, alloc=44.3MB, time=485.82 x[1] = 0.4475 1.562 h = 0.0001 0.003 y2[1] (numeric) = 11.9191189137 19.2488135399 y2[1] (closed_form) = 15.5520367882 17.6748757178 absolute error = 3.959 relative error = 16.82 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.24394153748 -0.98628984144 y1[1] (closed_form) = 2.24394153748 -0.98628984144 absolute error = 4.272e-63 relative error = 1.743e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.687 Order of pole (three term test) = 36.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.687 Order of pole (three term test) = 29.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40790.0MB, alloc=44.3MB, time=486.36 memory used=40836.8MB, alloc=44.3MB, time=486.92 x[1] = 0.4476 1.565 h = 0.001 0.001 y2[1] (numeric) = 11.9235926552 19.2976215319 y2[1] (closed_form) = 15.5562255151 17.7115178366 absolute error = 3.964 relative error = 16.81 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.25000826033 -0.98973155169 y1[1] (closed_form) = 2.25000826033 -0.98973155169 absolute error = 4.308e-63 relative error = 1.753e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.721 Order of pole (three term test) = 36.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.721 Order of pole (three term test) = 29.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40882.8MB, alloc=44.3MB, time=487.46 memory used=40929.1MB, alloc=44.3MB, time=488.01 x[1] = 0.4486 1.566 h = 0.001 0.003 y2[1] (numeric) = 11.9280927953 19.3464465095 y2[1] (closed_form) = 15.5694673168 17.722777032 absolute error = 3.987 relative error = 16.9 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.25098856187 -0.992875545377 y1[1] (closed_form) = 2.25098856187 -0.992875545377 absolute error = 4.272e-63 relative error = 1.736e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.732 Order of pole (three term test) = 36.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.732 Order of pole (three term test) = 29.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40975.0MB, alloc=44.3MB, time=488.54 memory used=41021.6MB, alloc=44.3MB, time=489.10 x[1] = 0.4496 1.569 h = 0.0001 0.004 y2[1] (numeric) = 11.9326195136 19.3952884417 y2[1] (closed_form) = 15.5847074669 17.7585421253 absolute error = 4.002 relative error = 16.94 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.25609945247 -0.998199461027 y1[1] (closed_form) = 2.25609945247 -0.998199461027 absolute error = 4.308e-63 relative error = 1.746e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.767 Order of pole (three term test) = 36.37 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.767 Order of pole (three term test) = 29.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41067.6MB, alloc=44.3MB, time=489.63 memory used=41114.0MB, alloc=44.3MB, time=490.18 memory used=41160.6MB, alloc=44.3MB, time=490.73 x[1] = 0.4497 1.573 h = 0.003 0.006 y2[1] (numeric) = 11.9371729904 19.444147297 y2[1] (closed_form) = 15.5899354188 17.8074828289 absolute error = 4.003 relative error = 16.91 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.26428240963 -1.00277004141 y1[1] (closed_form) = 2.26428240963 -1.00277004141 absolute error = 4.472e-63 relative error = 1.806e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.813 Order of pole (three term test) = 36.41 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.813 Order of pole (three term test) = 29.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41206.5MB, alloc=44.3MB, time=491.26 memory used=41253.3MB, alloc=44.3MB, time=491.82 x[1] = 0.4527 1.579 h = 0.0001 0.005 y2[1] (numeric) = 11.9417534072 19.4930230428 y2[1] (closed_form) = 15.6327971569 17.878068557 absolute error = 4.029 relative error = 16.96 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.27348098276 -1.01561450972 y1[1] (closed_form) = 2.27348098276 -1.01561450972 absolute error = 4.472e-63 relative error = 1.796e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.883 Order of pole (three term test) = 36.43 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.883 Order of pole (three term test) = 29.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41299.2MB, alloc=44.3MB, time=492.35 memory used=41345.8MB, alloc=44.3MB, time=492.90 x[1] = 0.4528 1.584 h = 0.0001 0.003 y2[1] (numeric) = 11.9463609463 19.5419156463 y2[1] (closed_form) = 15.6391174625 17.9393599841 absolute error = 4.025 relative error = 16.91 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.2838386873 -1.02136615485 y1[1] (closed_form) = 2.2838386873 -1.02136615485 absolute error = 4.472e-63 relative error = 1.788e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.942 Order of pole (three term test) = 36.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.942 Order of pole (three term test) = 29.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41392.0MB, alloc=44.3MB, time=493.44 memory used=41438.9MB, alloc=44.3MB, time=494.00 x[1] = 0.4529 1.587 h = 0.001 0.001 y2[1] (numeric) = 11.950995791 19.5908250735 y2[1] (closed_form) = 15.6434155747 17.9761184766 absolute error = 4.03 relative error = 16.91 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.29003562387 -1.02491472537 y1[1] (closed_form) = 2.29003562387 -1.02491472537 absolute error = 4.472e-63 relative error = 1.782e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.978 Order of pole (three term test) = 36.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.978 Order of pole (three term test) = 29.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41485.1MB, alloc=44.3MB, time=494.54 memory used=41531.8MB, alloc=44.3MB, time=495.10 x[1] = 0.4539 1.588 h = 0.0001 0.004 y2[1] (numeric) = 11.9556581256 19.63975129 y2[1] (closed_form) = 15.6567326316 17.987382482 absolute error = 4.053 relative error = 17 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.29102630078 -1.02813754978 y1[1] (closed_form) = 2.29102630078 -1.02813754978 absolute error = 4.123e-63 relative error = 1.642e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.99 Order of pole (three term test) = 36.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 5.99 Order of pole (three term test) = 29.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41578.1MB, alloc=44.3MB, time=495.63 memory used=41624.5MB, alloc=44.3MB, time=496.18 memory used=41671.2MB, alloc=44.3MB, time=496.73 x[1] = 0.454 1.592 h = 0.003 0.006 y2[1] (numeric) = 11.9603481353 19.6886942606 y2[1] (closed_form) = 15.6620840764 18.0364601984 absolute error = 4.054 relative error = 16.97 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.29936198451 -1.03282836853 y1[1] (closed_form) = 2.29936198451 -1.03282836853 absolute error = 4.472e-63 relative error = 1.774e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.038 Order of pole (three term test) = 36.53 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.038 Order of pole (three term test) = 29.17 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41717.2MB, alloc=44.3MB, time=497.26 memory used=41764.0MB, alloc=44.3MB, time=497.82 x[1] = 0.457 1.598 h = 0.0001 0.005 y2[1] (numeric) = 11.9650660064 19.7376539494 y2[1] (closed_form) = 15.7052325003 18.1071662294 absolute error = 4.08 relative error = 17.02 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.30870690732 -1.0459657003 y1[1] (closed_form) = 2.30870690732 -1.0459657003 absolute error = 4.472e-63 relative error = 1.764e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.111 Order of pole (three term test) = 36.56 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.111 Order of pole (three term test) = 29.17 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41809.8MB, alloc=44.3MB, time=498.36 memory used=41856.4MB, alloc=44.3MB, time=498.91 x[1] = 0.4571 1.603 h = 0.0001 0.003 y2[1] (numeric) = 11.9698119259 19.7866303198 y2[1] (closed_form) = 15.7117084725 18.1686312255 absolute error = 4.077 relative error = 16.97 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.31925758243 -1.05186882944 y1[1] (closed_form) = 2.31925758243 -1.05186882944 absolute error = 4.472e-63 relative error = 1.756e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.173 Order of pole (three term test) = 36.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.173 Order of pole (three term test) = 29.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41902.4MB, alloc=44.3MB, time=499.44 memory used=41949.4MB, alloc=44.3MB, time=500.01 x[1] = 0.4572 1.606 h = 0.001 0.001 y2[1] (numeric) = 11.9745860822 19.8356233344 y2[1] (closed_form) = 15.7161017796 18.2054930922 absolute error = 4.081 relative error = 16.97 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.32556952384 -1.05551024799 y1[1] (closed_form) = 2.32556952384 -1.05551024799 absolute error = 4.472e-63 relative error = 1.751e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.21 Order of pole (three term test) = 36.62 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.21 Order of pole (three term test) = 29.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41995.6MB, alloc=44.3MB, time=500.55 memory used=42042.1MB, alloc=44.3MB, time=501.11 x[1] = 0.4582 1.607 h = 0.001 0.003 y2[1] (numeric) = 11.9793886644 19.8846329551 y2[1] (closed_form) = 15.7294850053 18.2167620062 absolute error = 4.104 relative error = 17.05 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.32656985855 -1.05880216876 y1[1] (closed_form) = 2.32656985855 -1.05880216876 absolute error = 4.472e-63 relative error = 1.750e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.222 Order of pole (three term test) = 36.62 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.222 Order of pole (three term test) = 29.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42088.4MB, alloc=44.3MB, time=501.64 memory used=42134.7MB, alloc=44.3MB, time=502.19 memory used=42181.5MB, alloc=44.3MB, time=502.74 x[1] = 0.4592 1.61 h = 0.0001 0.004 y2[1] (numeric) = 11.9842198627 19.9336591432 y2[1] (closed_form) = 15.7449990251 18.2526880606 absolute error = 4.119 relative error = 17.09 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.3318687909 -1.06440261346 y1[1] (closed_form) = 2.3318687909 -1.06440261346 absolute error = 4.123e-63 relative error = 1.609e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.26 Order of pole (three term test) = 36.64 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.26 Order of pole (three term test) = 29.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42227.4MB, alloc=44.3MB, time=503.28 memory used=42273.9MB, alloc=44.3MB, time=503.82 x[1] = 0.4593 1.614 h = 0.003 0.006 y2[1] (numeric) = 11.9890798681 19.982701859 y2[1] (closed_form) = 15.750499915 18.3019258691 absolute error = 4.12 relative error = 17.06 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.34038248279 -1.06923933502 y1[1] (closed_form) = 2.34038248279 -1.06923933502 absolute error = 4.123e-63 relative error = 1.602e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.31 Order of pole (three term test) = 36.68 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.31 Order of pole (three term test) = 29.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42319.9MB, alloc=44.3MB, time=504.36 memory used=42366.5MB, alloc=44.3MB, time=504.91 x[1] = 0.4623 1.62 h = 0.0001 0.005 y2[1] (numeric) = 11.9939688728 20.0317610622 y2[1] (closed_form) = 15.793991165 18.372768765 absolute error = 4.146 relative error = 17.11 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.34989384914 -1.08272679133 y1[1] (closed_form) = 2.34989384914 -1.08272679133 absolute error = 4.472e-63 relative error = 1.728e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.386 Order of pole (three term test) = 36.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.386 Order of pole (three term test) = 29.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42412.5MB, alloc=44.3MB, time=505.44 memory used=42459.3MB, alloc=44.3MB, time=506.00 x[1] = 0.4624 1.625 h = 0.0001 0.003 y2[1] (numeric) = 11.99888707 20.080836712 y2[1] (closed_form) = 15.8006555317 18.4344365724 absolute error = 4.143 relative error = 17.06 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.36066945821 -1.08881375477 y1[1] (closed_form) = 2.36066945821 -1.08881375477 absolute error = 4.472e-63 relative error = 1.720e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.45 Order of pole (three term test) = 36.75 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.45 Order of pole (three term test) = 29.07 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42505.4MB, alloc=44.3MB, time=506.54 memory used=42552.2MB, alloc=44.3MB, time=507.10 x[1] = 0.4625 1.628 h = 0.001 0.001 y2[1] (numeric) = 12.0038346538 20.1299287663 y2[1] (closed_form) = 15.8051639903 18.4714191755 absolute error = 4.147 relative error = 17.06 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.36711539622 -1.0925677737 y1[1] (closed_form) = 2.36711539622 -1.0925677737 absolute error = 4.472e-63 relative error = 1.715e-61 % Correct digits = 63 memory used=42599.2MB, alloc=44.3MB, time=507.66 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.489 Order of pole (three term test) = 36.78 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.489 Order of pole (three term test) = 29.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42645.3MB, alloc=44.3MB, time=508.20 memory used=42691.8MB, alloc=44.3MB, time=508.75 x[1] = 0.4635 1.629 h = 0.001 0.003 y2[1] (numeric) = 12.0088118193 20.1790371828 y2[1] (closed_form) = 15.8186258653 18.4826925418 absolute error = 4.17 relative error = 17.14 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.36812555771 -1.09594172432 y1[1] (closed_form) = 2.36812555771 -1.09594172432 absolute error = 5.385e-63 relative error = 2.064e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.502 Order of pole (three term test) = 36.78 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.502 Order of pole (three term test) = 29.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42737.6MB, alloc=44.3MB, time=509.28 memory used=42784.3MB, alloc=44.3MB, time=509.84 x[1] = 0.4645 1.632 h = 0.0001 0.004 y2[1] (numeric) = 12.0138187627 20.228161918 y2[1] (closed_form) = 15.8342931422 18.518706199 absolute error = 4.185 relative error = 17.18 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.37352619559 -1.10169679566 y1[1] (closed_form) = 2.37352619559 -1.10169679566 absolute error = 5.099e-63 relative error = 1.949e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.541 Order of pole (three term test) = 36.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.541 Order of pole (three term test) = 29.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42830.2MB, alloc=44.3MB, time=510.37 memory used=42876.7MB, alloc=44.3MB, time=510.92 x[1] = 0.4646 1.636 h = 0.003 0.006 y2[1] (numeric) = 12.0188556811 20.2773029281 y2[1] (closed_form) = 15.8399476835 18.5681072615 absolute error = 4.186 relative error = 17.15 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.38222064922 -1.10668361076 y1[1] (closed_form) = 2.38222064922 -1.10668361076 absolute error = 5.099e-63 relative error = 1.941e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.594 Order of pole (three term test) = 36.83 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.594 Order of pole (three term test) = 29.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42922.6MB, alloc=44.3MB, time=511.45 memory used=42969.2MB, alloc=44.3MB, time=512.00 x[1] = 0.4676 1.642 h = 0.0001 0.005 y2[1] (numeric) = 12.0239227728 20.326460168 y2[1] (closed_form) = 15.8837904394 18.6390888194 absolute error = 4.213 relative error = 17.2 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.39189965004 -1.12052955906 y1[1] (closed_form) = 2.39189965004 -1.12052955906 absolute error = 5.099e-63 relative error = 1.930e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.673 Order of pole (three term test) = 36.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.673 Order of pole (three term test) = 29.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43015.5MB, alloc=44.3MB, time=512.53 memory used=43062.1MB, alloc=44.3MB, time=513.08 memory used=43108.8MB, alloc=44.3MB, time=513.64 x[1] = 0.4677 1.647 h = 0.0001 0.003 y2[1] (numeric) = 12.029020237 20.3756335924 y2[1] (closed_form) = 15.8906485043 18.7009634368 absolute error = 4.209 relative error = 17.15 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.40290368634 -1.12680564505 y1[1] (closed_form) = 2.40290368634 -1.12680564505 absolute error = 5.385e-63 relative error = 2.029e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.74 Order of pole (three term test) = 36.9 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.74 Order of pole (three term test) = 29.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43154.9MB, alloc=44.3MB, time=514.19 memory used=43201.8MB, alloc=44.3MB, time=514.75 x[1] = 0.4678 1.65 h = 0.001 0.001 y2[1] (numeric) = 12.0341482737 20.4248231548 y2[1] (closed_form) = 15.8952753424 18.7380691416 absolute error = 4.213 relative error = 17.15 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.40948568428 -1.13067547922 y1[1] (closed_form) = 2.40948568428 -1.13067547922 absolute error = 5.099e-63 relative error = 1.916e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.781 Order of pole (three term test) = 36.93 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.781 Order of pole (three term test) = 28.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43247.9MB, alloc=44.3MB, time=515.29 memory used=43294.6MB, alloc=44.3MB, time=515.85 x[1] = 0.4688 1.651 h = 0.001 0.003 y2[1] (numeric) = 12.0393070844 20.474028808 y2[1] (closed_form) = 15.9088177421 18.7493467334 absolute error = 4.236 relative error = 17.23 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.41050534625 -1.13413323353 y1[1] (closed_form) = 2.41050534625 -1.13413323353 absolute error = 5.099e-63 relative error = 1.914e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.794 Order of pole (three term test) = 36.93 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.794 Order of pole (three term test) = 29 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43340.4MB, alloc=44.3MB, time=516.38 memory used=43387.1MB, alloc=44.3MB, time=516.93 x[1] = 0.4698 1.654 h = 0.0001 0.004 y2[1] (numeric) = 12.0444968712 20.5232505042 y2[1] (closed_form) = 15.9246422623 18.7854494134 absolute error = 4.252 relative error = 17.26 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.41600880976 -1.14004681492 y1[1] (closed_form) = 2.41600880976 -1.14004681492 absolute error = 5.385e-63 relative error = 2.016e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.835 Order of pole (three term test) = 36.95 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.835 Order of pole (three term test) = 28.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43433.1MB, alloc=44.3MB, time=517.46 memory used=43479.7MB, alloc=44.3MB, time=518.01 x[1] = 0.4699 1.658 h = 0.003 0.006 y2[1] (numeric) = 12.0497178374 20.5724881947 y2[1] (closed_form) = 15.9304547697 18.8350169305 absolute error = 4.252 relative error = 17.24 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.4248868261 -1.14518802485 y1[1] (closed_form) = 2.4248868261 -1.14518802485 absolute error = 5.385e-63 relative error = 2.008e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.89 Order of pole (three term test) = 36.99 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.89 Order of pole (three term test) = 28.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43526.0MB, alloc=44.3MB, time=518.55 memory used=43572.2MB, alloc=44.3MB, time=519.10 memory used=43619.0MB, alloc=44.3MB, time=519.64 x[1] = 0.4729 1.664 h = 0.0001 0.005 y2[1] (numeric) = 12.0549701875 20.62174183 y2[1] (closed_form) = 15.9746579038 18.9061389289 absolute error = 4.279 relative error = 17.29 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.43473464515 -1.15940103514 y1[1] (closed_form) = 2.43473464515 -1.15940103514 absolute error = 5.385e-63 relative error = 1.997e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.973 Order of pole (three term test) = 37.02 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 6.973 Order of pole (three term test) = 28.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43664.9MB, alloc=44.3MB, time=520.18 memory used=43711.5MB, alloc=44.3MB, time=520.74 x[1] = 0.473 1.669 h = 0.0001 0.003 y2[1] (numeric) = 12.0602541267 20.6710113599 y2[1] (closed_form) = 15.9817151072 18.9682244039 absolute error = 4.275 relative error = 17.24 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.44597066198 -1.16587167142 y1[1] (closed_form) = 2.44597066198 -1.16587167142 absolute error = 5.831e-63 relative error = 2.152e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.043 Order of pole (three term test) = 37.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.043 Order of pole (three term test) = 28.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43757.7MB, alloc=44.3MB, time=521.28 memory used=43804.6MB, alloc=44.3MB, time=521.85 x[1] = 0.4731 1.672 h = 0.001 0.001 y2[1] (numeric) = 12.0655698615 20.7202967332 y2[1] (closed_form) = 15.9864636355 19.0054556043 absolute error = 4.279 relative error = 17.23 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.45269081822 -1.16986062021 y1[1] (closed_form) = 2.45269081822 -1.16986062021 absolute error = 5.831e-63 relative error = 2.146e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.086 Order of pole (three term test) = 37.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.086 Order of pole (three term test) = 28.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43850.7MB, alloc=44.3MB, time=522.39 memory used=43897.2MB, alloc=44.3MB, time=522.94 x[1] = 0.4741 1.673 h = 0.001 0.003 y2[1] (numeric) = 12.0709175994 20.7695978982 y2[1] (closed_form) = 16.0000884728 19.0167371778 absolute error = 4.302 relative error = 17.31 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.45371963914 -1.17340399249 y1[1] (closed_form) = 2.45371963914 -1.17340399249 absolute error = 5.831e-63 relative error = 2.144e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.1 Order of pole (three term test) = 37.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.1 Order of pole (three term test) = 28.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43943.1MB, alloc=44.3MB, time=523.47 memory used=43989.8MB, alloc=44.3MB, time=524.02 x[1] = 0.4751 1.676 h = 0.0001 0.004 y2[1] (numeric) = 12.0762975488 20.8189148021 y2[1] (closed_form) = 16.0160743152 19.0529303047 absolute error = 4.317 relative error = 17.35 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.45932705827 -1.17948006356 y1[1] (closed_form) = 2.45932705827 -1.17948006356 absolute error = 5.831e-63 relative error = 2.138e-61 % Correct digits = 63 memory used=44036.4MB, alloc=44.3MB, time=524.57 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.143 Order of pole (three term test) = 37.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.143 Order of pole (three term test) = 28.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44082.4MB, alloc=44.3MB, time=525.10 memory used=44128.9MB, alloc=44.3MB, time=525.65 x[1] = 0.4752 1.68 h = 0.003 0.006 y2[1] (numeric) = 12.0817099194 20.8682473915 y2[1] (closed_form) = 16.0220492141 19.1026675161 absolute error = 4.318 relative error = 17.32 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.46839148601 -1.18478008284 y1[1] (closed_form) = 2.46839148601 -1.18478008284 absolute error = 5.831e-63 relative error = 2.130e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.2 Order of pole (three term test) = 37.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.2 Order of pole (three term test) = 28.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44175.0MB, alloc=44.3MB, time=526.19 memory used=44221.7MB, alloc=44.3MB, time=526.75 x[1] = 0.4782 1.686 h = 0.0001 0.005 y2[1] (numeric) = 12.0871549217 20.917595612 y2[1] (closed_form) = 16.0666217958 19.1739317133 absolute error = 4.345 relative error = 17.37 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.47840929841 -1.19936893184 y1[1] (closed_form) = 2.47840929841 -1.19936893184 absolute error = 5.831e-63 relative error = 2.118e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.287 Order of pole (three term test) = 37.18 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.287 Order of pole (three term test) = 28.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44267.8MB, alloc=44.3MB, time=527.30 memory used=44314.5MB, alloc=44.3MB, time=527.85 x[1] = 0.4783 1.691 h = 0.0001 0.003 y2[1] (numeric) = 12.0926327674 20.9669594087 y2[1] (closed_form) = 16.0738837178 19.2362321433 absolute error = 4.341 relative error = 17.32 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.48988090945 -1.20603968896 y1[1] (closed_form) = 2.48988090945 -1.20603968896 absolute error = 5.831e-63 relative error = 2.108e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.36 Order of pole (three term test) = 37.23 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.36 Order of pole (three term test) = 28.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44360.5MB, alloc=44.3MB, time=528.38 memory used=44407.4MB, alloc=44.3MB, time=528.95 x[1] = 0.4784 1.694 h = 0.001 0.001 y2[1] (numeric) = 12.0981436693 21.0163387255 y2[1] (closed_form) = 16.0787573319 19.2735912619 absolute error = 4.345 relative error = 17.31 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.49674135757 -1.21015113829 y1[1] (closed_form) = 2.49674135757 -1.21015113829 absolute error = 5.831e-63 relative error = 2.102e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.405 Order of pole (three term test) = 37.26 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.405 Order of pole (three term test) = 28.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44453.9MB, alloc=44.3MB, time=529.50 memory used=44500.6MB, alloc=44.3MB, time=530.05 memory used=44547.2MB, alloc=44.3MB, time=530.60 x[1] = 0.4794 1.695 h = 0.0001 0.004 y2[1] (numeric) = 12.1036878412 21.0657335058 y2[1] (closed_form) = 16.0924665584 19.2848765561 absolute error = 4.368 relative error = 17.39 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.49777898014 -1.21378198397 y1[1] (closed_form) = 2.49777898014 -1.21378198397 absolute error = 5.385e-63 relative error = 1.939e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.419 Order of pole (three term test) = 37.26 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.419 Order of pole (three term test) = 28.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44593.0MB, alloc=44.3MB, time=531.13 memory used=44639.4MB, alloc=44.3MB, time=531.68 x[1] = 0.4795 1.699 h = 0.003 0.006 y2[1] (numeric) = 12.109265498 21.1151436919 y2[1] (closed_form) = 16.0985827943 19.3347644674 absolute error = 4.369 relative error = 17.36 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.50700814778 -1.21922005686 y1[1] (closed_form) = 2.50700814778 -1.21922005686 absolute error = 5.831e-63 relative error = 2.092e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.479 Order of pole (three term test) = 37.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.479 Order of pole (three term test) = 28.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44685.4MB, alloc=44.3MB, time=532.21 memory used=44732.0MB, alloc=44.3MB, time=532.76 x[1] = 0.4825 1.705 h = 0.0001 0.005 y2[1] (numeric) = 12.1148768555 21.1645692254 y2[1] (closed_form) = 16.1434790785 19.406157008 absolute error = 4.396 relative error = 17.41 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.51717784127 -1.23413756062 y1[1] (closed_form) = 2.51717784127 -1.23413756062 absolute error = 5.000e-63 relative error = 1.784e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.569 Order of pole (three term test) = 37.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.569 Order of pole (three term test) = 28.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44778.0MB, alloc=44.3MB, time=533.29 memory used=44824.6MB, alloc=44.3MB, time=533.84 x[1] = 0.4826 1.71 h = 0.0001 0.003 y2[1] (numeric) = 12.1205221309 21.2140100472 y2[1] (closed_form) = 16.1509191654 19.4686483153 absolute error = 4.392 relative error = 17.36 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.52885766091 -1.24098228127 y1[1] (closed_form) = 2.52885766091 -1.24098228127 absolute error = 5.000e-63 relative error = 1.775e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.645 Order of pole (three term test) = 37.39 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.645 Order of pole (three term test) = 28.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44870.6MB, alloc=44.3MB, time=534.38 memory used=44917.4MB, alloc=44.3MB, time=534.94 x[1] = 0.4827 1.713 h = 0.001 0.001 y2[1] (numeric) = 12.1262015423 21.2634660971 y2[1] (closed_form) = 16.1559016708 19.5061210504 absolute error = 4.396 relative error = 17.36 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.5358421189 -1.24520024748 y1[1] (closed_form) = 2.5358421189 -1.24520024748 absolute error = 6.403e-63 relative error = 2.267e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.691 Order of pole (three term test) = 37.42 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.691 Order of pole (three term test) = 28.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44964.0MB, alloc=44.3MB, time=535.49 memory used=45010.5MB, alloc=44.3MB, time=536.04 memory used=45056.9MB, alloc=44.3MB, time=536.62 x[1] = 0.4837 1.714 h = 0.001 0.003 y2[1] (numeric) = 12.1319153088 21.3129373141 y2[1] (closed_form) = 16.1696850897 19.5174103622 absolute error = 4.419 relative error = 17.44 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.53688809184 -1.24890780639 y1[1] (closed_form) = 2.53688809184 -1.24890780639 absolute error = 5.000e-63 relative error = 1.768e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.707 Order of pole (three term test) = 37.42 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.707 Order of pole (three term test) = 28.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45103.0MB, alloc=44.3MB, time=537.16 memory used=45149.7MB, alloc=44.3MB, time=537.71 x[1] = 0.4847 1.717 h = 0.0001 0.004 y2[1] (numeric) = 12.1376636508 21.3624236365 y2[1] (closed_form) = 16.185981179 19.5537776324 absolute error = 4.434 relative error = 17.47 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.54269404002 -1.25529589263 y1[1] (closed_form) = 2.54269404002 -1.25529589263 absolute error = 5.657e-63 relative error = 1.995e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.753 Order of pole (three term test) = 37.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.753 Order of pole (three term test) = 28.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45195.6MB, alloc=44.3MB, time=538.24 memory used=45242.1MB, alloc=44.3MB, time=538.79 x[1] = 0.4848 1.721 h = 0.003 0.006 y2[1] (numeric) = 12.1434467896 21.4119250016 y2[1] (closed_form) = 16.192268306 19.6038414278 absolute error = 4.434 relative error = 17.44 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.55211510349 -1.26090126446 y1[1] (closed_form) = 2.55211510349 -1.26090126446 absolute error = 5.000e-63 relative error = 1.756e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.815 Order of pole (three term test) = 37.48 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.815 Order of pole (three term test) = 28.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45288.1MB, alloc=44.3MB, time=539.32 memory used=45334.8MB, alloc=44.3MB, time=539.88 x[1] = 0.4878 1.727 h = 0.0001 0.005 y2[1] (numeric) = 12.1492649477 21.4614413459 y2[1] (closed_form) = 16.2375514335 19.675379495 absolute error = 4.461 relative error = 17.49 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.56245705931 -1.27621148959 y1[1] (closed_form) = 2.56245705931 -1.27621148959 absolute error = 5.657e-63 relative error = 1.976e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.91 Order of pole (three term test) = 37.51 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.91 Order of pole (three term test) = 28.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45381.0MB, alloc=44.3MB, time=540.41 memory used=45427.7MB, alloc=44.3MB, time=540.96 x[1] = 0.4879 1.732 h = 0.0001 0.003 y2[1] (numeric) = 12.1551183488 21.510972605 y2[1] (closed_form) = 16.2452069568 19.7380935864 absolute error = 4.458 relative error = 17.44 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.57437942985 -1.28326704353 y1[1] (closed_form) = 2.57437942985 -1.28326704353 absolute error = 5.657e-63 relative error = 1.967e-61 % Correct digits = 63 memory used=45474.4MB, alloc=44.3MB, time=541.51 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.989 Order of pole (three term test) = 37.57 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 7.989 Order of pole (three term test) = 28.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45520.7MB, alloc=44.3MB, time=542.08 memory used=45567.7MB, alloc=44.3MB, time=542.64 x[1] = 0.488 1.735 h = 0.001 0.001 y2[1] (numeric) = 12.1610072175 21.5605187136 y2[1] (closed_form) = 16.2503210693 19.7756988684 absolute error = 4.462 relative error = 17.43 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.58150828701 -1.28761402158 y1[1] (closed_form) = 2.58150828701 -1.28761402158 absolute error = 6.403e-63 relative error = 2.220e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.037 Order of pole (three term test) = 37.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.037 Order of pole (three term test) = 28.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45613.6MB, alloc=44.3MB, time=543.18 memory used=45660.2MB, alloc=44.3MB, time=543.73 x[1] = 0.489 1.736 h = 0.001 0.003 y2[1] (numeric) = 12.1669317795 21.6100796057 y2[1] (closed_form) = 16.2641926177 19.7869913911 absolute error = 4.485 relative error = 17.51 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.58256237593 -1.29141262338 y1[1] (closed_form) = 2.58256237593 -1.29141262338 absolute error = 5.657e-63 relative error = 1.959e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.053 Order of pole (three term test) = 37.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.053 Order of pole (three term test) = 28.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45706.0MB, alloc=44.3MB, time=544.26 memory used=45752.8MB, alloc=44.3MB, time=544.82 x[1] = 0.49 1.739 h = 0.0001 0.004 y2[1] (numeric) = 12.1728922618 21.6596552142 y2[1] (closed_form) = 16.2806622108 19.8234532531 absolute error = 4.499 relative error = 17.54 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.58847561482 -1.29797512061 y1[1] (closed_form) = 2.58847561482 -1.29797512061 absolute error = 5.657e-63 relative error = 1.954e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.102 Order of pole (three term test) = 37.62 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.102 Order of pole (three term test) = 28.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45798.8MB, alloc=44.3MB, time=545.35 memory used=45845.3MB, alloc=44.3MB, time=545.90 x[1] = 0.4901 1.743 h = 0.003 0.006 y2[1] (numeric) = 12.1788888925 21.7092454713 y2[1] (closed_form) = 16.2871249865 19.8736962878 absolute error = 4.5 relative error = 17.51 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.59809156211 -1.30375254414 y1[1] (closed_form) = 2.59809156211 -1.30375254414 absolute error = 5.657e-63 relative error = 1.946e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.167 Order of pole (three term test) = 37.66 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.167 Order of pole (three term test) = 28.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45891.3MB, alloc=44.3MB, time=546.42 memory used=45937.8MB, alloc=44.3MB, time=546.98 memory used=45984.4MB, alloc=44.3MB, time=547.53 x[1] = 0.4931 1.749 h = 0.0001 0.005 y2[1] (numeric) = 12.1849219007 21.758850308 y2[1] (closed_form) = 16.3328046162 19.9453815779 absolute error = 4.527 relative error = 17.56 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.60860692478 -1.31946488285 y1[1] (closed_form) = 2.60860692478 -1.31946488285 absolute error = 5.657e-63 relative error = 1.935e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.265 Order of pole (three term test) = 37.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.265 Order of pole (three term test) = 28.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46030.6MB, alloc=44.3MB, time=548.06 memory used=46077.3MB, alloc=44.3MB, time=548.62 x[1] = 0.4932 1.754 h = 0.0001 0.003 y2[1] (numeric) = 12.1909915165 21.8084696549 y2[1] (closed_form) = 16.3406815753 20.0083226978 absolute error = 4.523 relative error = 17.51 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.62077563643 -1.32673726738 y1[1] (closed_form) = 2.62077563643 -1.32673726738 absolute error = 5.000e-63 relative error = 1.702e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.348 Order of pole (three term test) = 37.75 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.348 Order of pole (three term test) = 28.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46123.6MB, alloc=44.3MB, time=549.16 memory used=46170.5MB, alloc=44.3MB, time=549.72 x[1] = 0.4933 1.757 h = 0.001 0.001 y2[1] (numeric) = 12.1970979715 21.8581034413 y2[1] (closed_form) = 16.3459309443 20.0460630346 absolute error = 4.527 relative error = 17.5 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.62805112917 -1.33121690173 y1[1] (closed_form) = 2.62805112917 -1.33121690173 absolute error = 5.000e-63 relative error = 1.697e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.399 Order of pole (three term test) = 37.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.399 Order of pole (three term test) = 28.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46216.7MB, alloc=44.3MB, time=550.27 memory used=46263.2MB, alloc=44.3MB, time=550.84 x[1] = 0.4943 1.758 h = 0.001 0.003 y2[1] (numeric) = 12.2032414981 21.9077515957 y2[1] (closed_form) = 16.3598926889 20.0573584546 absolute error = 4.55 relative error = 17.58 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.62911292875 -1.33510852412 y1[1] (closed_form) = 2.62911292875 -1.33510852412 absolute error = 5.000e-63 relative error = 1.696e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.415 Order of pole (three term test) = 37.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.415 Order of pole (three term test) = 28.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46309.2MB, alloc=44.3MB, time=551.38 memory used=46355.9MB, alloc=44.3MB, time=551.93 x[1] = 0.4953 1.761 h = 0.0001 0.004 y2[1] (numeric) = 12.20942233 21.9574140459 y2[1] (closed_form) = 16.3765402424 20.0939163457 absolute error = 4.565 relative error = 17.61 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.63513462384 -1.34184980341 y1[1] (closed_form) = 2.63513462384 -1.34184980341 absolute error = 5.385e-63 relative error = 1.821e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.466 Order of pole (three term test) = 37.81 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.466 Order of pole (three term test) = 28.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46402.1MB, alloc=44.3MB, time=552.46 memory used=46448.6MB, alloc=44.3MB, time=553.01 memory used=46495.2MB, alloc=44.3MB, time=553.56 x[1] = 0.4954 1.765 h = 0.003 0.006 y2[1] (numeric) = 12.2156407019 22.0070907184 y2[1] (closed_form) = 16.3831835463 20.1443420158 absolute error = 4.565 relative error = 17.58 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.64494849169 -1.34780415531 y1[1] (closed_form) = 2.64494849169 -1.34780415531 absolute error = 5.831e-63 relative error = 1.964e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.534 Order of pole (three term test) = 37.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.534 Order of pole (three term test) = 28.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46541.3MB, alloc=44.3MB, time=554.10 memory used=46587.9MB, alloc=44.3MB, time=554.65 x[1] = 0.4984 1.771 h = 0.0001 0.005 y2[1] (numeric) = 12.2218968498 22.056781539 y2[1] (closed_form) = 16.429269552 20.2161761995 absolute error = 4.592 relative error = 17.63 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.65563839101 -1.36392822358 y1[1] (closed_form) = 2.65563839101 -1.36392822358 absolute error = 5.831e-63 relative error = 1.953e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.637 Order of pole (three term test) = 37.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.637 Order of pole (three term test) = 28.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46633.9MB, alloc=44.3MB, time=555.18 memory used=46680.6MB, alloc=44.3MB, time=555.73 x[1] = 0.4985 1.776 h = 0.0001 0.003 y2[1] (numeric) = 12.2281910108 22.1064864328 y2[1] (closed_form) = 16.4373741005 20.2793486443 absolute error = 4.589 relative error = 17.58 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.6680572957 -1.37142359231 y1[1] (closed_form) = 2.6680572957 -1.37142359231 absolute error = 5.385e-63 relative error = 1.795e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.724 Order of pole (three term test) = 37.95 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.724 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46726.7MB, alloc=44.3MB, time=556.28 memory used=46773.6MB, alloc=44.3MB, time=556.85 x[1] = 0.4986 1.779 h = 0.001 0.001 y2[1] (numeric) = 12.2345234231 22.1562053236 y2[1] (closed_form) = 16.4427624686 20.3172265739 absolute error = 4.593 relative error = 17.57 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.67548169637 -1.3760396221 y1[1] (closed_form) = 2.67548169637 -1.3760396221 absolute error = 5.385e-63 relative error = 1.790e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.776 Order of pole (three term test) = 37.99 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.776 Order of pole (three term test) = 28.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46819.7MB, alloc=44.3MB, time=557.40 memory used=46866.2MB, alloc=44.3MB, time=557.94 x[1] = 0.4996 1.78 h = 0.001 0.003 y2[1] (numeric) = 12.240894326 22.2059381345 y2[1] (closed_form) = 16.4568165175 20.3285245579 absolute error = 4.615 relative error = 17.65 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.67655078311 -1.38002628698 y1[1] (closed_form) = 2.67655078311 -1.38002628698 absolute error = 5.385e-63 relative error = 1.788e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.794 Order of pole (three term test) = 37.98 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.794 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46912.5MB, alloc=44.3MB, time=558.49 memory used=46958.9MB, alloc=44.3MB, time=559.04 memory used=47005.6MB, alloc=44.3MB, time=559.59 x[1] = 0.5006 1.783 h = 0.0001 0.004 y2[1] (numeric) = 12.24730396 22.2556847875 y2[1] (closed_form) = 16.4736465918 20.3651799176 absolute error = 4.63 relative error = 17.68 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.68268210764 -1.3869508262 y1[1] (closed_form) = 2.68268210764 -1.3869508262 absolute error = 5.385e-63 relative error = 1.783e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.847 Order of pole (three term test) = 38.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.847 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47051.4MB, alloc=44.3MB, time=560.12 memory used=47097.9MB, alloc=44.3MB, time=560.67 x[1] = 0.5007 1.787 h = 0.003 0.006 y2[1] (numeric) = 12.2537525669 22.3054452038 y2[1] (closed_form) = 16.4804754281 20.4157916601 absolute error = 4.63 relative error = 17.65 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.69269698176 -1.39308710997 y1[1] (closed_form) = 2.69269698176 -1.39308710997 absolute error = 4.472e-63 relative error = 1.475e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.918 Order of pole (three term test) = 38.06 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 8.918 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47143.7MB, alloc=44.3MB, time=561.20 memory used=47190.5MB, alloc=44.3MB, time=561.76 x[1] = 0.5037 1.793 h = 0.0001 0.005 y2[1] (numeric) = 12.2602403895 22.3552193036 y2[1] (closed_form) = 16.5269779039 20.4877763814 absolute error = 4.658 relative error = 17.69 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.70356253107 -1.40963275221 y1[1] (closed_form) = 2.70356253107 -1.40963275221 absolute error = 4.472e-63 relative error = 1.467e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.025 Order of pole (three term test) = 38.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.025 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47236.5MB, alloc=44.3MB, time=562.29 memory used=47283.2MB, alloc=44.3MB, time=562.84 x[1] = 0.5038 1.798 h = 0.0001 0.003 y2[1] (numeric) = 12.2667676718 22.4050070063 y2[1] (closed_form) = 16.5353163528 20.5511844998 absolute error = 4.654 relative error = 17.64 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.71623554282 -1.41735741875 y1[1] (closed_form) = 2.71623554282 -1.41735741875 absolute error = 5.099e-63 relative error = 1.664e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.116 Order of pole (three term test) = 38.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.116 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47329.3MB, alloc=44.3MB, time=563.38 memory used=47376.3MB, alloc=44.3MB, time=563.94 x[1] = 0.5039 1.801 h = 0.001 0.001 y2[1] (numeric) = 12.273334659 22.45480823 y2[1] (closed_form) = 16.540847558 20.5892025905 absolute error = 4.657 relative error = 17.63 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.72381115982 -1.42211368003 y1[1] (closed_form) = 2.72381115982 -1.42211368003 absolute error = 5.385e-63 relative error = 1.753e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.171 Order of pole (three term test) = 38.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.171 Order of pole (three term test) = 28.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47423.0MB, alloc=44.3MB, time=564.50 memory used=47469.2MB, alloc=44.3MB, time=565.04 memory used=47516.0MB, alloc=44.3MB, time=565.60 x[1] = 0.5049 1.802 h = 0.0001 0.004 y2[1] (numeric) = 12.2799415973 22.5046228923 y2[1] (closed_form) = 16.5549960625 20.6005027848 absolute error = 4.68 relative error = 17.71 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.72488709138 -1.42619745435 y1[1] (closed_form) = 2.72488709138 -1.42619745435 absolute error = 5.385e-63 relative error = 1.751e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.189 Order of pole (three term test) = 38.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.189 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47561.9MB, alloc=44.3MB, time=566.13 memory used=47608.5MB, alloc=44.3MB, time=566.68 x[1] = 0.505 1.806 h = 0.003 0.006 y2[1] (numeric) = 12.2865887344 22.5544509093 y2[1] (closed_form) = 16.561986431 20.65127977 absolute error = 4.68 relative error = 17.68 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.7350797442 -1.4324919994 y1[1] (closed_form) = 2.7350797442 -1.4324919994 absolute error = 5.385e-63 relative error = 1.744e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.263 Order of pole (three term test) = 38.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.263 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47654.4MB, alloc=44.3MB, time=567.20 memory used=47701.1MB, alloc=44.3MB, time=567.76 x[1] = 0.508 1.812 h = 0.0001 0.005 y2[1] (numeric) = 12.293276319 22.6042921967 y2[1] (closed_form) = 16.6088538256 20.7234004925 absolute error = 4.708 relative error = 17.73 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.74610255054 -1.44940646943 y1[1] (closed_form) = 2.74610255054 -1.44940646943 absolute error = 5.385e-63 relative error = 1.734e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.375 Order of pole (three term test) = 38.28 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.375 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47747.0MB, alloc=44.3MB, time=568.29 memory used=47793.7MB, alloc=44.3MB, time=568.84 x[1] = 0.5081 1.817 h = 0.0001 0.003 y2[1] (numeric) = 12.300004601 22.6541466688 y2[1] (closed_form) = 16.6173959065 20.7870178851 absolute error = 4.704 relative error = 17.68 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.7590003078 -1.45733059711 y1[1] (closed_form) = 2.7590003078 -1.45733059711 absolute error = 5.385e-63 relative error = 1.726e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.469 Order of pole (three term test) = 38.34 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.469 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47840.0MB, alloc=44.3MB, time=569.39 memory used=47886.7MB, alloc=44.3MB, time=569.95 x[1] = 0.5082 1.82 h = 0.001 0.001 y2[1] (numeric) = 12.3067738313 22.7040142392 y2[1] (closed_form) = 16.6230514974 20.8251604672 absolute error = 4.707 relative error = 17.67 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.76670969743 -1.46220887309 y1[1] (closed_form) = 2.76670969743 -1.46220887309 absolute error = 6.083e-63 relative error = 1.944e-61 % Correct digits = 63 memory used=47933.7MB, alloc=44.3MB, time=570.51 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.526 Order of pole (three term test) = 38.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.526 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47979.6MB, alloc=44.3MB, time=571.05 memory used=48026.0MB, alloc=44.3MB, time=571.60 x[1] = 0.5092 1.821 h = 0.001 0.003 y2[1] (numeric) = 12.3135842624 22.7538948202 y2[1] (closed_form) = 16.6372830415 20.8364634256 absolute error = 4.73 relative error = 17.74 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.7677923428 -1.46637785212 y1[1] (closed_form) = 2.7677923428 -1.46637785212 absolute error = 6.325e-63 relative error = 2.019e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.545 Order of pole (three term test) = 38.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.545 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48071.9MB, alloc=44.3MB, time=572.14 memory used=48118.6MB, alloc=44.3MB, time=572.69 x[1] = 0.5102 1.824 h = 0.0001 0.004 y2[1] (numeric) = 12.3204361478 22.8037883235 y2[1] (closed_form) = 16.6544640443 20.8733062967 absolute error = 4.745 relative error = 17.77 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.77413312325 -1.47365434959 y1[1] (closed_form) = 2.77413312325 -1.47365434959 absolute error = 5.385e-63 relative error = 1.714e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.602 Order of pole (three term test) = 38.4 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.602 Order of pole (three term test) = 28.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48164.6MB, alloc=44.3MB, time=573.22 memory used=48211.2MB, alloc=44.3MB, time=573.78 x[1] = 0.5103 1.828 h = 0.003 0.006 y2[1] (numeric) = 12.327329742 22.8536946594 y2[1] (closed_form) = 16.6616495583 20.9242759245 absolute error = 4.744 relative error = 17.74 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.78453271859 -1.48014044657 y1[1] (closed_form) = 2.78453271859 -1.48014044657 absolute error = 6.083e-63 relative error = 1.929e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.679 Order of pole (three term test) = 38.46 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.679 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48257.0MB, alloc=44.3MB, time=574.30 memory used=48303.9MB, alloc=44.3MB, time=574.86 x[1] = 0.5133 1.834 h = 0.0001 0.005 y2[1] (numeric) = 12.334265301 22.9036137374 y2[1] (closed_form) = 16.7089527892 20.9965502931 absolute error = 4.772 relative error = 17.78 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.79573332059 -1.49749542029 y1[1] (closed_form) = 2.79573332059 -1.49749542029 absolute error = 6.083e-63 relative error = 1.918e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.796 Order of pole (three term test) = 38.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.796 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48350.3MB, alloc=44.3MB, time=575.40 memory used=48396.7MB, alloc=44.3MB, time=575.94 memory used=48443.4MB, alloc=44.3MB, time=576.50 x[1] = 0.5134 1.839 h = 0.0001 0.003 y2[1] (numeric) = 12.3412430819 22.9535454662 y2[1] (closed_form) = 16.7177408941 21.0604116721 absolute error = 4.768 relative error = 17.73 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.80889271409 -1.5056609845 y1[1] (closed_form) = 2.80889271409 -1.5056609845 absolute error = 6.325e-63 relative error = 1.984e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.895 Order of pole (three term test) = 38.56 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.895 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48489.5MB, alloc=44.3MB, time=577.04 memory used=48536.4MB, alloc=44.3MB, time=577.60 x[1] = 0.5135 1.842 h = 0.001 0.001 y2[1] (numeric) = 12.348263343 23.0034897531 y2[1] (closed_form) = 16.7235466944 21.0986993245 absolute error = 4.772 relative error = 17.72 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.81675776056 -1.51068686727 y1[1] (closed_form) = 2.81675776056 -1.51068686727 absolute error = 6.325e-63 relative error = 1.979e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.954 Order of pole (three term test) = 38.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.954 Order of pole (three term test) = 28.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48582.4MB, alloc=44.3MB, time=578.15 memory used=48629.0MB, alloc=44.3MB, time=578.70 x[1] = 0.5145 1.843 h = 0.001 0.003 y2[1] (numeric) = 12.3553263439 23.0534465047 y2[1] (closed_form) = 16.7378768181 21.1100038054 absolute error = 4.794 relative error = 17.8 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.81784640109 -1.51495693041 y1[1] (closed_form) = 2.81784640109 -1.51495693041 absolute error = 6.083e-63 relative error = 1.901e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.974 Order of pole (three term test) = 38.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 9.974 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48674.8MB, alloc=44.3MB, time=579.24 memory used=48721.5MB, alloc=44.3MB, time=579.79 x[1] = 0.5155 1.846 h = 0.0001 0.004 y2[1] (numeric) = 12.3624323452 23.1034156264 y2[1] (closed_form) = 16.7552539636 21.1469483309 absolute error = 4.809 relative error = 17.82 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.82430026333 -1.52243009444 y1[1] (closed_form) = 2.82430026333 -1.52243009444 absolute error = 6.083e-63 relative error = 1.896e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.03 Order of pole (three term test) = 38.63 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.03 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48767.6MB, alloc=44.3MB, time=580.32 memory used=48814.2MB, alloc=44.3MB, time=580.88 x[1] = 0.5156 1.85 h = 0.003 0.006 y2[1] (numeric) = 12.369581609 23.1533970225 y2[1] (closed_form) = 16.7626400013 21.1981141599 absolute error = 4.809 relative error = 17.79 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.83491002992 -1.52911312588 y1[1] (closed_form) = 2.83491002992 -1.52911312588 absolute error = 6.083e-63 relative error = 1.888e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.11 Order of pole (three term test) = 38.68 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.11 Order of pole (three term test) = 28.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48860.6MB, alloc=44.3MB, time=581.42 memory used=48906.7MB, alloc=44.3MB, time=581.96 memory used=48953.2MB, alloc=44.3MB, time=582.51 x[1] = 0.5186 1.856 h = 0.0001 0.005 y2[1] (numeric) = 12.3767743985 23.2033905966 y2[1] (closed_form) = 16.8103898201 21.2705437354 absolute error = 4.837 relative error = 17.84 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.84628948669 -1.54691912799 y1[1] (closed_form) = 2.84628948669 -1.54691912799 absolute error = 6.083e-63 relative error = 1.878e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.24 Order of pole (three term test) = 38.72 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.24 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48999.3MB, alloc=44.3MB, time=583.04 memory used=49045.9MB, alloc=44.3MB, time=583.59 x[1] = 0.5187 1.861 h = 0.0001 0.003 y2[1] (numeric) = 12.3840109781 23.253396251 y2[1] (closed_form) = 16.8194307325 21.3346536043 absolute error = 4.833 relative error = 17.79 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.85971461176 -1.5553329206 y1[1] (closed_form) = 2.85971461176 -1.5553329206 absolute error = 6.083e-63 relative error = 1.869e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.34 Order of pole (three term test) = 38.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.34 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49092.1MB, alloc=44.3MB, time=584.13 memory used=49138.9MB, alloc=44.3MB, time=584.70 x[1] = 0.5188 1.864 h = 0.001 0.001 y2[1] (numeric) = 12.3912916134 23.3034138869 y2[1] (closed_form) = 16.8253908662 21.3730889846 absolute error = 4.836 relative error = 17.78 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.86773772881 -1.56051053584 y1[1] (closed_form) = 2.86773772881 -1.56051053584 absolute error = 6e-63 relative error = 1.838e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.4 Order of pole (three term test) = 38.83 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.4 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49185.1MB, alloc=44.3MB, time=585.25 memory used=49231.8MB, alloc=44.3MB, time=585.80 x[1] = 0.5198 1.865 h = 0.001 0.003 y2[1] (numeric) = 12.3986165715 23.3534434048 y2[1] (closed_form) = 16.839821848 21.3843945729 absolute error = 4.858 relative error = 17.85 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.86883186496 -1.5648838838 y1[1] (closed_form) = 2.86883186496 -1.5648838838 absolute error = 6.083e-63 relative error = 1.861e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.42 Order of pole (three term test) = 38.83 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.42 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49277.7MB, alloc=44.3MB, time=586.34 memory used=49324.5MB, alloc=44.3MB, time=586.89 x[1] = 0.5208 1.868 h = 0.0001 0.004 y2[1] (numeric) = 12.4059861204 23.4034847037 y2[1] (closed_form) = 16.8574001191 21.4214421985 absolute error = 4.873 relative error = 17.88 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.87540000859 -1.57255862673 y1[1] (closed_form) = 2.87540000859 -1.57255862673 absolute error = 6e-63 relative error = 1.831e-61 % Correct digits = 63 memory used=49371.2MB, alloc=44.3MB, time=587.44 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.49 Order of pole (three term test) = 38.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.49 Order of pole (three term test) = 28.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49417.3MB, alloc=44.3MB, time=587.97 memory used=49463.9MB, alloc=44.3MB, time=588.52 x[1] = 0.5209 1.872 h = 0.003 0.006 y2[1] (numeric) = 12.4134005297 23.453537682 y2[1] (closed_form) = 16.8649921962 21.4728078302 absolute error = 4.872 relative error = 17.84 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.88622322507 -1.57944411397 y1[1] (closed_form) = 2.88622322507 -1.57944411397 absolute error = 6e-63 relative error = 1.824e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.57 Order of pole (three term test) = 38.92 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.57 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49509.8MB, alloc=44.3MB, time=589.05 memory used=49556.4MB, alloc=44.3MB, time=589.60 x[1] = 0.5239 1.878 h = 0.0001 0.005 y2[1] (numeric) = 12.4208600698 23.5036022366 y2[1] (closed_form) = 16.9131995943 21.5453941398 absolute error = 4.901 relative error = 17.89 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.89778257209 -1.59771191652 y1[1] (closed_form) = 2.89778257209 -1.59771191652 absolute error = 6e-63 relative error = 1.813e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.7 Order of pole (three term test) = 38.96 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.7 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49602.4MB, alloc=44.3MB, time=590.14 memory used=49649.0MB, alloc=44.3MB, time=590.69 x[1] = 0.524 1.883 h = 0.0001 0.003 y2[1] (numeric) = 12.4283650128 23.5536782637 y2[1] (closed_form) = 16.9225002709 21.6097570563 absolute error = 4.897 relative error = 17.84 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.91147758729 -1.60638090454 y1[1] (closed_form) = 2.91147758729 -1.60638090454 absolute error = 6e-63 relative error = 1.804e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.8 Order of pole (three term test) = 39.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.8 Order of pole (three term test) = 28.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49695.1MB, alloc=44.3MB, time=591.22 memory used=49742.0MB, alloc=44.3MB, time=591.79 x[1] = 0.5241 1.886 h = 0.001 0.001 y2[1] (numeric) = 12.4359156318 23.6037656583 y2[1] (closed_form) = 16.9286189666 21.6483428536 absolute error = 4.9 relative error = 17.83 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.91966122533 -1.61171448399 y1[1] (closed_form) = 2.91966122533 -1.61171448399 absolute error = 6e-63 relative error = 1.799e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.87 Order of pole (three term test) = 39.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.87 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49788.3MB, alloc=44.3MB, time=592.33 memory used=49834.7MB, alloc=44.3MB, time=592.88 memory used=49881.2MB, alloc=44.3MB, time=593.44 x[1] = 0.5251 1.887 h = 0.001 0.003 y2[1] (numeric) = 12.4435122013 23.6538643141 y2[1] (closed_form) = 16.9431531311 21.6596491112 absolute error = 4.922 relative error = 17.9 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.92076033601 -1.61619336584 y1[1] (closed_form) = 2.92076033601 -1.61619336584 absolute error = 7e-63 relative error = 2.097e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.89 Order of pole (three term test) = 39.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.89 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49927.2MB, alloc=44.3MB, time=593.97 memory used=49973.9MB, alloc=44.3MB, time=594.52 x[1] = 0.5261 1.89 h = 0.0001 0.004 y2[1] (numeric) = 12.4511549969 23.7039741242 y2[1] (closed_form) = 16.9609376266 21.6968012828 absolute error = 4.936 relative error = 17.92 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.9274439657 -1.62407471858 y1[1] (closed_form) = 2.9274439657 -1.62407471858 absolute error = 6.083e-63 relative error = 1.817e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.96 Order of pole (three term test) = 39.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 10.96 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50019.9MB, alloc=44.3MB, time=595.06 memory used=50066.5MB, alloc=44.3MB, time=595.60 x[1] = 0.5262 1.894 h = 0.003 0.006 y2[1] (numeric) = 12.4588442957 23.7540949801 y2[1] (closed_form) = 16.9687413993 21.7483703615 absolute error = 4.936 relative error = 17.89 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.9384839608 -1.63116832502 y1[1] (closed_form) = 2.9384839608 -1.63116832502 absolute error = 7.071e-63 relative error = 2.104e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.04 Order of pole (three term test) = 39.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.04 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50112.5MB, alloc=44.3MB, time=596.14 memory used=50159.3MB, alloc=44.3MB, time=596.69 x[1] = 0.5292 1.9 h = 0.0001 0.005 y2[1] (numeric) = 12.4665803759 23.8042267726 y2[1] (closed_form) = 17.0174176131 21.8211148974 absolute error = 4.964 relative error = 17.94 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.95022420787 -1.64990895256 y1[1] (closed_form) = 2.95022420787 -1.64990895256 absolute error = 6e-63 relative error = 1.775e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.18 Order of pole (three term test) = 39.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.18 Order of pole (three term test) = 28.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50205.3MB, alloc=44.3MB, time=597.23 memory used=50252.1MB, alloc=44.3MB, time=597.78 x[1] = 0.5293 1.905 h = 0.0001 0.003 y2[1] (numeric) = 12.474363517 23.8543693911 y2[1] (closed_form) = 17.026985188 21.8857354741 absolute error = 4.96 relative error = 17.89 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.96419333531 -1.65884028232 y1[1] (closed_form) = 2.96419333531 -1.65884028232 absolute error = 7e-63 relative error = 2.061e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.29 Order of pole (three term test) = 39.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.29 Order of pole (three term test) = 28.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50298.5MB, alloc=44.3MB, time=598.32 memory used=50344.9MB, alloc=44.3MB, time=598.88 memory used=50391.8MB, alloc=44.3MB, time=599.45 x[1] = 0.5294 1.908 h = 0.001 0.001 y2[1] (numeric) = 12.4821939998 23.9045227243 y2[1] (closed_form) = 17.0332667819 21.9244744091 absolute error = 4.963 relative error = 17.88 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.97253998156 -1.66433416623 y1[1] (closed_form) = 2.97253998156 -1.66433416623 absolute error = 6e-63 relative error = 1.761e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.36 Order of pole (three term test) = 39.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.36 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50437.9MB, alloc=44.3MB, time=599.99 memory used=50484.6MB, alloc=44.3MB, time=600.54 x[1] = 0.5304 1.909 h = 0.0001 0.004 y2[1] (numeric) = 12.4900721065 23.9546866593 y2[1] (closed_form) = 17.047906501 21.9357808741 absolute error = 4.985 relative error = 17.94 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.97364352332 -1.66892088033 y1[1] (closed_form) = 2.97364352332 -1.66892088033 absolute error = 6e-63 relative error = 1.760e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.38 Order of pole (three term test) = 39.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.38 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50530.5MB, alloc=44.3MB, time=601.08 memory used=50577.0MB, alloc=44.3MB, time=601.63 x[1] = 0.5305 1.913 h = 0.003 0.006 y2[1] (numeric) = 12.4979981205 24.0048610824 y2[1] (closed_form) = 17.0558946499 21.9875306409 absolute error = 4.984 relative error = 17.91 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.98487539181 -1.67619563777 y1[1] (closed_form) = 2.98487539181 -1.67619563777 absolute error = 6.083e-63 relative error = 1.777e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.47 Order of pole (three term test) = 39.39 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.47 Order of pole (three term test) = 28.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50623.0MB, alloc=44.3MB, time=602.16 memory used=50669.7MB, alloc=44.3MB, time=602.71 x[1] = 0.5335 1.919 h = 0.0001 0.005 y2[1] (numeric) = 12.5059723263 24.0550458788 y2[1] (closed_form) = 17.1049816856 22.0604183106 absolute error = 5.013 relative error = 17.96 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.99677795485 -1.6953501114 y1[1] (closed_form) = 2.99677795485 -1.6953501114 absolute error = 6e-63 relative error = 1.743e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.61 Order of pole (three term test) = 39.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.61 Order of pole (three term test) = 28.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50715.7MB, alloc=44.3MB, time=603.24 memory used=50762.3MB, alloc=44.3MB, time=603.80 x[1] = 0.5336 1.924 h = 0.0001 0.003 y2[1] (numeric) = 12.5139950101 24.1052409323 y2[1] (closed_form) = 17.1147817041 22.1252677065 absolute error = 5.009 relative error = 17.91 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.01098970289 -1.70450978391 y1[1] (closed_form) = 3.01098970289 -1.70450978391 absolute error = 6e-63 relative error = 1.734e-61 % Correct digits = 63 memory used=50808.9MB, alloc=44.3MB, time=604.35 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.73 Order of pole (three term test) = 39.52 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.73 Order of pole (three term test) = 28.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50855.1MB, alloc=44.3MB, time=604.90 memory used=50902.1MB, alloc=44.3MB, time=605.46 x[1] = 0.5337 1.927 h = 0.001 0.001 y2[1] (numeric) = 12.5220664592 24.1554461259 y2[1] (closed_form) = 17.1212052026 22.164142673 absolute error = 5.012 relative error = 17.89 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.01948066303 -1.71014323015 y1[1] (closed_form) = 3.01948066303 -1.71014323015 absolute error = 6e-63 relative error = 1.729e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.8 Order of pole (three term test) = 39.56 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.8 Order of pole (three term test) = 28.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50948.2MB, alloc=44.3MB, time=606.00 memory used=50994.8MB, alloc=44.3MB, time=606.56 x[1] = 0.5347 1.928 h = 0.001 0.003 y2[1] (numeric) = 12.530186962 24.2056613412 y2[1] (closed_form) = 17.1359377211 22.1754502247 absolute error = 5.033 relative error = 17.96 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.0205888888 -1.71482459787 y1[1] (closed_form) = 3.0205888888 -1.71482459787 absolute error = 5e-63 relative error = 1.440e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.82 Order of pole (three term test) = 39.56 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.82 Order of pole (three term test) = 28.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51040.8MB, alloc=44.3MB, time=607.09 memory used=51087.6MB, alloc=44.3MB, time=607.64 x[1] = 0.5357 1.931 h = 0.0001 0.004 y2[1] (numeric) = 12.5383568086 24.2558864588 y2[1] (closed_form) = 17.1541186441 22.2128033834 absolute error = 5.048 relative error = 17.99 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.02749324057 -1.72310280025 y1[1] (closed_form) = 3.02749324057 -1.72310280025 absolute error = 5e-63 relative error = 1.435e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.89 Order of pole (three term test) = 39.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.89 Order of pole (three term test) = 28.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51133.6MB, alloc=44.3MB, time=608.18 memory used=51180.2MB, alloc=44.3MB, time=608.72 x[1] = 0.5358 1.935 h = 0.003 0.006 y2[1] (numeric) = 12.5465762903 24.306121358 y2[1] (closed_form) = 17.1623293545 22.264763566 absolute error = 5.047 relative error = 17.95 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.0389482873 -1.73059656385 y1[1] (closed_form) = 3.0389482873 -1.73059656385 absolute error = 5.099e-63 relative error = 1.458e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.99 Order of pole (three term test) = 39.66 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 11.99 Order of pole (three term test) = 28.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51226.0MB, alloc=44.3MB, time=609.25 memory used=51272.7MB, alloc=44.3MB, time=609.80 memory used=51319.4MB, alloc=44.3MB, time=610.36 x[1] = 0.5388 1.941 h = 0.0001 0.005 y2[1] (numeric) = 12.5548456995 24.3563659172 y2[1] (closed_form) = 17.2119067692 22.3378122789 absolute error = 5.076 relative error = 18 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.0510336924 -1.75024505552 y1[1] (closed_form) = 3.0510336924 -1.75024505552 absolute error = 5e-63 relative error = 1.422e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.13 Order of pole (three term test) = 39.71 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.13 Order of pole (three term test) = 28.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51365.5MB, alloc=44.3MB, time=610.89 memory used=51412.2MB, alloc=44.3MB, time=611.45 x[1] = 0.5389 1.946 h = 0.0001 0.003 y2[1] (numeric) = 12.5631653302 24.4066200135 y2[1] (closed_form) = 17.2219873917 22.4029281553 absolute error = 5.071 relative error = 17.95 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.06552766938 -1.75968080709 y1[1] (closed_form) = 3.06552766938 -1.75968080709 absolute error = 5e-63 relative error = 1.415e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.26 Order of pole (three term test) = 39.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.26 Order of pole (three term test) = 28.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51458.3MB, alloc=44.3MB, time=611.99 memory used=51505.1MB, alloc=44.3MB, time=612.55 x[1] = 0.539 1.949 h = 0.001 0.001 y2[1] (numeric) = 12.5715354776 24.4568835227 y2[1] (closed_form) = 17.2285821184 22.4419614617 absolute error = 5.074 relative error = 17.93 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.07418641914 -1.76548290105 y1[1] (closed_form) = 3.07418641914 -1.76548290105 absolute error = 5.099e-63 relative error = 1.438e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.33 Order of pole (three term test) = 39.84 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.33 Order of pole (three term test) = 28.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51551.3MB, alloc=44.3MB, time=613.09 memory used=51597.8MB, alloc=44.3MB, time=613.64 x[1] = 0.54 1.95 h = 0.001 0.003 y2[1] (numeric) = 12.5799564382 24.5071563195 y2[1] (closed_form) = 17.2434247401 22.4532683251 absolute error = 5.096 relative error = 18 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.0752980314 -1.77027651919 y1[1] (closed_form) = 3.0752980314 -1.77027651919 absolute error = 6.083e-63 relative error = 1.714e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.35 Order of pole (three term test) = 39.84 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.35 Order of pole (three term test) = 28.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51643.7MB, alloc=44.3MB, time=614.18 memory used=51690.4MB, alloc=44.3MB, time=614.73 x[1] = 0.541 1.953 h = 0.0001 0.004 y2[1] (numeric) = 12.58842851 24.5574382777 y2[1] (closed_form) = 17.2618271198 22.490730227 absolute error = 5.11 relative error = 18.02 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.08232140286 -1.77877638708 y1[1] (closed_form) = 3.08232140286 -1.77877638708 absolute error = 6e-63 relative error = 1.686e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.43 Order of pole (three term test) = 39.87 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.43 Order of pole (three term test) = 28.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51736.5MB, alloc=44.3MB, time=615.26 memory used=51783.0MB, alloc=44.3MB, time=615.81 memory used=51829.6MB, alloc=44.3MB, time=616.36 x[1] = 0.5411 1.957 h = 0.003 0.006 y2[1] (numeric) = 12.5969519921 24.6077292694 y2[1] (closed_form) = 17.2702664686 22.5429045967 absolute error = 5.109 relative error = 17.99 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.09400310278 -1.78649524493 y1[1] (closed_form) = 3.09400310278 -1.78649524493 absolute error = 6e-63 relative error = 1.679e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.53 Order of pole (three term test) = 39.94 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.53 Order of pole (three term test) = 28.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51875.7MB, alloc=44.3MB, time=616.89 memory used=51922.4MB, alloc=44.3MB, time=617.44 x[1] = 0.5441 1.963 h = 0.0001 0.005 y2[1] (numeric) = 12.6055271853 24.6580291661 y2[1] (closed_form) = 17.3203462312 22.6161157362 absolute error = 5.138 relative error = 18.04 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.10627227759 -1.80664953138 y1[1] (closed_form) = 3.10627227759 -1.80664953138 absolute error = 7e-63 relative error = 1.948e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.68 Order of pole (three term test) = 39.99 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.68 Order of pole (three term test) = 28.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51968.6MB, alloc=44.3MB, time=617.98 memory used=52015.3MB, alloc=44.3MB, time=618.53 x[1] = 0.5442 1.968 h = 0.0001 0.003 y2[1] (numeric) = 12.6141543913 24.7083378375 y2[1] (closed_form) = 17.3307151231 22.6815028669 absolute error = 5.134 relative error = 17.98 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.12105289106 -1.81636904422 y1[1] (closed_form) = 3.12105289106 -1.81636904422 absolute error = 7e-63 relative error = 1.938e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.81 Order of pole (three term test) = 40.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.81 Order of pole (three term test) = 28.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52061.4MB, alloc=44.3MB, time=619.07 memory used=52108.2MB, alloc=44.3MB, time=619.63 x[1] = 0.5443 1.971 h = 0.001 0.001 y2[1] (numeric) = 12.6228339135 24.7586551526 y2[1] (closed_form) = 17.3374857353 22.720697327 absolute error = 5.136 relative error = 17.97 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.12988202499 -1.8223444506 y1[1] (closed_form) = 3.12988202499 -1.8223444506 absolute error = 7.071e-63 relative error = 1.952e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.88 Order of pole (three term test) = 40.13 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.88 Order of pole (three term test) = 28.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52154.4MB, alloc=44.3MB, time=620.18 memory used=52200.9MB, alloc=44.3MB, time=620.73 x[1] = 0.5453 1.972 h = 0.001 0.003 y2[1] (numeric) = 12.6315660566 24.808980979 y2[1] (closed_form) = 17.3524409729 22.7320029685 absolute error = 5.158 relative error = 18.03 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.1309964126 -1.82725276392 y1[1] (closed_form) = 3.1309964126 -1.82725276392 absolute error = 7.071e-63 relative error = 1.951e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.91 Order of pole (three term test) = 40.13 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.91 Order of pole (three term test) = 28.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52247.1MB, alloc=44.3MB, time=621.28 memory used=52293.4MB, alloc=44.3MB, time=621.82 memory used=52340.2MB, alloc=44.3MB, time=622.37 x[1] = 0.5463 1.975 h = 0.0001 0.004 y2[1] (numeric) = 12.6403511265 24.859315183 y2[1] (closed_form) = 17.3710703804 22.7695750561 absolute error = 5.172 relative error = 18.06 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.13814002356 -1.83597981057 y1[1] (closed_form) = 3.13814002356 -1.83597981057 absolute error = 7.071e-63 relative error = 1.945e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.99 Order of pole (three term test) = 40.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 12.99 Order of pole (three term test) = 28.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52386.0MB, alloc=44.3MB, time=622.90 memory used=52432.5MB, alloc=44.3MB, time=623.45 x[1] = 0.5464 1.979 h = 0.003 0.006 y2[1] (numeric) = 12.6491894307 24.9096576297 y2[1] (closed_form) = 17.3797445986 22.8219674284 absolute error = 5.171 relative error = 18.03 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.15005190244 -1.84393000626 y1[1] (closed_form) = 3.15005190244 -1.84393000626 absolute error = 6e-63 relative error = 1.644e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.09 Order of pole (three term test) = 40.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.09 Order of pole (three term test) = 28.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52478.5MB, alloc=44.3MB, time=623.99 memory used=52525.2MB, alloc=44.3MB, time=624.54 x[1] = 0.5494 1.985 h = 0.0001 0.005 y2[1] (numeric) = 12.6580812778 24.9600081831 y2[1] (closed_form) = 17.430338945 22.8953423348 absolute error = 5.2 relative error = 18.07 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.16250574041 -1.86460213767 y1[1] (closed_form) = 3.16250574041 -1.86460213767 absolute error = 7e-63 relative error = 1.907e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.25 Order of pole (three term test) = 40.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.25 Order of pole (three term test) = 28.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52571.3MB, alloc=44.3MB, time=625.07 memory used=52617.9MB, alloc=44.3MB, time=625.62 x[1] = 0.5495 1.99 h = 0.0001 0.003 y2[1] (numeric) = 12.6670269781 25.010366706 y2[1] (closed_form) = 17.4410039663 22.9610055503 absolute error = 5.195 relative error = 18.02 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.17757746242 -1.87461329023 y1[1] (closed_form) = 3.17757746242 -1.87461329023 absolute error = 7e-63 relative error = 1.897e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.38 Order of pole (three term test) = 40.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.38 Order of pole (three term test) = 28.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52664.0MB, alloc=44.3MB, time=626.16 memory used=52710.8MB, alloc=44.3MB, time=626.74 x[1] = 0.5496 1.993 h = 0.001 0.001 y2[1] (numeric) = 12.6760268429 25.0607330597 y2[1] (closed_form) = 17.4479552394 23.0003640102 absolute error = 5.198 relative error = 18 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.18657961237 -1.88076679246 y1[1] (closed_form) = 3.18657961237 -1.88076679246 absolute error = 7e-63 relative error = 1.892e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.46 Order of pole (three term test) = 40.43 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.46 Order of pole (three term test) = 28.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52757.6MB, alloc=44.3MB, time=627.29 memory used=52803.7MB, alloc=44.3MB, time=627.85 memory used=52850.3MB, alloc=44.3MB, time=628.40 x[1] = 0.5506 1.994 h = 0.001 0.003 y2[1] (numeric) = 12.6850811853 25.1111071046 y2[1] (closed_form) = 17.4630256566 23.0116678693 absolute error = 5.219 relative error = 18.07 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.1876961387 -1.88579229866 y1[1] (closed_form) = 3.1876961387 -1.88579229866 absolute error = 7e-63 relative error = 1.890e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.49 Order of pole (three term test) = 40.43 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.49 Order of pole (three term test) = 29 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52896.3MB, alloc=44.3MB, time=628.94 memory used=52942.9MB, alloc=44.3MB, time=629.48 x[1] = 0.5516 1.997 h = 0.0001 0.004 y2[1] (numeric) = 12.6941903194 25.1614886996 y2[1] (closed_form) = 17.4818877922 23.0493515824 absolute error = 5.233 relative error = 18.09 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.19496121079 -1.89475216896 y1[1] (closed_form) = 3.19496121079 -1.89475216896 absolute error = 7e-63 relative error = 1.884e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.57 Order of pole (three term test) = 40.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.57 Order of pole (three term test) = 29.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52988.8MB, alloc=44.3MB, time=630.02 memory used=53035.3MB, alloc=44.3MB, time=630.56 x[1] = 0.5517 2.001 h = 0.003 0.006 y2[1] (numeric) = 12.703354561 25.2118777024 y2[1] (closed_form) = 17.4908032688 23.1019658177 absolute error = 5.232 relative error = 18.06 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.2071068454 -1.90294010523 y1[1] (closed_form) = 3.2071068454 -1.90294010523 absolute error = 7e-63 relative error = 1.877e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.68 Order of pole (three term test) = 40.55 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.68 Order of pole (three term test) = 29.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53081.0MB, alloc=44.3MB, time=631.10 memory used=53127.7MB, alloc=44.3MB, time=631.65 x[1] = 0.5547 2.007 h = 0.0001 0.005 y2[1] (numeric) = 12.7125742271 25.2622739695 y2[1] (closed_form) = 17.5419247078 23.1755057859 absolute error = 5.261 relative error = 18.1 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.21974620341 -1.92414241094 y1[1] (closed_form) = 3.21974620341 -1.92414241094 absolute error = 7e-63 relative error = 1.866e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.84 Order of pole (three term test) = 40.6 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.84 Order of pole (three term test) = 29.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53173.8MB, alloc=44.3MB, time=632.18 memory used=53220.3MB, alloc=44.3MB, time=632.76 memory used=53267.0MB, alloc=44.3MB, time=633.31 x[1] = 0.5548 2.012 h = 0.0001 0.003 y2[1] (numeric) = 12.7218496362 25.3126773561 y2[1] (closed_form) = 17.5528939179 23.2414499732 absolute error = 5.256 relative error = 18.05 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.23511357073 -1.93445328254 y1[1] (closed_form) = 3.23511357073 -1.93445328254 absolute error = 8e-63 relative error = 2.122e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.98 Order of pole (three term test) = 40.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 13.98 Order of pole (three term test) = 29.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53313.0MB, alloc=44.3MB, time=633.85 memory used=53359.7MB, alloc=44.3MB, time=634.41 x[1] = 0.5549 2.015 h = 0.001 0.001 y2[1] (numeric) = 12.7311811081 25.3630877161 y2[1] (closed_form) = 17.5600307477 23.2809753117 absolute error = 5.259 relative error = 18.03 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.24429140587 -1.94078978559 y1[1] (closed_form) = 3.24429140587 -1.94078978559 absolute error = 8e-63 relative error = 2.116e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.07 Order of pole (three term test) = 40.75 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.07 Order of pole (three term test) = 29.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53406.0MB, alloc=44.3MB, time=634.96 memory used=53452.6MB, alloc=44.3MB, time=635.50 x[1] = 0.5559 2.016 h = 0.0001 0.004 y2[1] (numeric) = 12.7405689642 25.4135049022 y2[1] (closed_form) = 17.5752189603 23.2922768005 absolute error = 5.28 relative error = 18.09 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.24540940793 -1.94593503632 y1[1] (closed_form) = 3.24540940793 -1.94593503632 absolute error = 8e-63 relative error = 2.114e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.1 Order of pole (three term test) = 40.75 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.1 Order of pole (three term test) = 29.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53498.6MB, alloc=44.3MB, time=636.04 memory used=53545.0MB, alloc=44.3MB, time=636.59 x[1] = 0.556 2.02 h = 0.003 0.006 y2[1] (numeric) = 12.7500135271 25.4639287658 y2[1] (closed_form) = 17.5843446373 23.3450881138 absolute error = 5.278 relative error = 18.06 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.25776209368 -1.95433001975 y1[1] (closed_form) = 3.25776209368 -1.95433001975 absolute error = 8e-63 relative error = 2.106e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.21 Order of pole (three term test) = 40.83 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.21 Order of pole (three term test) = 29.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53590.8MB, alloc=44.3MB, time=637.13 memory used=53637.4MB, alloc=44.3MB, time=637.69 x[1] = 0.559 2.026 h = 0.0001 0.005 y2[1] (numeric) = 12.7595151209 25.5143591568 y2[1] (closed_form) = 17.635928023 23.4187776491 absolute error = 5.308 relative error = 18.1 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.27056831816 -1.97599654921 y1[1] (closed_form) = 3.27056831816 -1.97599654921 absolute error = 8e-63 relative error = 2.094e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.38 Order of pole (three term test) = 40.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.38 Order of pole (three term test) = 29.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53683.9MB, alloc=44.3MB, time=638.24 memory used=53730.2MB, alloc=44.3MB, time=638.80 memory used=53776.8MB, alloc=44.3MB, time=639.36 x[1] = 0.5591 2.031 h = 0.0001 0.003 y2[1] (numeric) = 12.7690740711 25.5647959242 y2[1] (closed_form) = 17.6471622511 23.4849714027 absolute error = 5.303 relative error = 18.05 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.28619755461 -1.98656843903 y1[1] (closed_form) = 3.28619755461 -1.98656843903 absolute error = 8e-63 relative error = 2.083e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.53 Order of pole (three term test) = 40.99 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.53 Order of pole (three term test) = 29.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53823.0MB, alloc=44.3MB, time=639.92 memory used=53869.7MB, alloc=44.3MB, time=640.50 x[1] = 0.5592 2.034 h = 0.001 0.001 y2[1] (numeric) = 12.7786907048 25.6152389153 y2[1] (closed_form) = 17.6544607815 23.524645007 absolute error = 5.305 relative error = 18.04 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.2955310414 -1.99306434906 y1[1] (closed_form) = 3.2955310414 -1.99306434906 absolute error = 9e-63 relative error = 2.337e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.61 Order of pole (three term test) = 41.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.61 Order of pole (three term test) = 29.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53915.8MB, alloc=44.3MB, time=641.05 memory used=53962.1MB, alloc=44.3MB, time=641.60 x[1] = 0.5602 2.035 h = 0.001 0.003 y2[1] (numeric) = 12.7883653503 25.6656879763 y2[1] (closed_form) = 17.669752562 23.5359454095 absolute error = 5.326 relative error = 18.1 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.29665123082 -1.99831475075 y1[1] (closed_form) = 3.29665123082 -1.99831475075 absolute error = 8e-63 relative error = 2.075e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.64 Order of pole (three term test) = 41.05 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.64 Order of pole (three term test) = 29.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54008.1MB, alloc=44.3MB, time=642.15 memory used=54054.7MB, alloc=44.3MB, time=643.08 x[1] = 0.5612 2.038 h = 0.0001 0.004 y2[1] (numeric) = 12.7980983375 25.716142952 y2[1] (closed_form) = 17.6890620066 23.5738435901 absolute error = 5.34 relative error = 18.12 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.30414850674 -2.00772185709 y1[1] (closed_form) = 3.30414850674 -2.00772185709 absolute error = 8.062e-63 relative error = 2.085e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.73 Order of pole (three term test) = 41.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.73 Order of pole (three term test) = 29.29 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54100.6MB, alloc=44.3MB, time=643.79 memory used=54147.2MB, alloc=44.3MB, time=644.35 x[1] = 0.5613 2.042 h = 0.003 0.006 y2[1] (numeric) = 12.8078899977 25.7666036859 y2[1] (closed_form) = 17.6984412165 23.6268841495 absolute error = 5.338 relative error = 18.08 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.31674182085 -2.01636688756 y1[1] (closed_form) = 3.31674182085 -2.01636688756 absolute error = 8e-63 relative error = 2.061e-61 % Correct digits = 63 memory used=54193.7MB, alloc=44.3MB, time=644.91 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.85 Order of pole (three term test) = 41.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 14.85 Order of pole (three term test) = 29.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54239.7MB, alloc=44.3MB, time=645.45 memory used=54286.3MB, alloc=44.3MB, time=646.01 x[1] = 0.5643 2.048 h = 0.0001 0.005 y2[1] (numeric) = 12.8177406635 25.8170700201 y2[1] (closed_form) = 17.7505757032 23.7007411846 absolute error = 5.368 relative error = 18.13 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.3297352089 -2.03858728735 y1[1] (closed_form) = 3.3297352089 -2.03858728735 absolute error = 8e-63 relative error = 2.049e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.03 Order of pole (three term test) = 41.23 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.03 Order of pole (three term test) = 29.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54332.3MB, alloc=44.3MB, time=646.56 memory used=54379.2MB, alloc=44.3MB, time=647.12 x[1] = 0.5644 2.053 h = 0.0001 0.003 y2[1] (numeric) = 12.8276506692 25.8675417955 y2[1] (closed_form) = 17.7621296044 23.7672252581 absolute error = 5.363 relative error = 18.07 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.34566880747 -2.04947442494 y1[1] (closed_form) = 3.34566880747 -2.04947442494 absolute error = 9e-63 relative error = 2.294e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.18 Order of pole (three term test) = 41.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.18 Order of pole (three term test) = 29.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54425.3MB, alloc=44.3MB, time=647.68 memory used=54472.1MB, alloc=44.3MB, time=648.25 x[1] = 0.5645 2.056 h = 0.001 0.001 y2[1] (numeric) = 12.8376203504 25.9180188517 y2[1] (closed_form) = 17.7696230974 23.8070712471 absolute error = 5.365 relative error = 18.06 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.3551831078 -2.05616276333 y1[1] (closed_form) = 3.3551831078 -2.05616276333 absolute error = 9.055e-63 relative error = 2.301e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.27 Order of pole (three term test) = 41.4 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.27 Order of pole (three term test) = 29.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54518.2MB, alloc=44.3MB, time=648.80 memory used=54564.7MB, alloc=44.3MB, time=649.36 x[1] = 0.5655 2.057 h = 0.001 0.003 y2[1] (numeric) = 12.8476500442 25.9685010266 y2[1] (closed_form) = 17.7850376908 23.818368141 absolute error = 5.385 relative error = 18.12 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.35630349799 -2.06153781323 y1[1] (closed_form) = 3.35630349799 -2.06153781323 absolute error = 8.062e-63 relative error = 2.047e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.3 Order of pole (three term test) = 41.4 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.3 Order of pole (three term test) = 29.44 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54610.6MB, alloc=44.3MB, time=649.91 memory used=54657.3MB, alloc=44.3MB, time=650.47 memory used=54704.0MB, alloc=44.3MB, time=651.03 x[1] = 0.5665 2.06 h = 0.0001 0.004 y2[1] (numeric) = 12.857740089 26.018988157 y2[1] (closed_form) = 17.8045968937 23.8563821182 absolute error = 5.399 relative error = 18.14 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.36392580584 -2.07119462999 y1[1] (closed_form) = 3.36392580584 -2.07119462999 absolute error = 8.062e-63 relative error = 2.041e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.39 Order of pole (three term test) = 41.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.39 Order of pole (three term test) = 29.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54749.9MB, alloc=44.3MB, time=651.57 memory used=54796.3MB, alloc=44.3MB, time=652.13 x[1] = 0.5666 2.064 h = 0.003 0.006 y2[1] (numeric) = 12.8678908251 26.0694800785 y2[1] (closed_form) = 17.8142364982 23.909655915 absolute error = 5.397 relative error = 18.1 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.37676347372 -2.08009658595 y1[1] (closed_form) = 3.37676347372 -2.08009658595 absolute error = 9.055e-63 relative error = 2.283e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.52 Order of pole (three term test) = 41.52 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.52 Order of pole (three term test) = 29.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54842.2MB, alloc=44.3MB, time=652.67 memory used=54888.7MB, alloc=44.3MB, time=653.23 x[1] = 0.5696 2.07 h = 0.0001 0.005 y2[1] (numeric) = 12.8781025938 26.1199766249 y2[1] (closed_form) = 17.8669354092 23.9836816054 absolute error = 5.427 relative error = 18.15 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.38994476712 -2.10288401714 y1[1] (closed_form) = 3.38994476712 -2.10288401714 absolute error = 8.246e-63 relative error = 2.067e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.7 Order of pole (three term test) = 41.59 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.7 Order of pole (three term test) = 29.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54934.7MB, alloc=44.3MB, time=653.77 memory used=54981.3MB, alloc=44.3MB, time=654.34 x[1] = 0.5697 2.075 h = 0.0001 0.003 y2[1] (numeric) = 12.8883757381 26.170477629 y2[1] (closed_form) = 17.8788176395 24.050461053 absolute error = 5.422 relative error = 18.09 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.40618745323 -2.1140950822 y1[1] (closed_form) = 3.40618745323 -2.1140950822 absolute error = 8.246e-63 relative error = 2.057e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.86 Order of pole (three term test) = 41.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.86 Order of pole (three term test) = 29.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55027.4MB, alloc=44.3MB, time=654.88 memory used=55074.1MB, alloc=44.3MB, time=655.45 x[1] = 0.5698 2.078 h = 0.001 0.001 y2[1] (numeric) = 12.8987106025 26.220982922 y2[1] (closed_form) = 17.8865113519 24.0904824012 absolute error = 5.424 relative error = 18.08 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.41588534504 -2.12098111721 y1[1] (closed_form) = 3.41588534504 -2.12098111721 absolute error = 8.246e-63 relative error = 2.051e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.96 Order of pole (three term test) = 41.76 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.96 Order of pole (three term test) = 29.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55120.6MB, alloc=44.3MB, time=656.01 memory used=55166.8MB, alloc=44.3MB, time=656.58 memory used=55213.3MB, alloc=44.3MB, time=657.15 x[1] = 0.5708 2.079 h = 0.001 0.003 y2[1] (numeric) = 12.9091075329 26.2714923338 y2[1] (closed_form) = 17.9020515293 24.101775115 absolute error = 5.444 relative error = 18.13 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.41700519327 -2.12648352722 y1[1] (closed_form) = 3.41700519327 -2.12648352722 absolute error = 8.246e-63 relative error = 2.049e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.99 Order of pole (three term test) = 41.76 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 15.99 Order of pole (three term test) = 29.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55259.4MB, alloc=44.3MB, time=658.20 memory used=55306.1MB, alloc=44.3MB, time=658.85 x[1] = 0.5718 2.082 h = 0.0001 0.004 y2[1] (numeric) = 12.9195668767 26.3220056929 y2[1] (closed_form) = 17.9218667178 24.1399063131 absolute error = 5.458 relative error = 18.15 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.42475375608 -2.13639623483 y1[1] (closed_form) = 3.42475375608 -2.13639623483 absolute error = 8.062e-63 relative error = 1.997e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.08 Order of pole (three term test) = 41.81 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 16.08 Order of pole (three term test) = 29.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55352.0MB, alloc=44.3MB, time=659.40 memory used=55398.3MB, alloc=44.3MB, time=659.97 x[1] = 0.5719 2.086 h = 0.003 0.006 y2[1] (numeric) = 12.9300889829 26.3725228264 y2[1] (closed_form) = 17.9317737515 24.1934173844 absolute error = 5.456 relative error = 18.12 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.43783955463 -2.14556216886 y1[1] (closed_form) = 3.43783955463 -2.14556216886 absolute error = 8.062e-63 relative error = 1.989e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.21 Order of pole (three term test) = 41.9 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 16.21 Order of pole (three term test) = 29.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55444.2MB, alloc=44.3MB, time=660.52 memory used=55490.9MB, alloc=44.3MB, time=661.09 x[1] = 0.5749 2.092 h = 0.0001 0.005 y2[1] (numeric) = 12.9406742018 26.4230435598 y2[1] (closed_form) = 17.9850507069 24.2676128309 absolute error = 5.486 relative error = 18.16 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.45120944861 -2.16893009487 y1[1] (closed_form) = 3.45120944861 -2.16893009487 absolute error = 9.055e-63 relative error = 2.222e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.41 Order of pole (three term test) = 41.97 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 16.41 Order of pole (three term test) = 29.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55537.0MB, alloc=44.3MB, time=661.64 memory used=55583.8MB, alloc=44.3MB, time=662.22 memory used=55630.6MB, alloc=44.3MB, time=662.79 x[1] = 0.575 2.097 h = 0.0001 0.003 y2[1] (numeric) = 12.9513228855 26.4735677176 y2[1] (closed_form) = 17.9972701411 24.3346927647 absolute error = 5.481 relative error = 18.11 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.46776601303 -2.18047398685 y1[1] (closed_form) = 3.46776601303 -2.18047398685 absolute error = 9.055e-63 relative error = 2.211e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.57 Order of pole (three term test) = 42.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 16.57 Order of pole (three term test) = 29.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55676.7MB, alloc=44.3MB, time=663.34 memory used=55723.7MB, alloc=44.3MB, time=663.93 x[1] = 0.5751 2.1 h = 0.001 0.001 y2[1] (numeric) = 12.9620353872 26.5240951225 y2[1] (closed_form) = 18.0051694619 24.37489248 absolute error = 5.482 relative error = 18.09 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.47765031187 -2.18756311972 y1[1] (closed_form) = 3.47765031187 -2.18756311972 absolute error = 9.055e-63 relative error = 2.204e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.67 Order of pole (three term test) = 42.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 16.67 Order of pole (three term test) = 29.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55769.7MB, alloc=44.3MB, time=664.48 memory used=55816.3MB, alloc=44.3MB, time=665.06 x[1] = 0.5761 2.101 h = 0.001 0.003 y2[1] (numeric) = 12.9728120621 26.5746255959 y2[1] (closed_form) = 18.0208380506 24.3861803112 absolute error = 5.502 relative error = 18.15 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.47876884545 -2.19319565968 y1[1] (closed_form) = 3.47876884545 -2.19319565968 absolute error = 9.055e-63 relative error = 2.202e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.71 Order of pole (three term test) = 42.15 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 16.71 Order of pole (three term test) = 29.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55862.2MB, alloc=44.3MB, time=665.62 memory used=55908.9MB, alloc=44.3MB, time=666.19 x[1] = 0.5771 2.104 h = 0.0001 0.004 y2[1] (numeric) = 12.9836532664 26.6251589578 y2[1] (closed_form) = 18.040915596 24.4244301482 absolute error = 5.515 relative error = 18.16 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.48664488415 -2.20337058466 y1[1] (closed_form) = 3.48664488415 -2.20337058466 absolute error = 9.220e-63 relative error = 2.235e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.81 Order of pole (three term test) = 42.2 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 16.81 Order of pole (three term test) = 29.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55955.0MB, alloc=44.3MB, time=666.74 memory used=56001.3MB, alloc=44.3MB, time=667.32 x[1] = 0.5772 2.108 h = 0.003 0.006 y2[1] (numeric) = 12.9945593582 26.6756950266 y2[1] (closed_form) = 18.0510972709 24.4781825766 absolute error = 5.513 relative error = 18.13 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.49998264181 -2.21280772757 y1[1] (closed_form) = 3.49998264181 -2.21280772757 absolute error = 9.055e-63 relative error = 2.187e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.94 Order of pole (three term test) = 42.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 16.94 Order of pole (three term test) = 29.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56047.4MB, alloc=44.3MB, time=667.87 memory used=56094.0MB, alloc=44.3MB, time=668.45 memory used=56140.5MB, alloc=44.3MB, time=669.02 x[1] = 0.5802 2.114 h = 0.0001 0.005 y2[1] (numeric) = 13.005530697 26.7262336195 y2[1] (closed_form) = 18.1049661936 24.5525488227 absolute error = 5.543 relative error = 18.17 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.51354178219 -2.23676992047 y1[1] (closed_form) = 3.51354178219 -2.23676992047 absolute error = 9.055e-63 relative error = 2.174e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.15 Order of pole (three term test) = 42.37 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 17.15 Order of pole (three term test) = 30.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56186.6MB, alloc=44.3MB, time=669.59 memory used=56233.3MB, alloc=44.3MB, time=670.18 x[1] = 0.5803 2.119 h = 0.0001 0.003 y2[1] (numeric) = 13.0165676439 26.7767745521 y2[1] (closed_form) = 18.1175319302 24.6199344133 absolute error = 5.538 relative error = 18.12 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.53041708123 -2.24865576378 y1[1] (closed_form) = 3.53041708123 -2.24865576378 absolute error = 9e-63 relative error = 2.150e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.32 Order of pole (three term test) = 42.49 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 17.32 Order of pole (three term test) = 30.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56279.4MB, alloc=44.3MB, time=670.75 memory used=56326.2MB, alloc=44.3MB, time=671.35 x[1] = 0.5804 2.122 h = 0.001 0.001 y2[1] (numeric) = 13.0276705613 26.8273176384 y2[1] (closed_form) = 18.1256423837 24.660315537 absolute error = 5.539 relative error = 18.1 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.54049064025 -2.25595353178 y1[1] (closed_form) = 3.54049064025 -2.25595353178 absolute error = 8e-63 relative error = 1.906e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.42 Order of pole (three term test) = 42.56 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 17.42 Order of pole (three term test) = 30.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56372.4MB, alloc=44.3MB, time=671.92 memory used=56419.1MB, alloc=44.3MB, time=672.51 x[1] = 0.5814 2.123 h = 0.0001 0.004 y2[1] (numeric) = 13.0388398135 26.8778626913 y2[1] (closed_form) = 18.1414422686 24.6715977505 absolute error = 5.559 relative error = 18.15 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.54160705553 -2.26171903056 y1[1] (closed_form) = 3.54160705553 -2.26171903056 absolute error = 8e-63 relative error = 1.904e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.46 Order of pole (three term test) = 42.56 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 17.46 Order of pole (three term test) = 30.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56465.1MB, alloc=44.3MB, time=673.07 memory used=56511.5MB, alloc=44.3MB, time=673.65 x[1] = 0.5815 2.127 h = 0.003 0.006 y2[1] (numeric) = 13.0500757659 26.9284095218 y2[1] (closed_form) = 18.151863317 24.7255646274 absolute error = 5.557 relative error = 18.12 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.55516814758 -2.27139248606 y1[1] (closed_form) = 3.55516814758 -2.27139248606 absolute error = 8.062e-63 relative error = 1.911e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.6 Order of pole (three term test) = 42.66 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 17.6 Order of pole (three term test) = 30.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56557.7MB, alloc=44.3MB, time=674.22 memory used=56604.2MB, alloc=44.3MB, time=674.79 memory used=56650.9MB, alloc=44.3MB, time=675.38 x[1] = 0.5845 2.133 h = 0.0001 0.005 y2[1] (numeric) = 13.0613787859 26.9789579397 y2[1] (closed_form) = 18.2062511208 24.8000859647 absolute error = 5.587 relative error = 18.16 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.56889797026 -2.29587520898 y1[1] (closed_form) = 3.56889797026 -2.29587520898 absolute error = 8.062e-63 relative error = 1.900e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.81 Order of pole (three term test) = 42.73 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 17.81 Order of pole (three term test) = 30.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56697.0MB, alloc=44.3MB, time=675.95 memory used=56743.7MB, alloc=44.3MB, time=676.54 x[1] = 0.5846 2.138 h = 0.0001 0.003 y2[1] (numeric) = 13.0727492422 27.0295077531 y2[1] (closed_form) = 18.2191186778 24.8677431166 absolute error = 5.582 relative error = 18.11 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.58605578976 -2.30805899813 y1[1] (closed_form) = 3.58605578976 -2.30805899813 absolute error = 8.062e-63 relative error = 1.891e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.99 Order of pole (three term test) = 42.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 17.99 Order of pole (three term test) = 30.37 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56789.8MB, alloc=44.3MB, time=677.11 memory used=56836.6MB, alloc=44.3MB, time=677.71 x[1] = 0.5847 2.141 h = 0.001 0.001 y2[1] (numeric) = 13.0841875051 27.0800587688 y2[1] (closed_form) = 18.2274131858 24.9082854586 absolute error = 5.583 relative error = 18.09 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.59629714873 -2.31553859124 y1[1] (closed_form) = 3.59629714873 -2.31553859124 absolute error = 8.062e-63 relative error = 1.885e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.1 Order of pole (three term test) = 42.93 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 18.1 Order of pole (three term test) = 30.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56882.7MB, alloc=44.3MB, time=678.28 memory used=56929.3MB, alloc=44.3MB, time=678.85 x[1] = 0.5857 2.142 h = 0.001 0.003 y2[1] (numeric) = 13.0956939465 27.130610792 y2[1] (closed_form) = 18.2433285203 24.9195638348 absolute error = 5.602 relative error = 18.14 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.5974127035 -2.32142088655 y1[1] (closed_form) = 3.5974127035 -2.32142088655 absolute error = 8.062e-63 relative error = 1.883e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.13 Order of pole (three term test) = 42.93 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 18.13 Order of pole (three term test) = 30.44 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56975.1MB, alloc=44.3MB, time=679.40 memory used=57021.8MB, alloc=44.3MB, time=679.96 x[1] = 0.5867 2.145 h = 0.0001 0.004 y2[1] (numeric) = 13.1072689398 27.1811636263 y2[1] (closed_form) = 18.2639102622 24.958041492 absolute error = 5.615 relative error = 18.16 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.60553249203 -2.33209953621 y1[1] (closed_form) = 3.60553249203 -2.33209953621 absolute error = 8.062e-63 relative error = 1.878e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.24 Order of pole (three term test) = 42.99 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 18.24 Order of pole (three term test) = 30.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57068.2MB, alloc=44.3MB, time=680.50 memory used=57114.4MB, alloc=44.3MB, time=681.06 memory used=57161.1MB, alloc=44.3MB, time=681.64 x[1] = 0.5868 2.149 h = 0.003 0.006 y2[1] (numeric) = 13.1189128601 27.2317170738 y2[1] (closed_form) = 18.2746198079 25.0122575366 absolute error = 5.613 relative error = 18.12 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.61935289583 -2.34205809711 y1[1] (closed_form) = 3.61935289583 -2.34205809711 absolute error = 9.055e-63 relative error = 2.101e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.39 Order of pole (three term test) = 43.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 18.39 Order of pole (three term test) = 30.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57207.0MB, alloc=44.3MB, time=682.19 memory used=57253.6MB, alloc=44.3MB, time=682.76 x[1] = 0.5898 2.155 h = 0.0001 0.005 y2[1] (numeric) = 13.1306260839 27.2822709352 y2[1] (closed_form) = 18.3296263056 25.0869516273 absolute error = 5.643 relative error = 18.16 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.63327319814 -2.36716155095 y1[1] (closed_form) = 3.63327319814 -2.36716155095 absolute error = 8.062e-63 relative error = 1.859e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.61 Order of pole (three term test) = 43.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 18.61 Order of pole (three term test) = 30.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57299.6MB, alloc=44.3MB, time=683.36 memory used=57346.4MB, alloc=44.3MB, time=683.93 x[1] = 0.5899 2.16 h = 0.0001 0.003 y2[1] (numeric) = 13.1424089895 27.3328250094 y2[1] (closed_form) = 18.3428576462 25.1549243283 absolute error = 5.638 relative error = 18.11 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.65075907846 -2.37970482705 y1[1] (closed_form) = 3.65075907846 -2.37970482705 absolute error = 8e-63 relative error = 1.836e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.8 Order of pole (three term test) = 43.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 18.8 Order of pole (three term test) = 30.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57392.4MB, alloc=44.3MB, time=684.49 memory used=57439.3MB, alloc=44.3MB, time=685.08 x[1] = 0.59 2.163 h = 0.001 0.001 y2[1] (numeric) = 13.1542619565 27.3833790942 y2[1] (closed_form) = 18.3513739005 25.1956538966 absolute error = 5.639 relative error = 18.09 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.66119517679 -2.38740369699 y1[1] (closed_form) = 3.66119517679 -2.38740369699 absolute error = 8e-63 relative error = 1.830e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.91 Order of pole (three term test) = 43.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 18.91 Order of pole (three term test) = 30.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57485.5MB, alloc=44.3MB, time=685.66 memory used=57532.0MB, alloc=44.3MB, time=686.24 x[1] = 0.591 2.164 h = 0.001 0.003 y2[1] (numeric) = 13.1661853664 27.4339329853 y2[1] (closed_form) = 18.3674260655 25.2069252347 absolute error = 5.658 relative error = 18.14 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.66230706737 -2.39342438636 y1[1] (closed_form) = 3.66230706737 -2.39342438636 absolute error = 8.062e-63 relative error = 1.843e-61 % Correct digits = 63 memory used=57578.6MB, alloc=44.3MB, time=686.82 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.95 Order of pole (three term test) = 43.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 18.95 Order of pole (three term test) = 30.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57624.6MB, alloc=44.3MB, time=687.38 memory used=57671.4MB, alloc=44.3MB, time=687.97 x[1] = 0.592 2.167 h = 0.0001 0.004 y2[1] (numeric) = 13.1781796021 27.4844864772 y2[1] (closed_form) = 18.3882891993 25.2455256275 absolute error = 5.671 relative error = 18.16 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.67055788601 -2.40438417325 y1[1] (closed_form) = 3.67055788601 -2.40438417325 absolute error = 9e-63 relative error = 2.051e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.06 Order of pole (three term test) = 43.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 19.06 Order of pole (three term test) = 30.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57717.5MB, alloc=44.3MB, time=688.53 memory used=57764.1MB, alloc=44.3MB, time=689.10 x[1] = 0.5921 2.171 h = 0.003 0.006 y2[1] (numeric) = 13.1902450483 27.5350393627 y2[1] (closed_form) = 18.3992949845 25.2999950569 absolute error = 5.668 relative error = 18.12 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.68464158009 -2.41463560306 y1[1] (closed_form) = 3.68464158009 -2.41463560306 absolute error = 9e-63 relative error = 2.043e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.22 Order of pole (three term test) = 43.55 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 19.22 Order of pole (three term test) = 30.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57810.0MB, alloc=44.3MB, time=689.67 memory used=57856.8MB, alloc=44.3MB, time=690.25 x[1] = 0.5951 2.177 h = 0.0001 0.005 y2[1] (numeric) = 13.2023820909 27.5855914331 y2[1] (closed_form) = 18.4549350041 25.3748627685 absolute error = 5.699 relative error = 18.16 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.69875285405 -2.44037447951 y1[1] (closed_form) = 3.69875285405 -2.44037447951 absolute error = 9e-63 relative error = 2.031e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.45 Order of pole (three term test) = 43.63 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 19.45 Order of pole (three term test) = 31.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57902.8MB, alloc=44.3MB, time=690.81 memory used=57949.4MB, alloc=44.3MB, time=691.38 x[1] = 0.5952 2.182 h = 0.0001 0.003 y2[1] (numeric) = 13.2145911179 27.636142478 y2[1] (closed_form) = 18.4685398964 25.4431563601 absolute error = 5.693 relative error = 18.11 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.7165718421 -2.45328703935 y1[1] (closed_form) = 3.7165718421 -2.45328703935 absolute error = 1.0e-62 relative error = 2.246e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.65 Order of pole (three term test) = 43.77 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 19.65 Order of pole (three term test) = 31.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57995.8MB, alloc=44.3MB, time=691.95 memory used=58042.5MB, alloc=44.3MB, time=692.54 memory used=58089.5MB, alloc=44.3MB, time=693.13 x[1] = 0.5953 2.185 h = 0.001 0.001 y2[1] (numeric) = 13.2268725186 27.6866922855 y2[1] (closed_form) = 18.4772838261 25.4840762937 absolute error = 5.694 relative error = 18.09 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.72720564232 -2.46121113009 y1[1] (closed_form) = 3.72720564232 -2.46121113009 absolute error = 1.005e-62 relative error = 2.250e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.76 Order of pole (three term test) = 43.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 19.76 Order of pole (three term test) = 31.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58135.4MB, alloc=44.3MB, time=693.70 memory used=58181.8MB, alloc=44.3MB, time=694.28 x[1] = 0.5963 2.186 h = 0.001 0.003 y2[1] (numeric) = 13.239226684 27.7372406422 y2[1] (closed_form) = 18.4934758774 25.4953397618 absolute error = 5.713 relative error = 18.14 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.72831297152 -2.46737321779 y1[1] (closed_form) = 3.72831297152 -2.46737321779 absolute error = 1.005e-62 relative error = 2.248e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.8 Order of pole (three term test) = 43.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 19.8 Order of pole (three term test) = 31.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58227.8MB, alloc=44.3MB, time=694.83 memory used=58274.4MB, alloc=44.3MB, time=695.40 x[1] = 0.5973 2.189 h = 0.0001 0.004 y2[1] (numeric) = 13.2516540067 27.7877873328 y2[1] (closed_form) = 18.5146273615 25.5340642779 absolute error = 5.725 relative error = 18.15 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.736696026 -2.47862106298 y1[1] (closed_form) = 3.736696026 -2.47862106298 absolute error = 1.005e-62 relative error = 2.241e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.92 Order of pole (three term test) = 43.92 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 19.92 Order of pole (three term test) = 31.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58320.4MB, alloc=44.3MB, time=695.95 memory used=58367.1MB, alloc=44.3MB, time=696.52 x[1] = 0.5974 2.193 h = 0.003 0.006 y2[1] (numeric) = 13.2641548811 27.8383321406 y2[1] (closed_form) = 18.5259373227 25.5887913554 absolute error = 5.722 relative error = 18.11 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.75104704061 -2.48917332011 y1[1] (closed_form) = 3.75104704061 -2.48917332011 absolute error = 1.005e-62 relative error = 2.232e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.08 Order of pole (three term test) = 44.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 20.08 Order of pole (three term test) = 31.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58413.2MB, alloc=44.3MB, time=697.07 memory used=58459.7MB, alloc=44.3MB, time=697.64 x[1] = 0.6004 2.199 h = 0.0001 0.005 y2[1] (numeric) = 13.276729703 27.8888748473 y2[1] (closed_form) = 18.5822260215 25.6638334868 absolute error = 5.753 relative error = 18.16 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.76534971711 -2.51556264512 y1[1] (closed_form) = 3.76534971711 -2.51556264512 absolute error = 1.005e-62 relative error = 2.219e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.32 Order of pole (three term test) = 44.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 20.32 Order of pole (three term test) = 31.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58506.2MB, alloc=44.3MB, time=698.20 memory used=58552.5MB, alloc=44.3MB, time=698.79 memory used=58599.3MB, alloc=44.3MB, time=699.37 x[1] = 0.6005 2.204 h = 0.0001 0.003 y2[1] (numeric) = 13.2893788699 27.9394152328 y2[1] (closed_form) = 18.5962144787 25.7324533698 absolute error = 5.747 relative error = 18.1 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.78350692552 -2.52885453152 y1[1] (closed_form) = 3.78350692552 -2.52885453152 absolute error = 1.005e-62 relative error = 2.208e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.53 Order of pole (three term test) = 44.27 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 20.53 Order of pole (three term test) = 31.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58645.5MB, alloc=44.3MB, time=699.93 memory used=58692.3MB, alloc=44.3MB, time=700.50 x[1] = 0.6006 2.207 h = 0.001 0.001 y2[1] (numeric) = 13.3021027811 27.9899530757 y2[1] (closed_form) = 18.6051921612 25.7735668412 absolute error = 5.748 relative error = 18.08 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.7943414278 -2.53700993584 y1[1] (closed_form) = 3.7943414278 -2.53700993584 absolute error = 1.005e-62 relative error = 2.202e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.65 Order of pole (three term test) = 44.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 20.65 Order of pole (three term test) = 31.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58738.3MB, alloc=44.3MB, time=701.05 memory used=58784.7MB, alloc=44.3MB, time=701.62 x[1] = 0.6016 2.208 h = 0.001 0.003 y2[1] (numeric) = 13.3149018373 28.0404881525 y2[1] (closed_form) = 18.6215272166 25.7848215714 absolute error = 5.766 relative error = 18.13 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.79544326336 -2.54331648955 y1[1] (closed_form) = 3.79544326336 -2.54331648955 absolute error = 1.005e-62 relative error = 2.200e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.69 Order of pole (three term test) = 44.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 20.69 Order of pole (three term test) = 31.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58830.4MB, alloc=44.3MB, time=702.16 memory used=58877.0MB, alloc=44.3MB, time=702.72 x[1] = 0.6026 2.211 h = 0.0001 0.004 y2[1] (numeric) = 13.327776441 28.0910202383 y2[1] (closed_form) = 18.64297417 25.8236715877 absolute error = 5.779 relative error = 18.14 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.8039597525 -2.55485947626 y1[1] (closed_form) = 3.8039597525 -2.55485947626 absolute error = 1.005e-62 relative error = 2.193e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.82 Order of pole (three term test) = 44.42 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 20.82 Order of pole (three term test) = 31.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58923.2MB, alloc=44.3MB, time=703.26 memory used=58969.9MB, alloc=44.3MB, time=703.82 x[1] = 0.6027 2.215 h = 0.003 0.006 y2[1] (numeric) = 13.3407269964 28.1415491066 y2[1] (closed_form) = 18.6545964423 25.8786606233 absolute error = 5.776 relative error = 18.1 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.81858216963 -2.56572071865 y1[1] (closed_form) = 3.81858216963 -2.56572071865 absolute error = 9.055e-63 relative error = 1.968e-61 % Correct digits = 63 memory used=59016.4MB, alloc=44.3MB, time=704.38 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.99 Order of pole (three term test) = 44.54 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 20.99 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59062.3MB, alloc=44.3MB, time=704.92 memory used=59109.0MB, alloc=44.3MB, time=705.48 x[1] = 0.6057 2.221 h = 0.0001 0.005 y2[1] (numeric) = 13.3537539093 28.1920745291 y2[1] (closed_form) = 18.7115493139 25.9538779014 absolute error = 5.807 relative error = 18.15 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.83307661513 -2.59277585934 y1[1] (closed_form) = 3.83307661513 -2.59277585934 absolute error = 1.0e-62 relative error = 2.161e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.24 Order of pole (three term test) = 44.64 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 21.24 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59155.0MB, alloc=44.3MB, time=706.03 memory used=59201.8MB, alloc=44.3MB, time=706.59 x[1] = 0.6058 2.226 h = 0.0001 0.003 y2[1] (numeric) = 13.3668575871 28.2425962759 y2[1] (closed_form) = 18.7259316003 26.022829536 absolute error = 5.801 relative error = 18.09 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.85157722229 -2.60645736697 y1[1] (closed_form) = 3.85157722229 -2.60645736697 absolute error = 1.005e-62 relative error = 2.161e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.45 Order of pole (three term test) = 44.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 21.45 Order of pole (three term test) = 32.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59247.8MB, alloc=44.3MB, time=707.14 memory used=59294.7MB, alloc=44.3MB, time=707.72 x[1] = 0.6059 2.229 h = 0.001 0.001 y2[1] (numeric) = 13.380038439 28.2931141155 y2[1] (closed_form) = 18.7351492647 26.0641397516 absolute error = 5.8 relative error = 18.07 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.86261546433 -2.61485032989 y1[1] (closed_form) = 3.86261546433 -2.61485032989 absolute error = 1.005e-62 relative error = 2.155e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.58 Order of pole (three term test) = 44.88 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 21.58 Order of pole (three term test) = 32.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59340.9MB, alloc=44.3MB, time=708.27 memory used=59387.5MB, alloc=44.3MB, time=708.82 x[1] = 0.6069 2.23 h = 0.0001 0.004 y2[1] (numeric) = 13.3932968757 28.3436278144 y2[1] (closed_form) = 18.7516305051 26.0753848384 absolute error = 5.819 relative error = 18.12 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.86371083781 -2.62130448189 y1[1] (closed_form) = 3.86371083781 -2.62130448189 absolute error = 1.005e-62 relative error = 2.152e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.62 Order of pole (three term test) = 44.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 21.62 Order of pole (three term test) = 32.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59433.7MB, alloc=44.3MB, time=709.36 memory used=59480.2MB, alloc=44.3MB, time=709.92 memory used=59526.7MB, alloc=44.3MB, time=710.48 x[1] = 0.607 2.234 h = 0.003 0.006 y2[1] (numeric) = 13.4066333099 28.3941371378 y2[1] (closed_form) = 18.7635250829 26.1306067015 absolute error = 5.815 relative error = 18.08 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.87857399405 -2.63243507682 y1[1] (closed_form) = 3.87857399405 -2.63243507682 absolute error = 1.005e-62 relative error = 2.144e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.8 Order of pole (three term test) = 45.01 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 21.8 Order of pole (three term test) = 32.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59572.7MB, alloc=44.3MB, time=711.02 memory used=59619.5MB, alloc=44.3MB, time=711.58 x[1] = 0.61 2.24 h = 0.0001 0.005 y2[1] (numeric) = 13.4200481555 28.4446418489 y2[1] (closed_form) = 18.8210602248 26.2059834343 absolute error = 5.847 relative error = 18.12 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.89324193641 -2.66007361175 y1[1] (closed_form) = 3.89324193641 -2.66007361175 absolute error = 1.005e-62 relative error = 2.131e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.06 Order of pole (three term test) = 45.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 22.06 Order of pole (three term test) = 32.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59665.5MB, alloc=44.3MB, time=712.12 memory used=59712.2MB, alloc=44.3MB, time=712.68 x[1] = 0.6101 2.245 h = 0.0001 0.003 y2[1] (numeric) = 13.4335418287 28.4951417092 y2[1] (closed_form) = 18.83578588 26.2752299096 absolute error = 5.841 relative error = 18.07 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.91204713947 -2.67409475692 y1[1] (closed_form) = 3.91204713947 -2.67409475692 absolute error = 1.005e-62 relative error = 2.121e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.28 Order of pole (three term test) = 45.28 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 22.28 Order of pole (three term test) = 32.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59758.2MB, alloc=44.3MB, time=713.23 memory used=59805.1MB, alloc=44.3MB, time=713.80 x[1] = 0.6102 2.248 h = 0.001 0.001 y2[1] (numeric) = 13.4471147468 28.5456364787 y2[1] (closed_form) = 18.8452128231 26.3167150319 absolute error = 5.84 relative error = 18.04 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.92326614897 -2.68269484522 y1[1] (closed_form) = 3.92326614897 -2.68269484522 absolute error = 1.005e-62 relative error = 2.115e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.42 Order of pole (three term test) = 45.37 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 22.42 Order of pole (three term test) = 32.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59851.5MB, alloc=44.3MB, time=714.37 memory used=59898.1MB, alloc=44.3MB, time=714.93 x[1] = 0.6112 2.249 h = 0.001 0.003 y2[1] (numeric) = 13.4607673292 28.5961259155 y2[1] (closed_form) = 18.8618226213 26.3279528578 absolute error = 5.858 relative error = 18.09 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.92435696629 -2.6892786967 y1[1] (closed_form) = 3.92435696629 -2.6892786967 absolute error = 1.005e-62 relative error = 2.112e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.46 Order of pole (three term test) = 45.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 22.46 Order of pole (three term test) = 32.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59944.2MB, alloc=44.3MB, time=715.48 memory used=59990.8MB, alloc=44.3MB, time=716.03 memory used=60037.4MB, alloc=44.3MB, time=716.58 x[1] = 0.6122 2.252 h = 0.0001 0.004 y2[1] (numeric) = 13.4744999969 28.6466097758 y2[1] (closed_form) = 18.8838373526 26.3670437525 absolute error = 5.87 relative error = 18.1 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.93312863143 -2.70138867251 y1[1] (closed_form) = 3.93312863143 -2.70138867251 absolute error = 1.005e-62 relative error = 2.106e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.6 Order of pole (three term test) = 45.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 22.6 Order of pole (three term test) = 32.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60083.3MB, alloc=44.3MB, time=717.12 memory used=60130.0MB, alloc=44.3MB, time=717.67 x[1] = 0.6123 2.256 h = 0.003 0.006 y2[1] (numeric) = 13.4883131726 28.6970878143 y2[1] (closed_form) = 18.8960598718 26.4225358203 absolute error = 5.867 relative error = 18.06 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.9482710263 -2.71284392966 y1[1] (closed_form) = 3.9482710263 -2.71284392966 absolute error = 1.005e-62 relative error = 2.098e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.78 Order of pole (three term test) = 45.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 22.78 Order of pole (three term test) = 32.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60176.0MB, alloc=44.3MB, time=718.21 memory used=60222.6MB, alloc=44.3MB, time=718.76 x[1] = 0.6153 2.262 h = 0.0001 0.005 y2[1] (numeric) = 13.5022072807 28.7475597839 y2[1] (closed_form) = 18.9542889305 26.4980890447 absolute error = 5.898 relative error = 18.1 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.96313142925 -2.74117780503 y1[1] (closed_form) = 3.96313142925 -2.74117780503 absolute error = 1.005e-62 relative error = 2.086e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.05 Order of pole (three term test) = 45.69 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 23.05 Order of pole (three term test) = 32.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60268.7MB, alloc=44.3MB, time=719.30 memory used=60315.4MB, alloc=44.3MB, time=719.85 x[1] = 0.6154 2.267 h = 0.0001 0.003 y2[1] (numeric) = 13.5161827474 28.7980254356 y2[1] (closed_form) = 18.9694281359 26.5676777193 absolute error = 5.892 relative error = 18.05 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.98228997162 -2.75560835439 y1[1] (closed_form) = 3.98228997162 -2.75560835439 absolute error = 1.005e-62 relative error = 2.075e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.28 Order of pole (three term test) = 45.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 23.28 Order of pole (three term test) = 33.07 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60361.4MB, alloc=44.3MB, time=720.39 memory used=60408.3MB, alloc=44.3MB, time=720.96 x[1] = 0.6155 2.27 h = 0.001 0.001 y2[1] (numeric) = 13.5302400005 28.8484845187 y2[1] (closed_form) = 18.9791070287 26.6093657204 absolute error = 5.891 relative error = 18.02 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.9937185519 -2.76445800211 y1[1] (closed_form) = 3.9937185519 -2.76445800211 absolute error = 1.005e-62 relative error = 2.069e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.42 Order of pole (three term test) = 45.96 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 23.42 Order of pole (three term test) = 33.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60454.8MB, alloc=44.3MB, time=721.52 memory used=60501.0MB, alloc=44.3MB, time=722.06 memory used=60547.7MB, alloc=44.3MB, time=722.63 x[1] = 0.6165 2.271 h = 0.001 0.003 y2[1] (numeric) = 13.5443794696 28.8989367809 y2[1] (closed_form) = 18.9958691151 26.6205921546 absolute error = 5.908 relative error = 18.07 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.99480104389 -2.77119546894 y1[1] (closed_form) = 3.99480104389 -2.77119546894 absolute error = 1.005e-62 relative error = 2.067e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.47 Order of pole (three term test) = 45.96 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 23.47 Order of pole (three term test) = 33.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60593.6MB, alloc=44.3MB, time=723.17 memory used=60640.2MB, alloc=44.3MB, time=723.72 x[1] = 0.6175 2.274 h = 0.0001 0.004 y2[1] (numeric) = 13.5586015861 28.9493819677 y2[1] (closed_form) = 19.0182005834 26.659812512 absolute error = 5.92 relative error = 18.08 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.00370961631 -2.78362176308 y1[1] (closed_form) = 4.00370961631 -2.78362176308 absolute error = 1.005e-62 relative error = 2.061e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.61 Order of pole (three term test) = 46.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 23.61 Order of pole (three term test) = 33.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60686.1MB, alloc=44.3MB, time=724.25 memory used=60732.6MB, alloc=44.3MB, time=724.80 x[1] = 0.6176 2.278 h = 0.003 0.006 y2[1] (numeric) = 13.5729067832 28.9998198231 y2[1] (closed_form) = 19.0307597736 26.7155792304 absolute error = 5.917 relative error = 18.04 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.01913548201 -2.79541043664 y1[1] (closed_form) = 4.01913548201 -2.79541043664 absolute error = 1.020e-62 relative error = 2.083e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.8 Order of pole (three term test) = 46.18 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 23.8 Order of pole (three term test) = 33.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60778.6MB, alloc=44.3MB, time=725.34 memory used=60825.4MB, alloc=44.3MB, time=725.89 x[1] = 0.6206 2.284 h = 0.0001 0.005 y2[1] (numeric) = 13.5872954955 29.0502500893 y2[1] (closed_form) = 19.0896992467 26.7913094541 absolute error = 5.948 relative error = 18.08 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.0341885128 -2.82445603622 y1[1] (closed_form) = 4.0341885128 -2.82445603622 absolute error = 1.020e-62 relative error = 2.071e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.09 Order of pole (three term test) = 46.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 24.09 Order of pole (three term test) = 33.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=60871.5MB, alloc=44.3MB, time=726.43 memory used=60918.2MB, alloc=44.3MB, time=726.99 memory used=60965.0MB, alloc=44.3MB, time=727.54 x[1] = 0.6207 2.289 h = 0.0001 0.003 y2[1] (numeric) = 13.6017681597 29.1006725065 y2[1] (closed_form) = 19.1052630171 26.8612459613 absolute error = 5.942 relative error = 18.03 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.05370576382 -2.83930703709 y1[1] (closed_form) = 4.05370576382 -2.83930703709 absolute error = 1.020e-62 relative error = 2.061e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.33 Order of pole (three term test) = 46.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 24.33 Order of pole (three term test) = 33.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61011.3MB, alloc=44.3MB, time=728.09 memory used=61058.3MB, alloc=44.3MB, time=728.66 x[1] = 0.6208 2.292 h = 0.001 0.001 y2[1] (numeric) = 13.6163252142 29.1510868133 y2[1] (closed_form) = 19.1152005424 26.9031401461 absolute error = 5.941 relative error = 18 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.06534706154 -2.84841294434 y1[1] (closed_form) = 4.06534706154 -2.84841294434 absolute error = 1.020e-62 relative error = 2.054e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.48 Order of pole (three term test) = 46.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 24.48 Order of pole (three term test) = 33.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61104.3MB, alloc=44.3MB, time=729.20 memory used=61151.0MB, alloc=44.3MB, time=729.75 x[1] = 0.6218 2.293 h = 0.001 0.003 y2[1] (numeric) = 13.6309670991 29.2014927462 y2[1] (closed_form) = 19.132118286 26.9143541707 absolute error = 5.958 relative error = 18.04 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.06642015043 -2.85530735073 y1[1] (closed_form) = 4.06642015043 -2.85530735073 absolute error = 1.105e-62 relative error = 2.223e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.53 Order of pole (three term test) = 46.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 24.53 Order of pole (three term test) = 33.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61196.9MB, alloc=44.3MB, time=730.29 memory used=61243.5MB, alloc=44.3MB, time=730.85 x[1] = 0.6228 2.296 h = 0.0001 0.004 y2[1] (numeric) = 13.6456942562 29.2518900401 y2[1] (closed_form) = 19.1547742639 26.9537053187 absolute error = 5.969 relative error = 18.05 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.07546679373 -2.86805770628 y1[1] (closed_form) = 4.07546679373 -2.86805770628 absolute error = 1.105e-62 relative error = 2.216e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.67 Order of pole (three term test) = 46.66 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 24.67 Order of pole (three term test) = 33.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61289.4MB, alloc=44.3MB, time=731.38 memory used=61336.0MB, alloc=44.3MB, time=731.93 x[1] = 0.6229 2.3 h = 0.003 0.006 y2[1] (numeric) = 13.6605071292 29.3022784279 y2[1] (closed_form) = 19.1676790723 27.0097511802 absolute error = 5.965 relative error = 18.01 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.09118041393 -2.88018876856 y1[1] (closed_form) = 4.09118041393 -2.88018876856 absolute error = 1.105e-62 relative error = 2.208e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.87 Order of pole (three term test) = 46.81 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 24.87 Order of pole (three term test) = 34.04 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61382.0MB, alloc=44.3MB, time=732.47 memory used=61428.6MB, alloc=44.3MB, time=733.02 memory used=61475.3MB, alloc=44.3MB, time=733.57 x[1] = 0.6259 2.306 h = 0.0001 0.005 y2[1] (numeric) = 13.6754061635 29.3526576407 y2[1] (closed_form) = 19.2273458225 27.0856588257 absolute error = 5.997 relative error = 18.05 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.10642616163 -2.90996284553 y1[1] (closed_form) = 4.10642616163 -2.90996284553 absolute error = 1.105e-62 relative error = 2.195e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.17 Order of pole (three term test) = 46.94 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 25.17 Order of pole (three term test) = 34.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61521.3MB, alloc=44.3MB, time=734.11 memory used=61568.0MB, alloc=44.3MB, time=734.66 x[1] = 0.626 2.311 h = 0.0001 0.003 y2[1] (numeric) = 13.6903918063 29.4030274077 y2[1] (closed_form) = 19.2433454475 27.1559488586 absolute error = 5.99 relative error = 18 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.12630755614 -2.9252456206 y1[1] (closed_form) = 4.12630755614 -2.9252456206 absolute error = 1.005e-62 relative error = 1.987e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.43 Order of pole (three term test) = 47.12 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 25.43 Order of pole (three term test) = 34.42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61614.0MB, alloc=44.3MB, time=735.21 memory used=61660.8MB, alloc=44.3MB, time=735.78 x[1] = 0.6261 2.314 h = 0.001 0.001 y2[1] (numeric) = 13.7054645067 29.4533874563 y2[1] (closed_form) = 19.253548454 27.1980525654 absolute error = 5.989 relative error = 17.97 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.13816475517 -2.93461465391 y1[1] (closed_form) = 4.13816475517 -2.93461465391 absolute error = 1.105e-62 relative error = 2.177e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.58 Order of pole (three term test) = 47.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 25.58 Order of pole (three term test) = 34.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61706.9MB, alloc=44.3MB, time=736.32 memory used=61753.5MB, alloc=44.3MB, time=736.88 x[1] = 0.6271 2.315 h = 0.001 0.003 y2[1] (numeric) = 13.7206247153 29.503737512 y2[1] (closed_form) = 19.2706252919 27.2092531206 absolute error = 6.006 relative error = 18.01 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.13922732232 -2.94166939345 y1[1] (closed_form) = 4.13922732232 -2.94166939345 absolute error = 1.020e-62 relative error = 2.008e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.63 Order of pole (three term test) = 47.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 25.63 Order of pole (three term test) = 34.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61799.3MB, alloc=44.3MB, time=737.42 memory used=61846.0MB, alloc=44.3MB, time=737.98 x[1] = 0.6281 2.318 h = 0.0001 0.004 y2[1] (numeric) = 13.7358728849 29.5540772983 y2[1] (closed_form) = 19.2936137304 27.248736371 absolute error = 6.017 relative error = 18.02 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.14841318746 -2.95475173342 y1[1] (closed_form) = 4.14841318746 -2.95475173342 absolute error = 1.020e-62 relative error = 2.002e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.78 Order of pole (three term test) = 47.32 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 25.78 Order of pole (three term test) = 34.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=61892.5MB, alloc=44.3MB, time=738.53 memory used=61938.8MB, alloc=44.3MB, time=739.07 memory used=61985.4MB, alloc=44.3MB, time=739.63 x[1] = 0.6282 2.322 h = 0.003 0.006 y2[1] (numeric) = 13.7512094698 29.6044065368 y2[1] (closed_form) = 19.3068733268 27.3050659149 absolute error = 6.013 relative error = 17.98 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.16441889718 -2.96723437995 y1[1] (closed_form) = 4.16441889718 -2.96723437995 absolute error = 1.118e-62 relative error = 2.186e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.99 Order of pole (three term test) = 47.48 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 25.99 Order of pole (three term test) = 34.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62031.4MB, alloc=44.3MB, time=740.17 memory used=62078.3MB, alloc=44.3MB, time=740.73 x[1] = 0.6312 2.328 h = 0.0001 0.005 y2[1] (numeric) = 13.7666349262 29.6547249473 y2[1] (closed_form) = 19.3672845899 27.3811513161 absolute error = 6.045 relative error = 18.02 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.17985736882 -2.99775406456 y1[1] (closed_form) = 4.17985736882 -2.99775406456 absolute error = 1.118e-62 relative error = 2.174e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.31 Order of pole (three term test) = 47.61 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 26.31 Order of pole (three term test) = 35.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62124.3MB, alloc=44.3MB, time=741.26 memory used=62171.1MB, alloc=44.3MB, time=741.82 x[1] = 0.6313 2.333 h = 0.0001 0.003 y2[1] (numeric) = 13.7821497121 29.7050322477 y2[1] (closed_form) = 19.38373164 27.4518006271 absolute error = 6.038 relative error = 17.97 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.20010840701 -3.01348021829 y1[1] (closed_form) = 4.20010840701 -3.01348021829 absolute error = 1.118e-62 relative error = 2.163e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.57 Order of pole (three term test) = 47.81 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 26.57 Order of pole (three term test) = 35.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62217.2MB, alloc=44.3MB, time=742.36 memory used=62264.0MB, alloc=44.3MB, time=742.92 x[1] = 0.6314 2.336 h = 0.001 0.001 y2[1] (numeric) = 13.7977542873 29.755328154 y2[1] (closed_form) = 19.3942071464 27.494117228 absolute error = 6.036 relative error = 17.94 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.21218472829 -3.02311941454 y1[1] (closed_form) = 4.21218472829 -3.02311941454 absolute error = 1.118e-62 relative error = 2.156e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.73 Order of pole (three term test) = 47.93 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 26.73 Order of pole (three term test) = 35.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62310.2MB, alloc=44.3MB, time=743.47 memory used=62356.9MB, alloc=44.3MB, time=744.02 x[1] = 0.6324 2.337 h = 0.0001 0.004 y2[1] (numeric) = 13.8134491135 29.8056123799 y2[1] (closed_form) = 19.411446585 27.5053032107 absolute error = 6.052 relative error = 17.98 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.21323561284 -3.03033795145 y1[1] (closed_form) = 4.21323561284 -3.03033795145 absolute error = 1.118e-62 relative error = 2.154e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.78 Order of pole (three term test) = 47.94 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 26.78 Order of pole (three term test) = 35.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62403.3MB, alloc=44.3MB, time=744.57 memory used=62449.4MB, alloc=44.3MB, time=745.12 memory used=62495.9MB, alloc=44.3MB, time=745.67 x[1] = 0.6325 2.341 h = 0.003 0.006 y2[1] (numeric) = 13.8292346541 29.8558846377 y2[1] (closed_form) = 19.4250156343 27.5618849886 absolute error = 6.048 relative error = 17.94 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.22950059531 -3.04312721717 y1[1] (closed_form) = 4.22950059531 -3.04312721717 absolute error = 1.118e-62 relative error = 2.146e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27 Order of pole (three term test) = 48.1 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 27 Order of pole (three term test) = 35.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62541.9MB, alloc=44.3MB, time=746.21 memory used=62588.5MB, alloc=44.3MB, time=746.76 x[1] = 0.6355 2.347 h = 0.0001 0.005 y2[1] (numeric) = 13.8451113746 29.9061446372 y2[1] (closed_form) = 19.4860797206 27.6381327478 absolute error = 6.08 relative error = 17.98 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.24511406388 -3.07430041286 y1[1] (closed_form) = 4.24511406388 -3.07430041286 absolute error = 1.140e-62 relative error = 2.175e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.32 Order of pole (three term test) = 48.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 27.32 Order of pole (three term test) = 35.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62634.6MB, alloc=44.3MB, time=747.30 memory used=62681.3MB, alloc=44.3MB, time=747.86 x[1] = 0.6356 2.352 h = 0.0001 0.003 y2[1] (numeric) = 13.8610797419 29.9563920867 y2[1] (closed_form) = 19.5029170103 27.7091014879 absolute error = 6.073 relative error = 17.92 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.26569320812 -3.09041323113 y1[1] (closed_form) = 4.26569320812 -3.09041323113 absolute error = 1.140e-62 relative error = 2.165e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.6 Order of pole (three term test) = 48.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 27.6 Order of pole (three term test) = 35.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62727.3MB, alloc=44.3MB, time=748.40 memory used=62774.1MB, alloc=44.3MB, time=748.96 x[1] = 0.6357 2.355 h = 0.001 0.001 y2[1] (numeric) = 13.8771402253 30.0066266923 y2[1] (closed_form) = 19.5136302372 27.7516074299 absolute error = 6.071 relative error = 17.89 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.27796408543 -3.10028807943 y1[1] (closed_form) = 4.27796408543 -3.10028807943 absolute error = 1.140e-62 relative error = 2.158e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.76 Order of pole (three term test) = 48.57 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 27.76 Order of pole (three term test) = 35.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62820.4MB, alloc=44.3MB, time=749.52 memory used=62867.0MB, alloc=44.3MB, time=750.07 x[1] = 0.6367 2.356 h = 0.001 0.003 y2[1] (numeric) = 13.8932932954 30.056848158 y2[1] (closed_form) = 19.5310126914 27.7627819469 absolute error = 6.087 relative error = 17.93 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.27900595988 -3.10765059541 memory used=62913.6MB, alloc=44.3MB, time=750.63 y1[1] (closed_form) = 4.27900595988 -3.10765059541 absolute error = 1.118e-62 relative error = 2.114e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.82 Order of pole (three term test) = 48.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 27.82 Order of pole (three term test) = 36.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=62959.7MB, alloc=44.3MB, time=751.16 memory used=63006.5MB, alloc=44.3MB, time=751.72 x[1] = 0.6377 2.359 h = 0.0001 0.004 y2[1] (numeric) = 13.909539425 30.107056186 y2[1] (closed_form) = 19.5546399414 27.8025186326 absolute error = 6.097 relative error = 17.94 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.28845808499 -3.12137071078 y1[1] (closed_form) = 4.28845808499 -3.12137071078 absolute error = 1.118e-62 relative error = 2.108e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.99 Order of pole (three term test) = 48.67 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 27.99 Order of pole (three term test) = 36.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63052.4MB, alloc=44.3MB, time=752.26 memory used=63098.9MB, alloc=44.3MB, time=752.81 x[1] = 0.6378 2.363 h = 0.003 0.006 y2[1] (numeric) = 13.9258790888 30.1572504763 y2[1] (closed_form) = 19.568581397 27.8593927791 absolute error = 6.093 relative error = 17.9 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.30502347555 -3.13452923039 y1[1] (closed_form) = 4.30502347555 -3.13452923039 absolute error = 1.217e-62 relative error = 2.284e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.21 Order of pole (three term test) = 48.84 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 28.21 Order of pole (three term test) = 36.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63144.9MB, alloc=44.3MB, time=753.35 memory used=63191.6MB, alloc=44.3MB, time=753.90 x[1] = 0.6408 2.369 h = 0.0001 0.005 y2[1] (numeric) = 13.942312763 30.2074307272 y2[1] (closed_form) = 19.6304230863 27.9358188818 absolute error = 6.125 relative error = 17.94 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.3208296641 -3.16648094202 y1[1] (closed_form) = 4.3208296641 -3.16648094202 absolute error = 1.237e-62 relative error = 2.309e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.55 Order of pole (three term test) = 49 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 28.55 Order of pole (three term test) = 36.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63237.7MB, alloc=44.3MB, time=754.44 memory used=63284.3MB, alloc=44.3MB, time=755.00 x[1] = 0.6409 2.374 h = 0.0001 0.003 y2[1] (numeric) = 13.9588409262 30.2575966345 y2[1] (closed_form) = 19.6477300325 28.0071579084 absolute error = 6.118 relative error = 17.88 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.34178900616 -3.18305943739 y1[1] (closed_form) = 4.34178900616 -3.18305943739 absolute error = 1.237e-62 relative error = 2.298e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.84 Order of pole (three term test) = 49.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 28.84 Order of pole (three term test) = 36.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63330.8MB, alloc=44.3MB, time=755.54 memory used=63377.3MB, alloc=44.3MB, time=756.10 memory used=63424.2MB, alloc=44.3MB, time=756.67 x[1] = 0.641 2.377 h = 0.001 0.001 y2[1] (numeric) = 13.9754640584 30.3077478925 y2[1] (closed_form) = 19.6587292442 28.0498831968 absolute error = 6.115 relative error = 17.85 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.354285186 -3.19321797012 y1[1] (closed_form) = 4.354285186 -3.19321797012 absolute error = 1.237e-62 relative error = 2.291e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.01 Order of pole (three term test) = 49.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 29.01 Order of pole (three term test) = 36.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63470.1MB, alloc=44.3MB, time=757.21 memory used=63516.7MB, alloc=44.3MB, time=757.77 x[1] = 0.642 2.378 h = 0.001 0.003 y2[1] (numeric) = 13.9921826417 30.3578841931 y2[1] (closed_form) = 19.6762810276 28.0610410128 absolute error = 6.131 relative error = 17.89 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.35531314422 -3.20075093719 y1[1] (closed_form) = 4.35531314422 -3.20075093719 absolute error = 1.237e-62 relative error = 2.289e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.07 Order of pole (three term test) = 49.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 29.07 Order of pole (three term test) = 36.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63562.7MB, alloc=44.3MB, time=758.30 memory used=63609.5MB, alloc=44.3MB, time=758.86 x[1] = 0.643 2.381 h = 0.0001 0.004 y2[1] (numeric) = 14.0089971602 30.4080052261 y2[1] (closed_form) = 19.7002644903 28.1009135558 absolute error = 6.141 relative error = 17.89 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.36490780396 -3.21482671857 y1[1] (closed_form) = 4.36490780396 -3.21482671857 absolute error = 1.237e-62 relative error = 2.282e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.25 Order of pole (three term test) = 49.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 29.25 Order of pole (three term test) = 37.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63655.3MB, alloc=44.3MB, time=759.40 memory used=63701.8MB, alloc=44.3MB, time=759.96 x[1] = 0.6431 2.385 h = 0.003 0.006 y2[1] (numeric) = 14.0259080996 30.4581106796 y2[1] (closed_form) = 19.7145881878 28.158084746 absolute error = 6.136 relative error = 17.85 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.38177808635 -3.22836435468 y1[1] (closed_form) = 4.38177808635 -3.22836435468 absolute error = 1.237e-62 relative error = 2.273e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.48 Order of pole (three term test) = 49.63 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 29.48 Order of pole (three term test) = 37.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63747.7MB, alloc=44.3MB, time=760.49 memory used=63794.4MB, alloc=44.3MB, time=761.04 x[1] = 0.6461 2.391 h = 0.0001 0.005 y2[1] (numeric) = 14.0429159477 30.5082002393 y2[1] (closed_form) = 19.7772258284 28.2346892553 absolute error = 6.169 relative error = 17.89 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.39777674958 -3.26111283605 y1[1] (closed_form) = 4.39777674958 -3.26111283605 absolute error = 1.237e-62 relative error = 2.259e-61 % Correct digits = 63 memory used=63840.9MB, alloc=44.3MB, time=761.59 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.84 Order of pole (three term test) = 49.8 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 29.84 Order of pole (three term test) = 37.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63887.1MB, alloc=44.3MB, time=762.13 memory used=63933.9MB, alloc=44.3MB, time=762.69 x[1] = 0.6462 2.396 h = 0.0001 0.003 y2[1] (numeric) = 14.0600211943 30.5582735888 y2[1] (closed_form) = 19.7950148423 28.3064044942 absolute error = 6.161 relative error = 17.84 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.41912197889 -3.27816945511 y1[1] (closed_form) = 4.41912197889 -3.27816945511 absolute error = 1.217e-62 relative error = 2.211e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.14 Order of pole (three term test) = 50.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 30.14 Order of pole (three term test) = 37.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=63980.0MB, alloc=44.3MB, time=763.24 memory used=64026.7MB, alloc=44.3MB, time=763.80 x[1] = 0.6463 2.399 h = 0.001 0.001 y2[1] (numeric) = 14.0772243308 30.60833041 y2[1] (closed_form) = 19.8063075654 28.3493525987 absolute error = 6.158 relative error = 17.81 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.43184678939 -3.28861921811 y1[1] (closed_form) = 4.43184678939 -3.28861921811 absolute error = 1.217e-62 relative error = 2.204e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.32 Order of pole (three term test) = 50.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 30.32 Order of pole (three term test) = 37.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64072.7MB, alloc=44.3MB, time=764.34 memory used=64119.4MB, alloc=44.3MB, time=764.90 x[1] = 0.6473 2.4 h = 0.001 0.003 y2[1] (numeric) = 14.0945258507 30.6583703823 y2[1] (closed_form) = 19.8240323911 28.3604924804 absolute error = 6.173 relative error = 17.84 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.43285954324 -3.29632631046 y1[1] (closed_form) = 4.43285954324 -3.29632631046 absolute error = 1.217e-62 relative error = 2.202e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.38 Order of pole (three term test) = 50.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 30.38 Order of pole (three term test) = 37.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64165.5MB, alloc=44.3MB, time=765.44 memory used=64212.3MB, alloc=44.3MB, time=766.00 x[1] = 0.6483 2.403 h = 0.0001 0.004 y2[1] (numeric) = 14.1119262495 30.7083931831 y2[1] (closed_form) = 19.8483807443 28.4005021206 absolute error = 6.183 relative error = 17.85 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.4425978293 -3.31076641297 y1[1] (closed_form) = 4.4425978293 -3.31076641297 absolute error = 1.315e-62 relative error = 2.374e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.56 Order of pole (three term test) = 50.28 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 30.56 Order of pole (three term test) = 38.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64258.3MB, alloc=44.3MB, time=766.54 memory used=64304.8MB, alloc=44.3MB, time=767.09 x[1] = 0.6484 2.407 h = 0.003 0.006 y2[1] (numeric) = 14.1294260244 30.7583984877 y2[1] (closed_form) = 19.863096763 28.457975076 absolute error = 6.178 relative error = 17.8 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.45977753786 -3.32469327214 y1[1] (closed_form) = 4.45977753786 -3.32469327214 absolute error = 1.217e-62 relative error = 2.187e-61 % Correct digits = 63 memory used=64351.6MB, alloc=44.3MB, time=767.64 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.81 Order of pole (three term test) = 50.47 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 30.81 Order of pole (three term test) = 38.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64397.6MB, alloc=44.3MB, time=768.18 memory used=64444.2MB, alloc=44.3MB, time=768.74 x[1] = 0.6514 2.413 h = 0.0001 0.005 y2[1] (numeric) = 14.1470256749 30.8083859693 y2[1] (closed_form) = 19.9265491076 28.5347579505 absolute error = 6.211 relative error = 17.84 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.47596833239 -3.3582571852 y1[1] (closed_form) = 4.47596833239 -3.3582571852 absolute error = 1.217e-62 relative error = 2.174e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.18 Order of pole (three term test) = 50.64 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 31.18 Order of pole (three term test) = 38.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64490.3MB, alloc=44.3MB, time=769.28 memory used=64537.1MB, alloc=44.3MB, time=769.84 x[1] = 0.6515 2.418 h = 0.0001 0.003 y2[1] (numeric) = 14.164725702 30.858355299 y2[1] (closed_form) = 19.9448329081 28.6068553866 absolute error = 6.203 relative error = 17.79 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.49770520283 -3.37580468256 y1[1] (closed_form) = 4.49770520283 -3.37580468256 absolute error = 1.315e-62 relative error = 2.339e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.49 Order of pole (three term test) = 50.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 31.49 Order of pole (three term test) = 38.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64583.1MB, alloc=44.3MB, time=770.39 memory used=64630.0MB, alloc=44.3MB, time=770.96 x[1] = 0.6516 2.421 h = 0.001 0.001 y2[1] (numeric) = 14.1825266088 30.9083061457 y2[1] (closed_form) = 19.956426855 28.6500298102 absolute error = 6.2 relative error = 17.76 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.51066200847 -3.38655340776 y1[1] (closed_form) = 4.51066200847 -3.38655340776 absolute error = 1.237e-62 relative error = 2.193e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.68 Order of pole (three term test) = 51.03 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 31.68 Order of pole (three term test) = 38.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64676.1MB, alloc=44.3MB, time=771.51 memory used=64722.7MB, alloc=44.3MB, time=772.07 x[1] = 0.6526 2.422 h = 0.001 0.003 y2[1] (numeric) = 14.2004289005 30.9582381761 y2[1] (closed_form) = 19.9743285108 28.6611504758 absolute error = 6.214 relative error = 17.79 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.51165822224 -3.39443837542 y1[1] (closed_form) = 4.51165822224 -3.39443837542 absolute error = 1.237e-62 relative error = 2.191e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.75 Order of pole (three term test) = 51.04 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 31.75 Order of pole (three term test) = 39.02 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64768.8MB, alloc=44.3MB, time=772.61 memory used=64815.6MB, alloc=44.3MB, time=773.17 memory used=64862.3MB, alloc=44.3MB, time=773.72 x[1] = 0.6536 2.425 h = 0.0001 0.004 y2[1] (numeric) = 14.2184330842 31.0081510547 y2[1] (closed_form) = 19.9990506307 28.7012984305 absolute error = 6.224 relative error = 17.79 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.52154120685 -3.40925165377 y1[1] (closed_form) = 4.52154120685 -3.40925165377 absolute error = 1.237e-62 relative error = 2.184e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.94 Order of pole (three term test) = 51.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 31.94 Order of pole (three term test) = 39.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=64908.2MB, alloc=44.3MB, time=774.26 memory used=64954.7MB, alloc=44.3MB, time=774.81 x[1] = 0.6537 2.429 h = 0.003 0.006 y2[1] (numeric) = 14.2365396687 31.0580444439 y2[1] (closed_form) = 20.014169299 28.7590779185 absolute error = 6.218 relative error = 17.75 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.53903492619 -3.42357809219 y1[1] (closed_form) = 4.53903492619 -3.42357809219 absolute error = 1.140e-62 relative error = 2.005e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.19 Order of pole (three term test) = 51.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 32.19 Order of pole (three term test) = 39.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65000.6MB, alloc=44.3MB, time=775.34 memory used=65047.3MB, alloc=44.3MB, time=775.90 x[1] = 0.6567 2.435 h = 0.0001 0.005 y2[1] (numeric) = 14.2547491651 31.107918004 y2[1] (closed_form) = 20.0784555133 28.8360390083 absolute error = 6.251 relative error = 17.79 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.55541740609 -3.45797651547 y1[1] (closed_form) = 4.55541740609 -3.45797651547 absolute error = 1.237e-62 relative error = 2.163e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.58 Order of pole (three term test) = 51.54 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 32.58 Order of pole (three term test) = 39.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65093.3MB, alloc=44.3MB, time=776.44 memory used=65140.1MB, alloc=44.3MB, time=777.00 x[1] = 0.6568 2.44 h = 0.0001 0.003 y2[1] (numeric) = 14.2730620862 31.157771393 y2[1] (closed_form) = 20.097247134 28.9085246856 absolute error = 6.243 relative error = 17.73 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.5775517356 -3.47602796084 y1[1] (closed_form) = 4.5775517356 -3.47602796084 absolute error = 1.237e-62 relative error = 2.152e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.91 Order of pole (three term test) = 51.8 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 32.91 Order of pole (three term test) = 39.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65186.0MB, alloc=44.3MB, time=777.54 memory used=65232.7MB, alloc=44.3MB, time=778.10 x[1] = 0.6569 2.443 h = 0.001 0.001 y2[1] (numeric) = 14.291478947 31.2076042668 y2[1] (closed_form) = 20.1091502072 28.951928964 absolute error = 6.24 relative error = 17.7 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.59074393688 -3.48708357059 y1[1] (closed_form) = 4.59074393688 -3.48708357059 absolute error = 1.237e-62 relative error = 2.146e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.11 Order of pole (three term test) = 51.95 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 33.11 Order of pole (three term test) = 40.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65279.2MB, alloc=44.3MB, time=778.66 memory used=65325.6MB, alloc=44.3MB, time=779.22 memory used=65372.2MB, alloc=44.3MB, time=779.77 x[1] = 0.6579 2.444 h = 0.0001 0.004 y2[1] (numeric) = 14.3100002643 31.2574162788 y2[1] (closed_form) = 20.127232557 28.9630290815 absolute error = 6.253 relative error = 17.73 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.59172222586 -3.49515024083 y1[1] (closed_form) = 4.59172222586 -3.49515024083 absolute error = 1.237e-62 relative error = 2.144e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.17 Order of pole (three term test) = 51.97 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 33.17 Order of pole (three term test) = 40.16 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65418.2MB, alloc=44.3MB, time=780.31 memory used=65464.9MB, alloc=44.3MB, time=780.87 x[1] = 0.658 2.448 h = 0.003 0.006 y2[1] (numeric) = 14.3286265571 31.3072070804 y2[1] (closed_form) = 20.1427025485 29.0210812439 absolute error = 6.247 relative error = 17.68 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.60949487706 -3.50982529582 y1[1] (closed_form) = 4.60949487706 -3.50982529582 absolute error = 1.334e-62 relative error = 2.303e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.44 Order of pole (three term test) = 52.17 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 33.44 Order of pole (three term test) = 40.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65511.0MB, alloc=44.3MB, time=781.40 memory used=65557.6MB, alloc=44.3MB, time=781.96 x[1] = 0.661 2.454 h = 0.0001 0.005 y2[1] (numeric) = 14.347358346 31.3569763208 y2[1] (closed_form) = 20.2077200809 29.0982057806 absolute error = 6.281 relative error = 17.73 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.62605217232 -3.54495536553 y1[1] (closed_form) = 4.62605217232 -3.54495536553 absolute error = 1.334e-62 relative error = 2.289e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.84 Order of pole (three term test) = 52.37 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 33.84 Order of pole (three term test) = 40.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65603.6MB, alloc=44.3MB, time=782.49 memory used=65650.5MB, alloc=44.3MB, time=783.05 x[1] = 0.6611 2.459 h = 0.0001 0.003 y2[1] (numeric) = 14.3661961541 31.4067236468 y2[1] (closed_form) = 20.2269547752 29.1710367937 absolute error = 6.273 relative error = 17.67 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.64853954973 -3.56344647442 y1[1] (closed_form) = 4.64853954973 -3.56344647442 absolute error = 1.360e-62 relative error = 2.322e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.18 Order of pole (three term test) = 52.64 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 34.18 Order of pole (three term test) = 40.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65696.5MB, alloc=44.3MB, time=783.59 memory used=65743.5MB, alloc=44.3MB, time=784.16 x[1] = 0.6612 2.462 h = 0.001 0.001 y2[1] (numeric) = 14.3851405061 31.456448703 y2[1] (closed_form) = 20.2391276147 29.214645594 absolute error = 6.269 relative error = 17.64 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.66194090971 -3.57476987297 y1[1] (closed_form) = 4.66194090971 -3.57476987297 absolute error = 1.360e-62 relative error = 2.315e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.39 Order of pole (three term test) = 52.8 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 34.39 Order of pole (three term test) = 41.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65790.1MB, alloc=44.3MB, time=784.71 memory used=65836.3MB, alloc=44.3MB, time=785.26 memory used=65882.9MB, alloc=44.3MB, time=785.81 x[1] = 0.6622 2.463 h = 0.001 0.003 y2[1] (numeric) = 14.4041919288 31.5061511319 y2[1] (closed_form) = 20.2573689205 29.2257291351 absolute error = 6.282 relative error = 17.67 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.66290485018 -3.58299630844 y1[1] (closed_form) = 4.66290485018 -3.58299630844 absolute error = 1.360e-62 relative error = 2.313e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.46 Order of pole (three term test) = 52.82 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 34.46 Order of pole (three term test) = 41.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=65928.8MB, alloc=44.3MB, time=786.35 memory used=65975.5MB, alloc=44.3MB, time=786.91 x[1] = 0.6632 2.466 h = 0.0001 0.004 y2[1] (numeric) = 14.4233509513 31.5558305732 y2[1] (closed_form) = 20.2828091739 29.2661423286 absolute error = 6.291 relative error = 17.67 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.67306456932 -3.59852649588 y1[1] (closed_form) = 4.67306456932 -3.59852649588 absolute error = 1.334e-62 relative error = 2.262e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.67 Order of pole (three term test) = 52.94 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 34.67 Order of pole (three term test) = 41.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66021.5MB, alloc=44.3MB, time=787.44 memory used=66068.0MB, alloc=44.3MB, time=788.00 x[1] = 0.6633 2.47 h = 0.003 0.006 y2[1] (numeric) = 14.4426181043 31.6054866649 y2[1] (closed_form) = 20.2987016591 29.324510147 absolute error = 6.285 relative error = 17.62 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.69116002563 -3.61362102885 y1[1] (closed_form) = 4.69116002563 -3.61362102885 absolute error = 1.432e-62 relative error = 2.418e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.94 Order of pole (three term test) = 53.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 34.94 Order of pole (three term test) = 41.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66113.9MB, alloc=44.3MB, time=788.53 memory used=66160.6MB, alloc=44.3MB, time=789.08 x[1] = 0.6663 2.476 h = 0.0001 0.005 y2[1] (numeric) = 14.4619939208 31.6551190423 y2[1] (closed_form) = 20.3645898585 29.4018125552 absolute error = 6.318 relative error = 17.67 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.70790812678 -3.64962225621 y1[1] (closed_form) = 4.70790812678 -3.64962225621 absolute error = 1.432e-62 relative error = 2.404e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.37 Order of pole (three term test) = 53.38 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 35.37 Order of pole (three term test) = 42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66206.6MB, alloc=44.3MB, time=789.62 memory used=66253.2MB, alloc=44.3MB, time=790.17 memory used=66299.9MB, alloc=44.3MB, time=790.73 x[1] = 0.6664 2.481 h = 0.0001 0.003 y2[1] (numeric) = 14.4814789358 31.7047273386 y2[1] (closed_form) = 20.3843574148 29.4750433758 absolute error = 6.31 relative error = 17.61 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.73080412314 -3.66864242567 y1[1] (closed_form) = 4.73080412314 -3.66864242567 absolute error = 1.432e-62 relative error = 2.392e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.72 Order of pole (three term test) = 53.66 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 35.72 Order of pole (three term test) = 42.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66346.1MB, alloc=44.3MB, time=791.28 memory used=66393.0MB, alloc=44.3MB, time=791.84 x[1] = 0.6665 2.484 h = 0.001 0.001 y2[1] (numeric) = 14.5010736862 31.7543111845 y2[1] (closed_form) = 20.3968545636 29.5188887968 absolute error = 6.305 relative error = 17.57 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.74444740117 -3.68028793084 y1[1] (closed_form) = 4.74444740117 -3.68028793084 absolute error = 1.552e-62 relative error = 2.585e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.94 Order of pole (three term test) = 53.83 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 35.94 Order of pole (three term test) = 42.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66439.0MB, alloc=44.3MB, time=792.38 memory used=66485.5MB, alloc=44.3MB, time=792.94 x[1] = 0.6675 2.485 h = 0.001 0.003 y2[1] (numeric) = 14.520778711 31.8038702086 y2[1] (closed_form) = 20.4152839782 29.5299492216 absolute error = 6.318 relative error = 17.6 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.74539075231 -3.68870341896 y1[1] (closed_form) = 4.74539075231 -3.68870341896 absolute error = 1.552e-62 relative error = 2.583e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.01 Order of pole (three term test) = 53.85 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 36.01 Order of pole (three term test) = 42.5 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66531.6MB, alloc=44.3MB, time=793.48 memory used=66578.3MB, alloc=44.3MB, time=794.03 x[1] = 0.6685 2.488 h = 0.0001 0.004 y2[1] (numeric) = 14.5405945514 31.8534040369 y2[1] (closed_form) = 20.4411245119 29.5705041876 absolute error = 6.327 relative error = 17.6 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.75569822927 -3.70463324263 y1[1] (closed_form) = 4.75569822927 -3.70463324263 absolute error = 1.552e-62 relative error = 2.575e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.22 Order of pole (three term test) = 53.98 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 36.22 Order of pole (three term test) = 42.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66624.4MB, alloc=44.3MB, time=794.56 memory used=66670.9MB, alloc=44.3MB, time=795.12 x[1] = 0.6686 2.492 h = 0.003 0.006 y2[1] (numeric) = 14.5605217505 31.9029122932 y2[1] (closed_form) = 20.4574505644 29.6291925631 absolute error = 6.32 relative error = 17.55 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.7741212205 -3.7201583557 y1[1] (closed_form) = 4.7741212205 -3.7201583557 absolute error = 1.581e-62 relative error = 2.612e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.52 Order of pole (three term test) = 54.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 36.52 Order of pole (three term test) = 42.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66717.1MB, alloc=44.3MB, time=795.66 memory used=66763.8MB, alloc=44.3MB, time=796.21 memory used=66810.6MB, alloc=44.3MB, time=796.76 x[1] = 0.6716 2.498 h = 0.0001 0.005 y2[1] (numeric) = 14.5805608534 31.9523945988 y2[1] (closed_form) = 20.5242298283 29.7066723617 absolute error = 6.354 relative error = 17.6 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.79105936726 -3.75705106045 y1[1] (closed_form) = 4.79105936726 -3.75705106045 absolute error = 1.552e-62 relative error = 2.550e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.96 Order of pole (three term test) = 54.44 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 36.96 Order of pole (three term test) = 43.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66856.5MB, alloc=44.3MB, time=797.29 memory used=66903.3MB, alloc=44.3MB, time=797.85 x[1] = 0.6717 2.503 h = 0.0001 0.003 y2[1] (numeric) = 14.6007124074 32.0018505728 y2[1] (closed_form) = 20.544544221 29.7803092042 absolute error = 6.345 relative error = 17.54 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.81436998555 -3.77661430197 y1[1] (closed_form) = 4.81436998555 -3.77661430197 absolute error = 1.581e-62 relative error = 2.584e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.33 Order of pole (three term test) = 54.74 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 37.33 Order of pole (three term test) = 43.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=66949.4MB, alloc=44.3MB, time=798.39 memory used=66996.4MB, alloc=44.3MB, time=798.96 x[1] = 0.6718 2.506 h = 0.001 0.001 y2[1] (numeric) = 14.6209769618 32.0512798318 y2[1] (closed_form) = 20.5573741499 29.824394877 absolute error = 6.34 relative error = 17.5 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.82825868595 -3.78859040506 y1[1] (closed_form) = 4.82825868595 -3.78859040506 absolute error = 1.676e-62 relative error = 2.731e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.55 Order of pole (three term test) = 54.92 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 37.55 Order of pole (three term test) = 43.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67042.5MB, alloc=44.3MB, time=799.50 memory used=67089.1MB, alloc=44.3MB, time=800.06 x[1] = 0.6728 2.507 h = 0.001 0.003 y2[1] (numeric) = 14.6413550681 32.10068199 y2[1] (closed_form) = 20.5759957637 29.835430703 absolute error = 6.352 relative error = 17.53 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.82917991522 -3.79719900265 y1[1] (closed_form) = 4.82917991522 -3.79719900265 absolute error = 1.676e-62 relative error = 2.729e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.63 Order of pole (three term test) = 54.94 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 37.63 Order of pole (three term test) = 43.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67135.1MB, alloc=44.3MB, time=800.60 memory used=67181.8MB, alloc=44.3MB, time=801.16 x[1] = 0.6738 2.51 h = 0.0001 0.004 y2[1] (numeric) = 14.6618472796 32.1500566593 y2[1] (closed_form) = 20.6022462613 29.8761285595 absolute error = 6.361 relative error = 17.53 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.8396361343 -3.8135381292 y1[1] (closed_form) = 4.8396361343 -3.8135381292 absolute error = 1.676e-62 relative error = 2.721e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.85 Order of pole (three term test) = 55.08 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 37.85 Order of pole (three term test) = 44.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67228.1MB, alloc=44.3MB, time=801.70 memory used=67274.4MB, alloc=44.3MB, time=802.24 memory used=67321.1MB, alloc=44.3MB, time=802.80 x[1] = 0.6739 2.514 h = 0.003 0.006 y2[1] (numeric) = 14.6824541521 32.1994034489 y2[1] (closed_form) = 20.619017227 29.9351424382 absolute error = 6.354 relative error = 17.48 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.85839143919 -3.8295051972 y1[1] (closed_form) = 4.85839143919 -3.8295051972 absolute error = 1.772e-62 relative error = 2.864e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.16 Order of pole (three term test) = 55.32 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 38.16 Order of pole (three term test) = 44.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67367.0MB, alloc=44.3MB, time=803.34 memory used=67413.6MB, alloc=44.3MB, time=803.89 x[1] = 0.6769 2.52 h = 0.0001 0.005 y2[1] (numeric) = 14.703176243 32.2487219658 y2[1] (closed_form) = 20.6867084006 30.0127990191 absolute error = 6.388 relative error = 17.52 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.87551875 -3.86731014983 y1[1] (closed_form) = 4.87551875 -3.86731014983 absolute error = 1.676e-62 relative error = 2.694e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.62 Order of pole (three term test) = 55.57 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 38.62 Order of pole (three term test) = 44.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67459.7MB, alloc=44.3MB, time=804.42 memory used=67506.3MB, alloc=44.3MB, time=804.98 x[1] = 0.677 2.525 h = 0.0001 0.003 y2[1] (numeric) = 14.7240141123 32.2980118147 y2[1] (closed_form) = 20.707583948 30.0868481557 absolute error = 6.379 relative error = 17.47 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.89925005558 -3.88743081918 y1[1] (closed_form) = 4.89925005558 -3.88743081918 absolute error = 1.676e-62 relative error = 2.680e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.01 Order of pole (three term test) = 55.88 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 39.01 Order of pole (three term test) = 45.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67552.4MB, alloc=44.3MB, time=805.52 memory used=67599.2MB, alloc=44.3MB, time=806.08 x[1] = 0.6771 2.528 h = 0.001 0.001 y2[1] (numeric) = 14.7449683216 32.3472725975 y2[1] (closed_form) = 20.7207553357 30.1311777434 absolute error = 6.373 relative error = 17.43 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.91338771749 -3.89974621946 y1[1] (closed_form) = 4.91338771749 -3.89974621946 absolute error = 1.676e-62 relative error = 2.672e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.24 Order of pole (three term test) = 56.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 39.24 Order of pole (three term test) = 45.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67645.4MB, alloc=44.3MB, time=806.64 memory used=67691.9MB, alloc=44.3MB, time=807.19 x[1] = 0.6781 2.529 h = 0.001 0.003 y2[1] (numeric) = 14.7660394351 32.3965039138 y2[1] (closed_form) = 20.7395733211 30.1421874322 absolute error = 6.385 relative error = 17.45 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.91428523721 -3.90855206623 y1[1] (closed_form) = 4.91428523721 -3.90855206623 absolute error = 1.581e-62 relative error = 2.518e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.32 Order of pole (three term test) = 56.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 39.32 Order of pole (three term test) = 45.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67738.3MB, alloc=44.3MB, time=807.74 memory used=67784.6MB, alloc=44.3MB, time=808.28 memory used=67831.3MB, alloc=44.3MB, time=808.84 x[1] = 0.6791 2.532 h = 0.0001 0.004 y2[1] (numeric) = 14.7872280187 32.4457053607 y2[1] (closed_form) = 20.7662436864 30.1830292666 absolute error = 6.393 relative error = 17.45 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.92489115507 -3.92531038362 y1[1] (closed_form) = 4.92489115507 -3.92531038362 absolute error = 1.676e-62 relative error = 2.662e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.56 Order of pole (three term test) = 56.24 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 39.56 Order of pole (three term test) = 45.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67877.3MB, alloc=44.3MB, time=809.37 memory used=67923.8MB, alloc=44.3MB, time=809.92 x[1] = 0.6792 2.536 h = 0.003 0.006 y2[1] (numeric) = 14.8085346407 32.494876533 y2[1] (closed_form) = 20.7834711902 30.2423736394 absolute error = 6.385 relative error = 17.4 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.94398360079 -3.94173106036 y1[1] (closed_form) = 4.94398360079 -3.94173106036 absolute error = 1.649e-62 relative error = 2.608e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.87 Order of pole (three term test) = 56.5 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 39.87 Order of pole (three term test) = 45.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=67969.9MB, alloc=44.3MB, time=810.46 memory used=68016.5MB, alloc=44.3MB, time=811.01 x[1] = 0.6822 2.542 h = 0.0001 0.005 y2[1] (numeric) = 14.8299598713 32.5440170226 y2[1] (closed_form) = 20.8520955754 30.3202062623 absolute error = 6.42 relative error = 17.45 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.9612990676 -3.9804694914 y1[1] (closed_form) = 4.9612990676 -3.9804694914 absolute error = 1.676e-62 relative error = 2.635e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.36 Order of pole (three term test) = 56.76 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 40.36 Order of pole (three term test) = 46.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68062.6MB, alloc=44.3MB, time=811.55 memory used=68109.3MB, alloc=44.3MB, time=812.10 x[1] = 0.6823 2.547 h = 0.0001 0.003 y2[1] (numeric) = 14.8515042832 32.5931264193 y2[1] (closed_form) = 20.8735469481 30.3946740221 absolute error = 6.411 relative error = 17.39 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.9854571876 -4.00116229662 y1[1] (closed_form) = 4.9854571876 -4.00116229662 absolute error = 1.676e-62 relative error = 2.622e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.76 Order of pole (three term test) = 57.1 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 40.76 Order of pole (three term test) = 46.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68155.6MB, alloc=44.3MB, time=812.64 memory used=68202.4MB, alloc=44.3MB, time=813.20 x[1] = 0.6824 2.55 h = 0.001 0.001 y2[1] (numeric) = 14.8731684507 32.6422043102 y2[1] (closed_form) = 20.8870686855 30.4392512193 absolute error = 6.405 relative error = 17.35 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.99984738453 -4.01382590613 y1[1] (closed_form) = 4.99984738453 -4.01382590613 absolute error = 1.676e-62 relative error = 2.614e-61 % Correct digits = 63 memory used=68249.5MB, alloc=44.3MB, time=813.77 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 41.01 Order of pole (three term test) = 57.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 41.01 Order of pole (three term test) = 46.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68295.5MB, alloc=44.3MB, time=814.31 memory used=68342.0MB, alloc=44.3MB, time=814.86 x[1] = 0.6834 2.551 h = 0.0001 0.004 y2[1] (numeric) = 14.8949529507 32.6912502798 y2[1] (closed_form) = 20.9060872984 30.4502331747 absolute error = 6.415 relative error = 17.37 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.00071955024 -4.02283322617 y1[1] (closed_form) = 5.00071955024 -4.02283322617 absolute error = 1.676e-62 relative error = 2.612e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 41.09 Order of pole (three term test) = 57.32 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 41.09 Order of pole (three term test) = 46.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68388.0MB, alloc=44.3MB, time=815.40 memory used=68434.5MB, alloc=44.3MB, time=815.96 x[1] = 0.6835 2.555 h = 0.003 0.006 y2[1] (numeric) = 14.9168583621 32.7402639101 y2[1] (closed_form) = 20.9237132825 30.5098716879 absolute error = 6.408 relative error = 17.32 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.02011169522 -4.03964980887 y1[1] (closed_form) = 5.02011169522 -4.03964980887 absolute error = 1.772e-62 relative error = 2.750e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 41.42 Order of pole (three term test) = 57.59 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 41.42 Order of pole (three term test) = 47.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68480.5MB, alloc=44.3MB, time=816.49 memory used=68527.2MB, alloc=44.3MB, time=817.04 x[1] = 0.6865 2.561 h = 0.0001 0.005 y2[1] (numeric) = 14.9388852658 32.7892447808 y2[1] (closed_form) = 20.9931562769 30.5878666149 absolute error = 6.442 relative error = 17.36 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.03759968511 -4.07920688354 y1[1] (closed_form) = 5.03759968511 -4.07920688354 absolute error = 1.676e-62 relative error = 2.586e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 41.92 Order of pole (three term test) = 57.87 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 41.92 Order of pole (three term test) = 47.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68573.3MB, alloc=44.3MB, time=817.58 memory used=68620.1MB, alloc=44.3MB, time=818.14 x[1] = 0.6866 2.566 h = 0.0001 0.003 y2[1] (numeric) = 14.9610342451 32.8381924685 y2[1] (closed_form) = 21.0151102329 30.6627069268 absolute error = 6.433 relative error = 17.31 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.0621372063 -4.10039903231 y1[1] (closed_form) = 5.0621372063 -4.10039903231 absolute error = 1.803e-62 relative error = 2.767e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.34 Order of pole (three term test) = 58.22 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 42.34 Order of pole (three term test) = 48.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68666.4MB, alloc=44.3MB, time=818.68 memory used=68712.9MB, alloc=44.3MB, time=819.24 memory used=68759.8MB, alloc=44.3MB, time=819.81 x[1] = 0.6867 2.569 h = 0.001 0.001 y2[1] (numeric) = 14.9833058854 32.8871065478 y2[1] (closed_form) = 21.0289378154 30.7075045619 absolute error = 6.427 relative error = 17.27 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.07675196083 -4.11336660451 y1[1] (closed_form) = 5.07675196083 -4.11336660451 absolute error = 1.803e-62 relative error = 2.759e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.6 Order of pole (three term test) = 58.42 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 42.6 Order of pole (three term test) = 48.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68805.8MB, alloc=44.3MB, time=820.35 memory used=68852.5MB, alloc=44.3MB, time=820.91 x[1] = 0.6877 2.57 h = 0.001 0.003 y2[1] (numeric) = 15.0057007742 32.9359865902 y2[1] (closed_form) = 21.0481329518 30.7184637822 absolute error = 6.436 relative error = 17.28 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.07760341115 -4.12255112393 y1[1] (closed_form) = 5.07760341115 -4.12255112393 absolute error = 1.803e-62 relative error = 2.756e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.68 Order of pole (three term test) = 58.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 42.68 Order of pole (three term test) = 48.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68898.4MB, alloc=44.3MB, time=821.44 memory used=68944.9MB, alloc=44.3MB, time=822.00 x[1] = 0.6887 2.573 h = 0.0001 0.004 y2[1] (numeric) = 15.0282195012 32.9848321648 y2[1] (closed_form) = 21.0756099829 30.7595815991 absolute error = 6.444 relative error = 17.28 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.08849560928 -4.14011474387 y1[1] (closed_form) = 5.08849560928 -4.14011474387 absolute error = 1.803e-62 relative error = 2.748e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.94 Order of pole (three term test) = 58.62 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 42.94 Order of pole (three term test) = 48.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=68990.9MB, alloc=44.3MB, time=822.53 memory used=69037.4MB, alloc=44.3MB, time=823.08 x[1] = 0.6888 2.577 h = 0.003 0.006 y2[1] (numeric) = 15.0508626584 33.0336428382 y2[1] (closed_form) = 21.0937148394 30.8195601571 absolute error = 6.436 relative error = 17.23 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.1082341514 -4.15740732624 y1[1] (closed_form) = 5.1082341514 -4.15740732624 absolute error = 1.803e-62 relative error = 2.737e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 43.28 Order of pole (three term test) = 58.9 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 43.28 Order of pole (three term test) = 48.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69083.4MB, alloc=44.3MB, time=823.62 memory used=69130.2MB, alloc=44.3MB, time=824.18 x[1] = 0.6918 2.583 h = 0.0001 0.005 y2[1] (numeric) = 15.0736308398 33.0824181741 y2[1] (closed_form) = 21.1641319457 30.8977296459 absolute error = 6.47 relative error = 17.28 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.12590833246 -4.19793865708 y1[1] (closed_form) = 5.12590833246 -4.19793865708 absolute error = 1.772e-62 relative error = 2.675e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 43.8 Order of pole (three term test) = 59.2 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 43.8 Order of pole (three term test) = 49.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69176.7MB, alloc=44.3MB, time=824.72 memory used=69223.0MB, alloc=44.3MB, time=825.27 memory used=69269.6MB, alloc=44.3MB, time=825.83 x[1] = 0.6919 2.588 h = 0.0001 0.003 y2[1] (numeric) = 15.0965246418 33.1311577339 y2[1] (closed_form) = 21.1866899129 30.9730006935 absolute error = 6.461 relative error = 17.22 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.15088441702 -4.21973120078 y1[1] (closed_form) = 5.15088441702 -4.21973120078 absolute error = 1.803e-62 relative error = 2.707e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.24 Order of pole (three term test) = 59.57 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 44.24 Order of pole (three term test) = 49.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69315.7MB, alloc=44.3MB, time=826.37 memory used=69362.6MB, alloc=44.3MB, time=826.94 x[1] = 0.692 2.591 h = 0.001 0.001 y2[1] (numeric) = 15.1195446629 33.179861076 y2[1] (closed_form) = 21.2008849274 31.0180530075 absolute error = 6.454 relative error = 17.18 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.16575855835 -4.23306410499 y1[1] (closed_form) = 5.16575855835 -4.23306410499 absolute error = 1.803e-62 relative error = 2.699e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.51 Order of pole (three term test) = 59.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 44.51 Order of pole (three term test) = 50 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69408.6MB, alloc=44.3MB, time=827.48 memory used=69455.3MB, alloc=44.3MB, time=828.04 x[1] = 0.693 2.592 h = 0.001 0.003 y2[1] (numeric) = 15.1426915038 33.2285277564 y2[1] (closed_form) = 21.2202888584 31.028981418 absolute error = 6.463 relative error = 17.19 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.16658149024 -4.24245820896 y1[1] (closed_form) = 5.16658149024 -4.24245820896 absolute error = 1.803e-62 relative error = 2.697e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.6 Order of pole (three term test) = 59.82 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 44.6 Order of pole (three term test) = 50.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69501.3MB, alloc=44.3MB, time=828.58 memory used=69548.1MB, alloc=44.3MB, time=829.13 x[1] = 0.694 2.595 h = 0.0001 0.004 y2[1] (numeric) = 15.1659657674 33.2771573281 y2[1] (closed_form) = 21.2482153378 31.0702462664 absolute error = 6.47 relative error = 17.19 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.17762608131 -4.26047056157 y1[1] (closed_form) = 5.17762608131 -4.26047056157 absolute error = 1.709e-62 relative error = 2.548e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.87 Order of pole (three term test) = 59.99 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 44.87 Order of pole (three term test) = 50.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69594.1MB, alloc=44.3MB, time=829.67 memory used=69640.7MB, alloc=44.3MB, time=830.22 x[1] = 0.6941 2.599 h = 0.003 0.006 y2[1] (numeric) = 15.1893680588 33.3257493419 y2[1] (closed_form) = 21.2668115245 31.1305699885 absolute error = 6.462 relative error = 17.14 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.19771598689 -4.27825163107 y1[1] (closed_form) = 5.19771598689 -4.27825163107 absolute error = 1.709e-62 relative error = 2.538e-61 % Correct digits = 63 memory used=69687.3MB, alloc=44.3MB, time=830.78 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.23 Order of pole (three term test) = 60.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 45.23 Order of pole (three term test) = 50.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69733.3MB, alloc=44.3MB, time=831.32 memory used=69780.0MB, alloc=44.3MB, time=831.87 x[1] = 0.6971 2.605 h = 0.0001 0.005 y2[1] (numeric) = 15.2128989856 33.3743033453 y2[1] (closed_form) = 21.338225407 31.2089128972 absolute error = 6.497 relative error = 17.18 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.21557496455 -4.31977981918 y1[1] (closed_form) = 5.21557496455 -4.31977981918 absolute error = 1.709e-62 relative error = 2.523e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.77 Order of pole (three term test) = 60.61 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 45.77 Order of pole (three term test) = 51.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69825.9MB, alloc=44.3MB, time=832.41 memory used=69872.6MB, alloc=44.3MB, time=832.97 x[1] = 0.6972 2.61 h = 0.0001 0.003 y2[1] (numeric) = 15.2365591572 33.4228188837 y2[1] (closed_form) = 21.3614031081 31.2846211743 absolute error = 6.487 relative error = 17.13 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.24099591723 -4.34218851839 y1[1] (closed_form) = 5.24099591723 -4.34218851839 absolute error = 1.746e-62 relative error = 2.566e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.23 Order of pole (three term test) = 61 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 46.23 Order of pole (three term test) = 51.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=69918.6MB, alloc=44.3MB, time=833.51 memory used=69965.4MB, alloc=44.3MB, time=834.07 x[1] = 0.6973 2.613 h = 0.001 0.001 y2[1] (numeric) = 15.2603491856 33.4712954993 y2[1] (closed_form) = 21.3759750809 31.3299319528 absolute error = 6.48 relative error = 17.08 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.25613311736 -4.3558963023 y1[1] (closed_form) = 5.25613311736 -4.3558963023 absolute error = 1.709e-62 relative error = 2.503e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.51 Order of pole (three term test) = 61.23 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 46.51 Order of pole (three term test) = 51.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70011.6MB, alloc=44.3MB, time=834.63 memory used=70058.2MB, alloc=44.3MB, time=835.18 x[1] = 0.6983 2.614 h = 0.001 0.003 y2[1] (numeric) = 15.2842696848 33.5197327318 y2[1] (closed_form) = 21.3955923105 31.3408277834 absolute error = 6.488 relative error = 17.1 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.25692571513 -4.36550446573 y1[1] (closed_form) = 5.25692571513 -4.36550446573 absolute error = 1.709e-62 relative error = 2.501e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.61 Order of pole (three term test) = 61.26 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 46.61 Order of pole (three term test) = 51.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70104.2MB, alloc=44.3MB, time=835.72 memory used=70151.0MB, alloc=44.3MB, time=836.28 memory used=70197.7MB, alloc=44.3MB, time=836.83 x[1] = 0.6993 2.617 h = 0.0001 0.004 y2[1] (numeric) = 15.3083212712 33.5681301181 y2[1] (closed_form) = 21.4239790384 31.3822406185 absolute error = 6.495 relative error = 17.09 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.26812353383 -4.38397633904 y1[1] (closed_form) = 5.26812353383 -4.38397633904 absolute error = 1.709e-62 relative error = 2.493e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.89 Order of pole (three term test) = 61.45 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 46.89 Order of pole (three term test) = 52.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70243.7MB, alloc=44.3MB, time=837.36 memory used=70290.3MB, alloc=44.3MB, time=837.92 x[1] = 0.6994 2.621 h = 0.003 0.006 y2[1] (numeric) = 15.3325045633 33.6164871922 y2[1] (closed_form) = 21.4430793176 31.4429146671 absolute error = 6.486 relative error = 17.04 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.28856981546 -4.4022586878 y1[1] (closed_form) = 5.28856981546 -4.4022586878 absolute error = 1.709e-62 relative error = 2.483e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.26 Order of pole (three term test) = 61.77 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 47.26 Order of pole (three term test) = 52.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70336.4MB, alloc=44.3MB, time=838.46 memory used=70383.2MB, alloc=44.3MB, time=839.01 x[1] = 0.7024 2.627 h = 0.0001 0.005 y2[1] (numeric) = 15.3568201822 33.6648034856 y2[1] (closed_form) = 21.5155131359 31.5214297 absolute error = 6.521 relative error = 17.09 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.30661204693 -4.44480683185 y1[1] (closed_form) = 5.30661204693 -4.44480683185 absolute error = 1.746e-62 relative error = 2.523e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.83 Order of pole (three term test) = 62.11 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 47.83 Order of pole (three term test) = 53.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70429.2MB, alloc=44.3MB, time=839.54 memory used=70476.0MB, alloc=44.3MB, time=840.10 x[1] = 0.7025 2.632 h = 0.0001 0.003 y2[1] (numeric) = 15.3812687508 33.7130785268 y2[1] (closed_form) = 21.5393266777 31.5975817554 absolute error = 6.511 relative error = 17.03 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.33248423162 -4.46784783182 y1[1] (closed_form) = 5.33248423162 -4.46784783182 absolute error = 1.746e-62 relative error = 2.510e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 48.31 Order of pole (three term test) = 62.52 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 48.31 Order of pole (three term test) = 53.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70522.0MB, alloc=44.3MB, time=840.64 memory used=70568.9MB, alloc=44.3MB, time=841.20 x[1] = 0.7026 2.635 h = 0.001 0.001 y2[1] (numeric) = 15.4058508946 33.7613118417 y2[1] (closed_form) = 21.5542853673 31.6431548137 absolute error = 6.503 relative error = 16.99 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.34788819504 -4.48194027538 y1[1] (closed_form) = 5.34788819504 -4.48194027538 absolute error = 1.746e-62 relative error = 2.503e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 48.61 Order of pole (three term test) = 62.76 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 48.61 Order of pole (three term test) = 53.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70615.3MB, alloc=44.3MB, time=841.76 memory used=70661.7MB, alloc=44.3MB, time=842.31 memory used=70708.3MB, alloc=44.3MB, time=842.86 x[1] = 0.7036 2.636 h = 0.001 0.003 y2[1] (numeric) = 15.4305672414 33.809502953 y2[1] (closed_form) = 21.5741204892 31.6540162301 absolute error = 6.511 relative error = 17 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.34864857927 -4.49176706371 y1[1] (closed_form) = 5.34864857927 -4.49176706371 absolute error = 1.709e-62 relative error = 2.447e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 48.7 Order of pole (three term test) = 62.8 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 48.7 Order of pole (three term test) = 53.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70754.3MB, alloc=44.3MB, time=843.40 memory used=70800.8MB, alloc=44.3MB, time=843.96 x[1] = 0.7046 2.639 h = 0.0001 0.004 y2[1] (numeric) = 15.455418421 33.857651381 y2[1] (closed_form) = 21.6029785102 31.695577967 absolute error = 6.517 relative error = 16.99 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.36000042297 -4.510709491 y1[1] (closed_form) = 5.36000042297 -4.510709491 absolute error = 1.746e-62 relative error = 2.493e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 49 Order of pole (three term test) = 63 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 49 Order of pole (three term test) = 54.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70846.6MB, alloc=44.3MB, time=844.49 memory used=70893.2MB, alloc=44.3MB, time=845.05 x[1] = 0.7047 2.643 h = 0.003 0.006 y2[1] (numeric) = 15.4804050657 33.905756643 y2[1] (closed_form) = 21.6225959558 31.7566075466 absolute error = 6.507 relative error = 16.94 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.3808081388 -4.52950622277 y1[1] (closed_form) = 5.3808081388 -4.52950622277 absolute error = 1.746e-62 relative error = 2.483e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 49.39 Order of pole (three term test) = 63.33 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 49.39 Order of pole (three term test) = 54.58 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=70939.3MB, alloc=44.3MB, time=845.58 memory used=70986.1MB, alloc=44.3MB, time=846.14 x[1] = 0.7077 2.649 h = 0.0001 0.005 y2[1] (numeric) = 15.5055278101 33.9538182534 y2[1] (closed_form) = 21.6960733745 31.8352932489 absolute error = 6.543 relative error = 16.98 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.39903192696 -4.57309792921 y1[1] (closed_form) = 5.39903192696 -4.57309792921 absolute error = 1.838e-62 relative error = 2.598e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 49.99 Order of pole (three term test) = 63.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 49.99 Order of pole (three term test) = 55.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71032.1MB, alloc=44.3MB, time=846.67 memory used=71078.8MB, alloc=44.3MB, time=847.23 x[1] = 0.7078 2.654 h = 0.0001 0.003 y2[1] (numeric) = 15.5307872912 34.0018357238 y2[1] (closed_form) = 21.7205392573 31.9118956854 absolute error = 6.533 relative error = 16.92 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.42536176581 -4.5967877687 y1[1] (closed_form) = 5.42536176581 -4.5967877687 absolute error = 1.746e-62 relative error = 2.456e-61 % Correct digits = 63 memory used=71125.5MB, alloc=44.3MB, time=847.78 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.49 Order of pole (three term test) = 64.13 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 50.49 Order of pole (three term test) = 55.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71171.8MB, alloc=44.3MB, time=848.34 memory used=71218.7MB, alloc=44.3MB, time=848.90 x[1] = 0.7079 2.657 h = 0.001 0.001 y2[1] (numeric) = 15.5561841479 34.049808563 y2[1] (closed_form) = 21.7358946597 31.9577348681 absolute error = 6.524 relative error = 16.88 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.44103622892 -4.61127488947 y1[1] (closed_form) = 5.44103622892 -4.61127488947 absolute error = 1.838e-62 relative error = 2.578e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.79 Order of pole (three term test) = 64.39 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 50.79 Order of pole (three term test) = 55.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71265.0MB, alloc=44.3MB, time=849.45 memory used=71311.7MB, alloc=44.3MB, time=850.00 x[1] = 0.7089 2.658 h = 0.0001 0.004 y2[1] (numeric) = 15.5817190219 34.0977362768 y2[1] (closed_form) = 21.7559523588 31.9685599692 absolute error = 6.531 relative error = 16.89 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.44176245451 -4.62132496028 y1[1] (closed_form) = 5.44176245451 -4.62132496028 absolute error = 1.746e-62 relative error = 2.446e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.89 Order of pole (three term test) = 64.42 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 50.89 Order of pole (three term test) = 56.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71357.7MB, alloc=44.3MB, time=850.54 memory used=71404.4MB, alloc=44.3MB, time=851.10 x[1] = 0.709 2.662 h = 0.003 0.006 y2[1] (numeric) = 15.607392557 34.145618368 y2[1] (closed_form) = 21.7760213562 32.0299061556 absolute error = 6.521 relative error = 16.84 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.4628917112 -4.64057080396 y1[1] (closed_form) = 5.4628917112 -4.64057080396 absolute error = 1.746e-62 relative error = 2.436e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 51.3 Order of pole (three term test) = 64.77 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 51.3 Order of pole (three term test) = 56.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71450.2MB, alloc=44.3MB, time=851.63 memory used=71496.8MB, alloc=44.3MB, time=852.18 x[1] = 0.712 2.668 h = 0.0001 0.005 y2[1] (numeric) = 15.6332053993 34.1934543367 y2[1] (closed_form) = 21.8504144083 32.1087502978 absolute error = 6.557 relative error = 16.88 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.48128311905 -4.68507794062 y1[1] (closed_form) = 5.48128311905 -4.68507794062 absolute error = 1.746e-62 relative error = 2.422e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 51.92 Order of pole (three term test) = 65.16 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 51.92 Order of pole (three term test) = 57.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71542.8MB, alloc=44.3MB, time=852.72 memory used=71589.5MB, alloc=44.3MB, time=853.27 memory used=71636.3MB, alloc=44.3MB, time=853.83 x[1] = 0.7121 2.673 h = 0.0001 0.003 y2[1] (numeric) = 15.6591581973 34.2412436801 y2[1] (closed_form) = 21.8754498517 32.1857537809 absolute error = 6.547 relative error = 16.82 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.50802008238 -4.70933427373 y1[1] (closed_form) = 5.50802008238 -4.70933427373 absolute error = 1.746e-62 relative error = 2.410e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 52.44 Order of pole (three term test) = 65.61 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 52.44 Order of pole (three term test) = 57.52 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71682.3MB, alloc=44.3MB, time=854.37 memory used=71729.2MB, alloc=44.3MB, time=854.94 x[1] = 0.7122 2.676 h = 0.001 0.001 y2[1] (numeric) = 15.6852516018 34.2889858921 y2[1] (closed_form) = 21.8911516881 32.2318300276 absolute error = 6.538 relative error = 16.78 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.52393526683 -4.72416604332 y1[1] (closed_form) = 5.52393526683 -4.72416604332 absolute error = 1.746e-62 relative error = 2.403e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 52.76 Order of pole (three term test) = 65.88 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 52.76 Order of pole (three term test) = 57.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71775.2MB, alloc=44.3MB, time=855.48 memory used=71821.7MB, alloc=44.3MB, time=856.03 x[1] = 0.7132 2.677 h = 0.001 0.003 y2[1] (numeric) = 15.711486266 34.3366804641 y2[1] (closed_form) = 21.9114052615 32.2426250243 absolute error = 6.544 relative error = 16.79 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.52463321759 -4.73441254921 y1[1] (closed_form) = 5.52463321759 -4.73441254921 absolute error = 1.709e-62 relative error = 2.349e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 52.86 Order of pole (three term test) = 65.92 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 52.86 Order of pole (three term test) = 57.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71867.9MB, alloc=44.3MB, time=856.58 memory used=71914.8MB, alloc=44.3MB, time=857.14 x[1] = 0.7142 2.68 h = 0.0001 0.004 y2[1] (numeric) = 15.7378628454 34.384326884 y2[1] (closed_form) = 21.941168706 32.2844720597 absolute error = 6.549 relative error = 16.78 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.53627957839 -4.75425893965 y1[1] (closed_form) = 5.53627957839 -4.75425893965 absolute error = 1.746e-62 relative error = 2.393e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 53.18 Order of pole (three term test) = 66.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 53.18 Order of pole (three term test) = 58.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=71960.7MB, alloc=44.3MB, time=857.68 memory used=72007.3MB, alloc=44.3MB, time=858.23 x[1] = 0.7143 2.684 h = 0.003 0.006 y2[1] (numeric) = 15.764381998 34.4319246372 y2[1] (closed_form) = 21.961779988 32.346183736 absolute error = 6.539 relative error = 16.72 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.55777996522 -4.77404434203 y1[1] (closed_form) = 5.55777996522 -4.77404434203 absolute error = 1.803e-62 relative error = 2.461e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 53.61 Order of pole (three term test) = 66.51 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 53.61 Order of pole (three term test) = 58.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72053.5MB, alloc=44.3MB, time=858.77 memory used=72100.0MB, alloc=44.3MB, time=859.32 memory used=72146.8MB, alloc=44.3MB, time=859.88 x[1] = 0.7173 2.69 h = 0.0001 0.005 y2[1] (numeric) = 15.791044384 34.4794732059 y2[1] (closed_form) = 22.0372620772 32.4251956914 absolute error = 6.575 relative error = 16.77 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.57634963541 -4.81964037906 y1[1] (closed_form) = 5.57634963541 -4.81964037906 absolute error = 1.803e-62 relative error = 2.446e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.26 Order of pole (three term test) = 66.92 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 54.26 Order of pole (three term test) = 59.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72192.8MB, alloc=44.3MB, time=860.42 memory used=72239.5MB, alloc=44.3MB, time=860.97 x[1] = 0.7174 2.695 h = 0.0001 0.003 y2[1] (numeric) = 15.817850666 34.5269720692 y2[1] (closed_form) = 22.062981563 32.5026621909 absolute error = 6.565 relative error = 16.71 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.60355656335 -4.84457732686 y1[1] (closed_form) = 5.60355656335 -4.84457732686 absolute error = 1.803e-62 relative error = 2.434e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.8 Order of pole (three term test) = 67.4 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 54.8 Order of pole (three term test) = 59.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72285.7MB, alloc=44.3MB, time=861.52 memory used=72332.4MB, alloc=44.3MB, time=862.08 x[1] = 0.7175 2.698 h = 0.001 0.001 y2[1] (numeric) = 15.8448015092 34.5744207033 y2[1] (closed_form) = 22.0790993167 32.5490119183 absolute error = 6.555 relative error = 16.67 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.6197494091 -4.85982301965 y1[1] (closed_form) = 5.6197494091 -4.85982301965 absolute error = 1.803e-62 relative error = 2.426e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 55.13 Order of pole (three term test) = 67.68 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 55.13 Order of pole (three term test) = 60.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72378.5MB, alloc=44.3MB, time=862.62 memory used=72424.9MB, alloc=44.3MB, time=863.17 x[1] = 0.7185 2.699 h = 0.001 0.003 y2[1] (numeric) = 15.8718975808 34.6218185814 y2[1] (closed_form) = 22.0995844583 32.5597669371 absolute error = 6.56 relative error = 16.67 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.62040945839 -4.87030175086 y1[1] (closed_form) = 5.62040945839 -4.87030175086 absolute error = 1.803e-62 relative error = 2.424e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 55.24 Order of pole (three term test) = 67.73 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 55.24 Order of pole (three term test) = 60.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72470.7MB, alloc=44.3MB, time=863.71 memory used=72517.3MB, alloc=44.3MB, time=864.27 x[1] = 0.7195 2.702 h = 0.0001 0.004 y2[1] (numeric) = 15.8991395507 34.6691651735 y2[1] (closed_form) = 22.1298521797 32.6017653948 absolute error = 6.565 relative error = 16.66 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.63221204088 -4.89065165251 y1[1] (closed_form) = 5.63221204088 -4.89065165251 absolute error = 1.803e-62 relative error = 2.417e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 55.57 Order of pole (three term test) = 67.97 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 55.57 Order of pole (three term test) = 60.58 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72563.9MB, alloc=44.3MB, time=864.82 memory used=72610.2MB, alloc=44.3MB, time=865.37 memory used=72656.7MB, alloc=44.3MB, time=865.92 x[1] = 0.7196 2.706 h = 0.003 0.006 y2[1] (numeric) = 15.926528091 34.7164599466 y2[1] (closed_form) = 22.151019751 32.6638478862 absolute error = 6.554 relative error = 16.61 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.65408874605 -4.91099064848 y1[1] (closed_form) = 5.65408874605 -4.91099064848 absolute error = 1.838e-62 relative error = 2.455e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 56.02 Order of pole (three term test) = 68.35 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 56.02 Order of pole (three term test) = 60.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72702.7MB, alloc=44.3MB, time=866.46 memory used=72749.5MB, alloc=44.3MB, time=867.02 x[1] = 0.7226 2.712 h = 0.0001 0.005 y2[1] (numeric) = 15.9540638765 34.7637023646 y2[1] (closed_form) = 22.2276160476 32.7430257156 absolute error = 6.591 relative error = 16.65 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.67283451111 -4.95770070494 y1[1] (closed_form) = 5.67283451111 -4.95770070494 absolute error = 1.803e-62 relative error = 2.393e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 56.7 Order of pole (three term test) = 68.79 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 56.7 Order of pole (three term test) = 61.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72795.6MB, alloc=44.3MB, time=867.55 memory used=72842.5MB, alloc=44.3MB, time=868.11 x[1] = 0.7227 2.717 h = 0.0001 0.003 y2[1] (numeric) = 15.9817475841 34.8108918885 y2[1] (closed_form) = 22.2540372516 32.8209619889 absolute error = 6.58 relative error = 16.59 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.70051799219 -4.98333598188 y1[1] (closed_form) = 5.70051799219 -4.98333598188 absolute error = 1.838e-62 relative error = 2.428e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 57.27 Order of pole (three term test) = 69.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 57.27 Order of pole (three term test) = 62.21 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72888.4MB, alloc=44.3MB, time=868.65 memory used=72935.2MB, alloc=44.3MB, time=869.22 x[1] = 0.7228 2.72 h = 0.001 0.001 y2[1] (numeric) = 16.0095798932 34.8580279759 y2[1] (closed_form) = 22.2705816281 32.8675891256 absolute error = 6.57 relative error = 16.55 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.71699232636 -4.99900632519 y1[1] (closed_form) = 5.71699232636 -4.99900632519 absolute error = 1.838e-62 relative error = 2.421e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 57.61 Order of pole (three term test) = 69.59 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 57.61 Order of pole (three term test) = 62.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=72981.5MB, alloc=44.3MB, time=869.77 memory used=73028.1MB, alloc=44.3MB, time=870.32 x[1] = 0.7238 2.721 h = 0.001 0.003 y2[1] (numeric) = 16.0375614857 34.9051100814 y2[1] (closed_form) = 22.2913032946 32.8783020654 absolute error = 6.574 relative error = 16.55 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.71761233128 -5.00972221315 y1[1] (closed_form) = 5.71761233128 -5.00972221315 absolute error = 1.931e-62 relative error = 2.541e-61 % Correct digits = 63 memory used=73074.5MB, alloc=44.3MB, time=870.87 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 57.73 Order of pole (three term test) = 69.64 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 57.73 Order of pole (three term test) = 62.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73121.0MB, alloc=44.3MB, time=871.42 memory used=73167.8MB, alloc=44.3MB, time=871.98 x[1] = 0.7248 2.724 h = 0.0001 0.004 y2[1] (numeric) = 16.0656930458 34.9521376565 y2[1] (closed_form) = 22.3220873315 32.920452689 absolute error = 6.578 relative error = 16.54 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.72957177056 -5.03058765657 y1[1] (closed_form) = 5.72957177056 -5.03058765657 absolute error = 1.879e-62 relative error = 2.464e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 58.07 Order of pole (three term test) = 69.89 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 58.07 Order of pole (three term test) = 63.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73213.7MB, alloc=44.3MB, time=872.52 memory used=73260.3MB, alloc=44.3MB, time=873.07 x[1] = 0.7249 2.728 h = 0.003 0.006 y2[1] (numeric) = 16.0939752604 34.9991101496 y2[1] (closed_form) = 22.343825537 32.9829113599 absolute error = 6.567 relative error = 16.48 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.75183002475 -5.05149462117 y1[1] (closed_form) = 5.75183002475 -5.05149462117 absolute error = 1.970e-62 relative error = 2.573e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 58.54 Order of pole (three term test) = 70.3 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 58.54 Order of pole (three term test) = 63.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73306.2MB, alloc=44.3MB, time=873.61 memory used=73353.0MB, alloc=44.3MB, time=874.16 x[1] = 0.7279 2.734 h = 0.0001 0.005 y2[1] (numeric) = 16.1224088185 35.0460270058 y2[1] (closed_form) = 22.4215617579 33.0622529398 absolute error = 6.604 relative error = 16.53 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.77074953768 -5.09934436508 y1[1] (closed_form) = 5.77074953768 -5.09934436508 absolute error = 1.879e-62 relative error = 2.440e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 59.25 Order of pole (three term test) = 70.77 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 59.25 Order of pole (three term test) = 64.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73399.0MB, alloc=44.3MB, time=874.70 memory used=73445.8MB, alloc=44.3MB, time=875.25 x[1] = 0.728 2.739 h = 0.0001 0.003 y2[1] (numeric) = 16.1509944118 35.0928876672 y2[1] (closed_form) = 22.4487027856 33.1406657952 absolute error = 6.593 relative error = 16.47 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.79891621483 -5.12569611516 y1[1] (closed_form) = 5.79891621483 -5.12569611516 absolute error = 2.012e-62 relative error = 2.600e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 59.84 Order of pole (three term test) = 71.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 59.84 Order of pole (three term test) = 64.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73492.1MB, alloc=44.3MB, time=875.79 memory used=73538.9MB, alloc=44.3MB, time=876.35 memory used=73585.8MB, alloc=44.3MB, time=876.92 x[1] = 0.7281 2.742 h = 0.001 0.001 y2[1] (numeric) = 16.1797327343 35.1396915725 y2[1] (closed_form) = 22.4656847497 33.1875742965 absolute error = 6.582 relative error = 16.42 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.81567589384 -5.14180209556 y1[1] (closed_form) = 5.81567589384 -5.14180209556 absolute error = 2.012e-62 relative error = 2.592e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 60.2 Order of pole (three term test) = 71.61 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 60.2 Order of pole (three term test) = 65.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73631.9MB, alloc=44.3MB, time=877.46 memory used=73678.5MB, alloc=44.3MB, time=878.01 x[1] = 0.7291 2.743 h = 0.001 0.003 y2[1] (numeric) = 16.2086244826 35.1864381574 y2[1] (closed_form) = 22.4866479955 33.198242982 absolute error = 6.585 relative error = 16.42 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.81625363793 -5.15276017047 y1[1] (closed_form) = 5.81625363793 -5.15276017047 absolute error = 2.012e-62 relative error = 2.590e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 60.32 Order of pole (three term test) = 71.66 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 60.32 Order of pole (three term test) = 65.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73724.6MB, alloc=44.3MB, time=878.55 memory used=73771.4MB, alloc=44.3MB, time=879.11 x[1] = 0.7301 2.746 h = 0.0001 0.004 y2[1] (numeric) = 16.2376703556 35.2331268543 y2[1] (closed_form) = 22.5179606577 33.2405464639 absolute error = 6.589 relative error = 16.41 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.8283705204 -5.17415345786 y1[1] (closed_form) = 5.8283705204 -5.17415345786 absolute error = 2.102e-62 relative error = 2.698e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 60.69 Order of pole (three term test) = 71.93 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 60.69 Order of pole (three term test) = 65.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73817.4MB, alloc=44.3MB, time=879.64 memory used=73863.9MB, alloc=44.3MB, time=880.20 x[1] = 0.7302 2.75 h = 0.003 0.006 y2[1] (numeric) = 16.2668710549 35.2797570923 y2[1] (closed_form) = 22.5402841902 33.3033867173 absolute error = 6.577 relative error = 16.36 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.85101559577 -5.19564311407 y1[1] (closed_form) = 5.85101559577 -5.19564311407 absolute error = 2.102e-62 relative error = 2.687e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.17 Order of pole (three term test) = 72.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 61.17 Order of pole (three term test) = 66.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=73909.9MB, alloc=44.3MB, time=880.73 memory used=73956.6MB, alloc=44.3MB, time=881.28 x[1] = 0.7332 2.756 h = 0.0001 0.005 y2[1] (numeric) = 16.2962272843 35.3263282974 y2[1] (closed_form) = 22.6191866102 33.382889733 absolute error = 6.615 relative error = 16.4 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.87010632302 -5.24465877359 y1[1] (closed_form) = 5.87010632302 -5.24465877359 absolute error = 2.102e-62 relative error = 2.671e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.91 Order of pole (three term test) = 72.86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 61.91 Order of pole (three term test) = 66.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74003.0MB, alloc=44.3MB, time=881.82 memory used=74049.5MB, alloc=44.3MB, time=882.38 memory used=74096.1MB, alloc=44.3MB, time=882.94 x[1] = 0.7333 2.761 h = 0.0001 0.003 y2[1] (numeric) = 16.3257397502 35.3728398922 y2[1] (closed_form) = 22.6470660061 33.4617860279 absolute error = 6.604 relative error = 16.34 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.89876289237 -5.27174558012 y1[1] (closed_form) = 5.89876289237 -5.27174558012 absolute error = 2.012e-62 relative error = 2.544e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 62.53 Order of pole (three term test) = 73.41 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 62.53 Order of pole (three term test) = 67.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74142.2MB, alloc=44.3MB, time=883.50 memory used=74189.0MB, alloc=44.3MB, time=884.06 x[1] = 0.7334 2.764 h = 0.001 0.001 y2[1] (numeric) = 16.3554091617 35.4192912962 y2[1] (closed_form) = 22.6644967877 33.5089798757 absolute error = 6.592 relative error = 16.29 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.91581180114 -5.28829844935 y1[1] (closed_form) = 5.91581180114 -5.28829844935 absolute error = 2.012e-62 relative error = 2.536e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 62.91 Order of pole (three term test) = 73.74 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 62.91 Order of pole (three term test) = 67.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74235.2MB, alloc=44.3MB, time=884.60 memory used=74281.9MB, alloc=44.3MB, time=885.16 x[1] = 0.7344 2.765 h = 0.0001 0.004 y2[1] (numeric) = 16.3852362301 35.4656819255 y2[1] (closed_form) = 22.6857067672 33.5196020548 absolute error = 6.594 relative error = 16.29 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.91634499219 -5.299503842 y1[1] (closed_form) = 5.91634499219 -5.299503842 absolute error = 2.102e-62 relative error = 2.647e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 63.04 Order of pole (three term test) = 73.8 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 63.04 Order of pole (three term test) = 67.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74327.9MB, alloc=44.3MB, time=885.70 memory used=74374.6MB, alloc=44.3MB, time=886.26 x[1] = 0.7345 2.769 h = 0.003 0.006 y2[1] (numeric) = 16.4152216694 35.5120111928 y2[1] (closed_form) = 22.708541533 33.582782334 absolute error = 6.582 relative error = 16.24 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.93933446939 -5.32150242698 y1[1] (closed_form) = 5.93933446939 -5.32150242698 absolute error = 2.102e-62 relative error = 2.636e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 63.54 Order of pole (three term test) = 74.25 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 63.54 Order of pole (three term test) = 68.37 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74420.5MB, alloc=44.3MB, time=886.79 memory used=74467.2MB, alloc=44.3MB, time=887.35 x[1] = 0.7375 2.775 h = 0.0001 0.005 y2[1] (numeric) = 16.4453661959 35.5582785077 y2[1] (closed_form) = 22.7884673712 33.6624366318 absolute error = 6.62 relative error = 16.29 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.95858471973 -5.3715411118 y1[1] (closed_form) = 5.95858471973 -5.3715411118 absolute error = 2.102e-62 relative error = 2.621e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 64.31 Order of pole (three term test) = 74.78 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 64.31 Order of pole (three term test) = 69.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74513.8MB, alloc=44.3MB, time=887.89 memory used=74560.2MB, alloc=44.3MB, time=888.44 memory used=74607.0MB, alloc=44.3MB, time=889.00 x[1] = 0.7376 2.78 h = 0.0001 0.003 y2[1] (numeric) = 16.4756705286 35.6044832764 y2[1] (closed_form) = 22.816991652 33.7417636879 absolute error = 6.609 relative error = 16.23 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.98767743931 -5.39926990921 y1[1] (closed_form) = 5.98767743931 -5.39926990921 absolute error = 2.102e-62 relative error = 2.608e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 64.96 Order of pole (three term test) = 75.36 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 64.96 Order of pole (three term test) = 69.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74653.1MB, alloc=44.3MB, time=889.54 memory used=74700.2MB, alloc=44.3MB, time=890.11 x[1] = 0.7377 2.783 h = 0.001 0.001 y2[1] (numeric) = 16.5061353891 35.6506249015 y2[1] (closed_form) = 22.8348144962 33.7892118936 absolute error = 6.597 relative error = 16.18 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.00498395025 -5.41621315365 y1[1] (closed_form) = 6.00498395025 -5.41621315365 absolute error = 2.102e-62 relative error = 2.600e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 65.35 Order of pole (three term test) = 75.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 65.35 Order of pole (three term test) = 70.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74746.2MB, alloc=44.3MB, time=890.65 memory used=74792.9MB, alloc=44.3MB, time=891.21 x[1] = 0.7387 2.784 h = 0.001 0.003 y2[1] (numeric) = 16.5367615013 35.6967027826 y2[1] (closed_form) = 22.8562416527 33.7997952027 absolute error = 6.598 relative error = 16.17 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.00547992763 -5.42763618519 y1[1] (closed_form) = 6.00547992763 -5.42763618519 absolute error = 2.102e-62 relative error = 2.597e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 65.48 Order of pole (three term test) = 75.77 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 65.48 Order of pole (three term test) = 70.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74838.9MB, alloc=44.3MB, time=891.75 memory used=74885.6MB, alloc=44.3MB, time=892.30 x[1] = 0.7397 2.787 h = 0.0001 0.004 y2[1] (numeric) = 16.5675495918 35.7427163156 y2[1] (closed_form) = 22.8885698399 33.8423914323 absolute error = 6.6 relative error = 16.16 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.01789780476 -5.4500434746 y1[1] (closed_form) = 6.01789780476 -5.4500434746 absolute error = 2.102e-62 relative error = 2.589e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 65.87 Order of pole (three term test) = 76.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 65.87 Order of pole (three term test) = 70.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=74931.6MB, alloc=44.3MB, time=892.84 memory used=74978.1MB, alloc=44.3MB, time=893.40 x[1] = 0.7398 2.791 h = 0.003 0.006 y2[1] (numeric) = 16.5985003897 35.7886648932 y2[1] (closed_form) = 22.9120181606 33.9059636316 absolute error = 6.588 relative error = 16.1 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.04128420583 -5.47265303667 y1[1] (closed_form) = 6.04128420583 -5.47265303667 absolute error = 2.102e-62 relative error = 2.579e-61 % Correct digits = 63 memory used=75024.7MB, alloc=44.3MB, time=893.94 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 66.4 Order of pole (three term test) = 76.54 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 66.4 Order of pole (three term test) = 71.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75070.9MB, alloc=44.3MB, time=894.48 memory used=75117.7MB, alloc=44.3MB, time=895.04 x[1] = 0.7428 2.797 h = 0.0001 0.005 y2[1] (numeric) = 16.6296146268 35.8345479046 y2[1] (closed_form) = 22.9931606466 33.9857748537 absolute error = 6.627 relative error = 16.15 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.06070076316 -5.52390800724 y1[1] (closed_form) = 6.06070076316 -5.52390800724 absolute error = 2.012e-62 relative error = 2.454e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 67.2 Order of pole (three term test) = 77.1 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 67.2 Order of pole (three term test) = 72.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75163.7MB, alloc=44.3MB, time=895.58 memory used=75210.4MB, alloc=44.3MB, time=896.14 x[1] = 0.7429 2.802 h = 0.0001 0.003 y2[1] (numeric) = 16.6608930371 35.8803647355 y2[1] (closed_form) = 23.022458924 34.0655984706 absolute error = 6.615 relative error = 16.09 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.09029620623 -5.55240756302 y1[1] (closed_form) = 6.09029620623 -5.55240756302 absolute error = 2.102e-62 relative error = 2.551e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 67.88 Order of pole (three term test) = 77.7 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 67.88 Order of pole (three term test) = 72.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75256.6MB, alloc=44.3MB, time=896.68 memory used=75303.4MB, alloc=44.3MB, time=897.24 x[1] = 0.743 2.805 h = 0.001 0.001 y2[1] (numeric) = 16.6923363574 35.9261147685 y2[1] (closed_form) = 23.0407521602 34.1133396403 absolute error = 6.602 relative error = 16.04 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.10789939053 -5.56981931263 y1[1] (closed_form) = 6.10789939053 -5.56981931263 absolute error = 2.147e-62 relative error = 2.597e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 68.29 Order of pole (three term test) = 78.07 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 68.29 Order of pole (three term test) = 73.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75349.6MB, alloc=44.3MB, time=897.79 memory used=75396.3MB, alloc=44.3MB, time=898.34 x[1] = 0.744 2.806 h = 0.001 0.003 y2[1] (numeric) = 16.7239453272 35.9717973822 y2[1] (closed_form) = 23.0624359425 34.1238721057 absolute error = 6.602 relative error = 16.03 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.1083464043 -5.58149951248 y1[1] (closed_form) = 6.1083464043 -5.58149951248 absolute error = 2.102e-62 relative error = 2.541e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 68.42 Order of pole (three term test) = 78.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 68.42 Order of pole (three term test) = 73.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75442.3MB, alloc=44.3MB, time=898.88 memory used=75489.0MB, alloc=44.3MB, time=899.44 memory used=75535.7MB, alloc=44.3MB, time=900.00 x[1] = 0.745 2.809 h = 0.0001 0.004 y2[1] (numeric) = 16.7557206884 36.0174119523 y2[1] (closed_form) = 23.095329512 34.1666230277 absolute error = 6.604 relative error = 16.01 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.12092326737 -5.60447138662 y1[1] (closed_form) = 6.12092326737 -5.60447138662 absolute error = 2.102e-62 relative error = 2.533e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 68.84 Order of pole (three term test) = 78.46 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 68.84 Order of pole (three term test) = 73.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75581.7MB, alloc=44.3MB, time=900.53 memory used=75628.4MB, alloc=44.3MB, time=901.08 x[1] = 0.7451 2.813 h = 0.003 0.006 y2[1] (numeric) = 16.7876631855 36.0629578504 y2[1] (closed_form) = 23.1194071196 34.2305926588 absolute error = 6.592 relative error = 15.96 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.14471198176 -5.62770768812 y1[1] (closed_form) = 6.14471198176 -5.62770768812 absolute error = 2.102e-62 relative error = 2.523e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 69.39 Order of pole (three term test) = 78.95 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 69.39 Order of pole (three term test) = 74.21 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75674.3MB, alloc=44.3MB, time=901.62 memory used=75721.0MB, alloc=44.3MB, time=902.17 x[1] = 0.7481 2.819 h = 0.0001 0.005 y2[1] (numeric) = 16.8197735655 36.1084344452 y2[1] (closed_form) = 23.201794191 34.3105579105 absolute error = 6.63 relative error = 16.01 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.16429174495 -5.68020684104 y1[1] (closed_form) = 6.16429174495 -5.68020684104 absolute error = 1.970e-62 relative error = 2.350e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 70.23 Order of pole (three term test) = 79.55 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 70.23 Order of pole (three term test) = 75.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75767.1MB, alloc=44.3MB, time=902.71 memory used=75813.8MB, alloc=44.3MB, time=903.26 x[1] = 0.7482 2.824 h = 0.0001 0.003 y2[1] (numeric) = 16.8520525783 36.1538411015 y2[1] (closed_form) = 23.231886322 34.3908850858 absolute error = 6.619 relative error = 15.95 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.19439675816 -5.70949705097 y1[1] (closed_form) = 6.19439675816 -5.70949705097 absolute error = 2.012e-62 relative error = 2.389e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 70.93 Order of pole (three term test) = 80.19 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 70.93 Order of pole (three term test) = 75.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75859.9MB, alloc=44.3MB, time=903.80 memory used=75906.8MB, alloc=44.3MB, time=904.37 x[1] = 0.7483 2.827 h = 0.001 0.001 y2[1] (numeric) = 16.8845009761 36.1991771807 y2[1] (closed_form) = 23.2506619723 34.4389232749 absolute error = 6.605 relative error = 15.9 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.21230058077 -5.72738934953 y1[1] (closed_form) = 6.21230058077 -5.72738934953 absolute error = 2.012e-62 relative error = 2.382e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 71.36 Order of pole (three term test) = 80.57 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 71.36 Order of pole (three term test) = 76.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=75953.2MB, alloc=44.3MB, time=904.92 memory used=75999.7MB, alloc=44.3MB, time=905.47 memory used=76046.4MB, alloc=44.3MB, time=906.02 x[1] = 0.7493 2.828 h = 0.001 0.003 y2[1] (numeric) = 16.9171195139 36.2444420407 y2[1] (closed_form) = 23.2726078313 34.4494024145 absolute error = 6.604 relative error = 15.89 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.2126961107 -5.73933214721 y1[1] (closed_form) = 6.2126961107 -5.73933214721 absolute error = 2.012e-62 relative error = 2.379e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 71.5 Order of pole (three term test) = 80.65 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 71.5 Order of pole (three term test) = 76.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76092.4MB, alloc=44.3MB, time=906.56 memory used=76139.0MB, alloc=44.3MB, time=907.12 x[1] = 0.7503 2.831 h = 0.0001 0.004 y2[1] (numeric) = 16.9499089491 36.2896350357 y2[1] (closed_form) = 23.3060801947 34.4923085032 absolute error = 6.605 relative error = 15.87 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.22543233635 -5.76288201264 y1[1] (closed_form) = 6.22543233635 -5.76288201264 absolute error = 2.012e-62 relative error = 2.372e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 71.93 Order of pole (three term test) = 80.98 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 71.93 Order of pole (three term test) = 76.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76184.9MB, alloc=44.3MB, time=907.65 memory used=76231.3MB, alloc=44.3MB, time=908.20 x[1] = 0.7504 2.835 h = 0.003 0.006 y2[1] (numeric) = 16.9828700421 36.3347555163 y2[1] (closed_form) = 23.3308032009 34.5566811124 absolute error = 6.592 relative error = 15.81 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.24962879076 -5.78676119548 y1[1] (closed_form) = 6.24962879076 -5.78676119548 absolute error = 2.012e-62 relative error = 2.363e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 72.51 Order of pole (three term test) = 81.51 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 72.51 Order of pole (three term test) = 77.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76277.1MB, alloc=44.3MB, time=908.75 memory used=76323.8MB, alloc=44.3MB, time=909.30 x[1] = 0.7534 2.841 h = 0.0001 0.005 y2[1] (numeric) = 17.0160035554 36.3798028297 y2[1] (closed_form) = 23.4144633983 34.6367972785 absolute error = 6.632 relative error = 15.86 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.26936844293 -5.84053303266 y1[1] (closed_form) = 6.26936844293 -5.84053303266 absolute error = 2.059e-62 relative error = 2.403e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 73.38 Order of pole (three term test) = 82.14 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 73.38 Order of pole (three term test) = 78.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76369.8MB, alloc=44.3MB, time=909.84 memory used=76416.5MB, alloc=44.3MB, time=910.39 x[1] = 0.7535 2.846 h = 0.0001 0.003 y2[1] (numeric) = 17.0493102547 36.4247763194 y2[1] (closed_form) = 23.4453697197 34.7176350543 absolute error = 6.62 relative error = 15.8 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.29998992085 -5.87063427183 y1[1] (closed_form) = 6.29998992085 -5.87063427183 absolute error = 2.059e-62 relative error = 2.391e-61 % Correct digits = 63 memory used=76463.0MB, alloc=44.3MB, time=910.94 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 74.12 Order of pole (three term test) = 82.81 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 74.12 Order of pole (three term test) = 79.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76509.5MB, alloc=44.3MB, time=911.50 memory used=76556.6MB, alloc=44.3MB, time=912.07 x[1] = 0.7536 2.849 h = 0.001 0.001 y2[1] (numeric) = 17.0827909079 36.4696753252 y2[1] (closed_form) = 23.4646400951 34.7659743412 absolute error = 6.605 relative error = 15.75 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.31819837173 -5.88901945234 y1[1] (closed_form) = 6.31819837173 -5.88901945234 absolute error = 2.102e-62 relative error = 2.434e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 74.57 Order of pole (three term test) = 83.21 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 74.57 Order of pole (three term test) = 79.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76602.6MB, alloc=44.3MB, time=912.61 memory used=76649.2MB, alloc=44.3MB, time=913.17 x[1] = 0.7546 2.85 h = 0.001 0.003 y2[1] (numeric) = 17.1164462858 36.5144991834 y2[1] (closed_form) = 23.486853589 34.7763975874 absolute error = 6.603 relative error = 15.74 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.31853981289 -5.90123038509 y1[1] (closed_form) = 6.31853981289 -5.90123038509 absolute error = 2.147e-62 relative error = 2.483e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 74.72 Order of pole (three term test) = 83.29 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 74.72 Order of pole (three term test) = 79.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76695.3MB, alloc=44.3MB, time=913.72 memory used=76742.0MB, alloc=44.3MB, time=914.27 x[1] = 0.7556 2.853 h = 0.0001 0.004 y2[1] (numeric) = 17.1502771618 36.5592472265 y2[1] (closed_form) = 23.5209184577 34.8194592529 absolute error = 6.604 relative error = 15.72 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.3314357156 -5.92537194904 y1[1] (closed_form) = 6.3314357156 -5.92537194904 absolute error = 2.147e-62 relative error = 2.476e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 75.17 Order of pole (three term test) = 83.65 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 75.17 Order of pole (three term test) = 80.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76788.0MB, alloc=44.3MB, time=914.81 memory used=76834.7MB, alloc=44.3MB, time=915.36 x[1] = 0.7557 2.857 h = 0.003 0.006 y2[1] (numeric) = 17.1842843119 36.6039187834 y2[1] (closed_form) = 23.5463033626 34.8842404195 absolute error = 6.59 relative error = 15.66 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.3560453727 -5.94991054332 y1[1] (closed_form) = 6.3560453727 -5.94991054332 absolute error = 2.102e-62 relative error = 2.415e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 75.77 Order of pole (three term test) = 84.2 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 75.77 Order of pole (three term test) = 80.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=76880.6MB, alloc=44.3MB, time=915.90 memory used=76927.3MB, alloc=44.3MB, time=916.45 memory used=76974.0MB, alloc=44.3MB, time=917.01 x[1] = 0.7587 2.863 h = 0.0001 0.005 y2[1] (numeric) = 17.2184685148 36.6485131793 y2[1] (closed_form) = 23.6312658424 34.964504157 absolute error = 6.63 relative error = 15.71 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.37594137307 -6.0049841842 y1[1] (closed_form) = 6.37594137307 -6.0049841842 absolute error = 2.147e-62 relative error = 2.451e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 76.69 Order of pole (three term test) = 84.87 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 76.69 Order of pole (three term test) = 81.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=77020.1MB, alloc=44.3MB, time=917.55 memory used=77066.7MB, alloc=44.3MB, time=918.11 x[1] = 0.7588 2.868 h = 0.0001 0.003 y2[1] (numeric) = 17.252830552 36.6930297358 y2[1] (closed_form) = 23.6630071809 35.0458596182 absolute error = 6.618 relative error = 15.65 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.40708625658 -6.03591731793 y1[1] (closed_form) = 6.40708625658 -6.03591731793 absolute error = 2.147e-62 relative error = 2.439e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 77.46 Order of pole (three term test) = 85.58 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 77.46 Order of pole (three term test) = 82.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=77112.8MB, alloc=44.3MB, time=918.65 memory used=77159.6MB, alloc=44.3MB, time=919.22 x[1] = 0.7589 2.871 h = 0.001 0.001 y2[1] (numeric) = 17.2873712074 36.7374677705 y2[1] (closed_form) = 23.6827848884 35.0945041033 absolute error = 6.603 relative error = 15.6 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.42560334963 -6.05480800915 y1[1] (closed_form) = 6.42560334963 -6.05480800915 absolute error = 2.236e-62 relative error = 2.533e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 77.92 Order of pole (three term test) = 86 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 77.92 Order of pole (three term test) = 82.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=77205.7MB, alloc=44.3MB, time=919.76 memory used=77252.2MB, alloc=44.3MB, time=920.32 x[1] = 0.7599 2.872 h = 0.001 0.003 y2[1] (numeric) = 17.3220912679 36.7818265977 y2[1] (closed_form) = 23.7052716844 35.1048688007 absolute error = 6.6 relative error = 15.58 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.42588800987 -6.06729272384 y1[1] (closed_form) = 6.42588800987 -6.06729272384 absolute error = 2.236e-62 relative error = 2.530e-61 % Correct digits = 63 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 78.08 Order of pole (three term test) = 86.09 0 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 78.08 Order of pole (three term test) = 83.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=77298.8MB, alloc=44.3MB, time=920.87 memory used=77347.0MB, alloc=44.3MB, time=921.52 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; Iterations = 754 Total Elapsed Time = 15 Minutes 21 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 15 Minutes 21 Seconds > quit memory used=77366.7MB, alloc=44.3MB, time=921.78